Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. III. Eigenvectors of the transfer matrix and hamiltonian

We obtain the eigenvectors of the transfer matrix of the zero-field eight vertex model. These are also the eigenvectors of the Hamiltonian of the corresponding one-dimensional anistropic Heisenberg chain.     

Spin transport in a one-dimensional anisotropic Heisenberg model

We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Δ is varied spin transport changes from ballistic for Δ<1 to anomalous at the isotropic point Δ=1, to diffusive for finite Δ>1, ending up as a perfect isolator in the Ising limit of infinite Δ. Using perturbation theory for large Δ a quantitative prediction is made for the dependence of diffusion constant on Δ.     

Field statistics in a one-dimensional Reverberation Chamber model

This work focuses on building a fairly simple yet physically appropriate 1D model for a Reverberation Chamber which claims to be able to analytically predict the statistical behavior of such a chamber, without forsaking to the benefits of deterministic models. The statistical properties are introduced by varying the size of a 1D stirrer or the cavity size itself. A validation analysis shows agreement with other theories and measured results on real RCs. Field statistics in undermoded regime is examined. A radiated emission test is defined and shows reliable matching with reality. The field performance near the conducting walls is investigated. To cite this article: R. Serra, F. Canavero, C. R. Physique 10 (2009).     

Anomalous wave function statistics on a one-dimensional lattice with power-law disorder

Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics.     

Polaron on a one-dimensional lattice: II. A moving polaron

Continuum-limit equations for moving polarons on a one-dimensional lattice with a harmonic interaction potential between adjacent particles and a simple nonlinear potential with a cubic nonlinearity are derived for the first time; for some particular cases, their solutions are obtained. For a harmonic lattice in the continuum limit, a system of integrable nonlinear partial differential equations is derived. A one-soliton solution to this system describes a polaron moving with a constant velocity. The speed of this polaron is uniquely related to its amplitude, with its values ranging from zero to the speed of sound. For a nonlinear lattice, the resulting system of differential equations is integrable at a certain ratio of the problem parameters. The one-soliton solution to this system, as in the harmonic case, describes a polaron moving with a constant velocity. At arbitrary values of the lattice parameters, the nonlinear lattice was studied by numerical methods. It turned out that, in the entire range of parameters, the nonlinear lattice gives rise to moving polarons, with the speed of the polaron being determined by the competition between the electron-photon interaction parameter α and the nonlinearity parameter β. At α ? β, the behavior of the polaron is very close to the dynamics on the harmonic lattice. In the opposite case, the dynamic nonlinearity begins to dominate, giving rise to dynamics inherent to solitons, so that speed of the polaron can exceed the speed of sound. In a certain range of α and β, numerical calculations revealed a family of polaron-type stable solutions, the envelope of which can have several peaks. The numerical and exact analytical solutions are in very good agreement for a sufficiently large radius of the polaron, when the system of equations obtained in the continuum approximation has a solution.     

Stark shift contribution to field statistics in a generalized Jaynes-Cummings model

The nonlinear and multiphoton interaction between a single two-level atom and two modes of radiation is studied in a generalized Jaynes-Cummings model. An intensity-dependent level shift is considered. The time evolution operator is obtained. The detuning has a photon number dependence. Different statistical aspects pertaining to either the atom or the fields are calculated. The dipole moment, the dipole-dipole correlation function, as well as the transient spectrum are obtained.     

Half-magnetization plateau stabilized by structural distortion in the antiferromagnetic heisenberg model on a pyrochlore lattice

Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half-magnetization plateau has been observed, is discussed.     

“Solidification” in a soluble model of bosons on a one-dimensional lattice: The “Boson-Hubbard chain”

Lieb and Liniger's soluble model of the 1-D Bose gas is put on a lattice, becoming a “boson-Hubbard model”. It remains soluble by the Bethe ansatz. When the coupling exceeds a critical value ($\text{U}\text{2πT}\text{)>}\text{2√3}\text{π}$, a gap is present when the density n bosons per site is 1.     

Superfluid to Mott-insulator transition in a one-dimensional optical lattice

Bose-Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ～ 13.7 E_r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.     

The statistics of dimers on a three-dimensional lattice. II. An improved lower bound

The model proposed in the previous paper is used to improve the Hammersley lower bound for three-dimensional dimer problem.     

一维反铁磁链中双亚格点模型的孤子解(英文)

求出了一维反铁磁链中双亚格点模型的孤子解,并求出了孤子宽度、峰值、静止能量和有效质量.在al=bl 和al=-bl 两种情况下求方程的精确解.     

Double-exchange ferromagnetism in the partially-filled one-dimensional Kondo lattice model

We investigate the incompletely saturated ferromagnetic phase which occurs at strong-coupling in the partially-filled one-dimensional (1D) Kondo lattice model. The double-exchange interaction responsible for the ferromagnetic ordering is absent in dilute Kondo systems, and is a missing element in nearly all theoretical treatments of the model. We discuss how: 1) double-exchange arises in the system, even though the Kondo coupling is antiferromagnetic, and show that at strong-coupling it favors an alignment of the spins of unpaired localized moments; and 2) how this determines the ground-state phase diagram, and properties of the localized moments.     

On the hydrodynamic limit of a one-dimensional Ginzburg-Landau lattice model. Thea priori bounds

The simplest Ginzburg-Landau model with conservation law is investigated. The initial state is specified by an inhomogeneous profile of the chemical potential associated with the conserved quantity, that is, the mean spin. It is shown that the mean spin satisfies a nonlinear diffusion equation in the hydrodynamic limit. The proof is based on the nice, parabolic structure of the model. A standard perturbation technique is used.     

Equivalence of the “Wilson expansion” and a generalized parton model

For a target made with constituents which interact via an asymptotically free theory, it is possible to define some parton densities in the deep inelastic region and at any order of the running coupling constant. These densities depend only on the structure of the target and their Q² dependence is governed by master equations. At first order the result of Altarelli and Parisi is recovered. The scattering of any current off the target is described by a convolution of these parton densities with some charge densities, depending on the couplings of the current to the partons. All those results are equivalent to those of the Wilson operator formalism. Some explicit examples are given.     

The statistics of dimers on a three-dimensional lattice. I. An exactly solvable model

A three-dimensional lattice model is proposed for which the constant occurring in the dimer problem can be evaluated exactly.     

Binding of holons and spinons in the one-dimensional anisotropic t-J model

We study the binding of a holon and a spinon in the one-dimensional anisotropic t-J model using a Bethe-Salpeter equation approach, exact diagonalization, and density matrix renormalization group methods on chains of up to 128 sites. We find that holon-spinon binding changes dramatically as a function of anisotropy parameter alpha=J( perpendicular)/J(z): it evolves from an exactly deducible impuritylike result in the Ising limit to an exponentially shallow bound state near the isotropic case. A remarkable agreement between the theory and numerical results suggests that such a change is controlled by the corresponding evolution of the spinon energy spectrum.     

Commensurate-incommensurate phase transition in one-dimensional quantum sine-Gordon model based on a lattice massive thirring model

The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sine-Gordon model at zero temperature is exactly solved with the use of the Bethe ansatz technique for the lattice massive Thirring model. The energy difference between C and IC phases is derived based on the same ground state which is valid in the whole parameter region. It is due to the fact that there is no change in the ground state of the lattice massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model. It is proved in the whole parameter region that the IC phase can be realized with the soliton density proportional to (E _s : formation energy of soliton), whenE _s becomes negative.     

Localization and level statistics in a one-dimensional solid state model with periodically modulated potential

For a solid state model described by a band matrix with diagonal elements depending periodically on the siteindex we determine the eigenstates and their localization length. The periodicity of the diagonal elements gives rise to the appearance of a pronounced peak structure of the eigenstates with the same period. The same type of peak-structure is present in the quasi-energy states of some periodically driven quantum systems, and can be associated with a nearly conversed quasi-momentum quantum number. We investigate the influence of the periodic peak structure on the nearest neighbor level spacing distribution and find that the nearly conserved quasi-momentum modifies but does not destroy the level repulsion expected for a Gaussian orthogonal ensemble.