bluuebunny/crossref_metadata_2025 huggingface dataset:
Conformal Birkhoff and Taub theorems in higher dimensions
Authors: Liang Can-bin
Published: July 2002

The result of a recent paper [Kuang and Liang, J. Math. Phys. 29, 2475 (1988)] is generalized to higher dimensions, i.e., it is proved that any conformally spherically (resp. plane-) symmetric solution to vacuum Einstein equations in higher dimensions must be the generalized Schwarzschild (resp. generalized Taub–Kasner or flat) metric.
Minimization of Landau potentials invariant under O(3).II
Authors: Brihaye Y. , Delaunois F. , Nuyts J.
Published: July 2002

In a previous paper, the absolute minima for Landau potentials were computed for the irreducible representations of SO(3) or O(3) of spin up to four. Here, this analysis is extended to the case of spin five and six. Some novel properties of the extrema are pointed out.
Corrections to the coherent state path integral: Comments upon a speculation of L. S. Schulman
Authors: Marchioro T. L.
Published: July 2002

Intuitively, the Feynman path integral corresponds to a weighted sum over classical paths, an interpretation that fails for the phase space path integral. To address the question of whether there exists a path integral expression conforming to a sum over paths in phase space, an examination of the discrete coherent state path integral (CSPI) is undertaken. Via an alternative formulation of the CSPI, it is shown that the coherent state action for a broad class Hamiltonians can be transformed from the variables (q,p) to (q,q̇). For these Hamiltonians, such a transformation along with the inclusion of all terms O(ε(zi−zi−1)) yields an expression which, for finite ε, can be interpreted as a sum over classical paths with Gaussian weight. The numerical evaluation of this expression through importance sampling (Monte Carlo) is demonstrated.
Bäcklund transformations for generalized nonlinear Schrödinger equations
Authors: Kingston J. G. , Sophocleous C.
Published: July 2002

A general class of Bäcklund transformations are considered for equations of the form izy+zxx+f(z,z̄)=0, where f(z,z̄) is a function of z=x+iy and z̄=x−iy. The nonlinear forms of this equation that admit such transformations are completely classified and shown to exist only when f(z,z̄)=z2z̄ (the nonlinear Schrödinger equation), z ln z̄, z ln z, (z+z̄)2, or suitable combinations of these functions. The form f(z,z̄)=(z+z̄)2 leads to auto-Bäcklund transformations for the Boussinesq equation.
Classical and quantum motion in an Eguchi–Hanson space
Authors: Mignemi S.
Published: July 2002

The motion of classical and quantum particles in a background constituted by an Eguchi–Hanson manifold is studied. The problem is separable in both cases, but analytic solutions are difficult to obtain. Some approximation methods are discussed and the formalism of scattering in four dimensions is introduced.
A class of exact solutions of the Einstein–Dirac equations
Authors: Wils Patrick
Published: July 2002

All exact solutions of the Einstein–Dirac field equations are given that satisfy the energy conditions and for which the spinor components of the Dirac bispinor are aligned but have different amplitude. They are all pure radiation fields of Kundt’s class.
Affine collineations in Riemannian spaces
Authors: Hojman Sergio A. , Núñez Darío
Published: July 2002

Sufficient conditions on the Christoffel symbols and metric tensors to insure the existence of affine collineations in Riemann spaces are obtained. A proof of the group property of affine collineations is given. Several examples of physically relevant Riemannian spaces admitting affine collineations are presented and the constants of motion are constructed.
Classification results and the Darboux theorem for low-order Hamiltonian operators
Authors: Cooke David B.
Published: July 2002

Hamiltonian operators and their behavior under differential substitutions are studied. Scalar Hamiltonian operators are classified up to fifth order, and it is shown that all such operators may be obtained from the first-order Gardner operator, Dx, by differential substitutions, thus proving an infinite-dimensional Darboux theorem for Hamiltonian systems of evolution equations corresponding to such operators.
Conformal invariance, extremals, and geodesics in two-dimensional gravity with torsion
Authors: Katanaev M. O.
Published: July 2002

The conformal symmetry transformations are elucidated for two-dimensional gravity with torsion in conformal gauge. The model is proved to describe one parameter family of surfaces with torsion. On these surfaces equations for extremal and geodesic lines are completely integrated and analyzed.
Solutions for the classical sigma model in the hedgehog ansatz
Authors: Ananias Neto Jorge , Ferreira Erasmo
Published: July 2002

All kinds of solution of the Euler–Lagrange equation obtained from the chiral nonlinear sigma model Lagrangian with the hedgehog ansatz for the SU(2) field are investigated. Making use of the scale invariance of the equation of motion, the solutions are classified in families, according to their analytic properties. It will be shown that the energy integral diverges for all possible classes of solution, and that a finite topological charge can be defined for only one class of solution, and has only one possible numerical value (and its negative).
Generalized gauge fields
Authors: Kerbrat Yvan , Kerbrat-Lunc Hélène , Śniatycki Jȩdrzej
Published: July 2002

Coupling constants in gauge theory are eigenvalues of invariant linear transformations in the Lie algebra 𝔤 of the structure group G. Generalized gauge fields are obtained by considering equivariant maps from the principal fiber bundle of the theory to the space of linear transformations in 𝔤 which take values in an orbit of G. Behavior of generalized gauge fields with respect to reduction and extension of the structure group is investigated. The induced symmetry breaking is analyzed, and the mass spectrum for G=SU(5) is computed.
Colliding gravitational plane waves with noncollinear polarizations
Authors: Li Wei , Hauser Isidore , Ernst Frederick J.
Published: July 2002

A method devised recently by Hauser and Ernst [J. Math. Phys. 31, 871 (1990)] is exploited to deduce an elegant generalization of the FIB/EGH family of colliding wave solutions [J. Math. Phys. 29, 681 (1988)] involving five parameters plus a real analytic function ψ0(z,ρ). All metrical and curvature quantities are evaluated explicitly, and solutions in which curvature singularities are avoidable are identified.
Thermodynamic variables of a relativisitic gas in collision-dominated equilibrium
Authors: Mason D. P. , Kgathi A. M.
Published: July 2002

The thermodynamic variables of a relativistic gas in collision-dominated equilibrium are investigated as functions of the particle number density n and the entropy per unit volume s. Two first-order linear partial differential equations are derived for the absolute temperature T(n,s) and the chemical potential per particle K(n,s). The equations depend on the pressure p that has to be specified through an equation of state. General solutions for T(n,s), K(n,s), and the total energy density μ(n,s) are obtained for a relativistic Maxwell–Boltzmann gas for which the perfect gas law p=nkT must hold, where k is Boltzmann’s constant, and for gases with equations of state p=(γ−1)μ(1≤γ≤2) and μ=ρ+[p/(γ−1)](1<γ≤2) where γ is a constant and ρ is the rest-mass density. It is shown that if p=(γ−1)μ then T is a homogeneous function of degree γ−1 in n and s, which extends from γ=2 to 1≤γ≤2 a result established by Oliver and Davis [Ann. Inst. H. Poincaré 30, 339 (1979)]. The modification of this result for the equation of state μ=ρ+p/(γ−1) is determined. For a relativistic Maxwell–Boltzmann gas for which both p=nkT and either p=(γ−1)μ or μ=ρ+p/(γ−1) are satisfied, T(n,s), K(n,s), and μ(n,s) are determined up to an arbitrary constant.
Uniqueness in some quasi-Goursat problems in 3+1 dimensions and the inverse scattering problem
Authors: Newton Roger G.
Published: July 2002

The plasma wave equation with boundary conditions either on the light cone, or on a tangent plane to it, or on both, is studied. These problems arise in solutions to the inverse scattering problem but are of independent interest.
Properties of block renormalization group operators for Euclidean Fermions in an external gauge field
Authors: Balaban Tadeusz , O’Carroll Michael , Schor Ricardo
Published: July 2002

The basis is laid for a block renormalization analysis of spinor electrodynamics in d=2,3 dimensions in a lattice approximation. The Fermion part of the renormalization group transformation gives rise to a sequence of localized Fermion action, fluctuation covariance, and minimizer operators in a regular external gauge field. It is shown that these operators are uniformly bounded analytic functions of complex-valued gauge fields with uniform exponentially decaying kernels.
Enhanced diffusivity and intercell transition layers in 2-D models of passive advection
Authors: Avellaneda Marco
Published: July 2002

A class of two-dimensional, isotropic, divergence-free vector fields is introduced and the effective diffusivity of the corresponding advection–diffusion equations is studied. These examples are very idealized flows, but they can be solved exactly in the limit Pe≫1. Scaling laws D*∝D0(Pe)α are obtained, where D0=molecular diffusion, Pe=Peclet number, with exponents in the range 0<α<1, and examples of ‘‘stream functions’’ with logarithmic singularities for which D*∝D0Pe. The exponent α is related by a simple formula to the shape of the stream function along cell boundaries, suggesting that similar scaling laws should hold for more general 2-D closed-cell flows.
Symmetry properties and solutions of nonlinear dispersive thin-film equations in three dimensions
Authors: Melkonian S. , Winternitz P.
Published: July 2002

The Lie point symmetries are obtained for each one of two, nonlinear, dispersive thin-film equations in 2+1 variables. By means of the invariants of the one- and two-dimensional subgroups, all reductions to ordinary differential equations and to partial differential equations in two variables are obtained. Solutions are provided for a number of the reduced equations. It is also ascertained that neither one of the two considered thin-film equations is integrable. In some cases, solitary- and periodic-wave solutions having curved wavecrests are obtained.
Geometric quantization of N=2 superstring
Authors: Merkulov Sergey A.
Published: July 2002

A nonperturbative geometric formulation of the N=2 Neveu–Schwarz superstring theory which has been recently interpreted by H. Ooguri and C. Vafa [Mod. Phys. Lett. A5, 1389 (1990)] as a consistent quantum theory of self-dual gravity in four dimensions, is constructed. It is shown that the natural complex structure over the loop superspace ΩMd‖d associated to the N=2 Neveu–Schwarz fermionic string, is invariant under symmetry group OSp(2‖2)⊆SuperdiffS1‖2. Moreover, it is proved that there is a unique Lorentz and OSp(2‖2) invariant complex structure on ΩMd‖d. This result implies that the superspace of all admissible complex structures over ΩMd‖d is isomorphic to the homogeneous Kähler supermanifold SuperdiffS1‖2/OSp(2‖2). The Ricci curvature of SuperdiffS1‖2/OSp(2‖2) is calculated. Applying the method of geometric quantization to the N=2 Neveu–Schwarz superstring theory along the lines suggested by M. J. Bowick and S. G. Rajeev [Nucl. Phys. B361, 469 (1991)], a representation is constructed of nonperturbative N=2 superstring vacua in terms of antiholomorphic and horizontal sections of a certain vector bundle over SuperdiffS1‖2/OSp(2‖2); it is proved that such sections exist only in complex dimension d=2.
A new boson realization for the isotropic three-dimensional oscillator
Authors: Marshalek Eugene R.
Published: July 2002

Two new closely related boson realizations of the Heisenberg–Weyl algebra are derived that are directly equivalent to the introduction of spherical coordinates for the isotropic three-dimensional harmonic oscillator. This provides another way to obtain matrix elements of all physical operators connecting angular-momentum eigenstates, which are represented here by simple products of boson operators acting on the vacuum. Two of these bosons carry the angular-momentum quantum numbers while the third is a novel ‘‘radial boson.’’ In this approach, one begins by finding the nonunitary Dyson and then the unitarized Holstein–Primakoff realizations for the spectrum-generating SU(1,1)×SO(3) algebra of the oscillator. The corresponding mappings of the Heisenberg–Weyl generators are then obtained from their tensor properties under SU(1,1)×SO(3). The Dyson map of the Heisenberg–Weyl generators is not uniquely determined in this way, but the Holstein–Primakoff map is nevertheless unique. The possibility exists for generalization to isotropic oscillators of higher dimension, which are of interest in connection with nuclear collective motion.
Dixon–Selberg summation over local number fields
Authors: Thiran E. , Weyers J.
Published: July 2002

The character summation formula analogous to Dixon’s theorem for the hypergeometric function 3F2 is derived for R and Qp.
Topological aspects of Liouville field theory and conformal anomaly
Authors: Roy Ashim , Bandyopadhyay Pratul
Published: July 2002

It is shown that conformal anomaly is connected with the topological properties of the Liouville field theory which arises out of the quantum geometry necessary for the quantization procedure. As in the particle picture, the quantization of a Fermi field can be achieved through the introduction of an anisotropic feature in the internal space so that it gives rise to two internal helicities corresponding to particle and antiparticle, in case of a string, also, this specific quantum geometry gives rise to two vortex lines at the endpoints of an open string which is manifested in the Liouville field theory. This helps one to represent a Polyakov string with a nonlinear σ model with the Wess–Zumino term, and the topological aspects of this Wess–Zumino term is found to be associated with those of a Liouville field. When in the Lagrangian formulation this specific quantum geometry is taken into account, it is found that anomaly vanishes.
Euclidean space-time diffeomorphisms and their Fueter subgroups
Authors: Gürsey Feza , Jiang Wenxin
Published: July 2002

Holomorphic Fueter functions of the position quaternion form a subgroup of Euclidean space-time diffeomorphisms. An O(4) covariant treatment of such mappings is presented with the quaternionic argument x being replaced by either p̄x or xp̄ involving self-dual and anti-self-dual structures and p denoting an arbitrary Euclidean time direction. An infinite group (the quasiconformal group) is exhibited that admits the conformal group SO(5,1) as a subgroup, in analogy to the two-dimensional case in which the Möbius group SO(3,1) is a subgroup of the infinite Virasoro group. The ensuing (3+1) covariant decomposition of diffeomorphisms suggests covariant gauges that throw the metric and the stress tensors in standard forms suitable for canonical quantization, leading to ‘‘improved’’ energy-momentum tensors. Other possible applications to current algebra and gravity will be mentioned.
Phase transition in aperiodic quantum Ising models
Authors: You J. Q. , Yan J. R. , Zhong J. X.
Published: July 2002

Phase transition in the aperiodic quantum Ising models were studied, in which the transverse magnetic fields are uniform and the couplings are arranged according to the aperiodic sequences that are generated by two types of two-tile inflation rules with initial condition {ApBq}: A → A′=Am11Bm12, B →B′=Am21Bm22, m12, m21≠0, and A → A′=Am11Bm12, B → B′=Bm21Am22, m12, m22≠0. When the inflation rules have the Pisot–Vijayaraghavan (PV) property in number theory, the generated aperiodic systems undergo phase transition at the critical points. When the inflation rules do not have the PV property, it is found that only by changing the initial conditions, the inflation rules can produce aperiodic systems exhibiting phase transition as well as aperiodic systems which do not exhibit any phase transition.
Oscillator realization of the strange superalgebras P(n) and Q(n)
Authors: Frappat L. , Sciarrino A.
Published: July 2002

The strange superalgebra P(n) is realized in terms of bilinear products of oscillators of bosonic and fermionic type. The even part is given by sums of bilinears in bosons and fermions, and the odd part by bilinears in one boson and one fermion. These oscillators can be used to build explicit realizations of some highest weight irreducible representations of P(n). This procedure is illustrated for P(3), where, in particular, the case of the adjoint representation of P(3) is worked out in detail. Finally, an oscillator realization of the strange superalgebra Q(n) is also given.
Approximate analytic solutions to the Skyrme equation
Authors: Linde Johan , Snellman Håkan
Published: July 2002

The asymptotic properties and the stability of the solutions of the Skyrme nonlinear differential equation for the profile function F are discussed. Using rational approximants for σ=cos F some different ways of finding approximate analytic solutions to the equation are discussed. For boundary conditions appropriate to soliton number 1 we construct a sequence of approximate analytic solutions that rapidly approaches the true solution according to several quality tests.
Multifold group integral for SU(2) character and sum rule among 6-j symbols
Authors: Tanimura N. , Tanimura O.
Published: July 2002

The sum rules among 6-j symbols are derived on the basis of the multifold group integral for the SU(2) characters. The formulas for simple multifold group integrals are derived by means of the graphic method.
Time-dependent rototranslational diffusion equation with multiple mixed boundary conditions: A formally exact analytical solution
Authors: Baldo M. , Grassi A. , Raudino A.
Published: July 2002

A formally exact analytical solution of the time-dependent rototranslational diffusion equation (RTDE) with mixed boundary conditions applied over both the translational and rotational variables has been derived. The approximation of isotropic translational motion has been imposed and no further approximations have been used in the calculations. The solution has been obtained in the form of a set of homogeneous linear algebraic equations.
Fluctuation path integrals in the generalized coherent states representation
Authors: Fukui Takahiro
Published: July 2002

Fluctuations around classical solutions are evaluated by the path integral method based on the generalized coherent states. A simple expression for the semiclassical propagator is derived and applied to the SU(2) character formula. It is also pointed out that several versions of the coherent states path integral can be considered owing to the nonorthogonal character of the coherent states, and they are compared by applying them to the SU(2) character formula.
Study on the one dimensional boson–fermion model
Authors: Wang Yupeng , Jin Duo
Published: July 2002

The one dimensional boson–fermion model is introduced and the general eigenstates of the model Hamiltonian are constructed. The Cooper-pairlike bound state is given. It is concluded that the present model is exactly soluble via the Bethe ansatz.
Caustics in 1+1 integrable systems
Authors: Kitaev A. V.
Published: July 2002

Caustics arising in the asymptotic description of rapidly decaying solutions of the equations integrable via the inverse scattering transform are defined. Different asymptotic approaches to the description are considered. The appearance of members (Ρn2) of the hierarchy of the second Painlevé equation as special functions of wave catastrophies is discussed. The ‘‘adjoining’’ problem Ρn2 → Ρk2(n≳k) for the simplest example Ρ22 → Ρ2 is considered in detail.
Bäcklund transformations and zero-curvature representations of systems of partial differential equations
Authors: Brandt Friedemann
Published: July 2002

It is shown that Bäcklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.
The canonical symmetry for integrable systems
Authors: Leznov A. N. , Razumov A. V.
Published: July 2002

The properties of discrete nonlinear symmetries of integrable equations are investigated. These symmetries are shown to be canonical transformations. On the basis of the considered examples, it is concluded, that the densities of the conservation laws are changed under these transformations by spatial divergencies.
Covariant flux-limited diffusion theory in Bianchi cosmologies
Authors: Bonanno Alfio , Romano Vittorio
Published: July 2002

A covariant flux-limited diffusion theory is presented for homogeneous and anisotropic cosmologies. Explicit formulas for radiation stress tensor and applications are given for Bianchi-type I model.
Coherent state approach to electron nuclear dynamics with an antisymmetrized geminal power state
Authors: Weiner B. , Deumens E. , Öhrn Y.
Published: July 2002

A formulation of the complete dynamics of electrons and nuclei is presented. The dynamical equations are derived using the time-dependent variational principle (TDVP). The approximate electronic state vectors are antisymmetrized geminal power (AGP) states parameterized as projected coherent states, while the nuclei are treated as classical point particles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree–Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the evolution equations (the classical harmonic approximation) which corresponds to a generalized random phase approximation (RPA) based on an AGP electronic reference state and which explicitly includes the dynamics of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic atomic basis thus avoiding any transformation to orthonormal molecular orbitals during the evolution.
High-energy asymptotics of resonances for three-dimensional Schrödinger operator with screened Coulomb potential
Authors: Shubov Marianna A.
Published: July 2002

Resonances for one-particle three-dimensional Schrödinger operators with Coulomb potential perturbed by a spherically symmetric compactly supported function q(r) are studied. The mth derivative of q(r) has a jump on the boundary of the support (m≥0). Resonances are defined as poles of an analytical continuation of the quadratic form of the resolvent to the second Riemann sheet through the branch cut along the continuous spectrum. It is shown that there exists an infinite set of resonance poles which splits into an infinite sequence of infinite series corresponding to different values of an angular momentum. Resonances in each series have the only point of accumulation at infinity. The main result of the work is an asymptotic formula for resonances in each series. It follows from this formula that high-energy resonances of the above operator are asymptotically close to those of the Schrödinger operator with the same potential q(r) but without Coulomb term. It was shown in one of the previous works of the author that, in contrast with the non-Coulomb case, some perturbations q(r) of the Coulomb potential can produce a sequence of resonances converging to zero. The result of this work together with the above result shows that the Coulomb part of the potential, while dramatically changing the geometry of resonances at low energies, does not destroy their asymptotic behavior at high energies.
Properties of solutions of the Kadomtsev–Petviashvili I equation
Authors: Boiti M. , Pempinelli F. , Pogrebkov A.
Published: July 2002

The Kadomtsev–Petviashvili I (KPI) equation is considered as a useful laboratory for experimenting with new theoretical tools able to handle the specific features of integrable models in 2+1 dimensions. The linearized version of the KPI equation is first considered by solving the initial value problem for different classes of initial data. Properties of the solutions in different cases are analyzed in details. The obtained results are used as a guideline for studying the properties of the solution u(t,x,y) of the Kadomtsev–Petviashvili I (KPI) equation with given initial data u(0,x,y) belonging to the Schwartz space. The spectral theory associated to KPI is studied in the space of the Fourier transform of the solutions. The variables p={p1,p2} of the Fourier space are shown to be the most convenient spectral variables to use for spectral data. Spectral data are shown to decay rapidly at large p but to be discontinuous at p=0. Direct and inverse problems are solved with special attention to the behavior of all the quantities involved in the neighborhood of t=0 and p=0. It is shown in particular that the solution u(t,x,y) has a time derivative discontinuous at t=0 and that at any t≠0 it does not belong to the Schwartz space no matter how small in norm and rapidly decaying at large distances the initial data are chosen.
Exactness in the Wentzel–Kramers–Brillouin approximation for some homogeneous spaces
Authors: Funahashi Kunio , Kashiwa Taro , Sakoda Seiji , Fujii Kazuyuki
Published: July 2002

Analysis of the Wentzel–Kramers–Brillouin (WKB) exactness in some homogeneous spaces is attempted. CPN as well as its noncompact counterpart DN,1 is studied. U(N+1) or U(N,1) based on the Schwinger bosons leads us to CPN or DN,1 path integral expression for the quantity tr e−iHT, with the aid of coherent states. The WKB approximation terminates in the leading order and yields the exact result provided that the Hamiltonian is given by a bilinear form of the creation and the annihilation operators. An argument on the WKB exactness to more general cases is also made.
Schlesinger transformations for Painlevé VI equation
Authors: Muğan U. , Sakka A.
Published: July 2002

A method to obtain the Schlesinger transformations for Painlevé VI equation is given. The procedure involves formulating a Riemann–Hilbert problem for a transformation matrix which transforms the solution of the linear problem but leaves the associated monodromy data the same.
Adelic integrable systems
Authors: Pigli Mircea
Published: July 2002

Incorporating the zonal spherical function (zsf) problems on real and p-adic hyperbolic planes into a Zakharov–Shabat integrable system setting, we find a wide class of integrable evolutions that respect the number-theoretic properties of the zsf problem. This means that at all times these real and p-adic systems can be unified into an adelic system with an S matrix that involves (Dirichlet, Langlands, Shimura,...) L functions.
𝒲-gauge structures and their anomalies: An algebraic approach
Authors: Garajeu Daniela , Grimm Richard , Lazzarini Serge
Published: July 2002

Starting from flat two-dimensional gauge potentials we propose the notion of 𝒲-gauge structure in terms of a nilpotent Becchi–Rouet–Stora (BRS) differential algebra. The decomposition of the underlying Lie algebra with respect to an SL(2) subalgebra is crucial for the discussion of conformal covariance, in particular the appearance of a projective connection. Different SL(2) embeddings lead to different 𝒲-gauge structures. We present a general soldering procedure which allows one to express zero curvature conditions for the 𝒲-currents in terms of conformally covariant differential operators acting on the 𝒲-gauge fields and to obtain, at the same time, the complete nilpotent BRS differential algebra generated by 𝒲-currents, gauge fields, and the ghost fields corresponding to 𝒲-diffeomorphisms. As illustrations we treat the cases of SL(2) itself and the two different SL(2) embeddings in SL(3), viz., the 𝒲 (1)3- and 𝒲 (2)3-gauge structures, in some detail. In these cases we determine algebraically 𝒲-anomalies as solutions of the consistency conditions and discuss their Chern–Simons origin.
The canonical connection in quantum mechanics
Authors: Lévay Péter , McMullan David , Tsutsui Izumi
Published: July 2002

In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G invariance is central to the emergence of the H connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-Abelian generalization of Berry’s phase, can also be found in systems that have slow variables taking values in such a coset space.
New no-scalar-hair theorem for black holes
Authors: Saa Alberto
Published: July 2002

A new no-hair theorem is formulated which rules out a very large class of nonminimally coupled finite scalar dressing of an asymptotically flat, static, and spherically symmetric black hole. The proof is very simple and based on a covariant method for generating solutions for nonminimally coupled scalar fields starting from the minimally coupled case. Such a method generalizes the Bekenstein method for conformal coupling and other recent ones. We also discuss the role of the finiteness assumption for the scalar field.
Determinants of Dirac operators with local boundary conditions
Authors: Falomir H. , Gamboa Saraví R. E. , Muschietti M. A. , Santangelo E. M. , Solomin J. E.
Published: July 2002

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green’s functions. We finally apply this result to the case of a bidimensional disk under baglike conditions.
On the structure of projective group representations in quaternionic Hilbert space
Authors: Tao Terry , Millard Andrew C.
Published: July 2002

A structure theorem concerning projective quaternionic representations is stated and proved. A corollary to the structure theorem is then proved, answering a question recently posed by Adler.
The canonical form of the Rabi Hamiltonian
Authors: Szopa M. , Mys G. , Ceulemans A.
Published: July 2002

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann–Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.
Microcanonical ensemble and algebra of conserved generators for generalized quantum dynamics
Authors: Adler Stephen L. , Horwitz L. P.
Published: July 2002

It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space.
Integration of thermodynamic identities for a relativistic general equation of state
Authors: Chattopadhyay Sankar , Ray Dipankar
Published: July 2002

In a recent paper Mason and Kgathi have integrated some well-known thermodynamic identities for an equation of state p=nkT and thereby have obtained some explicit expressions for the thermodynamic variables concerned. In the present paper we integrate the same identities for a more general equation of state p=p(n,T) and thereby obtain more general expressions for the same thermodynamic variables.
Gravitational and electromagnetic perturbations of the Schwarzschild solution
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that the complete metric and vector potential perturbations of the Schwarzschild solution can be expressed in terms of radial functions that share several differential properties. The energy flux of the incident, reflected, and absorbed gravitational and electromagnetic waves is given and the polarization changes are also analyzed.
Density conditions for quantum propositions
Authors: Havlicek Hans , Svozil Karl
Published: July 2002

As has already been pointed out by Birkhoff and von Neumann, quantum logic can be formulated in terms of projective geometry. In three-dimensional Hilbert space, elementary logical propositions are associated with one-dimensional subspaces, corresponding to points of the projective plane. It is shown that, starting with three such propositions corresponding to some basis {u,v,w}, successive application of the binary logical operation (x,y)⟼(x∨y)⊥ generates a set of elementary propositions which is countable infinite and dense in the projective plane if and only if no vector of the basis {u,v,w} is orthogonal to the other ones.
Berry’s phase on SU(n)/S(U(1)×U(n−1)) manifolds
Authors: Giller S. , Gonera C. , Kosiński P. , Maślanka P.
Published: July 2002

It is shown that the Berry phase/matrix for Hamiltonians parametrized by the points of M≡SU(n)/S(U(1)×U(n−1)) and having no accidental degeneracy is expressible in terms of Riemannian connection on M and representations of S(U(1)×U(n−1)).
Recovery of singularities from amplitude information
Authors: Sacks Paul E.
Published: July 2002

Let V(x) denote a potential in the one-dimensional Schrödinger equation, without bound states, for which (1) V(x)=0 for x<0 and (2) V(x) is piecewise continuous with adequate decay as x goes to infinity. We are interested in the problem of determining V given the reflectivity r(k)=|R(k)|, where R is the usual left-hand reflection coefficient. For very special classes of potentials it is known that r determines V uniquely. Here we show that under much more general (although still restrictive) assumptions, the location and magnitude of discontinuities of V can be determined from r. The nature of the restrictions is related to the behavior of R(k) for k in the upper half of the complex plane.
Advection–diffusion past a strip. II. Oblique incidence
Authors: Knessl Charles , Keller Joseph B.
Published: July 2002

Advection and diffusion of particles past an impenetrable strip is considered when the strip is oblique to the advection or drift velocity. The particle concentration p(x,y) is determined asymptotically for large values of vL/D, where v is the drift velocity, D is the diffusion coefficient, and 2L is the width of the strip. The results complement those of Part I, which treated a strip normal to the drift velocity.
Factorization of complex canonical transformations
Authors: Bruhn B.
Published: July 2002

We investigate the Lie series representation of the canonical transformations in a finite dimensional complex phase space. It is shown that any transformation of this type can be factorized into a product of three factors associated with a pure imaginary generating function, a holomorphic function, and an element of the cyclic group C4. The imaginary function can be considered as an observable in the sense of classical mechanics. Some hints are given which suggest that the holomorphic function can be connected with the notion of the state of a physical system. Moreover, a special kind of mappings is studied which provides a link between entropy, action, and state functions. The occurrence of these important physical quantities shows that the mathematical structure goes beyond a formal analogy to quantum physics at least in the finite dimensional case.
A new family of solvable self-dual Lie algebras
Authors: Pelc Oskar
Published: July 2002

A family of solvable self-dual Lie algebras is presented. There exist a few methods for the construction of nonreductive self-dual Lie algebras: an orthogonal direct product, a double extension of an Abelian algebra, and a Wigner contraction. It is shown that the presented algebras cannot be obtained by these methods.
Bott–Borel–Weil construction for quantum supergroup Uq(gl(m|n))
Authors: Zhang R. B.
Published: July 2002

The finite dimensional irreducible representations of the quantum supergroup Uq(gl(m|n)) are constructed geometrically using techniques from the Bott–Borel–Weil theory and vector coherent states.
New structures in the theory of the laser model. II. Microscopic dynamics and a nonequilibrium entropy principle
Authors: Bagarello Fabio , Sewell Geoffrey L.
Published: July 2002

In a recent article, Alli and Sewell [J. Math. Phys. 36, 5598 (1995)] formulated a new version of the Dicke–Hepp–Lieb laser model in terms of quantum dynamical semigroups, and thereby extended the macroscopic picture of the model. In the present article, we complement that picture with a corresponding microscopic one, which carries the following new results. (a) The local microscopic dynamics of the model is piloted by the classical, macroscopic field, generated by the collective action of its components; (b) the global state of the system carries no correlations between its constituent atoms after transient effects have died out; and (c) in the latter situation, the state of the system at any time t maximizes its entropy density, subject to the constraints imposed by the instantaneous values of its macroscopic variables.
Green’s function of the Fokker–Planck equation: General formula of frequency expansion
Authors: Miyazawa Toru
Published: July 2002

The one-variable Fokker–Planck equation is studied in its general form by means of an algebraic method. An expression of the Green’s function is derived as an expansion in powers of the square root of frequency. The expansion coefficient of arbitrary order is expressed as a functional of the potential in terms of integrals.
Magnetohydrodynamic boundary layer on a flat plate: Further analytic results
Authors: Shivamoggi Bhimsen K. , Rollins David K.
Published: July 2002

Further analytic results are deduced with the magnetohydrodynamic boundary layer equations for a flat plate. The asymptotic behavior of the solutions is deduced using the scaling group method. Then, an analytic perturbative procedure is used to determine an approximate solution that exhibits this asymptotic behavior.
Response to “Comment on ‘Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation’ ” [J. Math. Phys. 40, 3685 (1999)]
Authors: Lou Sen-yue , Weng Jian-ping
Published: July 2002

To verify the correctness of the high order symmetries for the Jimbo–Miwa–Kadomtsev–Petviashvilli system (JMKP) and the potential JMKP (PJMKP) system given in our paper [J. Math. Phys. 36, 3492–3497 (1995)], Ma’s definition of ∂x−1 may be used only for the general nonkernel solutions of the models. For some types of special solutions which are the kernels of some differential operators, one has to use ∂x−1 as the indefinite operator and selected the integral functions appropriately.
Equivalence classes of perturbations in cosmologies of Bianchi types I and V: Interpretation
Authors: Banach Zbigniew
Published: July 2002

In the preceding paper, 26 gauge-invariant variables were defined that characterize an almost-Bianchi type I or almost-Bianchi type V universe filled with a nonbarotropic perfect fluid. One can think of these basic variables, denoted collectively by D, as having at least two aspects. First, D gives an explicit (i.e., analytical) representation of the equivalence class of perturbations. In fact, this equivalence class is uniquely determined from D and vice versa. Second, any gauge-invariant quantity with respect to a Bianchi type I or Bianchi type V background model is obtainable linearly from D through purely algebraic and differential operations. Among many other things, the above properties of D facilitate new insights into the question of why a standard and well-known formulation based on the Stewart–Walker lemma does not enable one to describe the equivalence classes of perturbations and to find gauge-invariant variables independent of D. If we pose an analogous question in regard to almost-Robertson–Walker universe models, a different but none-the-less instructive answer is obtained. In this case, the Stewart–Walker lemma provides a complete framework both for constructing all gauge-invariant variables and for determining the equivalence classes of perturbations. Because of the sometimes confusing statements in the literature, nontrivial comparisons with other work on linear perturbations in anisotropic background models are made. We also present what we believe are some interesting applications of our ideas to the subject of quantum field theory in curved space–time.
Low frequency vibrational spectrum of CsDy(MoO4)2
Authors: Kut’ko V. I.
Published: July 2002

Transmission spectrum of CsDy(MoO4)2 single crystals is measured in polarized light in the longwave IR region (10–100 cm−1) at low temperatures 6–40 K. The change in the vibrational spectrum during first-order structural phase transition (Tc∼38 K) is detected experimentally. The vibrational spectrum of CsDy(MoO4)2 is analyzed in the model of “quasi-chipped off” vibrational modes.
Localization of helium around microscopic impurities in liquid helium
Authors: Gordon E. B. , Shestakov A. F.
Published: July 2002

The structure and properties of the environment of impurity atoms Im immersed in liquid helium are examined. It is demonstrated that there are two qualitatively different types of structure of the layer of helium atoms nearest to Im: structures characterized by attraction and repulsion. In the structures with attraction toward the center (for strong Im–He interaction) the Im–He distance is greater than the equilibrium distance for the Im–He pair potential, and the density and localization of helium atoms are greater than in the bulk. Here the number of helium atoms n in the layer is almost independent of the external pressure. In structures with repulsion, which exist for alkali metal atoms, the Im–He distances are shorter than the equilibrium ones, while the density is lower than in bulk helium. For T∼1 K several states with different n are populated, with energies differing only by ∼0.1 K, and n decreases substantially as the pressure is increased. On the basis of this analysis an interpretation is given for the optical and ESR spectra of atoms implanted in liquid and solid helium. A simple model is proposed for determining the characteristics of the helium environment from the experimental pressure dependence of the shifts of the atomic lines in the absorption and emission spectra. It is predicted that in He3-He4 mixtures the structure with attraction should be strongly enriched with He4 atoms, while the structures with repulsion should be enriched with He3. The possible existence of phase transitions in the helium shells surrounding impurity atoms is discussed.
The theoretical model for the annular jet instability—Revisited
Authors: Lee C. P. , Wang T. G.
Published: July 2002

Previously the instability of an annular jet [Proceedings of the 2nd International Colloquium on Drops and Bubbles, Monterey, California, 1981, edited by D. H. LeCroissette (Jet Propulsion Laboratory, Pasadena, CA, 1982), pp. 79–87; Phys. Fluids 29, 2086 (1986)] by a theoretical model [Phys. Fluids 29, 2076 (1986)] was described, in which the liquid layer of the jet is treated as a thin liquid sheet. Although the results are reasonable, the model is not completely satisfactory because certain discontinuities in the system occur as the jet collapses. In this study it is proposed that there is a missing piece of physics there, namely, that when the envelope is closing its bottleneck during collapsing the new envelope must experience a sharp pressure pulse from its gaseous core, which reverses the normal velocity of the sheet just enough to maintain a continuous constant gas flow. With this improved model the problem can be solved more thoroughly. In particular, it was found that if the liquid velocity UJ is high enough and if the gas velocity UG>UJ, then the bubble-formation frequency varies linearly with their difference ΔU=UG−UJ but not with their individual values.
Isothermal condensation on a spherical particle
Authors: Loyalka S. K. , Hamoodi S. A. , Tompson R. V.
Published: July 2002

The problem of isothermal condensation onto a spherical particle for a vapor diffusing through a background gas is considered. Accurate numerical results for the condensation rate and density profile in the Knudsen layer, for arbitrary mass ratio (background/vapor) and Knudsen number, are obtained by use of the SN method and the resulting theoretical values are compared with recent experimental data. The present theoretical results correspond to an assumption of rigid sphere molecular interactions, but the development is sufficiently general that results for other molecular force laws could also be obtained.
Upstream advancing columnar disturbances in two-dimensional stratified flow of finite depth
Authors: Hanazaki Hideshi
Published: July 2002

A numerical study of the two-dimensional flow of linearly stratified Boussinesq fluid past a vertical flat plate in a channel of finite depth is described. It is found that there are time-dependent oscillations in each vertical mode of the upstream advancing columnar disturbances which correspond to the unsteadiness in the drag coefficient found in previous experiments. The long-time behavior of the upstream columnar disturbances shows that the time-averaged strength of each mode approaches some constant value that is not zero. This determines the drag coefficient in the long-time limit. In many points the numerical solutions of the Navier–Stokes equation agree with the solutions of the forced Korteweg–de Vries (KdV) equation with a cubic nonlinear term or the forced KdV–Burgers equation. It is also suggested that the strong downstream columnar disturbances predicted by linear theory for steady flow do not exist.
A note on the generalized Rayleigh quotient for non-self-adjoint linear stability operators
Authors: Didwania A. K. , Goddard J. D.
Published: July 2002

As a generalization of the classical Rayleigh–Ritz technique for self-adjoint systems, a variational method that appears capable of providing rapid estimates of the dispersion relation for complicated, non-self-adjoint linear stability operators is outlined. The method is illustrated by examining the linear stability of Taylor–Dean flow against general three-dimensional disturbances. Relatively simple trial functions provide surprisingly accurate estimates for the dispersion relation.
On the transfer of energy to an unstable liquid jet in a coflowing compressible airstream
Authors: Li Hsi-Shang , Kelly Robert E.
Published: July 2002

The transfer of energy from a compressible airstream to a coflowing unstable liquid jet via the pressure perturbation at the interface is studied as the Mach number varies continuously from subsonic to supersonic values. The ‘‘lift’’ component of the pressure perturbation has been demonstrated to predominate up to slightly supersonic free-stream Mach numbers, after which the ‘‘drag’’ component predominates.