bluuebunny/crossref_metadata_2025 huggingface dataset:
Branching rules for a class of typical and atypical representations of gl(m‖n)
Authors: Gould M. D. , Jarvis P. D. , Bracken A. J.
Published: July 2002

The irreducible representations of the Lie superalgebra gl(m‖n) with highest weights of the form Λ=(λ1,λ2,...λm‖ω̇) are investigated using a recently introduced induced module construction for atypical modules. The gl(m‖n)↓gl(m‖n−1) branching rules are obtained and a suitable Gel’fand–Tsetlin basis is introduced. The class of representations considered includes some multiply atypical irreducible representations of gl(m‖n) and all irreducible representations of gl(m‖1).
Some remarks on the Feynman–Kac formula
Authors: Brzeźniak Zdzisl/aw
Published: July 2002

A simple necessary condition for the existence of the representation of solutions of partial differential equations is found. This condition is applied to obtain the known results on the Schrödinger equation and the Dirac system in a unified way. Applications for further equations are also possible (Weyl’s equations are discussed).
Adiabatic evolution of an irreversible two level system
Authors: Kvitsinsky Andrei , Putterman Seth
Published: July 2002

The adiabatic dynamics of a two level atom with spontaneous decay is studied. The existence of a complex adiabatic phase shift is established: The real part being the usual Berry’s phase. A closed-form expression for this phase and the adiabatic transition amplitudes is obtained. Incorporation of a finite preparation time for the initial state yields a new asymptotic form for the adiabatic transition amplitudes which is significantly different from the standard Landau–Zener–Dykhne formula.
Extension of unbounded left Hilbert algebras to partial *-algebras
Authors: Inoue A.
Published: July 2002

In this paper an unbounded generalization of left Hilbert algebras by partial *-algebras is considered, and the Tomita–Takesaki theory is extended to partial O*-algebras. While such a construction has been considered in previous papers [A. Inoue, Publ. RIMS, Kyoto Univ. 22, 725 (1986); 23, 673 (1987); ‘‘Modular Systems for algebras of unbounded operators, preprint, Fukuoka Univ. (1990)], the present one places emphasis on a rich class of unbounded operators, and is more applicable to examples.
Singularities in the solutions of the massive Skyrme model
Authors: Ferreira Erasmo , Neto Jorge Ananias
Published: July 2002

The equation of motion for the Skyrme model with a pion mass term is studied in the framework of the Painlevé analysis, and information is obtained about the singularity structure of its solutions. As in the massless case, singularities exist, consisting of a first-order pole term superposed to a logarithmic branch point. For the solitonic solutions, the singularities form an infinite sequence of points located on the negative real axis of the squared radial variable, accumulating at the origin. Based on this property and on the asymptotic behavior of the solitonic solutions, an approximate representation is built for the baryonic soliton, which is extremely accurate.
Some simple representations of the affine Lie superalgebra A(1)(1,0)
Authors: Su Yucai
Published: July 2002

In this paper, some simple modules of the affine Lie superalgebra A(1)(1,0) are considered which, although they are neither highest nor lowest weight modules, are constructed in a manner closely analogous to the construction of highest weight modules of the finite-dimensional Lie superalgebras A(m,n).
Diffusion in asymptotically logarithmic potentials
Authors: Miyazawa Toru
Published: July 2002

Behavior of solutions to the one-dimensional Fokker–Planck equation with potentials U(x) which diverge logarithmically as x→±∞ is investigated through the analysis of the frequency component of the Green’s function. It is shown that solutions of the equation decrease for large time t either logarithmically or as t−α, where α may take arbitrary positive value depending on a parameter.
Schlesinger transformations of Painlevé II-V
Authors: Mug̃an U. , Fokas A. S.
Published: July 2002

The explicit form of the Schlesinger transformations for the second, third, fourth, and fifth Painlevé equations is given.
P determinants and boundary values
Authors: Barraza O. , Falomir H. , Gamboa Saraví R. E. , Santangelo E. M.
Published: July 2002

It is shown that a regularized determinant based on Hilbert’s approach (which we call the ‘‘p determinant’’) of a quotient of elliptic operators defined on a manifold with boundary is equal to the ‘‘p determinant’’ of a quotient of pseudodifferential operators. The last ones are entirely expressible in terms of boundary values of solutions of the original differential operators. It is argued that, in the context of quantum field theory, these boundary values also determine the subtractions (i.e., the counterterms) to which this regularization scheme gives rise.
The supertrace of the steady asymptotic of the spinorial heat kernel
Authors: Bleecker David D.
Published: July 2002

An essentially self-contained, rigorous proof of the Atiyah–Singer index theorem is given for the case of the twisted Dirac operator. Indeed, the stronger local index theorem, which implies the general case, is proven here by computing the supertrace of the steady (time-independent) asymptotic of the twisted spinorial heat kernel. The computation is carried out in the spirit of Patodi’s proof of the Gauss–Bonnet–Chern theorem. Gilkey’s approach involving invariant theory is not used, but rather a generalization of Mehler’s formula is derived and utilized along with some elementary properties of Clifford algebras. The use of Mehler’s formula was inspired by work of Getzler, but families of Clifford algebra-valued pseudodifferential operators, and limits and estimates of families of heat kernels, are avoided here. Asymptotic expansions of heat kernels for operators on Euclidean fields are of fundamental importance in the computation of quantum corrections to the effective action for classical fields. Thus, the general formula developed here for the asymptotics may also be helpful in this regard.
Continuous integrable systems with multi-Poisson brackets
Authors: Okubo Susumu
Published: July 2002

For discrete finite systems, it is known that the zero Nijenhuis tensor condition can be used to explicitly construct conserved quantities in involution. Although the same method is not directly generalizable for continuous systems because of the divergence problem, the difficulty can be overcome with some minor modifications. In this way, various cases of KdV, nonlocal KdV, continuous Toda lattice, Kac–Moody hierarchy, and a model based upon a W3-algebra systematically by the same technique can be discussed.
On some mathematical problems in the evaluation of fields produced by currents which are generalized functions
Authors: Blaive B. , Barut A. O.
Published: July 2002

A method is given to overcome the ambiguities in the order of integration in the calculation of potentials as reciprocal Fourier transform by φ=ℱ̃ℱφ=∫dk0∫dk when generalized functions are involved.
Morse theory and gravitational microlensing
Authors: Petters A. O.
Published: July 2002

Morse theory is used to rigorously obtain counting formulas and lower bounds for the total number of images of a background point source, not on a caustic, undergoing lensing by a single-plane microlens system having compact bodies plus either subcritical or supercritical continuously distributed matter. An image-counting formula is also found for the case when external shear is added. In addition, it is proven that a microlens system consisting of k lens planes will generate N = 2M− + Πki=1(1 − gi) images of a background point source not on a caustic, where M− is the total number of critical points of odd index of the time-delay map and gi is the number of stars on the ith lens plane. Morse theoretic tools also yield that the smallest value N can have is Πi=1k(1+gi).
Computation of error effects in nonlinear Hamiltonian systems using Lie algebraic methods
Authors: Healy Liam M. , Dragt Alex J. , Gjaja Ivan M.
Published: July 2002

There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure.
Arithmetic features of 2-D strings
Authors: Freund Peter G. O.
Published: July 2002

The on-shell tree amplitudes of 2-D 𝒫-adic strings are constructed. Along with the recently obtained on-shell tree amplitudes of the ordinary (archimedean) 2-D string, they lead to adelic product formulas for all N-point amplitudes. This is in marked difference from 26-D critical strings, where such adelic formulas only obtain for four-point amplitudes. Certain much-discussed operator redefinitions are considered at the 𝒫-adic level where they change radically, the 𝒫-adic gamma function having only one rather than infinitely many real poles. Also considered are q-strings in 2-D.
Lattices and θ-function identities. II: Theta series
Authors: Gannon Terry , Lam C. S.
Published: July 2002

The gluing construction of lattices is used to generate and study a number of theta function densities. It is shown, for example, that Riemann’s formula, a fundamental degree 4 identity, can be derived from a degree 2 identity. It is proved that all in a large class of identities can be derived from these lattice techniques. A list of 24 independent quadratic identities in the Jacobi functions ϑ1 and ϑ3, conjectured to be complete, with all but two of them seeming to be new, is given. The theta series of glue classes is also investigated, and it is shown that all of them, as well as the functions ϑa, b, satisfy polynomials whose coefficients are linear combinations of theta series of lattices; these polynomials have some interesting properties.
The Painlevé classification of partial differential equations. III. Rational equations with several poles
Authors: Hlavatý Ladislav
Published: July 2002

Semilinear second-order partial differential equations in two independent variables with rational right-hand sides are investigated. It is found that the Painlevé admissible partial differential equations can be transformed to the form with maximally three poles and equations with two and three poles are classified. Results of a series of papers on the Painlevé classification are summarized.
Diffusion processes associated to a laser model
Authors: Rebolledo Rolando , Retamal Juan C. , Saavedra Carlos
Published: July 2002

A diffusion process is constructed as a model for the electromagnetic field in a laser. The process is characterized by means of a Martingale problem of Nelson’s type, under a finite entropy assumption.
Stability of Hamiltonian systems at high energy
Authors: Thomas Lawrence E. , Wassell Stephen R.
Published: July 2002

Let H=T(P)+U(P,φ) be the Hamiltonian for a classical mechanical system of l degrees of freedom, where T is an integrable Hamiltonian generating quasiperiodic motion in the first l−1 degrees of freedom which has the form
A relation between group- and Čech-cohomology in principal fiber bundles and anomalies
Authors: Kelnhofer Gerald
Published: July 2002

A natural map between group-cohomology of the structure group of a principal fiber bundle with coefficients in the space of functions from the total space into an Abelian group and Čech-cohomology of the base space is defined. A differential complex of local group-cochains is constructed and an analog of the Poincaré lemma for group-cohomology is proven. By using the machinery of spectral sequences the cohomology of this complex is calculated and the connection between group-cohomology and Čech-cohomology of the given principal fiber bundle is elucidated. Finally, the non-Abelian and Witten anomaly in this context is reviewed and the relevance of our results for lifting principal group actions is discussed.
Compact classical systems: so(n) systems
Authors: Fawcett R. J. B.
Published: July 2002

Compact quantum systems based on compact kinematical Lie algebras have been described previously [J. Math. Phys. 29, 1521 (1988)]. A ‘‘compact classical system’’ is obtained as the classical limit of such a compact quantum system. In this paper, compact classical systems obtained in this way from compact quantum systems based on the special orthogonal Lie algebras so(n) are considered; in particular, those based on so(3) and so(4). Such compact classical systems are shown to exhibit behavior strikingly different from that of corresponding noncompact systems in ordinary classical Hamiltonian dynamics.
Hidden symmetries and linearization of the modified Painlevé–Ince equation
Authors: Abraham-Shrauner Barbara
Published: July 2002

The linearization and hidden symmetries of the modified Painlevé–Ince equation, y″+σyy′+βy3=0, where σ and β are constants, are presented. The linearization of this equation by a nonlocal transformation yields a damped (stable) or growing (unstable) harmonic oscillator equation for β≳0. Hidden symmetries are analyzed by transforming the modified Painlevé–Ince equation to a third-order ordinary differential equation (ODE) which, in general, is invariant under a three-parameter group by a Riccati transformation. A type I hidden symmetry is found of a second-order ODE found from the third-order ODE where a symmetry is lost in the reduction of order by the non-normal subgroup invariants. A type II hidden symmetry occurs in the third-order ODE because the symmetries of a second-order ODE, reduced from the third-order ODE by another set of normal subgroup invariants, are increased.
Nodal-surface conjectures for the convex quantum billiard
Authors: Liboff Richard L.
Published: July 2002

Stemming from known properties of one-dimensional (1-D) and 2-D quantum billiards, it is conjectured that the nodal surface of the first-excited state of the convex 3-D quantum billiard intersects the billiard surface in a single simple closed curve. Examples of the validity of this conjecture are given for a number of elementary 3-D billiard configurations. From these examples a second conjecture is introduced that addresses convex quantum billiards which are figures of rotation and contain one and only one plane of mirror symmetry normal to the axis of rotation. Two characteristic displacement parameters are defined which are labeled an axis length, L, and diameter, a. It is conjectured that a parameter κ≊1, exists, whose exact value depends on the properties of the billiard, such that for L≳κa (‘‘prolatelike’’) the nodal surface of the first-excited state of a quantum billiard is a plane surface of mirror symmetry which divides the length of the billiard in half. For L<κa (‘‘oblatelike’’) the nodal surface of the first-excited state is a plane surface of mirror symmetry which contains the rotation axis and divides the diameter of the billiard in half. Arguments are given in support of a third conjecture which addresses the regular polyhedra quantum billiards, termed ‘‘spherical-like.’’ It is hypothesized that the nodal surface of the first-excited state for any of these billiards is any plane of reflection symmetry of the given polyhedron.
A generalized Henon–Heiles system and related integrable Newton equations
Authors: Bl/aszak Maciej , Rauch-Wojciechowski Stefan
Published: July 2002

A detailed description is given of integrable cases of the generalized Henon–Heiles systems which differs from the standard H–H ones by the term α/q22. Their connection with fifth-order one-component soliton equations is discussed. Lax representations are constructed, and the bi-Hamiltonian formulation of dynamics is given. It is also shown that the gH–H system can be mapped onto another system of Newton equations with a nonstandard Hamiltonian structure.
New integrable systems related to a Kupershmidt’s equation by Miura maps
Authors: Liu Q. P.
Published: July 2002

A multicomponent KdV system, Kupershmidt’s coupled KdV equation, is considered. The system is shown to be a modification of some system, and it can be modified.
A twistorial description of the processes of mass scattering of Dirac fields
Authors: Cardoso J. G.
Published: July 2002

A set of twistorial formulas for the null graphs that describe the mass scattering of Dirac fields in real Minkowski space is explicitly derived. By making particular use of two holomorphic expressions for the generalized mass-scattering differential forms the scattering integrals are transcribed directly into the framework of twistor theory.
On the connection between continuous Hahn polynomials and the Heisenberg algebra
Authors: Brambilla Nora , Montaldi Emilio
Published: July 2002

An elementary proof is given for the connection between a system of continuous Hahn polynomials and symmetrizations of elements in the Heisenberg algebra [Bender, Mead, and Pinsky, Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987); Koornwinder, ibid. 30, 767 (1989)].
On a class of homogeneous nonlinear Schrödinger equations
Authors: Auberson G. , Sabatier P. C.
Published: July 2002

A class of homogeneous, norm conserving, nonlinear wave equations of the Schrödinger type is studied. It is shown that those equations which derive from a Lagrangian can be linearized, but have no regular confined solutions, whereas the equations which cannot be obtained from a local Lagrangian do admit such confined solutions. The latter however are unstable against small perturbations of the initial data.
Extension of the de Sitter kink
Authors: Dunn K. A. , Harriott Tina A. , Williams J. G.
Published: July 2002

A space–time, locally identical to the usual de Sitter space–time but globally different because of a kink in its light cone field, is described in various coordinate systems. Two separate coordinate patches are needed. Each original patch is geodesically incomplete and so is extended by the Kruskal method. The space–time, which is not globally hyperbolic, is shown to be foliated by a family of hypersurfaces each of which is homeomorphic to a three-sphere but none of which is everywhere spacelike.
Reduced coefficients of quantum algebra SUq(4)
Authors: Yang Yaping , Yu Zurong
Published: July 2002

Irreducible representation and a recurrent formula to calculate reduced coefficients of quantum algebra SUq(4)⊇SUq(2)⊕SUq(2) has been obtained through a tensorlike method.
Total mass-momentum of arbitrary initial-data sets in general relativity
Authors: Geroch Robert , Perng Shyan-Ming
Published: July 2002

For an asymptotically flat initial-data set in general relativity, the total mass-momentum may be interpreted as a Hermitian quadratic form on the complex, two-dimensional vector space of ‘‘asymptotic spinors.’’ A generalization to an arbitrary initial-data set is obtained. The mass-momentum is retained as a Hermitian quadratic form, but the space of ‘‘asymptotic spinors’’ on which it is a function is modified. Indeed, the dimension of this space may range from zero to infinity, depending on the initial data. There is given a variety of examples and general properties of this generalized mass-momentum.
On the general solution of the d’Alembert equation with a nonlinear eikonal constraint and its applications
Authors: Zhdanov R. Z. , Revenko I. V. , Fushchych W. I.
Published: July 2002

We construct the general solutions of the system of nonlinear differential equations ⧠nu=0, uμuμ=0 in the four- and five-dimensional complex pseudo-Euclidean spaces. The results obtained are used to reduce the multidimensional nonlinear d’Alembert equation ⧠4u=F(u) to ordinary differential equations and to construct its new exact solutions.
On supersymmetry and radial equations for three-dimensional central problems
Authors: Beckers J. , Debergh N. , Ntibashirakandi L.
Published: July 2002

Supersymmetric three-dimensional Schrödinger equations describing central problems do not lead, in general, to supersymmetric one-dimensional radial equations. Such a context is discussed, in connection with the two main supersymmetrization procedures (with or without spin-orbit coupling terms). The inverse problem is also considered, starting from a supersymmetric radial equation.
Representations of the (2+1)-dimensional Galilean group
Authors: Bose S. K.
Published: July 2002

Using the Mackey theory of induced representations, the unitary irreducible representations of the proper Galilean group in 2+1 space–time dimensions are constructed. All representations, both true as well as the projective ones, are found. The concomitant representations of the Lie algebra are given.
Berry phase and supersymmetric topological index
Authors: Ilinski Kirill N. , Kalinin Gleb V. , Melezhik Vladislav V.
Published: July 2002

The sequences of supersymmetry for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian are revised. The condition (so-called supersymmetric adiabatic evolution condition) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek–Zee (degenerated case) phases of superpartners are taking place is pointed out. The analog of the Witten index (supersymmetric Berry index) is determined. The final expression for the new index has compact form of indBH=sDet U≡Det Uτ, where U is the cyclic evolution operator generated by supersymmetric Hamiltonian H and τ is a supersymmetric involution. As the examples of the suggested concept of the supersymmetric adiabatic evolution the holomorphic quantum mechanics on a complex plane and meromorphic quantum mechanics on Riemann surfaces are considered. The supersymmetric Berry indices for the models are calculated.
Removal of the resolvent-like energy dependence from interactions and invariant subspaces of a total Hamiltonian
Authors: Motovilov A. K.
Published: July 2002

The spectral problem (A+V(z))ψ=zψ is considered where the main Hamiltonian A is a self-adjoint operator of sufficiently arbitrary nature. The perturbation V(z)=−B(A′−z)−1B* depends on the energy z as resolvent of another self-adjoint operator A′. The latter is usually interpreted as a Hamiltonian describing an internal structure of physical system. The operator B is assumed to have a finite Hilbert–Schmidt norm. The conditions are formulated when one can replace the perturbation V(z) with an energy-independent ‘‘potential’’ W such that the Hamiltonian H=A+W has the same spectrum (more exactly a part of spectrum) and the same eigenfunctions as the initial spectral problem. The Hamiltonian H is constructed as a solution of the non-linear operator equation H=A+V(H). It is established that this equation is closely connected with the problem of searching for invariant subspaces of the Hamiltonian H=[B*AA′B]. The orthogonality and expansion theorems are proved for eigenfunction systems of the Hamiltonian H=A+W. Scattering theory is developed for this Hamiltonian in the case where the operator A has continuous spectrum.
‘‘Falling cat’’ connections and the momentum map
Authors: Fecko Marián
Published: July 2002

We consider a standard symplectic dynamics on TM generated by a natural Lagrangian L. The Lagrangian is assumed to be invariant with respect to the action TRg of a Lie group G lifted from the free and proper action Rg of G on M. It is shown that under these conditions a connection on principal bundle π:M → M/G can be constructed based on the momentum map corresponding to the action TRg. A simple explicit formula for the connection form is given. For the special case of the standard action of G=SO(3) on M=R3×...×R3 corresponding to a rigid rotation of an N-particle system the formula obtained earlier by Guichardet and Shapere and Wilczek is reproduced.
Homogeneity in integral representations for effective properties of composite materials
Authors: Sawicz Romuald
Published: July 2002

The effective complex conductivity σ* of an n-component composite material is considered. Recently, an integral representation that treats the component conductivities σ1,...,σn symmetrically was developed. This representation has the advantage that the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. However, the admissible class of measures has been difficult to characterize, due to the condition that σ* is a homogeneous function of the component conductivities. Here, this admissible class is characterized in terms of linear relations among the moments associated with tetrahedra in Fourier space Zn. The homogeneity is used to derive a new formula for σ* in the two-component case, in which σ* for general media is expressed in terms of the conductivities of laminates of second rank.
Boundary value problems for integrable equations compatible with the symmetry algebra
Authors: Gürel Burak , Gürses Metin , Habibullin Ismagil
Published: July 2002

Boundary value problems for integrable nonlinear partial differential equations are considered from the symmetry point of view. Families of boundary conditions compatible with the Harry-Dym, KdV, and mKdV equations and the Volterra chain are discussed. We also discuss the uniqueness of some of these boundary conditions.
Boussinesq solitary-wave as a multiple-time solution of the Korteweg–de Vries hierarchy
Authors: Kraenkel R. A. , Manna M. A. , Montero J. C. , Pereira J. G.
Published: July 2002

We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg–de Vries hierarchy, we show that the solitary-wave of the Boussinesq equation is a solitary-wave satisfying simultaneously all equations of the Korteweg–de Vries hierarchy, each one in an appropriate slow time variable.
Semiclassical sum rules and generalized coherent states
Authors: Combescure M. , Robert D.
Published: July 2002

Various semiclassical sum rules are obtained for matrix elements of smooth observables using semiclassical estimates of time evolved coherent states together with stationary phase theorems.
Fluids with spin and twist
Authors: Smalley Larry L. , Krisch Jean P.
Published: July 2002

Fluids with persistent vortices that exhibit shear plus expansion (or contraction) in noninertial frames are common physical phenomena. The concept of intrinsic rotation is commonly referred to as spin; the equivalent concept for shear would be shear momenta, referred to as twist in this work. The motion of the Earth’s atmosphere is a prime example of such motion in which the driving engine is the rotation of the Earth plus solar radiation. The general analytical features of persistent vortices that exhibit shear plus expansion and contraction are introduced using the methods of affine geometry. The same theoretical considerations can also be applied to astrophysical examples.
A uniform diffusion limit for random wave propagation with turning point
Authors: Kim Jeong-Hoon
Published: July 2002

A random wave propagation problem with turning point is considered for a refractive, layered random medium. The variations of the medium structure are assumed to have two spatial scales; microscopic random fluctuations are superposed upon slowly varying macroscopic variations. An extension of a limit theorem for stochastic differential equations with multiple spatial scales is derived and proved to obtain a uniformly valid diffusion limit for random multiple scattering up to the turning point region. The scale dependence of the infinitesimal generator of the backward Kolmogorov equation provides an insight into the interplay of internal refraction and random scattering as one approaches the turning point.
Stochastic mechanics of reciprocal diffusions
Authors: Levy Bernard C. , Krener Arthur J.
Published: July 2002

The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger’s equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner’s joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.
Geometrical aspect of topologically twisted two-dimensional conformal superalgebra
Authors: Ano Noriaki
Published: July 2002

We study the topologically twisted osp(2‖2)⊕osp(2‖2) conformal superalgebra. The algebra includes the Lagrangians which are intrinsic to the topological field theory and composed of fermionic generators. Studying the Lagrangians through a gauge system of osp(2‖2)⊕osp(2‖2), geometrical features inherent in the algebra are revealed: a moduli space associated with the algebra is derived and the crucial roles which the fermionic generators play in the moduli space are clarified. It is argued that there exists a specific relation between the topological twist and the moduli problem through a geometrical aspect of the algebra.
Analytic continuation from empirical data: A direct approach to the stabilization problem
Authors: Ciulli M. , Spearman T. D.
Published: July 2002

Analytic continuation plays a key role in many problems in physics. A central problem is the implementation of a stabilized continuation from approximate numerical data specified on an interior segment γ within the holomorphy domain. The solution to that problem presented in this paper is expressed in terms of a Fredholm integral equation of the second kind which refers only to the physical region γ ; in this latter respect it differs from other approaches to the same problem which are normally formulated on the boundary, and has the considerable advantage of dealing directly with the physically relevant functions.
Standard thermal statistics with q-entropies
Authors: Guerberoff G. R. , Raggio G. A.
Published: July 2002

We report results on the quantum thermal statistics à la Gibbs–Shannon–Szilard–Jaynes based on q-entropies Sq[ρ]=(q−1)−1(1−tr(ρq)) (0<q≠1) and the internal energy functional U[ρ]=tr(ρH) proposed by C. Tsallis [J. Stat. Phys. 52, 479–487 (1988)].
A quantum analog of the 𝒵 algebra
Authors: Bougourzi A. Hamid , Vinet Luc
Published: July 2002

We define a natural quantum analog for the 𝒵 algebra, and which we refer to as the 𝒵q algebra, by modding out the Heisenberg algebra from the quantum affine algebra Uq(sl(2)■) with level k. We discuss the representation theory of this 𝒵q algebra. In particular, we exhibit its reduction to a group algebra, and to a tensor product of a group algebra with a quantum Clifford algebra when k=1, and k=2, and thus we recover the explicit constructions of Uq(sl(2)■)-standard modules as achieved by Frenkel–Jing and Bernard, respectively. Moreover, for arbitrary nonzero level k, we show that the explicit basis for the simplest 𝒵-generalized Verma module as constructed by Lepowsky and Primc is also a basis for its corresponding 𝒵q-module, i.e., it is invariant under the q-deformation for generic q. We expect this 𝒵q algebra [associated with Uq(sl(2)■) at level k] to play the role of a dynamical symmetry in the off-critical Zk statistical models.
Fictitious level dynamics: A novel approach to spectral statistics in disordered conductors
Authors: Chalker John T. , Lerner Igor V. , Smith Robert A.
Published: July 2002

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker–Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order.
Models of the Hofstadter-type
Authors: Kreft Ch. , Seiler R.
Published: July 2002

Spectra and eigenfunctions of discrete Hamiltonians are computed using algebraic, analytic, and numerical tools. In particular, we consider the Hofstadter and the Second Neighbor Square Lattice model, the Triangular Lattice model in an inhomogenous magnetic field, the Doubly-discrete Quantum Pendulum, and the Honeycomb model. Qualitative properties of the spectra are related to symmetries. Semiclassical analysis in the algebraic setting for the Doubly-discrete Quantum Pendulum is shown to match numerical results well. The connection to integrable models is mentioned.
Entropy of a subalgebra and quantum estimation
Authors: Benatti Fabio
Published: July 2002

In this paper we compare the accessible information of quantum communication channels with the entropic content of finite-dimensional matrix algebras with respect to quantum states, as defined by Connes, Narnhofer, and Thirring. In particular, every Abelian n×n matrix algebra together with a density matrix define the input alphabet of a quantum communication channel whose accessible information equals the entropic content of the algebra with respect to the state. The cases n=2 and n=3 are concretely examined in connection with the problem of the best estimation.
Statistics of wave functions in mesoscopic systems
Authors: Fal’ko Vladimir I. , Efetov K. B.
Published: July 2002

We review the results of a recent study of fluctuations of wave functions in confined chaotic systems. The fluctuations can be due to a random potential or be a consequence of a chaotic scattering by the walls. The entire distribution function of the local amplitudes of the wave functions, f1, and the joint two-point distribution are calculated in various situations. The computation is performed using the supersymmetry technique and employs the studies of a reduced version of the non-linear supersymmetric σ-model developed especially for investigating the properties of a single eigenstate in a discrete spectrum of a chaotic quantum system. For not very large amplitudes, the complete description can be achieved using the zero-dimensional approximation of the σ-model. The distribution function calculated in the limit of various symmetry classes shows the universal behavior known as the Porter-Thomas statistics, and fluctuations at distant points do not correlate. In the crossover regime between the ensembles, the distribution of local amplitudes shows a somewhat more sophisticated behavior: the fluctuations in this case are correlated over distances exceeding the mean free path. For large amplitudes generated by the states the most affected by the localization (we call them prelocalized), the zero-dimensional approximation is no longer valid. Instead, the statistics of their wave functions is determined by nontrivial vacua of the reduced σ-model which is quite similar to the Liouville model known in conformal field theory. In particular, the vacuum state of the reduced σ-model obeys the Liouville equation, which indicates that in two dimensions the prelocalized states have nearly critical properties: we prove their multifractality and power-law statistically averaged envelope |φ(r)|2∝r−2μ at the intermediate range of distances below the localization length with a spectrum of exponents μ<1, as well as obtain a logarithmically-normal tail of the distribution function f1. We also find an evidence of prelocalized states in quasi-one-dimensional wires with the length shorter than the localization length: their statistically averaged envelope has power-law asymptotics, |φ(x)|2∝x−2, and the tail of the distribution function is similar to that describing localized states in the infinite wires.
q-deformation of the Lorentz group
Authors: Finkelstein Robert J.
Published: July 2002

We describe a q-deformation of the Lorentz group in terms of a q-deformation of the van der Waerden spinor algebra.
Advection diffusion past a strip. I. Normal incidence
Authors: Knessl Charles , Keller Joseph B.
Published: July 2002

The concentration p(x,y) of particles moving by diffusion and advection or drift is analyzed. The motion is impeded by an impenetrable strip that is parallel to the z axis. It is assumed that p satisfies the linear advection-diffusion equation with a boundary condition on the strip. It is also assumed that p=1 at infinity. This problem is solved asymptotically for vL/D≫1, where v is the drift velocity, D is the diffusion coefficient, and 2L is the strip width. It is found that p is large on the side of the strip facing the incident flow, that p is small in the shadow behind the strip, and that p is nearly constant elsewhere. The case of a strip normal to the incident flow is rather different from that of a strip oblique to the flow. Methods of asymptotic analysis are used.
Compact exponential product formulas and operator functional derivative
Authors: Suzuki Masuo
Published: July 2002

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin–Specht–Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians.
Periodic orbit theory analysis of a continuous family of quasi-circular billiards
Authors: Robinett R. W.
Published: July 2002

We compute the Fourier transform (ρ(L)) of the quantum mechanical energy level density for the problem of a particle in a two-dimensional circular infinite well (or circular billiard) as well as for several special generalizations of that geometry, namely the half-well, quarter-well, and the circular well with a thin, infinite wall along the positive x-axis (hereafter called a circular well plus baffle). The resulting peaks in plots of |ρ(L)|2 versus L are compared to the lengths of the classical closed trajectories in these geometries as a simple example of the application of periodic orbit (PO) theory to a billiard or infinite well system. We then solve the Schrödinger equation for the general case of a circular well with infinite walls both along the positive x-axis and at an arbitrary angle Θ (a circular “slice”) for which the half-well (Θ=π), quarter-well (Θ=π/2), and circular well plus baffle (Θ=2π) are then all special cases. We perform a PO theory analysis of this general system and calculate |ρ(L)|2 for many intermediate values of Θ to examine how the peaks in ρ(L) attributed to periodic orbits change as the quasi-circular wells are continuously transformed into each other. We explicitly examine the transitions from the half-circular well to the circle plus baffle case (half-well to quarter-circle case) as Θ changes continuously from π to 2π (from π to π/2) in detail. We then discuss the general Θ→0 limit, paying special attention to the cases where Θ=π/2n, as well as deriving the formulae for the lengths of closed orbits for the general case. We find that such a periodic orbit theory analysis is of great benefit in understanding and visualizing the increasingly complex pattern of closed orbits as Θ→0.
Multicomponent Wentzel–Kramers–Brillouin approximation on arbitrary symplectic manifolds: A star product approach
Authors: Emmrich C. , Römer H.
Published: July 2002

It is known that in the Wentzel–Kramers–Brillouin approximation of multicomponent systems like the Dirac equation or Born–Oppenheimer approximation, an additional phase appears apart from the Berry phase. So far, this phase was only examined in special cases, or under certain restrictive assumptions, namely, that the eigenspaces of the matrix or endomorphism valued symbol of the Hamiltonian form trivial bundles. We give a completely global derivation of this phase which does not depend on any choice of local trivializing sections. This is achieved using a star product approach to quantization. Furthermore, we give a systematic and global approach to a reduction of the problem to a problem defined completely on the different “polarizations.” Finally, we discuss to what extent it is actually possible to reduce the problem to a really scalar one, and make some comments on obstructions to the existence of global quasiclassical states.
Exponential stability for the energy exchange dynamics of the Holstein model
Authors: Hennig D.
Published: July 2002

We investigate the dynamics of the energy exchange between excitonic and vibrational degrees of freedom in the context of the Holstein model. Using Nekhoroshev-type arguments we derive bounds on the energy exchange for weak exciton–vibron coupling. It is shown that for large differences of the excitonic and vibronic frequencies the energy exchange is suppressed up to times growing exponentially with the ratio of the frequencies. Although the excitonic and vibronic energies are each for itself conserved there is equipartition of the excitonic energy among all lattice sites entailing an extended exciton. However, in the limit of large exciton–vibron coupling the excitonic actions are frozen separately, which leads to exciton localization. The action freezing is reflected in breather solutions.
Generalized plasma dispersion functions
Authors: Percival D. J. , Robinson P. A.
Published: July 2002

Generalized plasma dispersion functions have recently arisen in the derivation of an exact expression for the quadratic response tensor for a plasma with constituent species having Maxwellian velocity distributions. A range of mathematical properties satisfied by the generalized plasma dispersion functions are derived here, including recursion relations, series expansions, and approximate analytic forms, including Padé approximants. These properties are of central importance to the application of the exact quadratic response tensor to descriptions of second-order processes in weak and strong turbulence theory, such as three-wave interactions in warm plasmas.
Second harmonic generation: Hamiltonian structures and particular solutions
Authors: Khusnutdinova K. R. , Steudel H.
Published: July 2002

For the equations describing second harmonic generation (SHG), we find a linear system different from one found by Kaup (but connected with it by a gauge transformation), which enables us to consider the SHG equations as related to the first negative flow in the coupled KdV hierarchy and to find therefore the Hamiltonian structures and the recursion operator. With the help of the recursion operator we write down the simplest commuting flows and consider their stationary points in order to find particular solutions of the SHG equations. We also investigate some particular invariant solutions of the SHG equations that can be of physical interest, and find their connections with invariant solutions of the Tzitzéica equation. The latter are either connected with Painlevé III or solvable in elliptic functions.
On the Born-Infeld electron: Spin effects
Authors: Boillat Guy , Strumia Alberto
Published: July 2002

We start from a natural generalization of the Born–Infeld Lagrangian which involves two constants h,k and two parameters s,θ0 and show, by investigating static solutions of a first order approximation with respect to a small parameter (ε=h/k) that s=1/2 and that h is directly proportional to Planck’s constant. It seems reasonable to interpret s=1/2 as the spin of the electron and the angle θ0 as its orientation. Thus we obtain solutions that appear to reflect the influence of the states of spin on the electromagnetic field.
A rigorous real time Feynman path integral
Authors: Loo Ken
Published: July 2002

Using improper Riemann integrals, we will formulate a rigorous version of the real-time, time-sliced Feynman path integral for the L2 transition probability amplitude. We will do this for nonvector potential Hamiltonians with potential which has, at most, a finite number of discontinuities and singularities. We will also provide a Nonstandard Analysis version of our formulation.
Lie subalgebras of real and complex orthogonal groups in dimension four
Authors: Lastaria Federico G.
Published: July 2002

We give an explicit description of all Lie subalgebras of the Lie algebras so4R and so4C of the orthogonal groups O(4,R) and O(4,C).
Involutive automorphisms and Iwasawa decomposition of some hyperbolic Kac–Moody algebras
Authors: Pati K. C. , Parashar D. , Kaushal R. S.
Published: July 2002

The involutive automorphisms of hyperbolic Kac–Moody algebras are computed from Satake diagrams of these algebras which are then used to furnish a general procedure of their Iwasawa decomposition. In particular Â1(1) and Â2(1) are considered as representative examples to illustrate the efficacy of the underlying treatment.
Path integral for the relativistic three-dimensional Aharonov–Bohm–Coulomb system
Authors: Lin De-Hone
Published: July 2002

The path integral for the relativistic three-dimensional spinless Aharonov–Bohm–Coulomb system is solved, and the energy spectra are extracted from the resulting amplitude.
Closed forms for the exponential mapping on matrix Lie groups based on Putzer’s method
Authors: Leite F. Silva , Crouch P.
Published: July 2002

We present closed forms for the exponential of some infinitesimal generators of Lie groups which play an important role in physics and engineering applications. These explicit forms are based on the Putzer’s method. We also compare this methodology and results with related work by other authors.
Free field approach to the dilute AL models
Authors: Hara Yuji , Jimbo Michio , Konno Hitoshi , Odake Satoru , Shiraishi Jun’ichi
Published: July 2002

We construct a free field realization of vertex operators of the dilute AL models along with the Felder complex. For L=3, we also study an E8 structure in terms of the deformed Virasoro currents.