粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式.我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹.对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置.结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构.随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端.对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式.研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关.为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱.路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度.本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程有一定的参考价值.     

粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式。我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹。对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置。结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构。随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端。对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式。研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关。为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱。路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度。本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程可以提供一定的参考价值。     

Tunneling as a Classical Escape Rate Induced by the Vacuum Zero-point Radiation

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non-null escape rate over the potential barrier at low temperatures (T → 0). It is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results.     

Escape of Particles from an Open Square-Shaped Cavity

The escape of particles in an open square-shaped cavity has been examined. We consider a family of trajectories launched from the left bottom lead of the square cavity and escaped from the right boundary. For each escaping trajectories, we record the propagation time and the detector position. We find that the escape time graph exhibits a regular sawtooth structure. For a set of detector points, we search for the classical trajectories from the source point to the detector points. Then we use semiclassical theory to construct the wave function at different given points. The calculation results suggest that the escape probability density depends on the detector position and the momentum of the particle sensitively. The Fourier transform of the semiclassical wave function gives the path length spectrum. Each peak in the path length spectrum corresponds to the length of one escape trajectory of the particle. We hope that our results will be useful in understanding the escape and transport process of particles inside a microcavity.     

Directed transient long-range transport in a slowly driven Hamiltonian system of interacting particles

We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related force vanishes and hence, the system is effectively without bias which excludes any ratchet effect. We pay special attention to the escape of the entire chain when initially all of its units are distributed in a potential well. Moreover for an escaping chain we explore the possibility of the successive generation of a directed flow based on large accelerations. We find that for adiabatic slope-modulations due to the ac-field transient long-range transport dynamics arises whose direction is governed by the initial phase of the modulation. Most strikingly, that for the driven many particle Hamiltonian system directed collective motion is observed provides evidence for the existence of families of transporting invariant tori confining orbits in ballistic channels in the high-dimensional phase spaces.     

Influence of dark energy on time-like geodesic motion in Schwarzschild spacetime

In this paper we investigate the influence of the dark energy on the time-like geodesic motion of a particle in Schwarzschild spacetime by analysing the behaviour of the effective potential which appears in an equation of motion. For the non-radial time-like geodesics, we find a bound orbit when the particle energy is in an appropriate range, and also find another possible orbit, which is that the particle drops straightly into the singularity of a black hole or escapes to infinity. For the radial time-like geodesics, we find an unstable circular orbit when the particle energy is the critical value, in which case it is possible for the particle to escape to infinity.     

Multi-Resonant-Activation for a System Only Driven by Multi-State Noise

We consider the escape of the particles multi-state noise. It is shown that, the noise can make over fluctuating potential barrier for a system only driven by a the particles escape over the fluctuating potential barrier in some circumstances; but in other circumstances, it can not. If the noise can make the particle escape over the fluctuating potential barrier, the mean first passage time （MFPT） can display the phenomenon of multi-resonant-activation. For this phenomenon, there are two kinds of resonant activation to appear. One is resonant activation for the MFPTs as the function of the flipping rates of the fluctuating potential barrier; the other is that for the MFPTs as the functions of the transition rates of the multi-state noise.     

Possible manifestations of the quantum effect (Tunneling) in elementary events in the fracture kinetics of polymers

An elementary event in the kinetics of fracture of polymers, i.e., breaking of a stressed skeletal bond in a chain molecule, has been simulated by the decay of a loaded quantum anharmonic oscillator. The probability and the average time of expectation of the escape of a particle from the potential well in the Morse potential under the action of a tensile force have been calculated over a wide range of temperatures. It has been demonstrated that the escape of the particle occurs predominantly through the tunneling mechanism at low and medium temperatures and through a combination of the tunneling (under-barrier) and over-barrier (thermal-fluctuation) mechanisms with comparable contributions at high temperatures. The calculations have revealed that the participation of the tunneling mechanism in the kinetics of fracture of polymers manifests itself in a low-temperature athermal plateau in the temperature dependence of the breaking strength. A comparison between the calculated and experimental temperature dependences of the breaking strength for the oriented polymer polycaproamide has shown that the calculated and experimental results are in qualitative and quantitative agreement, which allows the conclusion that the tunneling mechanism can contribute to the fracture of polymers.     

Collective escape processes in many-particle systems

We study collective escape phenomena in nonlinear chain models. First we investigate the fragmentation of an overdamped polymer chain due to thermal fluctuations in the absence of an external force. We calculate the activation times of individual bonds in the coupled chain system and compare them with times obtained from Brownian dynamics simulations. We also consider a grafted chain exposed to an external force which monotonically grows as time goes on. In underdamped situations we show that collective localized excitations in a nonlinear force field with absorbing states can cause polymer fragmentation. In a similar fashion, localized modes assist a thermally activated escape of interacting particles in a metastable potential landscape which is additionally subjected to a periodic driving. The latter is necessary to obtain overcritical elongations which create localized modes even in case of stronger damping.     

Activated escape of periodically driven systems

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the activation energy of escape depends linearly on the force amplitude. This dependence is described by the logarithmic susceptibility, which is analyzed theoretically and through analog and digital simulations. A closed-form explicit expression for the escape rate of an overdamped Brownian particle is presented and shown to be in quantitative agreement with the simulations. We also describe experiments on a Brownian particle optically trapped in a double-well potential. A suitable periodic modulation of the optical intensity breaks the spatio-temporal symmetry of an otherwise spatially symmetric system. This has allowed us to localize a particle in one of the symmetric wells. (c) 2001 American Institute of Physics.     

Asymmetric Effects on Escape Rates of Bistable System

The asymmetric effects on the escape rates from the stable states x_± in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x_± of bistable. However, the asymmetric parameter r enhances the
particle escape from stable state x₊, and holds back the particle escape from stable state x_-.     

Asymptotic Behaviour of Randomly Reflecting Billiards in Unbounded Tubular Domains

We study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process originates with ideal gas models in the Knudsen regime, with particles reflecting off microscopically rough surfaces. We classify the process into recurrent and transient cases. We also give almost-sure results on the long-term behaviour of the location of the particle, including a super-diffusive rate of escape in the transient case. A key step in obtaining our results is to relate our process to an instance of a one-dimensional stochastic process with asymptotically zero drift, for which we prove some new almost-sure bounds of independent interest. We obtain some of these bounds via an application of general semimartingale criteria, also of some independent interest.     

粒子在 Hénon-Heiles势中的逃逸动力学模拟

利用庞加莱截面和相空间轨迹方法对粒子在Hénon-Heiles势中的逃逸动力学进行了模拟.粒子的动力学性质敏感地依赖于粒子的能量.数值计算表明当能量很小时,粒子的运动是规则的;随着能量的增加,粒子的运动开始出现混沌.当能量增加到鞍点能Es时,几乎所有的相空间轨迹都是混沌的.当粒子的能量E>Es,粒子可以越过势阱发生逃逸.对于给定的大于Es的能量, 我们画出了粒子的逃逸-时间曲线和逃逸轨迹.我们的研究对于研究混沌传输和逃逸动力学具有一定的参考价值.     

Nonlinear dynamics of charged particles in an oblique electromagnetic wave

We study dynamics of a charged particle under action of an electromagnetic wave that propagates obliquely to a background uniform magnetic field. The dynamics is described by a slow-fast Hamiltonian system. We show that long-term dynamics is dominated by phenomena of capture of particle into resonance with the wave and escape from this resonance, as well as of scattering on resonance. We find that the variation of the particle?s kinetic energy on the time interval between capture and escape is bounded and accumulated in the motion along the background field. We discuss possible applications of the obtained results.     

Free energy and scalings for polymer translocation through a nanopore: A molecular dynamics simulation study combined with milestoning

Coarse-grained molecular dynamics simulations combined with milestoning method are used to study the stochastic process of polymer chain translocation though a nanopore. We find that the scalings for polymer translocation process (the chain is initialized with the first monomer in the nanopore) and for polymer escape process (the chain is initialized with the middle monomer in the nanopore) are different. The translocation process is mainly controlled by the entropic barrier, while the polymer escape process is driven by the effective force due to free energy difference.     

Dynamics of Particles Around a Regular Black Hole with Nonlinear Electrodynamics

We investigate the dynamics of a charged particle being kicked off from its circular orbit around a regular black hole by an incoming massive particle in the presence of magnetic field. The resulting escape velocity, escape energy and the effective potential are analyzed. It is shown that the presence of even a very weak magnetic field helps the charged particles in escaping the gravitational field of the black hole. Moreover the effective force acting on the particle visibly reduces with distance. Thus particle near the black hole will experience higher effective force as compared to when it is far away.     

Quantum tunneling at zero temperature in the strong friction regime

In the large damping limit we derive a Fokker-Planck equation in configuration space (the so-called Smoluchowski equation) describing a Brownian particle immersed into a thermal environment and subjected to a nonlinear external force. We quantize this stochastic system and survey the problem of escape over a double-well potential barrier. Our finding is that the quantum Kramers rate does not depend on the friction coefficient at low temperatures; i.e., we predict a superfluidity phenomenon in overdamped open systems. Moreover, at zero temperature we show that the quantum escape rate does not vanish in the strong friction regime. This result, therefore, is in contrast with the work by Ankerhold et al. [Phys. Rev. Lett. 87, 086802 (2001)]] in which no quantum tunneling is predicted at zero temperature.     

A slowly moving particle in a two-dimensional magnetic field

We consider the behavior of a slowly moving classical point particle in a magnetic field in two dimensions, and show that, although energy conservation would permit the particle to escape to infinity, it in fact does not escape but is permanently trapped in the field. For any given magnetic field, this is true for particles of slow enough velocity. For such motion the magnetic flux enclosed by the Larmor orbits is an adiabatic invariant. Our results may be described by saying the deviations from conservation of this invariant are not cumulative but remain bounded over arbitrary time intervals, and are small if the velocity is small.