Non-Markovian relaxation of a three-level system: quantum trajectory approach

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schr?dinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.     

Exact c-number representation of non-Markovian quantum dissipation

The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schr?dinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born-Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.     

Relaxation dynamics of a quantum Brownian particle in an ideal gas

We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal gas by means of a translation-covariant master equation. We discuss the type of approximations required to obtain the generalized form of the Caldeira-Leggett master equation, along with their physical justification. Microscopic expressions for the diffusion and relaxation coefficients are obtained by analyzing the limiting form of the equation in both the Schr?dinger and the Heisenberg picture.     

Open quantum system approach for heavy quark thermalization

We treat heavy quark as an open quantum system in a hot medium and rederive the stochastic Schr?dinger equation (SSE) from the full Schr?dinger equation for both heavy quarks and the medium. We apply the SSE to the dynamical evolutions of a heavy quark (as a system) in the static hot medium (as an environment). Heavy quarks interact with the medium via random scatterings, which exchange the momentum and phase factor randomly between two wave functions of the system and the environment. The exchange of momentum and phase factor results in the transition between different eigenstates of the system. These are included via an external stochastic potential in the Hamiltonian of SSE. Stochastic wave functions of a heavy quark are evolved with the stochastic external potential. The mean wave functions and corresponding momentum distributions of heavy quarks are obtained after the ensemble average over a large set of stochastic wave functions. We present the thermalization of heavy quarks in the static medium with different coupling strengths.     

Exact solution for a non-Markovian dissipative quantum dynamics

We provide the exact analytic solution of the stochastic Schr?dinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.     

Finite Temperature Schr?dinger Equation

We know Schr?dinger equation describes the dynamics of quantum systems, which don’t include temperature. In this paper, we propose finite temperature Schr?dinger equation, which can describe the quantum systems in an arbitrary temperature. When the temperature T=0, it become Shr?dinger equation.     

一维定态薛定谔方程的宏观模拟解法

将实验模拟法引入量子力学.设计了一个弦振动系统,这个系统的定态方程与定态薛定谔方程数学形式一样,为定态薛定谔方程的模拟解法提供了理论和实验途径.宏观模拟的结果为理解薛定谔方程提供了宏观类比. 关键词： 薛定谔方程 宏观模拟解法     

Controlling ultracold Rydberg atoms in the quantum regime

We discuss the properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap being commonly used in ultracold atomic physics experiments. The Hamiltonian is derived, and it is demonstrated how tight traps alter the coupling of the atom to the magnetic field. We solve the underlying Schr?dinger equation of the system within a given n manifold and show that for a sufficiently large Ioffe field strength the 2n;{2}-dimensional system of coupled Schr?dinger equations decays into several decoupled multicomponent equations governing the center of mass motion. An analysis of the fully quantized center of mass and electronic states is undertaken. In particular, we discuss the situation of tight center of mass confinement outlining the procedure to generate a low-dimensional ultracold Rydberg gas.     

Monte Carlo wavefunction approach to the dissipative quantum-phase dynamics of two-component Bose-Einstein condensates

We investigate the relaxation effects on the dynamics of two-component dilute gas Bose-Einstein condensates (BEC) with relatively different two-body interactions and Josephson couplings between the two components. Three types of relaxation effects, i.e., one- and three-body losses and a pure phase relaxation caused by elastic two-body collision between condensed and noncondensed atoms, are examined on the dynamical behavior of a macroscopic superposition, i.e., Schr?dinger cat state, of two states with atom-number differences between the two components, which is known to be created by the time evolution in certain parameter regimes. Although three-body losses show a relatively large suppression of the revival behavior of Schr?dinger cat state and the Pegg-Barnett phase-difference distribution between the two components for a small-size Schr?dinger cat state, one- and three-body loss effects are not shown to directly depend on the size of Schr?dinger cat state. In contrast, the pure-phase relaxation effects, causing a reduction of phase-difference distribution and then decaying the Schr?dinger cat state, significantly increase with the increase of the size of Schr?dinger cat state. These features suggest that a detection of damped collapse-revival behavior is highly possible for medium-size Schr?dinger cat states in small-size two-component BECs.     

随机薛定谔级联方程：理论和应用

随机薛定谔级联方程是一种基于波函数的严格量子动力学方法,它可用于研究耦合到玻色子热库的复杂体系中的量子动力学过程. 本综述从开放量子体系费曼路径积分的影响泛函出发,概述了随机薛定谔级联方程的一般理论框架和各种具体表述形式,并通过对复杂体系中超快激发能量转移过程的模拟来展示方法的应用范例和计算效率.     

Quantum diffusion of H/Ni(111) through a Monte Carlo wave function formalism

We consider a quantum system coupled to a dissipative background with many degrees of freedom using the Monte Carlo wave function method. Instead of dealing with a density matrix which can be very highly dimensional, the method consists of integrating a stochastic Schr?dinger equation with a non-Hermitian damping term in the evolution operator, and with random quantum jumps. The method is applied to the diffusion of hydrogen on the Ni(111) surface below 100 K. We show that the recent experimental diffusion data for this system can be understood through an interband activation process, followed by quantum tunneling.     

Environmental recording of the angular momentum in quantum mechanics

We discuss the coupling of a quantum system through the angular momentum to the reservoir of quantum harmonic oscillators. In classical mechanics an observation of the oscillator trajectories allows one to determine the system's angular momentum. We discuss the quantum dynamics of the model. We show that the model of an observation of environmental coordinates can be related to some models of angular momentum measurement based on a stochastic Schrödinger equation.     

Classical chaos with Bose-Einstein condensates in tilted optical lattices

A widely accepted definition of "quantum chaos" is "the behavior of a quantum system whose classical limit is chaotic." The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical counterparts. A fundamental reason for that is the linearity of Schr?dinger equation. In this paper, we study the quantum dynamics of an ultracold quantum degenerate gas in a tilted optical lattice and show that it displays features very close to classical chaos. We show that its phase space is organized according to the Kolmogorov-Arnold-Moser theorem.     

Time-space fractional Schrödinger like equation with a nonlocal term

In this paper a time-space fractional Schr?dinger equation containing a nonlocal term has been studied. The time dependent solutions have been obtained in terms of the H-function. New general results include the results of integer Schr?dinger equation with a nonlocal term and the well-known quantum formulae for a free particle kernel.     

变量分离法与变系数非线性薛定谔方程的求解探索

把变量分离法应用于(1+1) 维非线性物理模型，构建了色散缓变光纤变系数非线性薛定谔方程的一类新的孤子解.作为特例，也得到了常系数非线性薛定谔方程的包络型孤子解，只是解的形式有点变化. 关键词： 变量分离法 变系数 薛定谔方程 孤子解     

Optimal stochastic enhancement of photoionization

The effect of noise on the nonlinear photoionization of an atom due to a femtosecond pulse is investigated in the framework of the stochastic Schr?dinger equation. A modest amount of white noise results in an enhancement of the net ionization yield by several orders of magnitude, giving rise to a form of quantum stochastic resonance. We demonstrate that this effect is preserved if the white noise is replaced by broadband chaotic light.     

The Supersymmetry Approaches to the Non-central Kratzer Plus Ring-Shaped Potential

In this paper, we study the Schr?dinger equation with non-central modified Kratzer potential plus a ring-shaped like potential, which is not spherically symmetric. We connect the corresponding Schr?dinger equation to the Laguerre and Jacobi equations. These lead us to have some raising and lowering operators which are first order equations. We take advantage from these first order equations and discuss the supersymmetry algebra. And also we obtain the corresponding partner Hamiltonian for Kratzer potential and investigate the commutation relation for the generators algebra.     

(2+1)维非线性薛定谔方程的环孤子,dromion,呼吸子和瞬子

利用分离变量法,研究了(2+1)维非线性薛定谔(NLS)方程的局域结构.由于在B?cklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了NLS方程丰富的局域结构.合适地选择任意函数,局域解可以是dromion,环孤子,呼吸子和瞬子.dromion解不仅可以存在于直线孤子的交叉点上,也可以存在于曲线孤子的最近邻点上.呼吸子在幅度和形状上都进行了呼吸 关键词： 非线性薛定谔方程 分离变量法 孤子结构     

联立薛定谔系统新精确解及其所描述的孤子脉冲和时间孤子

利用拓展的Riccati映射法，讨论了联立薛定谔系统，得到了其新的精确解，并根据所得到的解模拟出孤子脉冲、飞秒孤子和时间孤子，以及时间孤子间的弹性相互作用. 关键词： 联立薛定谔方程 拓展Riccati映射 孤子脉冲 时间孤子     

Non-markovian continuous quantum measurement of retarded observables

We reconsider the non-Markovian time-continuous measurement of a Heisenberg observable x[over ] and show for the first time that it can be realized by an infinite set of entangled von Neumann detectors. The concept of continuous readout is introduced and used to rederive the non-Markovian stochastic Schr?dinger equation. We can prove that, contrary to recent doubts, the resulting non-Markovian quantum trajectories are true single system trajectories and correspond to the continuous measurement of a retarded functional of x[over ].