Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap

We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the ground-state density distributions in the whole interaction regime for different atomic number ratio, intra- and inter-atomic interactions. For the case with equal intra- and inter-atomic interactions, our results clearly display the evolution of density distributions from a Bose condensate distribution to a Fermi-like distribution with the increase of the repulsive interaction. Particularly, we compare our result in the strong interaction regime to the exact result in the infinitely repulsive limit which can be obtained by a generalized Bose-Fermi mapping. We also discuss the general case with different intra- and inter-atomic interactions and show the rich configurations of the density profiles.     

Hysteresis behavior of the random-field Ising model with 2-spin-flip dynamics: exact results on a Bethe lattice

We present an exact treatment of the hysteresis behavior of the zero-temperature random-field Ising model on a Bethe lattice when it is driven by an external field and evolved according to a 2-spin-flip dynamics. We focus on lattice connectivities z=2 (the one-dimensional chain) and z=3. For the latter case, we demonstrate the existence of an out-of-equilibrium phase transition, in contrast with the situation found with the standard 1-spin-flip dynamics. We discuss the influence of the degree of cooperativity of the (local) spin dynamics of the nonequilibrium response on the system.     

Ground states versus low-temperature equilibria in random field Ising chains

Random walk arguments and exact numerical computations are used to study one-dimensional random field chains. The ground state structure is described with absorbing and non-absorbing random walk excursions. At low temperatures, the local magnetization follows the ground state except at regions where a local random field fluctuation makes thermal excitations easier. This is explained by the random walk picture, implying that the magnetization lengthscale is a product of the domain size and the thermal excitation scale. Received 16 October 2000 and Received in final form 7 June 2001     

Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.     

Flory radius of polymers in a periodic field: An exact analytic theory

We found an exact expression for the Flory radius R _F of Gaussian polymers placed in an external periodic field. This solution is expressed in terms of the two parameters η and a that describe the reduced strength of an external field and the period of the field to the polymer gyration radius ratio, respectively. R _F is found to be a decaying function of η for any values of a . Provided that the gyration radius is of the order of the period of an external field or less, the ground-state (GS) approximation of the exact result for R _F is shown to give qualitatively incorrect results. In addition to the “ground-state” contribution, the exact solution for R _F contains an additional term that is overlooked by the GS approximation. This term gives rise to the fact that R _F as a function of η exhibits power law behavior (rather than exponential decay obtained from the GS result) once η exceeds the threshold value η_con .     

Photon channelling in foams

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of ɛ.     

Transformation from the nonautonomous to standard NLS equations

In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schrödinger (NLS) equation. An integrable condition is first obtained by the Painlevé analysis, which is shown to be consistent with that obtained by the Lax pair method. Under this condition, we present a general transformation, which can directly convert all allowed exact solutions of the standard NLS equation into the corresponding exact solutions of the nonautonomous NLS equation. The method is quite powerful since the standard NLS equation has been well studied in the past decades and its exact solutions are vast in the literature. The result provides an effective way to control the soliton dynamics. Finally, the fundamental bright and dark solitons are taken as examples to demonstrate its explicit applications.     

Interacting gaps model,dynamics of order book,and stock-market fluctuations

Inspired by order-book models of financial fluctuations, we investigate the Interacting gaps model, which is the schematic one-dimensional system mimicking the order-book dynamics. We find by simulations the power-law tail in return distribution, power-law decay of volatility autocorrelation with exponent 0.5 and Hurst exponent close to 1/2. Surprisingly, when we make a mean-field approximation, i.e. replace the one-dimensional system by effectively infinite-dimensional one, we obtain analytically the return exponent 5/2, in perfect accord with one-dimensional simulations.     

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM).     

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process is studied in an arbitrary inertial reference frame. In particular, we derive directly from the stochastic equations of motion in an arbitrary inertial frame the transport equation for the distribution function of the diffusing particles in phase-space. We explain why this result is not trivial and has, at the very least, methodological interest. We also show that this result offers a conceptually new proof of the well-known fact that the relativistic one-particle distribution function in phase-space is a Lorentz scalar. Received 28 March 2000     

Exact Solutions of Schrödinger Equation for the Position-Dependent Effective Mass Harmonic Oscillator

A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration space, and the exact solutions to the corresponding Schrödinger equation are obtained analytically in terms of modified Hermite polynomials. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the position dependence of the mass vanishes.     

1D stability analysis of filtering and controlling the solitons in Bose-Einstein condensates

We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating the external potential well in the three-dimensional (3D) Gross–Pitaevskii equation (GPE). Within the framework of this method, under suitable conditions, the GPE can be exactly decomposed into a pair of coupled equations: a transverse two-dimensional (2D) linear Schr?dinger equation and a one-dimensional (1D) longitudinal nonlinear Schr?dinger equation (NLSE) with, in a general case, a time-dependent nonlinear coupling coefficient. We review the general idea how to filter and control localized solutions of the GPE. Then, the 1D longitudinal NLSE is numerically solved with suitable non-ideal controlling potentials that differ from the ideal one so as to introduce relatively small errors in the designed spatial profile. It is shown that a BEC with an asymmetric initial position in the confining potential exhibits breather-like oscillations in the longitudinal direction but, nevertheless, the BEC state remains confined within the potential well for a long time. In particular, while the condensate remains essentially stable, preserving its longitudinal soliton-like shape, only a small part is lost into “radiation”.     

Simple Method Obtaining Analytical Expressions of Particle and Kinetic—Energy Densities for One—Dimensional Confined Fermi Gases

We develop a simple approach to obtain explicitly exact analytical expressions of particle and kineticenergy densities for noninteracting Fermi gases in one-dimensional harmonic confinement,and in one-dimensional box confinement as well.     

Species segregation in one-dimensional granular-system simulations

We present one-dimensional molecular dynamics simulations of a two-species, initially uniform, freely evolving granular system. Colliding particles swap their relative position with a 50% probability allowing for the initial spatial ordering of the particles to evolve in time and frictional forces to operate. Unlike one-dimensional systems of identical particles, two-species one-dimensional systems of quasi-elastic particles are ergodic and the particles' velocity distributions tend to evolve towards Maxwell-Boltzmann distributions. Under such conditions, standard fluid equations with merely an additional sink term in the energy equation, reflecting the non-elasticity of the interparticle collisions, provide an excellent means to investigate the system's evolution. According to the predictions of fluid theory we find that the clustering instability is dominated by a non-propagating mode at a wavelength of the order 10πL/Nɛ , where N is the total number of particles, L the spatial extent of the system and ɛ the inelasticity coefficient. The typical fluid velocities at the time of inelastic collapse are seen to be supersonic, unless Nɛ ≲ 10π . Species segregation, driven by the frictional force occurs as a result of the strong temperature gradients within clusters which pushes the light particles towards the clusters' edges and the heavy particles towards the center. Segregation within clusters is complete at the time of inelastic collapse.     

Monte Carlo simulation of joint density of states in one-dimensional Lebwohl-Lasher model using Wang-Landau algorithm

Monte Carlo simulation using the Wang-Landau algorithm has been performed in an one-dimensional Lebwohl-Lasher model. Both one-dimensional and two-dimensional random walks have been carried out. The results are compared with the exact results which are available for this model.     

Spin Hall effect of light in one-dimensional photonic crystal

We established a general propagating model to investigate the spin Hall effect of light in one-dimensional photonic crystal. A polarized (spin dependent) Gaussian beam which was incident obliquely through one-dimensional photonic crystal was demonstrated. Having decomposed a polarized Gaussian beam into different plane wave components charactering individual wave vectors, we revealed the transmission coefficient and reflection coefficient of each plane wave which propagates through the one-dimensional photonic crystal. It enabled us to obtain exact solution to the electric field of transmitted and reflected beams, and the analytical formula of light intensity, accordingly. A method based upon the partial differentials with the intensity distribution of the transmitted and reflected Gaussian beams was presented to determine the transverse and longitude shifts explicitly. Spin dependent shifts in one-dimensional photonic crystal provide alternative evidence for the spin Hall effect of light.     

Magnetic susceptibility, heat capacity, and optical conductivity of LiPc and LiPcI

The magnetic susceptibility, using dc and electron spin resonance (ESR) methods, the specific heat, and the infrared properties of the one-dimensional molecular semiconductors lithium phthalocyanine (LiPc) and the iodinated compound LiPcI have been investigated for temperatures K. LiPc has a half-filled conduction band and is expected to be an organic metal. However, due to the strong Coulomb repulsion the system is a one-dimensional Mott-Hubbard insulator with a Hubbard gap of 0.75 eV as inferred from optical measurements. The localized electrons along the molecular stacks behave like a S = 1/2 antiferromagnetic spin chain. The spin susceptibility, as determined by ESR experiments, and the magnetic contribution to the heat capacity show a Bonner-Fisher type of behavior with an exchange constant K. LiPcI is an intrinsic narrow-gap semiconductor with an optical gap of 0.43 eV. In ESR experiments it is silent, indicating that all the unpaired electrons have been removed from the macrocycle via doping with iodine. Received: 16 June 1998 / Accepted: 14 July 1998     

Electromagnetically induced transparency and evolution of a two-level system under chaotic field of arbitrary intensity

The electromagnetically induced transparency (EIT) with a (near-)resonant chaotic (amplitude-phase fluctuating, Gaussian-Markovian) coupling field is studied theoretically. The Fourier transform of the steady-state EIT spectrum, which determines a nonstationary probe absorption, is also considered. This quantity equals the average diagonal element of the (reduced) evolution operator of the coupled transition (the evolution function). The exact solution in the form of a continued fraction is obtained and used to perform numerical calculations. Moreover, a number of approximate analytical results are obtained, which, together with the results of previous publications, describe the EIT and the evolution function in all possible regimes. In particular, in the constructive-interference case the EIT increases with the coupling-field bandwidth ν at sufficiently small ν. For a strong field, the maximum of the transparency as a function of ν is less than that for a monochromatic field of the same average intensity. In contrast, for a weak field, there is a range of ν values, where the field fluctuations do not affect the EIT. The latter result is shown to hold for a broad class of stochastic fields. Received 31 December 2000 and Received in final form 14 May 2001     

Exact X-wave solutions of the hyperbolic nonlinear Schrödinger equation with a supporting potential

We find exact solutions of the two- and three-dimensional nonlinear Schrödinger equation with a supporting potential. We focus in the case where the diffraction operator is of the hyperbolic type and both the potential and the solution have the form of an X-wave. Following similar arguments, several additional families of exact solutions can also can be found irrespectively of the type of the diffraction operator (hyperbolic or elliptic) or the dimensionality of the problem. In particular we present two such examples: The one-dimensional nonlinear Schrödinger equation with a stationary and a “breathing” potential and the two-dimensional nonlinear Schrödinger with a Bessel potential.     

Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps

A cholesteric liquid crystal can be considered as a one-dimensional photonic crystal with a refractive index that is regularly modulated along the helix axis because of the particular arrangement of the molecules. The result is that the propagation of light is suppressed for a particular range of wavelengths (bandgap). A polymer-stabilized cholesteric liquid crystal (PSCLC), which is obtained by in situ photopolymerization of reactive liquid-crystal molecules in the presence of non-reactive liquid-crystal molecules in an oriented Bragg planar texture, is elaborated by combining the UV-curing with a thermally induced pitch variation. As a consequence, it is shown here that memory effects are introduced into the characteristics of the reflection band of the material at room temperature. In the visible spectrum, the reflection bandwidth can be tuned in agreement with the thermal ramp and broadened. In addition, the bandgap filters can be switched between broadband reflective, scattering and transparent states by subjecting them to an electric field. Related application fields of these functional materials are switchable smart windows for the control of the solar-light spectrum and white-or-black polarizer-free reflective displays.