Ionization of atoms in electric and magnetic fields and the imaginary time method

A semiclassical theory is developed for the ionization of atoms and negative ions in constant, uniform electric and magnetic fields, including the Coulomb interaction between the electron and the atomic core during tunneling. The case of crossed fields (Lorentz ionization) is examined specially, as well as the limit of a strong magnetic field. Analytic equations are derived for arbitrary fields ℰ and ℋ that are weak compared to the characteristic intraatomic fields. The major results of this paper are obtained using the “imaginary time” method (ITM), in which tunneling is described using the classical equations of motion but with purely imaginary “time.” The possibility of generalizing the ITM to the relativistic case, as well as to states with nonzero angular momentum, is pointed out. Zh. éksp. Teor. Fiz. 113, 1579–1605 (May 1998)     

Nonlocal charges in susy integrable models

We study systematically the general properties of theB-extension of any integrable model and its properties as Hamiltonian structures etc. We clarify the origin of “exotic” changes in such models. We show that in such models there exist at least two sets of non-local conserved charges and that the “exotic” charges are part of this non-local charge hierarchy. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Variational wave equations of two fermions interacting via scalar,pseudoscalar, vector,pseudovector and tensor fields

We consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.     

Glimmers of a Pre-geometric Perspective

Spacetime measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about spacetime is in fact an assertion about the degrees of freedom of the matter (i.e. non gravitational) fields; those, say for definiteness, of the Standard Model of particle physics. As for any quantum theory, the dynamics of the matter fields can be described in terms of a unitary evolution of a state vector in a Hilbert space. By writing the Hilbert space as a generic tensor product of “subsystems” we analyse the evolution of a state vector on an information theoretical basis and attempt to recover the usual spacetime relations from the information exchanges between these subsystems. We consider generic interacting second quantized models with a finite number of fermionic degrees of freedom and characterize on physical grounds the tensor product structure associated with the class of “localized systems” and therefore with “position”. We find that in the case of free theories no spacetime relation is operationally definable. On the contrary, by applying the same procedure to the simple interacting model of a one-dimensional Heisenberg spin chain we recover the tensor product structure usually associated with “position”. Finally, we discuss the possible role of gravity in this framework.     

What is “System”: Some Decoherence-Theory Arguments

We discuss the possibility of making the initial definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical system as well as point out complementarity of the different possible divisions of a composite system into “subsystems,” thus eventually sharpening the issue of “what is system.”     

Static and quasistatic solutions of the real Proca field

We consider the theory of the massive real vector field with spin 1 (the real Proca field) and its solutions. First the field equations with dual symmetry [1] are written and the 4-pseudo vector is chosen to be zero. The constants of motion for the real Proca field, the constant “electric” real Proca field, the uniform motion of a point charge in the real Proca field, uniform motions in the “Coulomb” field, dipole and multipole free-momentum, constant “magnetic” field, and the field of a point charge in motion are presented.     

Valid for Much of “Realistic” Fields: A Non-Generational Conjecture for Deriving All First-Class Constraints at Once

We propose a single-step non-generational conjecture for derivation of all first class constraints, (involving, only, variables compatible with canonical Poisson brackets), of a realistic gauge (singular) field theory. We verify our conjecture for the free electromagnetic field, the Yang-Mills fields in interaction with spinor and scalar fields, and we also verify our conjecture in the case of gravitational field. We show that the first class constraints, which were reached at using the standard Dirac’s multi-generational algorithm, will be reproduced using the proposed conjecture. We make no claim that this conjecture is valid for all “mathematically” plausible Lagrangians; but, nevertheless, the examples we consider here show that this conjecture is valid for a “wide” range or much of realistic fields of Physical interest that are known to exist and be manifested in nature.     

On the Stability of a Quantum Dynamics of a Bose-Einstein Condensate Trapped in a One-Dimensional Toroidal Geometry

We rigorously analyze the stability of the “quasi-classical” dynamics of a Bose-Einstein condensate with repulsive and attractive interactions, trapped in an effective 1D toroidal geometry. The “classical” dynamics, which corresponds to the Gross-Pitaevskii mean field theory, is stable in the case of repulsive interaction, and unstable (under some conditions) in the case of attractive interaction. The corresponding quantum dynamics for observables is described by using a closed system of linear partial differential equations. In both cases of stable and unstable quasi-classical dynamics the quantum effects represent a singular perturbation to the quasi-classical solutions, and are described by the terms in these equations which consist of a small quasi-classical parameter which multiplies high-order “spatial” derivatives. We demonstrate that as a result of the quantum singularity for observables a convergence of quantum solutions to the corresponding classical solutions exists only for limited times, and estimate the characteristic time-scales of the convergence.     

Composite boson many-body theory for Frenkel excitons

We present a many-body theory for Frenkel excitons which takes into account their composite nature exactly. Our approach is based on four commutators similar to the ones we previously proposed for Wannier excitons. They allow us to calculate any physical quantity dealing with N excitons in terms of “Pauli scatterings” for carrier exchange in the absence of carrier interaction and “interaction scatterings” for carrier interactions in the absence of carrier exchange. We show that Frenkel excitons have a novel “transfer assisted exchange scattering”, specific to these excitons. It comes from indirect Coulomb processes between localized atomic states. These indirect processes, commonly called “electron-hole exchange” in the case of Wannier excitons and most often neglected, are crucial for Frenkel excitons, as they are the only ones responsible for the excitation transfer. We also show that in spite of the fact that Frenkel excitons are made of electrons and holes on the same atomic site, so that we could naively see them as elementary particles, they definitely are composite objects, their composite nature appearing through various properties, not always easy to guess. The present many-body theory for Frenkel excitons is thus going to appear as highly valuable to securely tackle their many-body physics, as in the case of nonlinear optical effects in organic semiconductors.     

The renormalization group in the problem of turbulent convection of a passive scalar impurity with nonlinear diffusion

The problem of turbulent mixing of a passive scalar impurity is studied within the renormalization-group approach to the stochastic theory of developed turbulence for the case where the diffusion coefficient is an arbitrary function of the impurity concentration. Such a problem incorporates an infinite number of coupling constants (“charges”). A one-loop calculation shows that in the infinite-dimensional space of the charges there is a two-dimensional surface of fixed points of the renormalization-group equations. When the surface has an IR-stability region, the problem has scaling with universal critical dimensionalities, corresponding to the phenomenological laws of Kolmogorov and Richardson, but with nonuniversal (i.e., depending on the Prandtl number and the explicit form of the nonlinearity in the diffusion equation) scaling functions, amplitude factors in the power laws, and value of the “effective Prandtl turbulence number.” Zh. éksp. Teor. Fiz. 112, 1649–1663 (November 1997)     

Forward and Backward Bellman Equations Improve the Efficiency of the EM Algorithm for DEC-POMDP

Decentralized partially observable Markov decision process (DEC-POMDP) models sequential decision making problems by a team of agents. Since the planning of DEC-POMDP can be interpreted as the maximum likelihood estimation for the latent variable model, DEC-POMDP can be solved by the EM algorithm. However, in EM for DEC-POMDP, the forward–backward algorithm needs to be calculated up to the infinite horizon, which impairs the computational efficiency. In this paper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EM algorithm (MBEM) by introducing the forward and backward Bellman equations into EM. BEM can be more efficient than EM because BEM calculates the forward and backward Bellman equations instead of the forward–backward algorithm up to the infinite horizon. However, BEM cannot always be more efficient than EM when the size of problems is large because BEM calculates an inverse matrix. We circumvent this shortcoming in MBEM by calculating the forward and backward Bellman equations without the inverse matrix. Our numerical experiments demonstrate that the convergence of MBEM is faster than that of EM.     

On “Gauge Renormalization” in Classical Electrodynamics

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined.     

Higher equations of motion in the N = 1 SUSY Liouville field theory

As in the ordinary bosonic Liouville field theory, in its N = 1 supersymmetric version, an infinite set of operator valued relations, the “higher equations of motions,” hold. The equations are in one to one correspondence with the singular representations of the super Virasoro algebra and enumerated by a pair of natural numbers (m, n). We explicitly demonstrate these equations in the classical case, where the equations of type (1, n) survive and can be interpreted directly as relations for classical fields. The general form of higher equations of motion is established in the quantum case, both for the Neveu-Schwarz and Ramond series. The text was submitted by the authors in English.     

On the geometry of relativistic magnetofluid flows

This paper deals with the construction of “magnetic vorticity” vector using Greenberg's theory of spacelike congruences for the trajectories of magnetic fields. A set of propagation equations is derived for the geometrical invariants associated with the congruences of magnetic field lines and fluid flow lines. Some applications of these propagation equations are made. A generalization of Ferraro's law of isorotation is obtained employing the propagation equation forω ² along the magnetic field lines.     

Space-time structure and bound-charge fields

Together with a “postulate of equivalent situations,” the exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) makes it possible to find the space-time structure and fields of charged conductors of arbitrary shape without using the Einstein equations. The energy of the electric field outside of a charged plane, which is equal to the rest energy of the masses of the charges creating the field, is determined. The space-time metric outside of the charged plane is established; it could also have been found from the exact solution of the Einstein-Maxwell equations. This solution describes the equilibrium of charged dust in parallel electric and gravitational fields. The field and metric are found outside of a charged conducting sphere. While it eliminates the self-energy divergence, the proposed method renders the classical electrodynamics internally consistent on transition to any short distance. All-Russian Scientific Research Institute of Opticophysical Measurements. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 63–74, October, 1997.     

Particles and events in classical off-shell electrodynamics

Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10⁻⁶ seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics.     

Wave-Corpuscle Mechanics for Electric Charges

It is well known that the concept of a point charge interacting with the electromagnetic (EM) field has a problem. To address that problem we introduce the concept of wave-corpuscle to describe spinless elementary charges interacting with the classical EM field. Every charge interacts only with the EM field and is described by a complex valued wave function over the 4-dimensional space time continuum. A system of many charges interacting with the EM field is defined by a local, gauge and Lorentz invariant Lagrangian with a key ingredient—a nonlinear self-interaction term providing for a cohesive force assigned to every charge. An ideal wave-corpuscle is an exact solution to the Euler-Lagrange equations describing both free and accelerated motions. It carries explicitly features of a point charge and the de Broglie wave. Our analysis shows that a system of well separated charges moving with nonrelativistic velocities are represented accurately as wave-corpuscles governed by the Newton equations of motion for point charges interacting with the Lorentz forces. In this regime the nonlinearities are “stealthy” and don’t show explicitly anywhere, but they provide for the binding forces that keep localized every individual charge. The theory can also be applied to closely interacting charges as in hydrogen atom where it produces discrete energy spectrum.     

On the <Emphasis Type="Italic">SU</Emphasis>(2)×<Emphasis Type="Italic">SU</Emphasis>(2) symmetry in the Hubbard model

We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.     

Three-Point Functions for MN/SN Orbifolds¶with?= 4 Supersymmetry

The D1–D5 system is believed to have an “orbifold point” in its moduli space where its low energy theory is a ?=4 supersymmetric sigma model with target space M ^N /S _N , where M is T ⁴ or K3. We study correlation functions of chiral operators in CFTs arising from such a theory. We construct a basic class of chiral operators from twist fields of the symmetric group and the generators of the superconformal algebra. We find explicitly the 3-point functions for these chiral fields at large N; these expressions are “universal” in that they are independent of the choice of M. We observe that the result is a significantly simpler expression than the corresponding expression for the bosonic theory based on the same orbifold target space. Received: 29 March 2001 / Accepted: 20 January 2002