bluuebunny/crossref_metadata_2025 huggingface dataset:
The effect of isotopic substitution and detailed balance on the infrared spectroscopy of water: A combined time correlation function and instantaneous normal mode analysis
Authors: Ahlborn Heather , Space Brian , Moore Preston B.
Published: July 2002

We have recently demonstrated that simple classical molecular dynamics methods are capable of nearly quantitatively reproducing most of the intermolecular and intramolecular infrared (IR) spectroscopy of water [H. Ahlborn, X. Ji, B. Space, and P. B. Moore, J. Chem. Phys. 111, 10622 (1999)]. Here it is demonstrated that the result is robust by quantitatively reproducing experimentally measured D2O IR spectroscopy utilizing the same models. This suggests that the quantum effects associated with light atom motion are relatively unimportant. Instantaneous normal mode (INM) theory and the time correlation function (TCF) methodology are used in a complimentary fashion to analyze the molecular origin of the IR spectroscopy of deuterated water (D2O). The TCF methods demonstrate that our models of the dynamics and the system dipole are reasonable by successful quantitative comparison of the theoretical spectrum with experimental results. INM methodology is then employed to analyze what condensed phase motions are responsible for the observed O–D stretching line shapes. It is surprising that classical models can reproduce the complex spectroscopy of both liquid H2O and D2O, and this result implies that the motions responsible for the signal must be effectively harmonic in nature. This assertion is supported by the drastic impact that is seen on both the intensity and line shape through the choice of detailed balance correction factor that is used to quantum correct the classical vibrational line shape.
Three-dimensional measurements of the nuclear magnetic resonance chemical shift and a new analytic data transform for the shift anisotropy
Authors: de Swiet Thomas M.
Published: July 2002

Three-dimensional measurements of the C13 nuclear magnetic resonance (NMR) chemical shift in methyl-α-D-glucopyranoside are presented. One dimension measures the isotropic shift under ordinary magic angle spinning. In the remaining two dimensions, the chemical shift anisotropy (CSA) is recoupled in two complementary ways. An analytic transform is constructed which takes the time-domain data directly to the three isotropic shift parameters, which can then be read off the resulting plot. The possibility of using such an experiment to resolve chemical sites by the CSA alone in powdered samples is discussed.
Interfacial profiles of mismatched lamellae in thin diblock copolymer films
Authors: Pereira G. G. , Williams D. R. M. , Chakrabarti A.
Published: July 2002

A number of recent experiments have allowed direct study of diblock copolymer morphology on patterned surfaces. Here we examine, by computer simulation, the morphology of a diblock thin film in contact with a substrate having large stripes. The diblock aligns parallel to the surface but is frustrated at the point where two stripes join. We show here that at the joint one of the phases is continuous while the other is discontinuous. In the region of the join the lamellae form a kink with a length scale of the same size as the lamellar period. Within the kink the ordering is suppressed.
New propagators for quantum-classical molecular dynamics simulations
Authors: Jiang Hong , Zhao Xin Sheng
Published: July 2002

The propagation of quantum/classical molecular dynamics equations is investigated from two different points of view. One is to take into account the time-dependence of effective Hamiltonians of quantum and classical subsystems by the combination of Zhu and Zhao’s time-independentlike split operator method [J. Chem. Phys. 105, 9536 (1996)] and a predictor-corrector technique. The other one is to introduce a time-independent quasi-Hamiltonian operator for the total system based on which new split-operator propagators are constructed. High-order quantum wave-packet propagators and the multiple time scale technique can be easily employed in our algorithms. Four new quantum/classical propagators are proposed and tested in a simple model system. It is found that combinations of our algorithms with high-order quantum propagators or the multiple time scale technique can give good results even with very large time steps. These new schemes will be particularly powerful in the case when the propagation of the classical subsystem is most time-consuming.
Angular resolved studies of the Lyman-α photodissociation of HCN and DCN: New dynamical insights
Authors: Cook Phillip A. , Langford Stephen R. , Ashfold Michael N. R. , Dixon Richard N.
Published: July 2002

The photochemistries of HCN and DCN at the H(D) Lyman-α wavelength have been reinvestigated using the technique of H(D) Rydberg atom time-of-flight spectroscopy, with angular resolution of the H/D atom signal about the polarization vector of the photolysis radiation. In the case of HCN photodissociation, the previous assignment of substantial branching to H+CN(A 2Π)v=0 products is confirmed. Analysis of the profile taken under parallel polarization of the Lyman-α radiation relative to the time of flight axis reveals additional structure attributable both to a progression in CN(A) products with high rovibrational excitation (v=4–9, with N∼26–41, for all v), and to various rotationally excited levels associated with CN(B 2Σ+)v=0,1. From these various assignments an improved value for the dissociation energy, D0(H–CN)=43 710±70 cm−1, is obtained. The determined β parameter, which is a measure of the angular part of the photofragment velocity distribution about the polarization vector of the photolysis radiation, shows an increasingly parallel distribution of H atom velocities with increasing CN internal energy. DCN photolysis at the D Lyman-α wavelength yields both CN(A)v=0 and a range of rovibrationally excited CN(A) products but, in contrast to HCN, no significant branching to CN(B) products is observed. The corresponding β parameter, which is found to be relatively invariant with CN internal energy, indicates a near limiting perpendicular distribution of D atom velocities about the photolysis radiation. These results are interpreted with reference to the available ab initio calculated potential energy surfaces of A′ and A″ symmetry, and the relative propensities for excitation to, and the likely dynamics on, these various excited states is discussed.
Analysis on generalized superspaces
Authors: Kobayashi Yuji , Nagamachi Shigeaki
Published: July 2002

The analysis over σ-commutative algebras (generalized supercommutative algebras), that is, differentiation and integration for functions defined on superspace over a σ-commutative algebra, is studied.
Compatibility of weak rigidity with some types of elastic schemes
Authors: del Olmo V. , Olivert J.
Published: July 2002

The behavior of the hypoelastic-Synge, hypoelastic-Maugin, and hypoelastic-Carter and Quintana almost-thermodynamic material schemes, under weak rigidity hypotheses, is studied. In every case, the absence of principal transverse shock waves (or the vanishing of the corresponding speeds) is obtained. The same result follows for the longitudinal shock waves when the Lamé coefficient μ does not vanish. A definition of an elastic almost-thermodynamic material scheme based on the Fermi–Walker transport is proposed and compared with the above elastic schemes. The speeds of the principal shock waves associated are attained and its compatibility with the Ferrando–Olivert incompressibility condition is proved. In the presence of weak rigidity the elastic schemes here defined lead (assuming μ≠0) to the Born-rigidity condition.
A generalization of Penrose’s helicity theorem for space-times with nonzero dual mass
Authors: Magnon Anne
Published: July 2002

An algebraic definition of the helicity operator ℋ is proposed for vacuum stationary and asymptotically flat wormholes (i.e., space-times where the manifold of orbits of the stationary Killing field has S2×R topology). The definition avoids the use of momentum space or Fourier decomposition of the gravitational degrees of freedom into positive and negative frequency parts, and is essentially geared to emphasize the role of nontrivial topology. It is obtained via the introduction of a total spin vector Sα derived from the dual Bondi four-momentum *Pα, both vectors originating in the presence of nontrivial homotopy groups. (Space-times with nonzero dual mass can be characterized by a conformal null boundary ℐ having the topology of an S1 fiber bundle over S2 with possible identifications along the fiber—lens space—or equivalently vanishing Bondi–News.) It is shown that Sα is a constant multiple of Pα, the total Bondi four-momentum, and if in addition the space-time admits a point at spacelike infinity, there is strong support for the past limit of Sα to be a null vector. This can be viewed as a generalization of Penrose’s result on the Pauli–Lubanski vector for classical zero rest-mass particles. The helicity operator at null infinity is rooted in the topology and turns out to be essentially the Hodge duality operator(*). The notion of duality appears as a global concept. Under such conditions, self- and anti-self-dual modes of the Weyl curvature could be viewed as states originating in the nontrivial topology. These results depend crucially on the presence of topological charges; it is tempting to speculate that such wormholes might be basic building blocks.
An approximation formula in the inverse scattering problem
Authors: Saitō Yoshimi
Published: July 2002

An approximate formula is given by which the potential Q(x) can be recovered with any accuracy if only the scattering data of the Schrödinger operator −Δ+Q(x) is known for some sufficiently high energy value k. Thus the scattering data for all k around k=∞ is not needed in order to get a good approximate value for the potential. The main tools for the proof are an asymptotic formula for the S-matrix [Y. Saitō, J. Math. Phys. 25, 3105 (1984)] and the spectral decomposition theorem for the Schrödinger operator −Δ+Q(x) based on the limiting absorption principle.
Volterra algebra and the Bethe–Salpeter equation
Authors: Faraut J. , Viano G. A.
Published: July 2002

The diagonalization of the Bethe–Salpeter equation for the absorptive part of the amplitude is reconsidered. In particular the mathematical tools required by the diagonalization, like the Volterra algebra and the related spherical Laplace transform, are investigated in detail.
Solution of a generalized Chandrasekhar H-equation
Authors: Willis B. L.
Published: July 2002

The Chandrasekhar H-equations are generalized to problems relevant to multigroup transport equations that have nondiagonal cross-section matrices. These equations are shown to have a unique solution in a ball of a Banach space, which satisfies the necessary analyticity properties.
Soliton transformations for axially symmetric higher-dimensional gravity. II. Belinskii–Zakharov N-soliton transformations
Authors: Lee S.-C.
Published: July 2002

The solutions of vacuum Einstein equations in 4+K dimensions with 2+K commuting Killing vectors under the Abelian Kaluza–Klein ansatz are considered. This system admits Belinskii–Zakharov-type soliton transformations. The explicit formulas for general N-soliton transformations are obtained by iterating the formulas for one-soliton transformation.
Stationary axisymmetric Kaluza–Klein black hole
Authors: Mazur P. O. , Bombelli Luca
Published: July 2002

Stationary, rotating Kaluza–Klein black hole solutions are studied in the case of vanishing electric charge. It is shown that in this case the field equations decouple and consist of the vacuum Ernst equations and the Laplace equation for the scalar (dilaton) field. The regular, electrically neutral, rotating Kaluza–Klein black hole is described uniquely by the trivial embedding of the Kerr metric in the five-dimensional space-time.
Locally operating realizations of nonconnected transformation Lie groups
Authors: García-Prada Oscar , del Olmo Mariano A. , Santander Mariano
Published: July 2002

A systematic study of locally operating multiplier realizations of nonconnected Lie groups of transformations is presented that generalizes previous results on connected groups. The semilinear locally operating multiplier realizations of a nonconnected group G are those obtained through an induction process from the finite-dimensional semilinear representations of a given subgroup of a representation group Ḡ for G.
Meixner–Pollaczek polynomials and the Heisenberg algebra
Authors: Koornwinder Tom H.
Published: July 2002

An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)]. The continuous Hahn polynomials turn out to be Meixner–Pollaczek polynomials. Use is made of the connection between Laguerre polynomials and Meixner–Pollaczek polynomials, the Rodrigues formula for Laguerre polynomials, an operational formula involving Meixner–Pollaczek polynomials, and the Schrödinger model for the irreducible unitary representations of the three-dimensional Heisenberg group.
Integral bounds for radar ambiguity functions and Wigner distributions
Authors: Lieb Elliott H.
Published: July 2002

An upper bound is proved for the Lp norm of Woodward’s ambiguity function in radar signal analysis and of the Wigner distribution in quantum mechanics when p>2. A lower bound is proved for 1≤p<2. In addition, a lower bound is proved for the entropy. These bounds set limits to the sharpness of the peaking of the ambiguity function or Wigner distribution. The bounds are best possible and equality is achieved in the Lp bounds if and only if the functions f and g that enter the definition are both Gaussians.
Real representations of finite Clifford algebras. II. Explicit construction and pseudo-octonion
Authors: Okubo Susumu
Published: July 2002

It has been shown that any real irreducible representation of any C(p,q) can be, in principle, explicitly constructed inductively. The relation between the pseudo-octonion algebra and C(8,0) as well as C(0,8) has also been investigated in some detail. Finally, dimensions of the real spinor representations of SO(p,q) have been studied.
Anomalous basis for representations of the Poincaré group
Authors: Moshinsky M. , Loyola G. , Villegas C.
Published: July 2002

The basis for irreducible representations of groups can have many realizations. Usually those presented in textbooks are the simpler ones based on eigenstates of one-particle Casimir operators. There are of course other types of operators, involving occasionally many particles, that may be invariant under a given group, and their eigenstates then provide a new basis, to which the name of anomalous shall be given, for irreducible representations. This paper shall first illustrate the concept for the simple case of the two-dimensional Euclidean group E(2). The main objective though will be to show that an operator, to which the name of the many-body Dirac oscillator is given, is invariant under the Poincaré group. Thus its eigenstates, which will be discussed explicitly in the case of two bodies, are an anomalous basis for irreducible representations of this group, and the representations are derived explicitly. The many-body Dirac oscillator can then be used with confidence in relativistic problems involving several interacting particles.
The zero-dimensional problem in Φ4 field theory
Authors: Manolessou M.
Published: July 2002

This article describes a new approach to the study of a Φ4 scalar field theory. A previous work addressed the problem of equations of motion of the Schwinger functions proving the existence of a unique nontrivial solution in 0≤r≤2 dimensions. Here, the zero dimensions (i.e., no momentum dependence) are focused on a greatly simplified version of the proof of the existence and uniqueness of the solution is presented, which, moreover, can be extended to the case of r=1,2 dimensions in a straightforward way.
Relativistic interactions by means of boundary conditions: The Breit–Wigner formula
Authors: Moshinsky M. , Laurrabaquio G. López
Published: July 2002

The relativistic generalization of the Breit–Wigner formula presented in this paper is not based on perturbative quantum field theory. Rather, it starts with two free Klein–Gordon or Dirac particles interacting only at the point of coincidence in space-time. This state has then two components, the two-particle one just mentioned and a single-particle one representing the compound system. From considerations of conservation of probability the boundary condition is derived relating the two-particle component at coincidence with the one-particle component of this state. From this boundary condition, the R and S matrices of the problems are obtained as well as a Breit–Wigner type of cross section. The present paper is restricted to a scalar compound particle so its spin is 0 and its parity +. In the concluding section, the generalization to one-point, but still Poincaré invariant, boundary conditions is mentioned. This generalization allows one to go to compound particles with arbitrary spin and parity and, in particular to the case 1− which may be of some practical interest.
Transcendentally small reflection of waves for problems with/without turning points near infinity: A new uniform approach
Authors: Gingold Harry , Hu Jishan
Published: July 2002

In this paper the generalized Liouville–Green approximation is used to study the wave reflection with a turning point at infinity. The method provided here unifies the work by many authors in finding the nontrivial behavior of the reflection coefficient for high-energy particles above barrier in the semiclassical limit.
Hyperbolicity of invariant wave equations
Authors: Darkhosh Teymour
Published: July 2002

The method of characteristics is used to construct the fundamental solution to a system of second-order partial differential equations. Conditions that the coefficients have to satisfy to preserve the hyperbolicity are determined and the influence of lower-order terms is indicated. As an example, the Proca wave equation in an external field is analyzed.
Families of invariants of the motion for the Lotka–Volterra equations: The linear polynomials family
Authors: Cairó L. , Feix M. R.
Published: July 2002

The modified Carleman embedding method already introduced by the authors to find first integrals (invariants of the motion) of polynomial form to the Lotka–Volterra system is described in detail, and its efficiency to treat the N-dimensional system proved. Using this method, an extensive investigation is performed for polynomials of the first degree, which allow a classification of the integrals in three families. For some systems possessing one invariant it is possible to find a second invariant using rescaling methods. They represent very restrictive solutions, implying that there exists a great number of conditions among the equation’s coefficients to satisfy. A proof is given that the Volterra invariants can be deduced as a limit. Finally, the interesting properties of the solutions of these systems are studied in detail.
A new topology on space-time
Authors: Fullwood D. T.
Published: July 2002

A new topology, 𝒫̃, is suggested on space-time definable solely in terms of the causal structure, thus combining ideas of both Zeeman (and more specifically Hawking, King, and McCarthy) and Alexandrov to create a very ‘‘physical’’ topology. It is proved that the distinguishing condition holds on a manifold if and only if this new topology is equivalent to the path topology of Hawking, King, and McCarthy. It is also found that the homeomorphism group of 𝒫̃ is the group of chronological and antichronological bijections in the case that the chronology condition holds on the space-time manifold. Thus, if the chronology condition holds 𝒫̃ determines the causal structure, and if the distinguishing condition holds 𝒫̃ determines the causal, differential, and conformal structures of space-time.
Real trajectories in complex-time method and barrier penetrationlike phenomena
Authors: Radosz A. , Magierski W.
Published: July 2002

Various applications of the real trajectories in the complex-time method are discussed. It is shown that the proper way of summation over semiclassical orbits removes existing doubts and leads to the more general formulas than the standard WKB-type one in the energy eigenvalue problem. This method is also used in the description of explicitly time-dependent phenomena. In the problem of escaping from a metastable state, the estimation of a lifetime is in a good agreement with the inverse width of a false ground state energy.
Bounds for the exact matrix elements for radiation processes in hydrogenic atoms
Authors: Moses Harry E. , Prosser Reese T.
Published: July 2002

The exact matrix elements for transitions from the ground state to some excited state of a nonrelativistic hydrogenic atom, accompanied by the emission or absorption of a real or virtual photon, are here obtained in closed form. The matrix elements are simple rational functions of the photon energy if the excited state is bound, or have a simple transcendental factor if the excited state is unbound. It follows from the form of these elements that the contribution of each such process to the second-order radiative correction to the ground state energy level is always finite, without renormalization. It also follows that the sum of these contributions over all bound intermediate states is finite, while the sum over all unbound intermediate states diverges at most logarithmically without renormalization.
Methods to determine generators and defining relations for an n-dimensional point group
Authors: Wijnands Frank , Thiers Ad
Published: July 2002

Four methods to determine a generating set of matrices satisfying defining relations of an n-dimensional point group are described, given all point group elements or given a generating set, but without knowing defining relations. The first method makes use of the stepwise construction of the point group, adding a new generator at each step. Defining relations are achieved by making a coset decomposition at each step. Another approach is by use of the lower central series, yielding generators and relations according to a well-known technique. If the point group is nonsolvable, there is a nontrivial subgroup which has itself as commutator group. The first method is then used to treat this subgroup. This approach is denoted as the second method. The third new method is a depth-first search method. At each step in the construction, a certain element is multiplied with a certain generator according to the depth-first search rule. In the fourth method, which is similar to the third method, the point group is constructed according to a breadth-first search rule. The first method gives better results than the other methods with regard to (w.r.t.) the number of defining relations and the computer time.
Geometrization of a general collineation
Authors: Tsamparlis M.
Published: July 2002

Geometrization of a general collineation means to express the collineation as necessary and sufficient conditions on the kinematic quantities (shear, vorticity, expansion) of the congruence of the vector field generating the collineation. It is shown that the generic form of a collineation is Lξgab = 2ψgab + Hab where Hab is a traceless symmetric tensor. A general theorem concerning the geometrization of the generic collineation is presented and its applications are discussed.
Power series everywhere convergent on R and all Qp
Authors: Dragović Branko G.
Published: July 2002

Power series are introduced that are simultaneously convergent for all real and all p-adic numbers. Our expansions are in some aspects similar to those of exponential, trigonometric, and hyperbolic functions. Starting from these series and using their factorial structure new and summable series with rational sums are obtained. For arguments x∈Q adeles of series are constructed. Possible applications at the Planck scale are also considered.
On SO(8)± valued Yang–Mills fields and multi-instanton solutions in eight-dimensional curved space
Authors: Dündarer A. Reşit
Published: July 2002

SO(8)± valued Yang–Mills multi-instantons are generalized to include three more winding numbers by parametrizing S8=CP1+×CP3 and performing the map x = (u,v1,v2,v3) → w = (un,vm11,vm22,vm33), so that the action is proportional to the product nm1m2m3. The fields that emerge in this parametrization form local representations of SO(8) at every point (v,m) of CP3×(Z+)3 through the decomposition SO(8)=SO(8)/SO(7)×SO(7)/SO(6)×SO(6)/U(3)×U(3). Beside the duality relation FΛF=±*FΛF), these fields also satisfy FΛFΛF∼±*F.
Integrable nonlinear evolution equations with time-dependent coefficients
Authors: Fuchssteiner Benno
Published: July 2002

A simple and straightforward method for generating completely integrable nonlinear evolution equations with time-dependent coefficients is presented herein. For the equations under consideration, the solutions to those given by vector fields which are independent of time are given, thus explicit links between equations are obtained. As an application of the proposed method it is shown that the linear superposition, with arbitrary time-dependent coefficients, of different members of an integrable hierarchy is again integrable. Furthermore, it turns out that for some integrable equations [like the Korteweg–de Vries (KdV), the Benjamin–Ono (BO), or the Kadomtsev–Petviashvili (KP) the resolvent operator of lower order flows can be explicitly obtained from that of any higher order flow. Those flows (demonstrated for the KdV) which can be generated by Lie homomorphisms coming from first order problems are completely classified. Many well-known equations which can be found in the literature are of that type. As an application of such a first order link a direct link is given from KdV to the cylindrical KdV, and from there to the KP with nontrivial dependence on the second spatial variable.
Stable and unstable manifolds in a zone of instability
Authors: Tanikawa Kiyotaka , Yamaguchi Yoshihiro
Published: July 2002

Applying Birkhoff’s twist map theorem, it is shown that the closure of each of stable and unstable manifolds of any homoclinic Birkhoff saddle (see text for definition) in a zone of instability contains the boundary curves of the zone. It is shown as corollaries that (1) all the stable and unstable manifolds of different homoclinic Birkhoff saddles have heteroclinic points; (2) as soon as the boundary invariant curve, which separates two adjacent zones of instability, disintegrates, stable and unstable manifolds of all the homoclinic Birkhoff saddles of both zones intersect with each other; and (3) the stable and unstable manifolds of any homoclinic Birkhoff saddle have an infinite number of disjoint arcs which start in an ε-neighborhood of one boundary of the zone and end in an ε-neighborhood of the other boundary for any ε≳0.
Asymptotic level state density for parabosonic strings
Authors: Bytsenko A. A. , Odintsov S. D. , Zerbini S.
Published: July 2002

Making use of some results concerning the theory of partitions, relevant in number theory, the complete asymptotic behavior, for large N, of the level density of states for a parabosonic string is derived. It is also pointed out that there is a similarity between parabosonic strings and membranes.
Compressional oscillation frequency of an anharmonic oscillator: The spherical non-neutral plasma
Authors: Turner Leaf , Tiouririne T. N. , Lau A. W. C.
Published: July 2002

The physics of ultrahigh density compressional oscillations of a non-neutral plasma has already been discussed. Here, one technical facet will be analytically plumbed; namely the frequency of such oscillations. These oscillations are governed by differential equations whose solutions involve elliptic integrals of the third kind. Nevertheless, without studying the properties of these integrals, a procedure is demonstrated which permits the development of an analytic formula for the frequency of these anharmonic oscillations. This frequency is shown to be proportional to the cyclotron frequency ωc with a constant of proportionality that depends on the ratio of the difference between the radii of the outer and inner turning points divided by the sum of the radii of the two turning points. These radii, in turn, depend on two constants of integration that represent the energy of the compressional oscillations and the amount of charge in the plasma cloud. The final result of the analysis is that the frequency varies only from ωc/√2 when the above ratio is small to (2/3)1/2ωc when the ratio is large. These limits are also obtained intuitively.
Almost commutative algebra and differential calculus on the quantum hyperplane
Authors: Bongaarts P. J. M. , Pijls H. G. J.
Published: July 2002

A notion of almost commutative algebra is given that makes it possible to extend differential geometric ideas associated with commutative algebras in a simple manner to certain classes of noncommutative algebras. As an example differential calculus on the N-dimensional quantum hyperplane is discussed.
Integral formulas for wave functions of quantum many-body problems and representations of 𝔤l
n
Authors: Etingof Pavel
Published: July 2002

Explicit integral formulas are derived for eigenfunctions of quantum integrals of the Calogero–Sutherland–Moser operator with a trigonometric interaction potential. In particular, explicit formulas for Jack’s symmetric functions are derived. To obtain such formulas, one must use the representation of these eigenfunctions by means of traces of intertwining operators between certain modules over the Lie algebra 𝔤ln, and the realization of these modules on functions of many variables.
Hamilton’s principle in stochastic mechanics
Authors: Pavon Michele
Published: July 2002

In this paper we establish three variational principles that provide new foundations for Nelson’s stochastic mechanics in the case of nonrelativistic particles without spin. The resulting variational picture is much richer and of a different nature with respect to the one previously considered in the literature. We first develop two stochastic variational principles whose Hamilton–Jacobi-like equations are precisely the two coupled partial differential equations that are obtained from the Schrödinger equation (Madelung equations). The two problems are zero-sum, noncooperative, stochastic differential games that are familiar in the control theory literature. They are solved here by means of a new, absolutely elementary method based on Lagrange functionals. For both games the saddle-point equilibrium solution is given by the Nelson’s process and the optimal controls for the two competing players are precisely Nelson’s current velocity v and osmotic velocity u, respectively. The first variational principle includes as special cases both the Guerra–Morato variational principle [Phys. Rev. D 27, 1774 (1983)] and Schrödinger original variational derivation of the time-independent equation.

It also reduces to the classical least action principle when the intensity of the underlying noise tends to zero. It appears as a saddle-point action principle. In the second variational principle the action is simply the difference between the initial and final configurational entropy. It is therefore a saddle-point entropy production principle. From the variational principles it follows, in particular, that both v(x,t) and u(x,t) are gradients of appropriate principal functions. In the variational principles, the role of the background noise has the intuitive meaning of attempting to contrast the more classical mechanical features of the system by trying to maximize the action in the first principle and by trying to increase the entropy in the second. Combining the two variational principles, we get the quantum Hamilton principle, i.e., a variational characterization of the logarithm of the wave function ψ. The Lagrangian is the Lagrangian of classical mechanics with the complex-valued velocity v−iu replacing the classical velocity. The dynamics is given by a stochastic differential equation for real-valued diffusions with complex-valued drift and driving noise processes. From the variational principle we derive a Newton-type law. We finally define the momentum process and show that its mean and variance coincide with those of the quantum momentum operator.
Group quantization on configuration space
Authors: Navarro Miguel , Aldaya Víctor , Calixto Manuel
Published: July 2002

New features of a previously introduced group approach to quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the ‘‘quantizing group’’) does not require, in general, the explicit construction of the phase space of the system, i.e., does not require the actual knowledge of the general solution of the classical equations of motion; in many relevant cases an implicit construction of the group can be given, directly, on configuration space. To show an application, we construct the symmetry group for the conformally invariant massless scalar and electromagnetic fields and the scalar and Dirac fields evolving in a symmetric curved space-time or interacting with symmetric classical electromagnetic fields. Further generalizations of the present procedure are also discussed and in particular the conditions under which non-Abelian groups (mainly affine groups and more general gauge groups) can be included.
The projective unitary irreducible representations of the Galilei group in 1+2 dimensions
Authors: Grigore D. R.
Published: July 2002

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions 𝒢+↑. For a nontrivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of 𝒢+↑.
Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra
Authors: van den Hijligenberg N. , Martini R.
Published: July 2002

We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of U(g). The construction of such differential structures is interpreted in terms of color Lie superalgebras.
Feynman–Kac kernels in Markovian representations of the Schrödinger interpolating dynamics
Authors: Garbaczewski Piotr , Olkiewicz Robert
Published: July 2002

Probabilistic solutions of the so-called Schrödinger boundary data problem provide for a unique Markovian interpolation between any two strictly positive probability densities designed to form the input–output statistics data for the process taking place in a finite-time interval. The key issue is to select the jointly continuous in all variables positive Feynman–Kac kernel, appropriate for the phenomenological (physical) situation. We extend the existing formulations of the problem to cases when the kernel is not a fundamental solution of a parabolic equation, and prove the existence of a continuous Markovian interpolation in this case. Next, we analyze the compatibility of this stochastic evolution with the original parabolic dynamics, which is assumed to be governed by the temporally adjoint pair of (parabolic) partial differential equations, and prove that the pertinent random motion is a diffusion process. In particular, in conjunction with Born’s statistical interpretation postulate in quantum theory, we consider stochastic processes which are compatible with the Schrödinger picture quantum evolution.
Higher-order Melnikov theory for adiabatic systems
Authors: Soto-Treviño Cristina , Kaper Tasso J.
Published: July 2002

In this paper, we study adiabatic Hamiltonian systems including those subject to small-amplitude forcing and damping. It is known that simple zeroes of the adiabatic Poincare–Arnold–Melnikov function imply the existence of primary intersection points of the stable and unstable manifolds of hyperbolic orbits. Here, we present an Nth-order Melnikov function whose simple zeroes correspond to Nth-order transverse intersection points and hence to N-pulse homoclinic orbits. Using this function, it can be shown that N-pulse homoclinic orbits arise in a plethora of adiabatic models, including systems with slowly varying potentials. The theory is illustrated on a damped Hamiltonian system with a slowly varying cubic potential. In addition, the Nth-order adiabatic Melnikov function is useful for showing the existence of multi-pulse resonant periodic orbits in the special class of slow, time-periodic systems.
Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies
Authors: Shaw Jiin-Chang , Tu Ming-Hsien
Published: July 2002

We construct the Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies. Both the eigenfunctions and the adjoint eigenfunctions of the hierarchies are used to trigger the transformations. The canonical properties of the constructed Miura and auto-Bäcklund transformations are also investigated.
Gamow vectors for degenerate scattering resonances
Authors: Antoniou I. E. , Gadella M. , Pronko G. P.
Published: July 2002

In this paper we construct Gamow vectors for resonances given by poles of the analytic continuation of the S matrix of any finite order. We study their modes of decay (or growth). We obtain Jordan block structures for the extended Hamiltonians and evolution operators on the subspaces spanned by these Gamow vectors. We perform this study within the context of the rigged Hilbert space extension of quantum theory. We construct an explicit Friedrichs model with a double pole resonance to illustrate the general formulation.
Coupling constant thresholds of perturbed periodic Hamiltonians
Authors: Fassari Silvestro , Klaus Martin
Published: July 2002

We consider Schrödinger operators of the form Hλ=−Δ+V+λW on L2(Rν) (ν=1, 2, or 3) with V periodic, W short range, and λ a real non-negative parameter. Then the continuous spectrum of Hλ has the typical band structure consisting of intervals, separated by gaps. In the gaps there may be discrete eigenvalues of Hλ that are functions of the parameter λ. Let (a,b) be a gap and E(λ)∈(a,b) an eigenvalue of Hλ. We study the asymptotic behavior of E(λ) as λ approaches a critical value λ0, called a coupling constant threshold, at which the eigenvalue either emerges from or is absorbed into the continuous spectrum. A typical question is the following: Assuming E(λ)↓a as λ↓λ0, is E(λ)−a∼c(λ−λ0)α for some α>0 and c≠0, or is there an expansion in some other quantity? As one expects from previous work in the case V=0, the answer strongly depends on ν.
q-phase-coherent states and their squeezing properties
Authors: Yang Yaping , Lin Zhixin , Xie Shuangyuan , Feng Weiguo , Wu Xiang
Published: July 2002

Some kinds of q-phase-coherent states of a q-harmonic osscillator in a finite-dimensional Hilbert space are constructed. Some properties of these states are discussed. Second-order squeezing properties of these states with respect to the phase quadrature operators are studied. The number-phase squeezing and number-phase uncertainty relations are also studied in detail for a two-state system. Some new number-phase minimum uncertainty states are found.
The quantum canonical ensemble
Authors: Brody Dorje C. , Hughston Lane P.
Published: July 2002

The phase space Γ of quantum mechanics can be viewed as the complex projective space CPn endowed with a Kählerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrödinger equation as generating a Hamiltonian dynamics on Γ. Based upon the geometric structure of the quantum phase space we introduce the corresponding natural microcanonical and canonical ensembles. The resulting density matrix for the canonical Γ-ensemble differs from the density matrix of the conventional approach. As an illustration, the results are applied to the case of a spin one-half particle in a heat bath with an applied magnetic field.
Bifurcations of new eigenvalues for the Benjamin–Ono equation
Authors: Pelinovsky Dmitry E. , Sulem Catherine
Published: July 2002

A criterion for the emergence of new eigenvalues is found for the linear scattering problem associated with the Benjamin–Ono (BO) equation. This bifurcation occurs due to perturbations of nongeneric potentials which include the soliton solutions of the BO equation. The asymptotic approximation of an exponentially small new eigenvalue is derived. The method is based on the expansion of a localized function through a complete set of unperturbed eigenfunctions. Explicit expressions are obtained for the soliton potentials.
Conservation laws for linear equations on braided linear spaces
Authors: Klimek M.
Published: July 2002

The properties of linear equations on braided linear spaces are investigated and conservation laws for them are derived. The conserved currents are given in the explicit form. The procedure is then applied to scalar wave equations on a quantum plane and on q-Minkowski space.
Onset of nonlinear waves on falling films
Authors: Chang Hsueh-Chia
Published: July 2002

Steady waves on a thin liquid film flowing down an inclined plane are analyzed near the critical Reynolds number. A second-order bifurcation analysis of an interface equation, which is valid to third order in the long-wave expansion, reveals two sets of waves near criticality. One set travels faster than twice the interfacial velocity, while the other set is symmetrically slower for the vertical film. Each set contains two families of shocks, one family of periodic waves, and a single solitary wave. Local analytical estimates of the velocity, amplitude, and wavelength are obtained for all waves. These estimates are favorably compared to numerical solutions of the steady waves and to experimental data near criticality. An interesting result is that naturally excited waves with wavelengths close to the maximum growing linear mode should not be studied with a local analysis near the neutral curve. Instead, they are better approximated by a Melnikov perturbation of the solitary wave solution.
Response of a filamentary vortex to sound
Authors: Lund Fernando
Published: July 2002

The motion of a test vortex filament induced by a sound wave of frequency high in comparison with the vortex time scales, at low Mach numbers, is studied. To leading order the filament moves with the local speed of the sound wave. The small but finite compressibility introduces retardation effects that modify this behavior: for example, there is a self-induction effect for a point vortex. A differential equation, depending on one cutoff parameter that quantifies this assertion both in two and three dimensions, is derived in a localized induction approximation. This is done by use of a variational principle that governs inviscid irrotational adiabatic flow. The velocity and pressure, generated by the vortex, are expressed in terms of a multivalued velocity potential, as convolutions of a Green’s function and a source localized on the filament. Substitution of these expressions into the action, whose extrema give the equations of fluid flow, renders it a functional of the vortex filament history. Its extrema, with respect to variations of this history, determine the equation of vortex evolution. The multivalued velocity potential is used to recast the usual theory of vortex sound. Incompressible vortex dynamics is used as an example to introduce and illustrate these methods.
Leveling of thin films over uneven substrates during spin coating
Authors: Stillwagon L. E. , Larson R. G.
Published: July 2002

The planarization, that is leveling, of 1–4 μm thick liquid epoxy films over 25–200 μm wide isolated trenches on a silicon substrate during spin coating is determined by photochemically hardening the film and measuring the film profiles over the trenches with a profilometer. The profiles are quantitatively described by a simple lubrication theory that takes advantage of the thinness of the film compared to the feature width, the narrowness of the feature width compared with the distance of the feature from the substrate center, and the rapidity of change in the film profile compared to the overall rate of centrifugally driven film thinning. For a fixed ratio of film thickness to trench depth hf/d, the experimental data fall on a single curve when planarization is plotted against a dimensionless parameter Ω2≡ρω2w3r0/γhf, where ρ is the density of the liquid film, ω is the substrate angular velocity, w is the trench width, r0 is the radial position of the trench, and γ is the film surface tension. For a fixed value of Ω2, planarization improves with decreasing hf/d ratios. Theoretical planarization versus Ω2 curves agree reasonably well with the experimental data. Data for a positive photoresist film form a similar curve to that formed by the epoxy data, but at lower planarization values because of spinning solvent evaporation that causes film shrinkage and degradation of planarization. The effects of evaporation can be accounted for by dividing the spin-coating process into two stages. In the first the film remains fluid and the profile equilibrates with the overall film thickness. In the second the film is immobile and thins only by evaporation.
Fluctuation-response relations in systems with chaotic behavior
Authors: Carnevale G. F. , Falcioni M. , Isola S. , Purini R. , Vulpiani A.
Published: July 2002

The statistics of systems with good chaotic properties obey a formal fluctuation-response relation which gives the average linear response of a dynamical system to an external perturbation in terms of two-time correlation functions. Unfortunately, except for particularly simple cases, the appropriate form of correlation function is unknown because an analytic expression for the invariant density is lacking. The simplest situation is that in which the probability distribution is Gaussian. In that case, the fluctuation-response relation is a linear relation between the response matrix and the two-time two-point correlation matrix. Some numerical computations have been carried out in low-dimensional models of hydrodynamic systems. The results show that fluctuation-response relation for Gaussian distributions is not a useful approximation. Nevertheless, these calculations show that, even for non-Gaussian statistics, the response function and the two-time correlations can have similar qualitative features, which may be attributed to the existence of the more general fluctuation-response relation.
The effect of boundary-layer turbulence on mixing in heated jets
Authors: Strykowski P. J. , Russ S.
Published: July 2002

The mixing properties of a heated axisymmetric jet at a density ratio of 0.55 were examined for initially laminar and turbulent separated boundary layers. Initially laminar jets displayed large intermittent spread rates with half-angles up to 45° and a corresponding rapid decay of the streamwise velocity and temperature on the jet axis. When the boundary layer was disturbed upstream of the nozzle exit, creating an initially turbulent separated layer, the jet mixing was significantly reduced. Flow visualization revealed that the turbulent conditions eliminated the intermittent nature of the jet spreading, producing constant spreading rates at half-angles near 10°.