Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential

Multistability, i.e., the coexistence of several attractors for a given set of system parameters, is one of the most important phenomena occurring in dynamical systems. We consider it in the velocity dynamics of a Brownian particle, driven by thermal fluctuations and moving in a biased periodic potential. In doing so, we focus on the impact of ergodicity—A concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and, as a consequence, the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken, and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperatures the ergodicity is, in principle, restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperatures, the multistability is robust with respect to the choice of the starting position and velocity of the particle.     

A Brownian Particle in a Microscopic Periodic Potential

We study a model for a massive test particle in a microscopic periodic potential and interacting with a reservoir of light particles. In the regime considered, the fluctuations in the test particle’s momentum resulting from collisions typically outweigh the shifts in momentum generated by the periodic force, so the force is effectively a perturbative contribution. The mathematical starting point is an idealized reduced dynamics for the test particle given by a linear Boltzmann equation. In the limit that the mass ratio of a single reservoir particle to the test particle tends to zero, we show that there is convergence to the Ornstein–Uhlenbeck process under the standard normalizations for the test particle variables. Our analysis is primarily directed towards bounding the perturbative effect of the periodic potential on the particle’s momentum.     

Sedimentation of Brownian Particles in a Gravitational Potential

The settling of a Brownian particle in a semi-infinite fluid bounded by a bottom plane is studied on the basis of Smoluchowski's exact solution of the equation describing diffusion in the gravitational potential. Expressions are derived for the mean height and the variance of height at some time after starting at an initial height. These quantities show interesting behavior as a function of time. It is shown that for certain initial heights the Boltzmann entropy does not increase steadily. It increases at first but then decreases to its equilibrium value.     

Current Reversals of an Underdamped Brownian Particle in an Asymmetric Deformable Potential

Transport of an underdamped Brownian particle in a one-dimensional asymmetric deformable potential is investigated in the presence of both an ac force and a static force,respectively.From numerical simulations,we obtain the current average velocity.The current reversals and the absolute negative mobility are presented.The increasing of the deformation of the potential can cause the absolute negative mobility to be suppressed and even disappear.When the static force is small,the increase of the potential deformation suppresses the absolute negative mobility.When the force is large,the absolute negative mobility disappears.In particular,when the potential deformation is equal to0.015,the two current reversals present with the increasing of the force.Remarkably,when the potential deformation is small,there are three current reversals with the increasing of the friction coefficient and the average velocity presents a oscillation behavior.     

Escape rate of an active Brownian particle in a rough potential

We discuss the escape problem with the consideration of both the activity of particles and the roughness of potentials. We derive analytic expressions for the escape rate of an active Brownian particle in two types of rough potentials by employing the effective equilibrium approach and the Zwanzig method. We find that activity enhances the escape rate, but both the oscillating perturbation and the random amplitude hinder escaping.     

光阱中布朗粒子动力学分析

通过对光阱中的布朗粒子进行动力学方程求解,由解的结果分析得到观测系统的性能要求．结果表明：光阱中布朗颗粒服从Boltzmann分布;对其运动的观测需要纳米量级的空间分辨率和毫秒量级的时间分辨率．     

The CWKB Method of Particle Production in a Periodic Potential

In this work we study the particle production in time dependent periodic potential using the method of complex time WKB (CWKB) approximation. In the inflationary cosmology at the end of the inflationary stage, the potential becomes time dependent as well as periodic. Reheating occurs due to particle production by the oscillating inflaton field. Using CWKB we obtain almost identical results on catastrophic particle production as obtained by others.     

Chaotic Behavior and Instability of Perturbed sine-Gordon Solitons

Solitons of the sine-Gordon system interacting with a disturbed external field are handled by using a direct method. Theoretical analysis reveals that the single soliton perturbed by a periodic field leads to chaotic behavior of the system, and the perturbed double soliton is unstable for most of physically interesting spacetime disturbances.     

A Comparative Study of the Determination of Ferrofluid Particle Size by Means of Rotational Brownian Motion and Translational Brownian Motion

Two methods, the Toroidal Technique and the Forced Rayleigh Scattering (FRS) method, were used in the determination of the size of magnetic particles and their aggregates in magnetic fluids. The toroidal technique was used in the determination of the complex, frequency dependent magnetic susceptibility, x(w)=x'(w) - ix"(w) of magnetic fluids consisting of two colloidal suspensions of cobalt ferrite in hexadecene and a colloidal suspension of magnetite in isopar m with corresponding saturation magnetisation of 45.5 mT, 20 mT and 90 mT, respectively. Plots of the susceptibility components against frequency f over the range 10 Hz to 1 MHz, are shown to have approximate Debye-type profiles with the presence of relaxation components being indicated by the frequency, f _max, of the maximum of the loss-peak in the x"(w) profiles. The FRS method (the interference of two intense laser beams in the thin film of magnetic fluid) was used to create the periodical structure of needle like clusters of magnetic particles. This creation is caused by a thermodiffusion effect known as the Soret effect. The obtained structures are indicative of as a self diffraction effect of the used primary laser beams. The relaxation phenomena arising from the switching off of the laser interference field is discussed in terms of a spectrum of relaxation times. This spectrum is proportional to the hydrodynamic particle size distribution. Corresponding calculations of particle hydrodynamic radius obtained by both mentioned methods indicate the presence of aggregates of magnetic particles.     

带电粒子束的等时周期场聚焦

在质子直线加速器中经常利用等时周期场对粒子束进行聚焦. 这种周期场的特点是周期长度不等而粒子经过每一周期的时间为常数,本文讨论等时周期场聚焦的基本理论,并将它推广到周期长度缓慢变化的周期场.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.     

Eigenvalue Spectrum of a Dirac Particle in Static and Spherical Complex Potential

It has been observed that a quantum theory need not be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many complex potentials, and obtain the real relativistic energy eigenvalues and corresponding eigenfunctions of a Dirac-charged particle in complex statically and spherically symmetric potentials. Complex Dirac–Eckart, complex Dirac–Rosen–Morse II, complex Dirac–Scarf and complex Dirac–Poschl–Teller potential are investigated.     

Velocity spectrum for non-Markovian Brownian motion in a periodic potential

Non-Markovian Brownian motion in a periodic potential is studied by means of an electronic analogue simulator. Velocity spectra, the Fourier transforms of velocity autocorrelation functions, are obtained for three types of random force, that is, a white noise, an Ornstein—Uhlenbeck process, and a quasimonochromatic noise. The analogue results are in good agreement both with theoretical ones calculated with the use of a matrix-continued-fraction method, and with the results of digital simulations. An unexpected extra peak in the velocity spectrum is observed for Ornstein-Uhlenbeck noise with large correlation time. The peak is attributed to a slow oscillatory motion of the Brownian particle as it moves back and forth over several lattice spaces. Its relationship to an approximate Langevin equation is discussed.     

Fermion Particle Production in a Periodic Potential

In this paper we study fermion particle production in the early universe. The present work is motivated to restudy the fermion particle production from the basics and compare the results in the literature through another method developed by one of the present author. One of the authors (SB) has developed a method, known as complex trajectory WKB method, to study particle production in curved as well as flat spacetime. In the present work we have tried to compare the CWKB method with that of other works, current in the literature. In this work we have obtained the particle production amplitude starting from the basics and test our results through both analytical and numerical calculations. For fermion particle production, we first do analytical calculations with a toy example to calculate the production amplitude and verify the same doing fourth order Runge-Kutta calculation. As most problems relevant to early universe are not amenable to analytical calculations, we then take up to study the particle production in periodic potential, generally used in inflationary cosmology. We recheck two recent approaches and obtain almost identical results as that obtained by Greene and Kofman. We also verify the result through CWKB method. Boson particle production has been discussed elsewhere, we discuss it briefly in connection with CWKB. In the present work we generalize the CWKB results of boson production to fermion production. Our works will enable one to understand the various phenomena in early universe related to particle production. Using CWKB we calculate the occupation number and some other results for fermion particle production. The present work will help us clarify the variant results of fermion production current in the literature.     

Effective Potential of a Two-State Model for Molecular Motor

We study force generation and motion of molecular motors using a simple two-state model in the paper. Asymmetric and periodic potential is adopted to describe the interaction between motor proteins and filaments that are periodic and polar. The current and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the current is also calculated. It is shown that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states.     

Rotation-translation coupling of a double-headed Brownian motor in a traveling-wave potential

Frontiers of Physics - We use an interferometic scheme to extract the phase distribution of the electron wave packet from above-threshold ionization in elliptically polarized laser fields. In this...     

Exact Electronic Bands for a Periodic Pöschl-Teller Potential

We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic Pöschl-Teller potential, and to find out the exact energy spectra and the corresponding band structure.     

Equilibrium measure and Brownian escape process

The probability density of Brownian escape process has been obtained recently by R. K. Getoor. In this note we illustrate that Getoor's result can also be obtained by considering equilibrium charge distribution on a metal ball of radiusr>0. This approach reveals a connection between Brownian escape process and classical potential theory.     

Chaotic Behavior of a Model of the Hypothalamo-Pituitary-Gonad Axis in Human Male

A nonlinear dynamical model for the pulsatile secretion of the hypothalamo-pituitary-gonad axis in human male is proposed and chaotic solutions are obtained. We investigate the bifurcation character of the solution and calculate the Lyapunov exponents. Some deductions of this model are obtained and compared ,with experimental results. All the results show that the model is a quite reasonable one.