Quantum Solitons Research Articles

Skyrme-like solitons with absolute scale in 2+1 dimensions.

A family of models involving a complex scalar field in 2+1 dimensions is considered. The most important feature of these models is their quartic kinetic term which makes them simple analogues of systems involving Skyrme-like kinetic terms in dimensions d>2. Their static field configurations in ${\mathit{openR}}_{2}$ have topological stability. These are studied in some detail, followed by a preliminary formulation of the soliton quantization in 2+1 dimensions. In the Appendix it is demonstrated that the models under discussion are subsystems of the generalization of the Yang-Mills model in higher dimensions.

Breathing vortex solitons in nonrelativistic Chern-Simons gauge theory.

We present exact solutions for breather solitons in the (2+1)-dimensional Chern-Simons gauge theory with external magnetic field B. The breather soliton is a time-dependent solution whose size is oscillating and whose center of mass moves ina cyclotron motion. These solitions describe how the Jackiw-Pi solitons behave in the external magnetic field. We then apply the Bohr-Sommerfeld semiclassical quantization to the breathing mode and the cyclotron motion. It is found that the orbital angular momentum takes on an integer value and that the quantum soliton is in the Landau level.

Quantum solitons in a Hamiltonian framework: John A. Parmentola. Physics Department, West Virginia University, Morgantown, West Virginia 26506; Xin-Hua Yang. School of Physics and Astronomy, 116 Church Street, Minneapolis, Minnesota 55455; and Ismail Zahed. Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3800

Quantum solitons in a Hamiltonian framework: John A. Parmentola. Physics Department, West Virginia University, Morgantown, West Virginia 26506; Xin-Hua Yang. School of Physics and Astronomy, 116 Church Street, Minneapolis, Minnesota 55455; and Ismail Zahed. Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3800

Quantum solitons and anyons in lattice field theories

We briefly report some results obtained in a joint work with J. Fröhlich on quantization and particle structure analysis of solitons in Lattice Field Theories. In particular we discuss abelian gauge theories with Chern-Simons term coupled to Higgs fields in three space-time dimensions. The solitons of such models are electrically charged vortices and they correspond to anyons (particles with any real spin in d = 2+1, see [1]) in the (formal) continuum limit. Such kind of particle excitations are believed to appear in the Fractional Quantum Hall Effect [2]. Furthermore a gas of free anyons with spin 8ϵ Qβ 1 2 Z seems to be a superconductor of a new type, which may describe (essentially) two-dimensional high T c superconductors [3].

Phase-noise scaling in quantum soliton propagation.

We treat the scaling of thermal phase-noise effects and quantum fluctuations for solitons in optical fibers. The central result is that the size of the thermal noise relative to quantum noise is reduced in proportion to the soliton duration for solitons whose duration is less than the thermal correlation times, suggesting that squeezed quantum solitons should be realizable in optical fibers. The physical basis for this effect is largely the fact that squeezing, which is nonlinear, occurs more rapidly for shorter pulses.

Variational problems on vector bundles

A variety of problems in quantum physics and classical statistical mechanics, in particular the quantization of topological solitons and the statistical mechanics of defects in ordered media, are described. These problems can be studied within a semi-classical approximation, or with the help of low-temperature expansions, respectively. The calculation of the leading term in such expansions gives rise to variational problems for sections of vector bundles characterized by certain topological constraints. Examples of such problems are the quantization of kinks in the two-dimensional λϕ4-theory and the analysis of Bloch walls in a Landau-Ginzburg model of a threedimensional anisotropic ferromagnet. We state a general existence result for variational problems of this kind and develop regularity and decay estimates for solutions of the Landau-Ginzburg model describing Bloch walls with prescribed boundaries. For certain boundary configurations stability results are established. The relation between the minimizers of the Landau-Ginzburg model in a certain strong-coupling limit and minimal surfaces is pursued in some detail. An open question is whether, asymptotically, the stability of the limit (minimal) surface will imply the stability of the minimizers of the Landau-Ginzburg model.

Gauge condition and constraint in collective coordinate quantization of solitons

We present a canonical quantization of solitons. The gauge-fixing condition on the field fluctuation and the constraint on its conjugate momentum are set forth in such a way that infrared divergences contained in the continuum meson wavefunctions are removed from the quantum field variables. We show by using the meson-soliton interactions in the quantized hamiltonian that the perturbation calculation exactly reproduces the Born term of the meson-soliton scattering amplitude.

Simulation of solitons in an Ising-like S=(1/2 antiferromagnet on a linear chain.

The dynamics of quantum solitons in an Ising-like S=(1/2 antiferromagnet on finite linear chains with spins N (\ensuremath{\le}15) is studied by integrating the Schr\"odinger equation of motion. Space-time correlation functions ${S}^{\mathrm{zz}}$(r,t) and their Fourier transforms, i.e., dynamical structure factor ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of ${S}^{\mathrm{zz}}$(r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) on ${\mathrm{CsCoCl}}_{3}$ and ${\mathrm{CsCoBr}}_{3}$ very well over a wide temperature range.

SOLITONS AND LORENTZ COVARIANCE AT A QUANTUM LEVEL

An explicit form for the boost operator is derived based upon the Christ-Lee formulation of soliton quantization and we argue that the boost operator along with the other Lorentz generators satisfies the Lorentz group algebra perturbatively in a dimensionless parameter.

Dynamics of solitons in nearly integrable systems

A detailed survey of the technique of perturbation theory for nearly integrable systems, based upon the inverse scattering transform, and a minute account of results obtained by means of that technique and alternative methods are given. Attention is focused on four classical nonlinear equations: the Korteweg-de Vries, nonlinear Schr\"odinger, sine-Gordon, and Landau-Lifshitz equations perturbed by various Hamiltonian and/or dissipative terms; a comprehensive list of physical applications of these perturbed equations is compiled. Systems of weakly coupled equations, which become exactly integrable when decoupled, are also considered in detail. Adiabatic and radiative effects in dynamics of one and several solitons (both simple and compound) are analyzed. Generalizations of the perturbation theory to quasi-one-dimensional and quantum (semiclassical) solitons, as well as to nonsoliton nonlinear wave packets, are also considered.

Quantization and soliton charge in the Peierls model

We have considered a quasiclassical quantization of solitons (kinks, polarons, bipolarons) for the Peierls model with both a degenerate and a nondegenerate ground state. We have calculated the electric current and the charge of quantum excitations, which, as is proved, is distinct from the local charge of classical excitations.

Quantum-nondemolition measurement of optical solitons

Quantization of optical solitons is discussed, using the nonlinear Fourier-transform (inverse-scattering) method. A quantum soliton is described in terms of two sets of conjugate variables such as the photon number and the phase, and the momentum and the center position. The theory of a soliton collision is extended to describe the quantum-nondemolition measurement of soliton photon number and momentum. These two variables are indeed quantum-nondemolition observables and can be measured by means of the phase and the center position of the probe soliton. It is demonstrated that the measurement error and backaction noise on the conjugate variable satisfy an uncertainty product.

Solitons in one-dimensional antiferromagnetic chains.

We study the quantum-statistical mechanics, at low temperatures, of a one-dimensional antiferromagnetic Heisenberg model with two anisotropies. In the weak-coupling limit we determine the temperature dependences of the soliton energy and the soliton density. We have found that the leading correction to the sine-Gordon (SG) expression for the soliton density and the quantum soliton energy comes from the out-of-plane magnon mode, not present in the pure SG model. We also show that when an external magnetic field is applied, the chain supports a new type of kink, where the sublattices rotate in opposite directions.

Soliton quantization in chiral models with vector mesons

A canonical quantization of the skyrmion with ω-mesons is presented using Dirac theory of quantization under constraints. After removing the spurious spin-isospin zero modes from the meson spectrum, an explicit meson-nucleon hamiltonian is constructed. In the strong ω-coupling limit the semi-classical results are recovered. The relevance of this approach to low-energy meson-nucleon physics is stressed.

Stationary phase approximation and quantum soliton families

It is shown that solitons in the anisotropic λ(φ ∗φ) 2 2 model correspond to critical behaviour in a related dynamical system: they are present in the separatrix dividing the phase space of a completely integrable system into parts of bound and unbound motion. The topology of the configuration space is fully described in terms of the topology of the space of paths in S 2, whose geodesics with fixed endpoints give rise to the same Morse series as the family of solitons of the model, according to their asymptotic behaviour. When computed by the Stationary Phase Approximation to the Functional Integral, quantum observables, such as energy and wavefunctions, of quantum states corresponding to the different kinds of solitons exhibit properties which are directly related to the topological structure previously discovered. Using an appropriate coordinate system the model is equivalent to one with two nearly independent fields; once a ground state has been chosen the second field behaves exactly as though it were governed by the sine-Gordon Lagrangian. It is thus discovered that the model contains time-dependent solutions which are multisoliton scattering states.

Stationary phase approximation and quantum soliton families: Juan Mateos Guilarte. Departamento de Física, Facultad de Ciencias, Universidad de Salamanca, Salamanca 37008, Spain

Stationary phase approximation and quantum soliton families: Juan Mateos Guilarte. Departamento de Física, Facultad de Ciencias, Universidad de Salamanca, Salamanca 37008, Spain

The effective lagrangian of the charge-density-wave and macroscopic quantum tunneling in random media

It is shown within the microscopical model that the classical lagrangian of the CDW is independent of the characteristics of the random field of weak impurities. The correction to the quantum lagrangian produced by the forward scattering impurities is obtained exactly. It originates from the chiral anomaly phenomenon. The random renormalization of the tunnel exponent, defining the quantum soliton conductivity, is also obtained.

Quantum field theories of vortices and anyons

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be “anyons,” i.e. particles with arbitrary real spin and intermediate (Θ) statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of HighTcsuperconductors.

Nonperturbative treatment of the functional Schrödinger equation in QCD.

Use of the functional Schroedinger equation in QCD is complicated by the need to maintain gauge invariance at the same time one is dealing with nonperturbative effects (at least at long distances). Moreover, asymptotic freedom must be recovered at short distances. In this paper we show how to set up and solve a set of Ward identities which ensure gauge invariance of the wave functional, which can then be parametrized simply and used with various nonperturbative algorithms (e.g., variational). Parametrizations are found both for the vacuum wave functional and for J/sup P//sup C/ = 0/sup +- //sup +/ quantum soliton states of QCD. A nonperturbative algorithm, based on the observation that a wave functional is really a partition function in the presence of a special kind of source, is set up and applied; this algorithm is based on dressed-loop expansions of partition functions. One recovers this way some earlier results found from the study of Schwinger-Dyson equations, plus some new results concerning the 0/sup -+/ soliton, whose wave functional involves the Chern-Simons secondary class function.

Semiclassical excitation spectrum of an integrable discrete spin chain

The classically integrable discrete spin model with a logarithmic ferromagnetic nearest-neighbor interaction is semiclassically quantized. The resulting spectrum consists of linear magnons and nonlinear quantum solitons. The lowest soliton branch is identical with the magnon as S→∞; in practice, deviations amount to a maximum of 10% for S = 1. The early termination points in momentum space proposed by Haldane as a result of lattice discreteness are found. The singular case m = 2 S is characterized by a logarithmic divergence of the energy at the cutoff wavevector.