From effective BCS action to vortex dynamics

The topological term in the effective action for the electrically neutral BCS system is discussed. It is applied for the calculation of the transverse force acting on a vortex in the limit of a smooth vortex core and vanishing interlevel distance in the vortex core. The controversy between the topological terms in the articles by I. J. R. Aitchison et al., Phys. Rev. B 51, 6531 (1995) and A. van Otterlo et al., cond-mat/9703124 is resolved. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 641–646 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Topological interpretation of quantum numbers

The paper shows how vector topological charges for topological excitations in nonlinear σ-models on compact one-dimensional spaces T _G and G/T _G can be defined (here G is a simple compact Lie group and T _G is its maximal commutative subgroup). Explicit solutions, their energies and interactions between different topological charges have been obtained. A possibility of topological interpretation of quantum numbers of groups and particles is discussed. Zh. éksp. Teor. Fiz. 116, 1131–1147 (October 1999)     

Symbolic Dynamics for the General Quartic Map

The general quartic map is studied by symbolic dynamics in the three parameter space, joints are obtained in terms of the kneading theory. We describe the skeleton of superstable. kneading sequences corresponding to a joint and all allowed superstable kneading sequences in the kneading space in details. A criterion for the existence of chaos has been given according to the topological entropy.     

Random Unitary Matrices, Permutations and Painlevé

This paper is concerned with certain connections between the ensemble of n×n unitary matrices – specifically the characteristic function of the random variable tr(U) – and combinatorics – specifically Ulam's problem concerning the distribution of the length of the longest increasing subsequence in permutation groups – and the appearance of Painlevé functions in the answers to apparently unrelated questions. Among the results is a representation in terms of a Painlevé V function for the characteristic function of tr(U) and (using recent results of Baik, Deift and Johansson) an expression in terms of a Painlevé II function for the limiting distribution of the length of the longest increasing subsequence in the hyperoctahedral groups. Received: 2 December 1998 / Accepted: 12 May 1999     

Elliptic Linear Problem for the Calogero—Inozemtsev Model and Painlevé VI Equation

We introduce a 3N × 3N Lax pair with spectral parameter for the Calogero—Inozemtsev model. The case of one degree freedom appears to have 2 × 2 Lax representation. We derive it from the elliptic Gaudin model via some reduction procedure and prove algebraic integrability. This Lax pair provides an elliptic linear problem for the Painlevé VI equation in elliptic form.     

On topological excitations with isovector topological charges

It is shown that degenerate systems with order parameter ψ taking on values in compact homogeneous subspaces T _G or G/T _G (where G is a simple compact group and T _G is its maximum commutative subgroup) possess a rich collection of topological excitations (vortices or, correspondingly, instantons) with isovector topological charges. The corresponding homotopy groups are found for all G. The possibility of a topological interpretation of the quantum numbers of the groups and particles is discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 758–762 (25 May 1996)     

On Integrability of a (2+1)-Dimensional Perturbed KdV Equation

Abstract

A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlevé; test for integrability well, and its 4×4 Lax pair with two spectral parameters is found. The results show that the Painlevé; classification of coupled KdV equations by A. Karasu should be revised.     

Ground-state instability in systems of strongly interacting fermions

The stability of a fermion system is analyzed for a model repulsive pair interaction potential. The possibility of different types of restructuring of the Fermi ground state (at sufficiently great coupling constant) is related to the analyticity properties of such potential. In particular, for the screened Coulomb law it is shown that the restructuring cannot be of the Fermi condensation type, known earlier for some exactly solvable models, but instead belongs to the class of topological transitions. A phase diagram constructed for this model in the variables “screening parameter-coupling constant” displays two kinds of topological transitions: a “5/2” kind, similar to the known Lifshitz transitions in metals, and a “2” kind, characteristic for a uniform strongly interacting system. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 893–899 (25 December 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On “Hodge” topological strings at genus zero

A “Hodge strings” construction of solutions to associativity equations based on the t-part of t−t* equations is proposed. This construction formalizes and generalizes the “integration over the position of the marked point” procedure for computation of amplitudes in topological conformal theories coupled to topological gravity. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 374–379 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The Generalized Milnor–Thurston Conjecture and Equal Topological Entropy Class in Symbolic Dynamics of Order Topological Space of Three Letters

This paper presents an answer to an open problem in the dynamical systems of three letters: the generalized Milnor–Thurston conjecture on the existence of infinitely many plateaus of topological entropy in the two-dimensional parameter plane. The concept of equal topological entropy class is introduced by the dual star product which is a generalization of the Derrida–Gervois–Pomeau star product to the symbolic dynamics of three letters for the endomorphisms on the interval. The algebraic rules established by the dual star products for the doubly superstable kneading sequences are equivalent to the normal factorization of the Milnor–Thurston characteristic polynomials. Moreover, the classification theory of symbolic primitive and compound sequences based on the topological conjugacy in the meaning of equal entropy is completed in the topological space Σ₃ of three letters. Received: 4 February 1998 / Accepted: 1 March 2000     

Abelian dyons in the maximal Abelian projection of SU(2) gluodynamics

Correlations of the topological charge Q, the electric current J ^e, and the magnetic current J ^m in SU(2) lattice gauge theory in the maximal Abelian projection are investigated. It is found that the correlator 〈〈QJ ^eJ^m〉〉 is nonzero for a wide range of values of the bare charge. It is shown that: (i) the Abelian monopoles in the maximal Abelian projection are dyons which carry fluctuating electric charge; (ii) the sign of the electric charge e(x) coincides with that of the product of the monopole charge m(x) and the topological charge density Q(x). Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 161–165 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Symmetries and causes of the coincidence of the emission spectra of mirrors and charges in 1+1 and 3+1 spaces

This paper discusses the symmetry of the wave field that lies to the right and left of a two-sided accelerated mirror in 1+1 space and satisfies a single condition on it. The symmetry is embodied in the Bogolyubov matrix coefficients α and β that connect the two complete sets of solutions of the wave equations. The amplitudes of the quantum processes in the right and left half-spaces are expressed in terms of α and β and are related to each other by the transformation (12). The coefficient β _ω′ω ^* plays the role of the source amplitude of a pair of oppositely directed particles with frequencies ω and ω′ of which one is in the left half-space and the other is in the right half-space because one of them has undergone reflection. Such an interpretation makes β _ω′ω ^* observable and explains why, as shown by Eq. (1) and found earlier by Nikishov and Ritus [Zh. éksp. Teor. Fiz. 108, 1121 (1995); transl. JETP 81, 615 (1995)] and by Ritus [Zh. éksp. Teor. Fiz. 110, 526 (1996); transl. JETP 83, 282 (1996)], the emission spectra of a mirror in 1+1 space coincide with those of charges in 3+1 space. The reason is that the angular momentum of the pair emitted by the mirror coincides with the angular momentum of the single particle emitted by the charge. Zh. éksp. Teor. Fiz. 114, 46–62 (July 1998)     

Solutions of the Yvon-Born-Green equation for a system of square-well molecules at a temperature below the triple point

The Yvon-Born-Green equation (with superposition approximation) is solved numerically for the pair correlation function for a system of molecules interacting via the square-well potential (with σ₂/σ₁ = 1·85), for an isotherm below the triple point, and over a broad range of densities. The correlation function data and attendant thermodynamics generated for this isotherm are compared with results reported previously by the authors for several supercritical and subcritical isotherms of the square-well fluid. To facilitate the interpretation of these results, particularly in those regions of (T, ρ) space where phase transitions may occur, a geometrical representation of the data is presented (motivated, in part, by recent work by René Thom), and the location of the triple point is discussed in terms of this construction. The differences anticipated between results reported here and those that would be obtained in an exact statistical mechanical analysis, are identified.     

On phase ordering behind the propagating front of a second-order transition

In a real system the heating is nonuniform, and a second-order phase transition to a broken-symmetry phase occurs by propagation of a temperature front. Two parameters, the cooling rate τ _Q and the transition front velocity ν _T determine the nucleation of topological defects. Depending on the relation of these parameters, two regimes are found: in the regime of fast propagation defects are created according to the Zurek scenario for the homogeneous case, while in the slow-propagation regime vortex formation is suppressed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 96–101 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Nucleation of Topological Dipoles¶in Nematic Liquid Crystals

A topological dipole is a pair of point defects with opposite topological charges. In this paper we show by example how the nucleation of such a dipole within a smooth field can drive a metastable state into a stable one. Building on our previous work, we construct a mathematical model for the dynamics of both monopoles and dipoles in a capillary filled with a nematic liquid crystal. Though our analysis is fit for liquid crystals, a similar mechanism is also likely to apply to the field theory for other ordered media. Received: 10 July 1997 / Accepted: 25 June 1998     

The quantum group structure of 2D gravity and minimal models I

On the unit circle, an infinite family of chiral operators is constructed, whose exchange algebra is given by the universalR-matrix of the quantum groupSL(2) _q . This establishes the precise connection between the chiral algebra of two dimensional gravity or minimal models and this quantum group. The method is to relate the monodromy properties of the operator differential equations satisfied by the generalized vertex operators with the exchange algebra ofSL(2) _q . The formulae so derived, which generalize an earlier particular case worked out by Babelon, are remarkably compact and may be entirely written in terms of “q-deformed” factorials and binomial coefficients. Laboratoire Propre du Centre National de la Recherche Scientifique, associé à l'école Normale Supérieure et à l'Université de Paris-Sud     

Nuclear β-decay and photoproduction of e + e − pairs in intense electromagnetic fields with a complex configuration

The effect of an intense electromagnetic field formed by the superposition of a constant magnetic field and a laser-type field on nuclear β-decay and on pair production by two g-rays with different polarizations is studied. Time integral representations are obtained for the total probabilities of these processes without restrictions on the strengths of the fields making up the configuration. Despite the different nature of these reactions, in the nonrelativistic limitthese expressions contain similar dependences on the field characteristics and the differences reduce to different power-law singularities in the behavior of the integrands at zero. At low fields, complete asymptotic expansions of the probabilities of these processes, including perturbation theory terms and oscillatory field contributions, are obtained in terms of parameters characterizing the fields. It is shown that the oscillatory corrections can be enhanced owing to the effect of a combination external field. The analysis of the probabilities of the various processes given here in terms of nonlinear functions of the field is illustrated by numerical calculations and graphs. Zh. éksp. Teor. Fiz. 113, 21–42 (January 1998)     

Thermopower of concentrated AuCr alloys

Measurements are presented of the thermopower of three concentrated $\text{Au}$Cr (0.9, 4.9 and 10.6 at.%Cr) alloys between 4 and 500°K. Considerable differences are observed in the thermopower compared with $\text{Au}$Fe alloys in a similar concentration range. Possible reasons for these differences are discussed in terms of current ideas on spin glasses and the pair model of Matho and Béal-Monod.