Atomic tunneling states and low-temperature anomalies of thermal properties in amorphous materials

A general theory of local atomic non-single-well potential in amorphous materials is presented. It is shown that the potentials practically are critical double-well potentials with low spring constants. Two essentially different types of two-level tunneling states in such potentials are found. The spectral density of the states is shown to be smooth under realistic conditions. The respective specific heat logarithmically deviates from the linear temperature dependence and logarithmically or more weakly depends on the measurement time. Both types of the tunneling states can essentially contribute to the specific heat, whereas one of the types is rather more strongly coupled with phonons and determines the phononic thermal conductivity. Some other questions are also discussed.     

Localization or tunneling in asymmetric double-well potentials

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the exact wave functions of the parabolic wells on both sides of the barrier, for two almost degenerate states, we find a quantization condition for the energy levels which reproduces the known energy splitting formula between the two states. For the other low-lying non-degenerate states, we show that the eigenfunction should be primarily localized in one of the wells with negligible magnitude in the other. Using Dekker’s method (Dekker, 1987), the present analysis generalizes earlier results for weakly biased double-well potentials to systems with arbitrary asymmetry.     

Vibrational resonance in Duffing systems with fractional-order damping

The phenomenon of vibrational resonance (VR) is investigated in over- and under-damped Duffing systems with fractional-order damping. It is found that the factional-order damping can induce change in the number of the steady stable states and then lead to single- or double-resonance behavior. Compared with vibrational resonance in the ordinary systems, the following new results are found in the fractional-order systems. (1) In the overdamped system with double-well potential and ordinary damping, there is only one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for these new resonance behaviors is the value of the fractional-order satisfies α?>?1. (2) In the overdamped system with single-well potential and ordinary damping, there is no resonance, whereas there is a single-resonance for the case of fractional-order damping. The necessary condition for the new result is α?>?1. (3) In the underdamped system with double-well potential and ordinary damping, there are double-resonance and one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for the new single-resonance is α?相似文献   

Pareto distribution in dynamical systems subjected to noise perturbation

Possible mechanisms for formation of the Pareto distribution in dynamical systems subjected to noise perturbation are studied. The effect of external noise characteristics on dimensions of the dynamic variable range where the system response can be approximated by this distribution with a good accuracy is discussed. Systems described by specific forms of the double-well potential are examined.     

Tunnelling in asymmetric double-well potentials: varying initial states

Tunnelling in a double-well potential has features which are not derivable through a mere extension of the concepts used in the context of a single potential barrier with no confining walls on either side. Furthermore, an asymmetric double-well potential, relevant in many contemporary areas of physics and chemistry, possesses certain distinctive aspects in contrast to the relatively simple case of a symmetric double-well potential. In this paper a self-contained numerical and analytical study of these features is reported, and a theoretical model is presented with special attention being given to a unified treatment of both the symmetric and asymmetric cases. The popularly used pair-state model is critically examined, and the important role of the initial state (which is rarely discussed in the literature) is highlighted with specific examples.     

氢键铁电体中的孤子电导性

Gordon首先采用带有非对称双阱势的氢键链模型研究了氢键铁电体的电导性,给出了扭结解和迁移率的表达式.但是对于电导有贡献的扭结孤子应该对应于质子在两个阱底之间的转移,基于这种考虑,修正了Gordon的结果,重新导出了低能态的扭结解,给出了迁移率的一个新的表达式.当非对称双阱势转化为对称双阱势时,这个表达式恰与以前的研究结果一致.这个表达式表明,相变临界指数是1. 关键词： 氢键铁电体 铁电相 孤子迁移率     

有效质量法调控原子玻色-爱因斯坦凝聚体的双阱动力学

操控原子玻色-爱因斯坦凝聚体在双势阱中的动力学通常是通过改变势阱深度来实现,本文提出了一种基于调节原子有效质量的控制方案,可以在不改变双阱势的前提下操控凝聚体的双阱动力学.利用双模近似,本文解析地导出了超冷原子在双阱势中的隧穿强度和相互作用强度对有效质量的依赖关系,并基于平均场近似数值模拟了在有效质量调节下的凝聚体动力学演化,展示了隧穿振荡和自束缚等典型的双阱动力学行为.此外,本文的研究还发现,借助负有效质量效应,这一方案甚至可以等效地实现对负散射长度原子凝聚体双阱动力学行为的操控.     

A controllable double-well optical trap for cold atoms (or molecules) using a binary <Emphasis Type="Italic">π</Emphasis>-phase plate: experimental demonstration and Monte Carlo simulation

We experimentally demonstrate a practical scheme to form a controllable double-well optical dipole trap for cold atoms (or cold molecules), and give some experimental results as well as the fabrication method of a binary π-phase plate. The dependence of the double-well characteristics on the phase etching error of the π-phase plate and the evolution of the double-well optical trap from two wells to a single one are studied both theoretically and experimentally, and the experimental results are consistent with the theoretical prediction. Furthermore, the dynamic process of loading and splitting of cold ⁸⁷Rb atoms from a standard magneto-optical trap (MOT) into our controllable double-well one are studied by Monte Carlo simulations. Our study shows that the loading efficiency of cold atoms from the standard MOT into our single-well trap can reach 100%, and the relative atomic density will be reduced from 1.0 to ∼0.5 during the evolution of our double-well trap, in which the temperature of cold atoms is reduced from 20 μK to ∼15 μK. In final, some potential applications of our controllable double-well optical trap in atom and molecule optics are briefly discussed.     

一种新型双势和周期势模型的构造及其精确解

提出了一种构造并精确求解新型势函数的方法.采用这种方法.讨论了一维二次型函数的通解,将这种二次型函数分段连接构造出一种新型一维双势阱模型和新型一维周期势模型,在此基础上得出了这两种新型势模型的精确解.     

Feedback control in a coupled Brownian ratchet

On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.     

Distribution of escape times for a deterministically driven bistable system

In this paper, we analyze the sequence of escape times for a particle in a symmetric double-well potential coupled to a chain of monodimensional oscillators and we find that, in some range of energies, the probability of escape exhibits the multimodal form that is characteristic of bistable systems driven by a periodic signal embedded in noise. We identify two different modes contributing to the overall hopping dynamics of the particle, each one having a definite dependence on the energy of the chain. Those findings suggest a model for internal fluctuations that could be useful in the study of some problems of interest in physics and biology.     

Spontaneous symmetry breaking of a Boseben Fermi mixture in a two-dimensional double-well potential

We study the spontaneous symmetry breaking of a superfluid Bose-Fermi mixture in a two-dimensional double-well potential. The mixture is described by a set of coupled Gross-Pitaevskii equations. The symmetry breaking phenomenon is demonstrated in the two-dimensional double-well potential in the mixture. The results are summarized in the phase diagrams of the mixture particle numbers, which are divided into symmetric and asymmetric regions by the asymmetry ratios. The dynamical pictures of the spontaneous symmetry breaking induced by a gradual transformation of the single-well potential into a double-well one are also illustrated. The properties of the quantum degenerate mixture are explored using the realistic parameters for a ⁴⁰K-⁸⁷Rb system.     

Condensation of Fermions in the double-well potential

The density distribution of ultracold two-component fermionic gases 6Li, which are confined in a gradient magnetic field and a symmetrical double-well potential, is investigated by employing local-density approximation. It is found that three different regimes including quasi-molecular Bose-Einstein condensation （BECm）, the dimers in the unitarity limit （ULd）, and Bardeen-Cooper-Schrieffer superfluid （BCS） can coexist at the same time. Furthermore, the ranges of these regimes can be controlled to some extent by tuning the gradient of the magnetic field and the parameters characterizing the properties of the double-well potential. This study is of guidance and significance for experimentally realizing the coexistence of BECm, ULd, and BCS in the double-well potential.     

Stochastic resonance and heat fluctuations in a driven double-well system

We study a periodically driven (symmetric as well as asymmetric) double-well potential system at finite temperature. We show that mean heat loss by the system to the environment (bath) per period of the applied field is a good quantifier of stochastic resonance. It is found that the heat fluctuations over a single period are always larger than the work fluctuations. The observed distributions of work and heat exhibit pronounced asymmetry near resonance. The heat loss over a large number of periods satisfies the conventional steady-state fluctuation theorem.     

Physical meaning for Mandelbrot and Julia sets

We consider the dynamics of a kicked charged particle moving in a double-well potential and a time-dependent magnetic field. In certain cases the stroboscopic dynamics reduces to the complex logistic map, thus providing physical meaning for the Mandelbrot set. In other cases we obtain iterated function systems consisting of the inverse complex logistic map, thus providing physical meaning for Julia sets. Our approach can be generalized to complex mappings with a maximum of order q.     

基于Laguerre多项式逼近法的随机双势阱Duffing系统的分岔和混沌研究

应用Laguerre正交多项式逼近法研究了含有随机参数的双势阱Duffing系统的分岔和混沌行为.系统参数为指数分布随机变量的非线性动力系统首先被转化为等价的确定性扩阶系统，然后通过数值方法求得其响应.数值模拟结果的比较表明，含有随机参数的双势阱Duffing系统保持着与确定性系统相类似的倍周期分岔和混沌行为，但是由于随机因素的影响，在局部小区域内随机参数系统的动力学行为会发生突变. 关键词： 双势阱Duffing系统 指数分布概率密度函数 Laguerre多项式逼近 随机分岔     

Multi-instantons and exact results II: specific cases, higher-order effects, and numerical calculations

In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton contributions to the partition function, using the formalism introduced in the first part of the treatise [Ann. Phys. (N. Y.) (previous issue) (2004)]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker-Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is non-zero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited.     

Strongly correlated bistable sublattice and temperature hysteresis of elastic and thermal crystal properties

It is shown that in crystal lattices with a basis the cooperative behavior of a certain type of atoms performing optical long-wavelength vibrations in a double-well potential of the field of the matrix lattice may lead to the formation of a bistable sublattice. As a result of the interaction of the metastable states of such a sublattice with the vibrational states of the matrix lattice, the elastic and thermal properties of the crystal acquire anomalous, hysteresis-like, temperature curves. The concepts developed in the paper make it possible to obtain a qualitative interpretation, which agrees with the experimental data, of the hysteresis-like temperature dependence of the speed and absorption of ultrasonic waves, the specific heat, and the thermal conductivity in superconducting yttrium and bismuth cuprates. Zh. éksp. Teor. Fiz. 116, 168–193 (July 1999)     

Eigenvalues and eigenfunctions of the Fokker-Planck equation for the extremely underdamped Brownian motion in a double-well potential

The eigenvalues and eigenfunctions of the Fokker-Planck equation describing the extremely underdamped Brownian motion in a symmetric double-well potential are investigated. By transforming the Fokker-Planck equation to energy and position coordinates and by performing a suitable averaging over the position coordinate, a differential equation depending only on energy is derived. For finite temperatures this equation is solved by numerical integration, whereas in the weak-noise limit an analytic result for the lowest nonzero eigenvalue is obtained. Furthermore, by using a boundary-layer theory near the critical trajectory, the correction term to the zero-friction-limit result is found.