Solitonic solutions for the generalized two-velocity Boltzmann equation

We obtain solitonic solutions for an inhomogeneous model Boltzmann equation which describes a two velocity one-dimensional gas diffusing in a background when remotion and regeneration processes are allowed. These solutions are obtained as a series expansion in the similarity variable, whose coefficients can be exactly found within a recursive scheme. The solitons describe a shape-preserving distribution function which approaches a stationary value as time elapses. The particular case in which remotion and regeneration events are neglected can be solved in a closed form.     

One-dimensional inhomogeneous Ising model: A new approach

We present a new method for the study of a one-dimensional inhomogeneous Ising chain with nonconstant nearest neighbor interactions. The external field required to produce a given magnetization profile is derived exactly. Some properties of the pair direct correlation function are derived. Our findings generalize previous results of Percus.     

非匀强磁场中双量子位Heisenberg XY链的基态纠缠和热纠缠(英文)

研究了非匀强磁场中各向异性Heisenberg XY链的基态纠缠和热纠缠.结果表明对双量子位情形,纠缠与格点间耦合常数J、外部磁场B、各向异性参数γ和b的正负无关.对绝对零度情形,我们给出了纠缠C的解析表达式,并指出临界磁场Bc随磁场各向异性参数b的增大而增大.对有限温度情形,我们给出了γ=0时C的解析表达式和γ≠0时的数值模拟结果,结果发现引进非匀强磁场可以使纠缠在某些区域明显增大;同时我们还指出当γ=0时,纠缠存在的临界温度Tc仅是b的增函数,而当γ≠0时,它却由B和b共同决定.     

Numerical determination of the density profile of an inhomogeneous membrane: solution of the inverse vibration problem

Given one or more vibrational modes of a membrane, the free vibration equation can be applied to infer the mass surface density. This paper considers determining the surface density of an inhomogeneous membrane from digitized holographic projections (interferograms) of the modeshapes. Spatially discrete numerical models of the membrane surface are presented, which can be used to solve both forward and inverse vibration problems. The accuracy of the discrete models is examined for exactly solvable free vibration problems involving inhomogeneous membranes. For the solution of the inverse problem, error estimates are given for the mass surface density deduced from modeshape interferograms. The practicability of the method is investigated using simulated experimental data for membranes with composite and continuously inhomogeneous density profiles. Strategies are discussed for reducing errors in the reconstructed densities.     

Exact ground-state correlation functions of one-dimensional strongly correlated electron models with resonating-valence-bond ground state

We investigate one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding noninteracting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing.     

Spinless fermion model on diamond chain

The decoration or iteration transformation were widely applied to solve exactly the magnetic spin models in one-dimensional and two-dimensional lattice. The motif of this Letter is to extend the decoration transformation approach for models that describe interacting electron systems instead of spin magnetic systems, one illustrative model to be studied, will be the spinless fermion model on diamond chain. Using the decoration transformation, we are able to solve this model exactly. The phase diagram of this model was explored at zero temperature as well as the thermodynamic properties of the model for any particle density. The particular case when particle-hole symmetry is satisfied was also discussed.     

Pauli principle for one-dimensional bosons and the algebraic bethe ansatz

For the construction of the physical vacuum in exactly solvable one-dimensional models of interacting bosons it is important that the momenta of all the particles be different. We give a formal proof that they are indeed different.     

Composite-fermionization of the mixture composed of Tonks gas and Fermi gas

This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks-Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose-Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson-fermion interaction, the system exhibits composite-fermionization crossover.     

Multiple Quantum NMR in One-Dimensional and Nano-Scale Systems: Theory and Computer Simulations

We investigate several exactly solvable models of multiple quantum (MQ) NMR dynamics. We study MQ NMR dynamics of one-dimensional systems (chains and rings) and nano-voids filled with spin-carrying atoms or molecules in a strong external magnetic field. Our focus is the problem of the profile of MQ NMR coherences (i.e., the dependence of the intensities of MQ NMR coherences on their orders). We find that integrable one-dimensional systems exhibit peculiar behavior that does not shed much light on a more generic situation. On the other hand, important lessons can be extracted from our solution for the nano-scale systems. We find that the profile of the intensities of the MQ NMR coherences is rather exponential than Gaussian as was proposed earlier. We also address the cluster growth in the course of the evolution of MQ NMR coherences.     

Multiple-quantum NMR spin dynamics of inhomogeneous one-dimensional systems in solids

Multiple-quantum NMR spin dynamics of inhomogeneous one-dimensional systems in solids is investigated by analytical and numerical methods. A fermion approach for MQ spin dynamics of one-dimensional inhomogeneous systems is developed in the approximation of the dipole–dipole interactions (DDI) of nearest neighbors. It is shown that only MQ coherences of the zeroth and plus/minus second orders appear in the approximation of the DDI of the nearest neighbors even in inhomogeneous one-dimensional systems. We also investigate MQ dynamics of inhomogeneous chains numerically. Intensities of MQ NMR coherences for a linear chain consisting of 3000 spins are calculated.     

FDTD Simulation of Electromagnetic Reflection of Conductive Plane Covered with Imhomogeneous Time-Varying Plasma

A finite-difference time-domain (FDTD) algorithm is applied to study the electromagnetic reflection of conduction plane covered with inhomogeneous, collision, warm, time-varying plasma. The collision frequency of plasma is a function of electron density and plasma temperature. Under the one-dimensional case, transient electromagnetic propagation through various plasmas have been obtained, and the reflection coefficient of EM wave through inhomogeneous time-varying plasma (ITVP), homogeneous time-varying plasma (HTVP) and inhomogeneous plasma (IP) are calculated under different conditions. The results illustrate that a plasma cloaking system can successfully absorb the incident EM wave.     

Quantum phase diagram of the t-J(z) chain model

We present the quantum phase diagram of the one-dimensional t- J(z) model for arbitrary spin (integer or half-integer) and sign of the spin-spin interaction J(z), using an exact mapping to a spinless fermion model that can be solved exactly using the Bethe ansatz. We discuss its superconducting phase as a function of hole doping nu. Motivated by the new paradigm of high temperature superconductivity, the stripe phase, we also consider the effect the antiferromagnetic background has on the t- J(z) chain intended to mimic the stripe segments.     

倾斜入射光入射于一维非线性光子晶体中带宽加宽的二次谐波的产生

研究了置于空气中的含缺陷的一维非线性光子晶体中二次谐波的产生.由于反射的二次谐波很强而不能忽略,缓变振幅近似在系统中是不适用的.本文提出了一种不采用缓变振幅近似来处理二次谐波产生问题的方法,并应用这种方法计算相关的二次谐波转换效率.结果表明:随着入射波角度的增加,缺陷模对应的波长将变短,并且通过调整基频波入射的角度,可以产生宽带宽并且高转换效率的二次谐波.这个方法适用于任何一维非均匀系统,可以简单方便地计算出二次谐波转换效率.     

Self-similar potentials and Ising models

A new link between soliton solutions of integrable nonlinear equations and one-dimensional Ising models is established. Translational invariance of the spin lattice associated with the KdV equation is related to self-similar potentials of the Schrödinger equation. This gives antiferromagnets with exponentially decaying interaction between the spins. The partition function is calculated exactly for a uniform magnetic field and two discrete values of the temperature.     

Photothermal waves in a periodically modulated structure

The generation of thermal waves in a one-dimensional structure with a sinusoidal variation in thermal diffusivity can be described by an inhomogeneous Mathieu equation. An exact solution to the frequency-domain Mathieu equation can be found by using a variation of parameters method to give the alternating component of the temperature along the structure. From the theory of Mathieu functions a dispersion relation for the thermal waves is found, which does not display band gaps, but which shows damping that departs from that for thermal waves in a uniform medium.     

Inhomogeneous Ising model on a multiconnected network

We first generalize the inhomogeneous external field Ising model on a ring to include inhomogeneous couplings. We then further generalize the one-dimensional periodic lattice to the simplest multiconnected networks. The fundamental idea and techniques developed here may be also applicable to other problems where topological collective (nonlocal) modes are many fewer in number than total degrees of freedom.     

Equations for the distributions of functionals of a random-walk trajectory in an inhomogeneous medium

Based on the random-trap model and using the mean-field approximation, we derive an equation that allows the distribution of a functional of the trajectory of a particle making random walks over inhomogeneous-lattice site to be calculated. The derived equation is a generalization of the Feynman-Kac equation to an inhomogeneous medium. We also derive a backward equation in which not the final position of the particle but its position at the initial time is used as an independent variable. As an example of applying the derived equations, we consider the one-dimensional problem of calculating the first-passage time distribution. We show that the average first-passage times for homogeneous and inhomogeneous media with identical diffusion coefficients coincide, but the variance of the distribution for an inhomogeneous medium can be many times larger than that for a homogeneous one.     

On spin and matrix models in the complex plane

We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of two-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-N partition function zeros in the complex plane.     

Transport property of inhomogeneous strained graphene

In analogy to real magnetic field, the pseudo-magnetic field (PMF) induced by inhomogeneous strain can also formthe Landau levels and edge states. In this paper, the transport properties of graphene under inhomogeneous strain arestudied. We find that the Landau levels have non-zero group velocity, and construct one-dimensional conducting channels.In addition, the edge states and the Landau level states in PMF are both fragile under disorder. We also confirm that thebackscattering of these states could be suppressed by applying a real magnetic filed (MF). Therefore, the transmissioncoefficient for each conducting channel can be manipulated by adjusting the MF strength, which indicates the applicationof switching devices.