bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantum Monte Carlo simulations of the structure in the liquid-vapor interface of BiGa binary alloys
Authors: Zhao M , Chekmarev D , Rice S A
Published: November 2023

The liquid vapor interface of a pure metal has been the subject of a number of simulations by both molecular dynamics and Monte Carlo methods. In this work quantum :t\fonte Carlo calculations for an interface were carried out for electrons and ions in a self-consistent manner, making use of pseudopotentials for the ions, a jellium approximation to determine their densities, and a KohnSham treatment of the electrons. The quantum Monte Carlo aspect appears in the solution of Kohn-Sham equation, which is the same as the one-dimensional Schrodinger equation in this application, which relates the electron wavefunction 1/Jn to the position z normal to the surface and the effective electron potential Veir, which in turn depends on the electron density ne ( z). The solution of this equation for 1/Jn (z) and the energy En may be determined in variational QMC by the Metropolis sampling method. With ne(z) freshly determined and Veir revised, the process may be repeated, a new ne(z) determined, and so forth to achieve self-consistency. For a pure metal, the development of the ionic interactions and the pseudopotential is a rather complex procedure, and it is even more complex for the bismuth-gallium alloy described in this paper. The end results are structures of the interface expressed in terms of longitudinal distributions (normal to the surface) of each of the atomic species, a transverse pair distribution, and the electron densities. Experimental measurements of the structure of alloys such as these are available from grazing incidence x-ray studies. In this case, the measured and predicted longitudinal density profiles are in “rather good” agreement, but differ somewhat in the details.
Selective correlation scheme within diffusion quantum Monte Carlo
Authors: Schautz F , Flad H J
Published: November 2023

This paper describes the development of a new scheme for using an effective model potential to reduce the number of electrons explicitly treated in a QMC calculation for a molecular system. Like other pseudopotential and model-potential approaches it is based on differing treatments of core and valence (or frozen and explicitly correlated) electrons. It differs from the earlier schemes of Yoshida and co-workers0 in that it is adapted to multicenter systems and includes a projectionlike operator to enforce orthogonality between orbitals for the two sets of electrons. The model potential includes Coulomb and exchange terms and the projectionlike operator. The latter two are nonlocal. For these a localization procedure, similar to those used in pseudopotential calculations, was derived. In implementing the scheme the authors had to explore a number of questions, such as those related to nonequivalent nodal domains, and to devise a number of approximations to simplify the calculations. The triple-bonded nitrogen molecule N2, with correlation for the electrons of the bonding orgitals and with the nonbonding orbitals frozen, was used as a test case. A coupled cluster [CCSD(T)] calculation with a large basis set provided a benchmark with a correlation energy of 228 mhartree for the triple bond estimated to be accurate within a few mhartree. The corresponding result for the QMC calculation using the best approximations differed by 2-6 mhartree. Thus, quantitative agreement was obtained within the limits of statistical error. The authors indicated a “good chance” for further development to enable efficient treatment of problems involving solids and surfaces.
Assessing the Quality of a Wavefunction using Quantum Monte Carlo
Authors: Mcdowell K
Published: November 2023

These two papers introduced the term “Quantum Monte Carlo” to the scientific literature. Earlier in the same year McDowell0 and Berneb had used the term in abstracts for an American Chemical Society meeting, and later in the year Gordon, Rothstein, and Proctorc used it in the title of a paper submitted to the Journal of Computational Physics. The papers report investigations of variational QMC methods with Metropolis sampling using the hydride ion H- and the helium atom He as examples. As had been found by earlier workers it is shown that relatively simple trial functions explicitly incorporating the interelectron distance rij can produce a high level of accuracy comparable to those of configuration interaction (CI) calculations based on many-term trial functions without rij
Green’s function Monte Carlo for few fermion problems
Authors: Arnow D M , Kalos M H , Lee M A , Schmidt K E
Published: November 2023

A method for treating the nodes for small systems was described in this paper. The general procedure involves the use of both positive and negative walkers in Green’s function QMC, along with cancellation of walkers of opposite sign in close proximity. The method is illustrated for the first excited state of a particle in a one-dimensional box and for three model problems with three particles in three dimensions, interacting with each other through square-well potentials with repulsive and attractive parts. The calculations were executed with the Green’s function procedure, made convenient by availability of known Green’s functions satisfying the conditions of the sample problems. A partial cancellation of positive and negative walkers was made on the basis of overlapping Green’s functions, and the distributions of steps for the walkers involved were altered accordingly. Without cancellations, the distributions of positive and negative walkers proceed to the boson ground-state distribution. With cancellation and with control of their numbers, the positive and negative walkers tend to accumulate in separate regions and to commingle in the vicinity of a node. The arithmetic sum of the walkers yields the excited or fermion wavefunction with a node separating positive and negative regions. For the model problems the method successfully produced accuracies within a few percent of the exact energies, where known. It was noted that for larger problems, the total number of walkers required to maintain an adequate density for sufficient cancellation might be prohibitive.
Monte Carlo variational study of Be: A survey of correlated wavefunctions
Authors: Moskowitz J W , Schmidt K E
Published: November 2023

This paper reports a successful attempt to construct simple but accurate wavefunctions for an atomic system by taking advantage of explicit electron-electron distances rij which can be incorporated into wavefunctions intended for QMC calculations which do not require analytic integrations. The principal advance reported is success with the use of functional forms more complex than that of earlier “Jastrow” functions such as exp[brij/(l+crij)]. In this case the forms are the “transcorrelated” expressions of Boys and Handy° which include exponential terms involving rm  ijrn  ik, mixed powers of electron-electron and electron-nucleus distances. The results were not particularly impressive because the coefficients within these terms were not optimized. Multiplying a Slater determinant by a typical Jastrow term tends to favor the overall expansion of the electron cloud as it keeps electrons apart, but it usually fails to give much improvement unless a corresponding adjustment shrinking the cloud is made. The slight improvements for the Be atom seen in this work were soon superceded in the authors’ later work in which such adjustments produced very much improved wavefunctions.b
A new look at correlation energy in atomic and molecular systems. II. The application of the Green’s function Monte Carlo method to LiH
Authors: Moskowitz J W , Schmidt K E
Published: November 2023

This paper describes the use of a combination of importance sampling with fixed-node diffusion QMC for a molecular system. Although the two devices had been used separately for several four-electron systems, a the combination gives the important advantages of low values of multiplication of walkers and nearly complete elimination of node crossing. The authors derive the Green’s function approach to importance sampling and use the short-time approximation to obtain a calculation procedure essentially the same as that for diffusion with drift. The calculations for LiH were carried out with two different trial functions t/JT specifying the node locations: an SCF function of Slater orbitals and a generalized valence bond function, each multiplied by a simple Jastrow function. This allowed a comparison of results for the two node structures, accompanied with the recognition that the energies represented upper bounds to the true energy which would be given for the correct node locations. At the equilibrium internuclear distance, the calculated energies were the same within their statistical uncertainties. A complete potential energy curve was plotted for the generalized valence bond case. At the equilibrium distance of 3.015 bohr, the energy found was -8.0727 ± 0.0006 hartrees, with an additional uncertainty of about ±0.01 hartree due to time-step error. Within the uncertainties this calculated energy agrees with more recent estimatesb of the exact Born-Oppenheimer energy at 3.015 bohr.
Binding Energy Of Positively Charged Acceptors In Germanium - A Green’s Function Monte Carlo Calculation
Authors: Kalia R K , Vashishta P , Lee M A
Published: November 2023

Spectroscopic measurements of germanium crystals have revealed some of the characteristics of impurity complexes which can be explained in terms of charge acceptors interacting with surrounding holes to form so-called pseudoatoms. With suitable modifications, these complexes can be treated in the same way as real atoms and ions by conventional quantum methods, as described in earlier work, and by QMC methods as described first in this paper. The complexes of interest include double acceptor impurities Be and Zn binding three holes and quadruple acceptors binding four holes, equivalent to negatively charged infinite-mass nuclei (of charge -Z) surrounded by positively charged holes (of charge +1). with use of effective masses for the holes, an effective dielectric constant, and a modification of Fermi statistics to allow four holes in ls orbitals, these systems may be treated as simple atoms and ions in diffusion QMC with importance sampling. The systems treated were equivalent to nodeless H-, He+, He, He-, Li+, Li, and Li-. Both variational and diffusion calculations used the same trial wavefunctions, which were symmetrized ls orbital products with added correlation terms linear in the interelectron distances. For the one- and two-hole systems, the energies could be deduced from the analogous systems. For these the diffusion QMC calculations gave equivalent results. In all cases the diffusion calculations gave slightly lower energies than the variational calculations. In comparisons with experiment, agreement was good for double acceptors and poor for triple acceptors, for which the pseudoatom model was judged to be inadequate.
The infrared predissociation spectra of water clusters
Authors: Coker D F , Miller R E , Watts R O
Published: November 2023

Coker, Miller, and watts carried out experimental measurements of the infrared predissociation spectra of small water clusters in molecular beams formed with free jet expansions of water vapor in helium. The spectra include several O-H stretch absorptions and an H-O-H bend overtone. Theoretical analyses based on empirical intramolecular/intermolecular potential energy surfaces were made using normal mode theory, local mode theory, and a novel extension of the simple random-walk procedure without importance sampling. The normal mode analysis was found inadequate and the local mode analysis not quite satisfactory, but the QMC-based quantum simulation procedure predicted the observed vibrational bands for the dimer and trimer very accurately. The simple QMC method was used to generate a large number of walkers with a distribution corresponding to the ground state wavefunction 7/J0. This many-body function was then projected onto the local vibrational coordinates for each molecule to give single-variable functions, each then fit by a Morse function. A variational calculation including cross terms for low-lying excited states was then made with this reference state. The results gave unambiguous assignments for the observed O-H stretching vibrations in the dimer, good agreement for the bending overtones, and satisfactory agreement for the O-H vibrations in the trimer. Repetition using a different pair interaction potential established that the experiment could provide a sensitive method for testing pair interactions.
Auxiliary field Monte Carlo for quantum many-body ground states
Authors: Sugiya G , Koonin S E
Published: November 2023

This paper describes a different Q11C method for solving the Schrödinger equation, one unlike variational, diffusion, and Green’s function methods. It can be applied to many-body systems to produce solutions for ground states. For systems of fermions, antisymmetrization can be imposed to overcome the problem of node location, but the instability of the method is a serious shortcoming, so that the method as described is limited to treating relatively simple systems. Nevertheless, this auxiliary field quantum 1,fonte Carlo (AFMC) method was demonstrated to be successful for test cases reported in this paper, and in time has been improved to allow treatment of realistic systemsa. The method makes use of the imaginary-time propagation of an initial wavefunction toward the ground-state function. It requires use of a trial wavefunction which is the product of single-particle orbitals for bosons or an antisymmetrized product for fermions. A Hubbard-Stratonovich transformation of the propagator changes the many-body problem to a problem of a collection of single particles interacting with a fluctuating (auxiliary) field which replaces the many-body interactions. The authors developed an integral expression for the energy which, after discretization, could be evaluated by a Metropolis Monte Carlo integration forward in time. The algorithm was tested for one-dimensional systems of particles: 6 to 20 bosons with varied interactions, 2 to 6 neutron-proton pairs, others with repulsive potentials. Importance sampling was found to be critical and computational requirements to be large. For spin systems on a lattice the AFMC method was considered feasible, but for general multidimensional systems the method appeared to be limited by its computation requirements.
Validity of random walk methods in the limit of small time steps
Authors: Anderson J B , Garmer D R
Published: November 2023

These three notes each offer evidence against an earlier claim, added as an appendix to a paper by Moskowitz and Schmidt,a that the discretization of the imaginary-time Schrödinger equation was in error even for infinitesimal time-step sizes and that all results with this short-time approximation were incorrect. As acknowledged by Moskowitz and Schmidt, there was an error in their analysis and they agreed that the short-time approximation was correct after all.
Potential energies for the reaction F + H2 HF + H by the random walk method
Authors: Garmer D R , Garmer D R
Published: November 2023

If the reaction H + H2 H2 + H is number one on the list of interesting chemical reactions, then number two is the reaction F + H2 HF + H. It is very fast, it is highly exothermic, it drives chemical lasers, it can be studied in crossed molecular beams, it can be studied by infrared spectroscopy, and it involves only 11 electrons. This paper, and its companion paper a year earlier, report fixed-node diffusion QMC calculations of the ground-state potential energy surface for the F-H-H systems, with emphasis on the region of the barrier to reaction. At the time this work was completed, it was clear from experiments that the barrier height must be in the range of 1 to 2 kcal/mol. Calculations by a variety of methods gave barrier heights in the range of 1 to 6 kcal/mole for collinear reactions. More recent high-level calculations, QMC and others, place the collinear barrier at about 3 kcal/mol, with a lower height of about 2 kcal/mol for slightly bent configurations. The QMC calculations were fixed-node diffusion calculations with importance sampling, using single-determinant trial functions with orbitals represented by cubic spline functions fit to Gaussian orbitals. Recovery of correlation energy was about 96% for the isolated F atom and for the HF molecule. Total energies for reactions and products were about 40 kcal/mol lower than the lowest energy
Model Hamiltonians for atomic and molecular systems
Authors: Carlson J , Moskowitz J W , Schmidt K E
Published: November 2023

The aim of this study was to reduce the variance in the energies for QMC calculations for atomic and molecular systems by replacing the electron-electron potential energy terms for core electrons by averaged values. The complete Hamiltonian expression was thus altered to become a model Hamiltonian, and while total energies from such calculations may have little meaning, energy differences for similar systems obtained with the same model may give fairly good agreement with those from calculations for the full Hamiltonian. The work reported in this paper indicated that is the case for Li, LiH, and Li2. The average electron-electron potential was expressed as a two-parameter function decreasing with increasing distance from a nucleus. Importance sampling was carried out with a trial function consisting of an unaltered Slater determinant specifying node locations multiplied by a modified Jastrow function. The random walk of configurations was executed with Green’s function sampling for the full set of electrons. Energy differences for LiH versus (Li + H) and Li2 versus (Li + Li) were accurate within about 1 millihartree. The reduction in variance in local energies led to increases in calculation efficiency by a factor of 5 to 7 for these systems. The results indicated such an approach might be successful for larger systems.
H. Sun & R. 0. Watts: Diffusion Monte Carlo simulations of hydrogen fluoride dimers
Authors: Sun H
Published: November 2023

This is one of the earlier QMC papers to describe calculations of molecular vibrational states. As noted by the authors, harmonic oscillator models for vibration are not adequate for treating floppy molecules, and the principal motivation for their study was to “give up the harmonic oscillator assumption and use quantum Monte Carlo to calculate accurate vibrational frequencies for the HF and DF dimers.” Clearly, they were successful in meeting that objective. In doing so they devised several new approaches to the general problem of treating vibrational motion. Diffusion QMC with importance sampling was used with an improved short-time approximation based on an added multiplication term second order in the time-step size. Excited states for which node locations could be specified from consideration of symmetry arguments, as for torsion states, were simulated in fixed-node calculations. For other states an orthogonalization methoda based on cancellation of positive and negative walkers as well as orthogonality with lower states was used. For these it was necessary to simulate the excited states successively, and calculations were limited to four different states. The states involved in tunneling splitting for the dimers were distinguished by an added fixed node. The calculations were carried out for three different potential energy surfaces and results were compared with spectroscopic data. Each one gave reasonable values for low-lying vibrations. Modification of one surface gave still better values.
Wave functions of helium clusters
Authors: Rama M V
Published: November 2023

This paper describes improved trial wavefunctions for helium clusters and their use in variational QMC calculations of their binding energies, structural properties, and breathing mode vibrational excited states, for clusters of 3 to 270 atoms. The wavefunctions developed were similar to those of earlier work but included convenient analytic functions for two- and three-body correlations. All terms were of the Jastrow exponential form, based on sums of one-, two-, and three-body terms t1(ri), t2(rij), and t3(rij, rjk,rki), expressed as functions of interparticle distances. Excited-state wavefunctions for the breathing vibrational mode were obtained with the aid of procedures adapted from treatment of the quantum mechanics of liquid drop models. The interactions of helium atoms were specified as pairwise-additive with an accurate semi-empirical pair potential. Optimizations of parameters in the trial wavefunctions were carried out for individual cluster sizes with an exhaustive search procedure in a series of trial variational calculations, in which the parameters were varied to minimize the energy. A partial correlation of results was obtained by use of identical initial coordinates and random number seeds in these optimization calculations. Once the wavefunctions were optimized, longer calculations were used to determine properties of the clusters. In addition, diffusion QMC calculations were used to obtain more accurate nonvariational energies for comparisons.
Variational quantum Monte Carlo nonlocal pseudopotential approach to solids: Formulation and application to diamond, graphite, and silicon
Authors: Fahy S , Wang X W , Louie S G
Published: November 2023

This paper describes the use of nonlocal pseudopotentials with variational QMC to calculate the binding energies of the solids diamond, graphite, and silicon. While nonlocal pseudopotentials have the advantage of elimination of core electrons and the large fluctuations of local energies associated with core electrons, they produce several types of difficulties in diffusion and Green’s function QMC. As shown in this paper, the use of variational QMC avoids many of these. The calculations used pseudopotentials of the standard form developed for use in density functional calculations. The trial functions were based on mixtures of short-range Gaussian orbitals and long-range plane-wave functions in single determinants multiplied by Jastrow functions. Metropolis sampling was carried out for movement of one electron at a time, along with its images, in order to take advantage of the efficiencies associated with changing one row of the determinant for a single electron. The solids were treated as cells of up to 54 atoms (216 valence electrons) with periodic boundary conditions. For each of the three systems - diamond, graphite, and silicon - the VQMC structural properties were found in excellent agreement with experiment. Density functional calculations at the LDA level were similarly successful. More important, the VQMC binding energies and energy differences were found in excellent agreement with experiment. For these quantities density functional calculations at the LDA level were far less successful.
Magnetic structure and equation of state of bee solid hydrogen: A variational quantum Monte Carlo study
Authors: Wang X W , Zhu J , Louie S G , Fahy S
Published: November 2023

Solid hydrogen in its atomic bee structure provides an interesting testing ground for various theoretical methods in predicting the properties of its several electronic states. These include three possible magnetic phases: paramagnetic (PM), ferromagnetic (FM), and antiferromagnetic (AFM). The system is simple enough to permit reliable calculations for all three phases to determine their energies as functions of the density and to predict the transitions between phases. The calculations reported in this paper were variational QMC calculations performed primarily on a 54-atom cluster in the bee structure with periodic boundary conditions. The protons were fixed in position. The trial wavefunction was constructed from a product of spin-up and spin-down determinants based on single particle wave functions from density-functional calculations for the system, multiplied by a symmetric Jastrow factor. The specification of magnetic phase was made through modifications of the single-particle orbitals within the determinants and localization of orbitals to one or the other of the cubic sublattices. The calculations for all three phases were performed for a range of densities in which earlier calculations had predicted magnetic and metalinsulator transitions. At the lowest densities, the FM and AFM energies approached the value for free hydrogen atoms, with AFM lower than FM. With increasing density the PM phase drops below the AFM and becomes the ground state. Across the range, the ferromagnetic phase was never the lowest-energy phase.
Nonlocal pseudo potentials and diffusion Monte Carlo
Authors: Mitáš L , Shirley E L , Ceperley D M
Published: November 2023

This paper reports improvements which overcome some of the problems encountered in the use of nonlocal pseudopotentials in QMC. These increase the reliability of the method by reducing or eliminating several approximations of earlier treatments, reduce the variance in local energies, and increase the recovery of correlation energy. Calculations for Si, Sc, and Cu neutrals and ions in several states and the dimer Si2 were used to test the revised method. One key improvement was the use of correlated trial wavefunctions making use of Schmidt-Moskowitz expressions for two- and three-body terms. Additional exponential terms were added in some cases. Atomic orbitals for the determinants were obtained in density functional calculations. Another key improvement was in the procedure for integrating the trial function over a sphere in determining the electron-pseudopotential energetics. For the complete correlated trial function the integrals were determined with numerical quadrature, settling on 18-point quadrature with random orientation on the sphere. Except for these changes, the calculations were similar to those of the earlier studies. Both variational and fixed-node diffusion calculations were made. The recovery of valence conelation energy for atoms and ions was 80%-90% in the variational calculations and estimated to be greater than 95% in the diffusion calculations. Comparison of ionization potentials and electron affinities with experimental values showed agreement within 1% for Si, a few percent for Sc, and about 20% for Cu. The general conclusion was that the method was stable and feasible even for the difficult case of Cu.
Quantum Monte Carlo perturbation calculations of interaction energies
Authors: Caffarel M , HESS O
Published: November 2023

The perturbation approach to predicting interaction energies between molecules avoids many of the problems associated with accurate calculations of total energies for subtraction to obtain energy differences, but it has many problems of its own. This paper reports a slightly successful first attempt to combine the perturbation approach with QMC methods for such calculations. The basis for the development is the nth-order Rayleigh Schri:idinger perturb bation theory, which in principle can be formulated to give a series of energy corrections !}.E(n) that can be expressed as integrals involving the perturbing potential and the unperturbed wavefunctions. In practice this is difficult for interactions of molecules, but the authors succeeded in reformulating the problem so that the required quantities could be determined in diffusion QMC calculations. The interaction energy was split into Rayleigh Schri:idinger and exchange parts which could be separately evaluated. The QMC aspects were carried out in diffusion QMC with importance sampling using Jastrow like trial functions and conditional acceptance of moves to enforce detailed balance. This produced the expectation values required in the expressions for the interaction energy.
Binding energies of positronium fluoride and positronium bromide by the model potential quantum Monte Carlo method
Authors: Schrader D M , Yoshida T , Iguchi K
Published: November 2023

This paper and a companion paper0 describe three pseudopotential QMC calculations for the positronium halides PsF, PsCl, and PsBr with accuracies and reliabilities not previously available. These three compounds have a fleeting lifetime sufficiently long that time-independent nonrelativistic quantum mechanics should give good estimates of their energies but too short to allow direct measurements of those energies. Earlier estimates of several types and calculations at the Hartree-Fock level had given a wide spread in predictions of the binding energies of positronium to the halide ions, mostly in the range of 1 to 3 eV for the three molecules. The calculations were fixed-node diffusion QMC calculations for the eight valence electrons and the positron with a model potential expression replacing the core electrons and halide nucleus. The model or pseudopotential used was a simplified version without valence-core correlation and with several lesser terms eliminated in order to make it a local pseudopotential. This modelb had been used previously in successful predictions of the electron affinity of the Cl atom. An importance sampling trial wavefunction was constructed of Hartree-Fock orbitals for the halide ion and a 2s orbital for the positron, along with an electron-positron term but no electron-electron correlation terms. Checks of the consistency of the calculations with independent estimates of the correlation energies were entirely satisfactory. The results, in terms of binding energies, were obtained in the range of 1-2 eV (with uncertainties of 0.1-0.2 eV) in an order consistent with competitive formation experiments.
Quantum annealing: A new method for minimizing multidimensional functions
Authors: Finnila A B , Gomez M A , Sebenik C , Stenson C , Doll J D
Published: November 2023

Quantum Monte Carlo has found a new application far afield from the solution of the Schrodinger equation for many-body problems. In this paper the authors report a method for solving multidimensional optimization problems that is superior, in many cases, to other methods such as conjugate gradient methods, the simplex method, direction-set methods, genetic methods, and classical simulated annealing. The new approach, aptly titled “quantum annealing,” is closely related to classical annealing, in which a physical system such as a metal cluster is slowly cooled and finds its lowest-energy configuration as the temperature drops to zero. In classical annealing the system follows classical-mechanical dynamics as the temperature drops. In quantum annealing a collection of configurations evolves in the the same way as walkers undergoing diffusion and multiplication in diffusion QMC with the added feature of a slowly dropping value for Planck’s constant h. Classical annealing allows the escape from local minima with the aid of thermal fluctuations. Quantum annealing allows such escape by delocalization and tunneling. Since a QMC walker can multiply in number on entering a low-energy region, a single walker can populate an entire region.
Quantum Monte Carlo simulation of molecular vibrations: Application to formaldehyde
Authors: Lewerenz M , Watts R O
Published: November 2023

The formaldehyde molecule is an often used test system for methods of predicting vibrational levels of polyatomic molecules. It was the first four-atom molecule to be treated in analytic variational calculations and it was the subject of early QMC variational calculations by Bernu et al.a It has also been the subject of several perturbational studies. The study reported in this paper has taken advantage of a preexisting accurate global potential energy surface, providing good descriptions of the several local minima, for fully QMC calculations using the fixed-node diffusion method. The fixed nodes for several of the excited states treated could be specified exactly from symmetry considerations. For the others approximate node locations were used. Importance-sampling trial wavefunctions were assembled from diatomic and triatomic subunits in “modular” constructions. Calculations for a total of eight different vibrational states gave lower energies than variational calculations for the same surface but good agreement in frequencies except for two combination states. Agreement with experiment in terms of vibrational frequencies was good, especially for the lowest states of a given symmetry.
Driven Two-Dimensional Dynamical Systems
Authors: Gilmore Robert , Letellier Christophe
Published: November 2023

There is a general structure theory for dynamical systems-sets of coupled nonlinear ordinary differential equations-that remains to be worked out. This theory takes the form of the structure theory that is well known for algebraic systems-in particular, the structure theory that exists for groups and their representations. Groups may be nonsemisimple, semisimple, or simple [31]. Representations of groups can be reducible, fully reducible, or irreducible. We will adopt the language of representations to describe the structure theory for dynamical systems,on the grounds that such equations form representations of physical processes. We summarize schematically the structure theory for groups, representations, and dynamical systems in Table 8.1.
Group Theory Basics
Authors: Gilmore Robert , Letellier Christophe
Published: November 2023

The parameters c = ( c1, c2, · · · , ck) are called control parameters. They are parameters that typically appear in the dynamical systems equations. For example, for the Lorenz equations (2.1) the three control parameters are c = ( c1 , c2, c3) = (R, u, b) and for the Rossler equations (5.7) they are c = ( c1, c2, c3) = ( a, b, c). The control parameters are points in a k-dimensional manifold whose global topology is less important than that of the phase space. The dynamical systems equations (10.1) are typically coupled nonlinear equations. They are deterministic under mild conditions on the source functions f(x; c). Trajec­tories exist through any point at which a Lipschitz condition is satisfied. Such tra­jectories are locally extendable and unique. Specifically, the theorem is as follows [S].
Equivariant Dynamics in RN
Authors: Gilmore Robert , Letellier Christophe
Published: November 2023

The properties of equivariant dynamical systems X = F(X) are highly constrained by the sylllllletry group Q. The number of fixed points is to some extent determined by Q. The singular set SS(Q) is completely determined by the action of Q on JRN through the defining matrix representation rDe f (Q). Most important, the structure of the forcing functions F(X) is determined by ro e f (Q), the spectrum of irreducible representations of Q, and the ring basis functions R(a ) ( X) that transform under these irreducible representations
All the Covers of the Horseshoe
Authors: Gilmore Robert , Letellier Christophe
Published: November 2023

This book covers them. All of them. As we have progressed through the chapters our understanding and appreciation of covers has become increasingly complex. At first, covers were dynamical systems with some symmetry that could be mapped to a dynamical systems without symmetry in a locally one to one way. Many examples of such symmetric dynamical systems, and their images, were given in Chapter 3. Fig. 16.1 shows two symmetric attractors, the Lorenz attractor and the Burke and Shaw attractor, and their 2 , 1 images, the proto-Lorenz, and the proto-Burke and Shaw attractors. The original attractors are the covers, the proto attractors are the images. As a next step, the cover-image mapping could be inverted. This allows us to lift an attractor without symmetry, and the dynamical equations that generate that attractor, to attractors with symmetry, and the equations that generate the symmetric attractors. At this stage we encountered our first enriching experience.
Five Days that Changed My Life
Authors: Ford Emily , Liebowitz Michael R , Andrews Linda Wasmer
Published: November 2023

The money I was costing my parents had been steadily adding up. By the spring of 2005, I had drained tens of thousands of dollars from their bank accounts by pursuing failed stays in faraway places and start-up businesses that would have allowed me to work completely by myself, but that never seemed to get off the ground. My medical insurance covered none of the cost of monthly visits to the psychiatrist or the medication I was taking, so my parents paid for those, too. They had also financed my undergraduate degree as well as the graduate degree that I hadn’t finished, and they had paid the security deposits and monthly rent for no fewer than five apartments. The cost was straining my relationship not only with my parents, but also with my sisters, who implied that my constant financial demands were extremely selfish.
My Life Today, Your Life Tomorrow
Authors: Ford Emily , Liebowitz Michael R , Andrews Linda Wasmer
Published: November 2023

As a child, Emily was incomparable, unusual, even precocious. At age four she was writing little poems and stories, enjoying music, art, and a myriad of creative pastimes. The breadth of her imagination along with her joie de vivre was a charming combination. Then in her teens, Emily became increasingly self-conscious. Immediate post-college days marked the beginning of her deep depression. I think of it as her dark period. During this time she frequently slept by day and was up all night. Emotional reactions were almost nonexistent. Emily withdrew socially; personal interactions became rare. Anxiety plagued her to the point of refusing to talk on the phone, which, of course, was a detriment to work situations. Her eating habits became bizarre, eating all oatmeal one week, and toast and coffee the next. Remarkably, Emily has abandoned her dark despair and reemerged into the radiance of self-delight and that of the world around her. Of her own accord she found and put herself under the aegis of an anxiety treatment center. Through psychotherapy and medication Emily has become a ‘‘new’’ person, ironically by becoming her ‘‘old’’ self.
The Loss of Sadness
Authors: Horwitz Allan V , Wakefield Jerome C
Published: November 2023

The Loss of Sadness argues that the increased prevalence of major depressive disorder is due not to a genuine rise in mental disease, but to the way that normal human sadness has been 'pathologised' since 1980. That year saw the publication of the landmark third edition of The Diagnostic and Statistical Manual of Mental Disorders (DSM-III), which has since become a dominant force behind our current understanding of mental illness overall. As concerns at least major depression, the authors argue that the DSM's definition of the condition is too broad and that as a result virtually all research and clinical approaches to the condition have been based on a flawed understanding about it. The social, political, and scientific implications of this are far-reaching - from the overselling of antidepressants to treat ordinary sadness, as Big Pharma exploits the DSM for its own purposes; to intrusive and expensive depression screening programs at all levels of society, as well-meaning but misguided initiatives translate the DSM into simple terms to catch any whiff of depressive pathology in our midst; and funded research into the 'epidemic' of depression, which advances the field very litttle and the public even less. Ultimately, the definition of depression that is in operation today has formed the basis for an entire system of social control (e.g. community-wide screening initiatives, intrusive public health policy) that benefits psychiatry, primary care providers, and the pharmaceutical and insurance industries by turning everyone else into a potential consumer of services, needed or not. The authors do recognise that depression is a devastating illness that affects some people. Their chief concern is with the use of this diagnosis as a catch-all for anyone who has experienced sadness for more than a few weeks at a time. The result is a pointed yet nuanced critique of modern psychiatry that will stir controversy of the sort that will reacquaint us with sadness as a primary human emotion and that could productively influence the way that depression the actual illness is characterised in the future.
Sadness With and Without Cause Depression From Ancient Times Through the Nineteenth Century
Authors: Horwitz Allan V , Wakefield Jerome C
Published: November 2023

Depression has been an omnipresent phenomenon over several millennia of human history. For virtually all of that time, from the earliest writings of the ancient Greek physicians to the late twentieth century, Western diagnosticians routinely distinguished depressive disorders, as a form of madness, from symptomatically similar but nondisordered, normal sad­ ness responses to a wide range of painful circumstances. Then, in 1980, seeking a more scientific foundation for diagnosis by focusing on decontextualized criteria based on symptoms, the DSM-III inadvertently abandoned this critical traditional distinction, which is now essentially lost in current thinking about depression. This chapter and the next trace the history leading up to this momentous and, we argue, ultimately detrimental conceptual shift.
Depression in the Twentieth Century
Authors: Horwitz Allan V , Wakefield Jerome C
Published: November 2023

Until the end of the nineteenth century, psychiatry generally used the relationship of symptoms to their provoking causes as an essential part of definitions of melancholic disorder. Although some kinds of cases, such as psychotic depressions, almost always displayed symptoms that implied disorder, diagnosticians understood that they had to consider context, because depressive disorder could often be symptomatically indistinguishable from profound normal sadness. In the late 1800s, the traditional contextual approach to diagnosis of depressive disorder began to divide into two distinct schools. On one side, Sigmund Freud and his followers emphasized the psychological etiology of all mental disorders, including depression, and their continuity with normal functioning. Adherents of this school studied and interpreted the patient’s reported thoughts to surmise the existence of under­ lying unconscious pathogenic meanings and wishes. On the other side, Emil Kraepelin applied a classical medical model that examined the symptoms, course, and prognosis of depression and other disorders to define distinct physical pathologies. Kraepelin’s approach inspired a cadre of researchers to trans­ late it into a research program that often used statistical techniques to infer discrete disorders from manifest symptoms.
Importing Pathology into the Community
Authors: Horwitz Allan V , Wakefield Jerome C
Published: November 2023

The transformation of intense normal sadness into depressive dis­ order occurred in several stages. The development of influential symptom-based research criteria for affective disorders in the Feighner criteria and RDC provided an initial step. Such criteria lacked the contextual assessment that had traditionally protected diagnosis from misclassifying intense sadness as disorder and thus created the potential for false positives. Research on depression was, however, primarily concerned with hospitalized patients and quite severely afflicted community members who were clearly disordered. Within this context, the symptom-based criteria worked well to distinguish affective disorders from other serious disorders, and the potential for false positives was not immediately realized. The second step occurred when the DSM-III applied the symptom-based logic to clinical practice in general, including burgeoning out­ patient practices and community clinics in which therapists might see all forms of mental distress. Applying decontextualized criteria to this heterogeneous group of outpatients made it more likely that these diagnoses would be applied to those suffering from normal sadness.
The Surveillance of Sadness
Authors: Horwitz Allan V , Wakefield Jerome C
Published: November 2023

If you are a typical resident of New York City, the chances are that you’ll visit your primary care physician at some point over the next year. If your doctor follows the advice of the New York City Commissioner of Mental Health, he or she will ask you to fill out a questionnaire that asks: “Over the past 2 weeks, how often have you been bothered by any of the following problems?”1 Each of nine symptoms are rated as O (not at all), 1 (several days), 2 (more than half the days), or 3 (nearly every day).
The Failure of the Social Sciences to Distinguish Sadness From Depressive Disorder
Authors: Horwitz Allan V , Wakefield Jerome C
Published: November 2023

The field of psychiatry does not exist in a vacuum; it depends on other disciplines for much of the intellectual underpinnings of its clinical theory. One might thus expect that disciplines such as anthropology and sociology should be in good positions to help correct the confusion in psychiatric nosology about the distinction between depressive disorder and normal intense sadness. Anthropologists could identify universal emotional mechanisms that are part of human nature and elaborate the cultural variations in their expression, and they could pinpoint when these normal variations lead to mistaken labeling of disorder. Sociologists could demonstrate how stressful social arrangements often produce nondisordered sadness, which can sometimes be severe enough to meet DSM criteria, and could distinguish between the study of normal emotional responses to social stress and the study of mental disorder.
Love Stories of Later Life
Authors: Barusch Amanda Smith
Published: November 2023

Even with baby boomers retiring and greater media and research attention being lavished on older people, most gerontologists have studiously avoided examining romance among the elderly. Love Stories of Later Life is an appealing and eye-opening remedy to this neglect, as leading gerontologist Amanda Smith Barusch presents original research into what love and romance mean in older people’s lives. The result is a glimpse into a world many people didn’t know existed—that of romantic love in later life. Unlike superficial guidebooks that purport to help older people find a new mate, Love Stories of Later Life integrates theory and the latest research on love and the aging process. Drawing on a wealth of personal narratives collected during a landmark five-year study, the book presents the lived experiences of older adults from all walks of life. It addresses the impact of common age-related changes, both emotional and physical, on romantic relationships, and argues that love continues to sculpt our personalities and our lives, even in life’s later decades. Each chapter includes practical tools, including exercises designed to increase self-awareness and relationship-building as well as annotated lists of suggested reading that are at once comprehensive and accessible. Barusch’s fresh perspective, engaging voice, and in-depth qualitative research make Love Stories of Later Life an important contribution to the study of individual lives and the aging process.
Looking for Love
Authors: Barusch Amanda Smith
Published: November 2023

Candy is a tall, energetic 62-year-old, retired from her job and deeply involved with gay and lesbian organizations in her community. For the first time in her life, she is actively looking for a balanced, “50–50” relationship. “I would love to be in love. Have dinner with somebody, go to a show—I have an idea that if love comes again, which I pray that it will, it’s going to be much more low key.” Her early love experiences were anything but low key.
The Thought That Counts
Authors: Kant Jared Douglas , Franklin Martin , Andrews Linda Wasmer
Published: November 2023

In this book for young people who have been diagnosed with obsessive-compulsive disorder (OCD), Jared Kant discusses his own experiences with the illness, and the disruption and distress that it brought to his life as an adolescent. Combining this personal story with a candid and easy-to-understand description of the science behind OCD, Kant (now an adult who healthily and successfully manages his illness) also provides the facts that young people diagnosed with OCD need, such as how to find professional help, what types of therapies are available for this disorder, and how to deal with stressful situations at home and at school.