On quantum solitons and their classical relatives: Bethe Ansatz states in soliton sectors of the sine-Gordon system

Previously we have found that the semiclassical sine-Gordon/Thirring spectrum can be received in the absence of quantum solitons via the spin $\text{1}\text{2}$ approximation of the quantized sine-Gordon system on a lattice. Later on, we have recovered the Hilbert space of quantum soliton states for the sine-Gordon system. In the present paper we present a derivation of the Bethe Ansatz eigenstates for the generalized ice model in this soliton Hilbert space. We demonstrate that via “Wick rotation” of a fundamental parameter of the ice model one arrives at the Bethe Ansatz eigenstates of the quantum sine-Gordon system. The latter is a “local transition matrix” ancestor of the conventional sine-Gordon /Thirring model, as derived by Faddeev et al. within the quantum inverse-scattering method. Our result is essentially based on the N < ∞, Δ = 1, m ? 1 regime. Consequently, the spectrum received, though resembling the semiclassical one, does not coincide with it at all.     

On the dynamics of a quantum system which is classically chaotic

We investigate the dynamics of one anisotropic spin in an external time-dependent magnetic field. The classical dynamics of the system is nonintegrable (and very similar to the standard map). We present results on this model for a quantum spin (i.e. for finite values of the spin lengthS). In particular we discuss the semiclassical regime,S1, using the concept of Wigner functions to define a suitable probability distribution. In regular regions of phase space the time evolution of the probability distribution shows an algebraic decay of correlations as in quantum mechanics. In chaotic regions of phase space it is characterised by a positive Lyapunov exponent which depends onS. In these regions semiclassical trajectories coincide with classical ones fort <₀ where ₀InS.     

Two-loop quantum corrections to the soliton mass in two-dimensional scalar field theories

We study higher-order corrections to the soliton mass in two-dimensional scalar field theories.We show that the second quantum correction (two-loop graphs) to the soliton mass (M_S) is finite provided one orders correctly the non-commuting operators in the effective hamiltonian. That is, the vacuum sector UV counterterm suffices to eliminate the ultraviolet and infinite volume divergences of the one-soliton sector.We evaluate explicitly the finite part of the second quantum correction to M_S in the sine-Gordon model. We find that the ratio of the soliton mass to the meson mass is the same in our perturbative calculation, as in the semiclassical one by Dashen, Hasslacher and Neveu, up to two-loop contributions.     

Model for Topological Fermions

 We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S ³. These solitons behave like particles with relativistic properties like Lorentz contraction and velocity dependence of mass. This mass is defined by the energy of the soliton. In this sense this model is a generalization of the Sine-Gordon model¹(We do not chase the aim to give a four-dimensional generalization of Coleman’s isomorphism between the Sine-Gordon model and the Thirring model which was shown in 2-dimensional space-time) from 1 + 1-dimensions to 3 + 1-dimensions, from S ¹ to S ³. For large distances from the centre of solitons this model tends to a dual U(1)-theory with freely propagating electromagnetic waves. Already at the classical level it describes important effects, which usually have to be explained by quantum field theory, like particle-antiparticle annihilation and the running of the coupling. Received November 30, 1999; revised June 20, 2000; accepted for publication October 2, 2000     

Transport through artificial single-molecule magnets: Spin-pair state sequential tunneling and Kondo effects

The transport properties of an artificial single-molecule magnet based on a CdTe quantum dot doped with a single Mn+2 ion(S=5/2) are investigated by the non-equilibrium Green function method.We consider a minimal model where the Mn-hole exchange coupling is strongly anisotropic so that spin-flip is suppressed and the impurity spin S and a hole spin s entering the quantum dot are coupled into spin pair states with(2S+1) sublevels.In the sequential tunneling regime,the differential conductance exhibits(2S+1) possible peaks,corresponding to resonance tunneling via(2S+1) sublevels.At low temperature,Kondo physics dominates transport and(2S+1) Kondo peaks occur in the local density of states and conductance.These peaks originate from the spin-singlet state formed by the holes in the leads and on the dot via higher-order processes and are related to the parallel and antiparallel spin pair states.     

Quasiclassical Hamiltonians for large-spin systems

We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion. Received 5 May 1999 and received in final form 24 September 1999     

Entangled solitons and stochastic q-bits

Stochastic realization of the wave function in quantum mechanics with the inclusion of soliton representation of extended particles is discussed. Two-soliton configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles. The concept of stochastic qubits is used for quantum computing modeling. The text was submitted by the authors in English.     

Solitons and magnons in Sine-Gordon like magnetic chains

We present theoretical results on the dynamic structure factors of both the classical Sine-Gordon chain and thexy-like ferromagnetic chain in a symmetry breaking magnetic field. We investigate the lowest order corrections to the noninteracting soliton/magnon picture and show that interference effects between solitons and magnons considerably reduce the intensity of the soliton induced central peak. We discuss the additional contribution of two magnon processes to the central peak and find that the combined strength is in agreement with numerical results. We calculate magnon intensities including quantum effects and find that the intensity depends strongly on temperature and wavevector. Quantitative results are given for the one-dimensional magnet CsNiF₃ and compared to neutron scattering data. The soliton induced line-width of the long wavelength magnon is also given.     

Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons

We report results of the first analysis of collisions between stable fundamental (alias spinless) and vortical (spinning) three-dimensional dissipative solitons in a model of a laser cavity. The systematic analysis is carried out for values S=1 and S=2 of the vorticity of the latter soliton. With the increase of the collision momentum, Χ, the same generic scenarios are observed in either case: merger into a single fundamental soliton at both small and relatively large values of Χ, and the formation of two fundamental solitons in an intermediate interval of variation of the collision momentum Χ. At very large values of Χ, the collision seems quasi-elastic, but the vortex soliton eventually splits into two nonspinning fragments.     

Internal structure of a quantum soliton and classical excitations due to trap opening

We analytically solve two problems that may be useful in the context of the recent observation of matter wave bright solitons in a one-dimensional attractive atomic Bose gas. The first problem is strictly beyond mean field: from the Bethe ansatz solution we extract the internal correlation function of the particle positions in the quantum soliton, that is for a fixed center of mass position. The second problem is solved in the limit of a large number of particles, where the mean field theory is asymptotically correct: it deals with the number of excitations created by the opening of the trap, starting from a pure soliton in a weakly curved harmonic potential.     

Stability of vortex solitons in the cubic-quintic model

We investigate one-parameter families of two-dimensional bright spinning solitons (ring vortices) in dispersive media combining cubic self-focusing and quintic self-defocusing nonlinearities. In direct simulations, the spinning solitons display a symmetry-breaking azimuthal instability, which leads to breakup of a soliton into a set of fragments, each being a stable nonspinning soliton. The fragments fly out tangentially to the circular crest of the original vortex ring. If the soliton’s energy is large enough, the instability develops so slowly that the spinning solitons may be regarded as virtually stable ones, in accord with earlier published results. Growth rates of perturbation eigenmodes with different azimuthal “quantum numbers” are calculated as a function of the soliton’s propagation constant κ from a numerical solution of the linearized equations. As a result, a narrow (in terms of κ) stability window is found for extremely broad solitons with values of the “spin” s=1 and 2. However, analytical consideration of a special perturbation mode in the form of a spontaneous shift of the soliton’s central “bubble” (core of the vortex embedded in a broad soliton) demonstrates that even extremely broad solitons are subject to an exponentially weak instability against this mode. In actual simulations, a manifestation of this instability is found in a three-dimensional soliton with s=1. In the case when the two-dimensional spinning solitons are subject to tangible azimuthal instability, the number of the nonspinning fragments into which the soliton splits is usually, but not always, equal to the azimuthal number of the instability eigenmode with the largest growth rate.     

Topological and dynamical excitations in a classical 2D easy-axis Heisenberg model

The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of applicability of the continuum approach are discussed. Received 22 August 2000     

Quantum monte carlo studies of electron-electron interaction effects in conducting polymers

We discuss recent studies, using the quantum ensemble projector Monte Carlo (EPMC) method, of theoretical models of conducting polymers. Our focus is on the consequences of incorporating direct electron-electron interactions into the “standard” electron-phonon interaction models. Among the observables we examine one energetics of purely dimerized ground states, single solitons, soliton pairs, averaged spin and charge distributions, and local correlation functions.     

Exact vortex solitons in a quasi-two-dimensional Bose–Einstein condensate with spatially inhomogeneous cubic–quintic nonlinearity

The exact vortex soliton solutions of the quasi-two-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities are constructed by similarity transformation. It is demonstrated that spatially inhomogeneous cubic–quintic nonlinearity can support exact vortex solitons in which there are two quantum numbers S and m. The radius structures and density distributions of these vortex solitons are studied, and it is shown that the number of ring structure of the vortex solitons increases by one with increasing the “radial quantum number” m by one.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

Fast Soliton Scattering by Delta Impurities

We study the Gross-Pitaevskii equation with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L ² norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998     

Quantum analogue of the spin-flop transition for a spin pair

Quantum (step) magnetization curves have been analyzed for a spin pair with antiferromagnetic interaction in the presence of a magnetic field that is parallel to the easy magnetization axis. Both semiclassical and numerical analyses have been performed for a wide range of the anisotropy parameter and spins up to S ? 100. In the dependence of the anisotropy character (single-ion or exchange), a spin jump larger than unity can appear in the magnetization curve or jumps can be concentrated in a narrow range of the field. In addition, regions of the problem parameters have been revealed where behavior is semiclassical for low spins on the order of S = 5 and where behavior is substantially quantum even for S → ∞.     

Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model

We study the stabilization of the soliton transported bio-energy by the dynamic equations in the improved Davydov theory from four aspects containing the feature of free motion and states of the soliton at the long-time motion and at biological temperature 300 K and behaviors of collision of the solitons by Runge-Kutta method and physical parameter values appropriate to the $\alpha$-helix protein molecules. We prove that the new solitons can move without dispersion at a constant speed retaining its shape and energy in free and long-time motions and can go through each other without scattering. If considering further influence of the temperature effect of heat bath on the soliton, it is still thermally stable at biological temperature 300 K and in a time as long as 300 ps and amino acid spacings as large as 400, which shows that the lifetime of the new soliton is at least 300 ps, which is consistent with analytic result obtained by quantum perturbation theory. These results exhibit that the new soliton is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.     

Ground states, solitons and spin textures in spin-1 Bose-Einstein condensates

We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.