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 共查询到20条相似文献,搜索用时 78 毫秒
1.
A. Isar  W. Scheid 《Physica A》2002,310(3-4):364-376
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady-state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.  相似文献   

2.
The paper reexamines the treatment of irreversible quantum systems by master equations. Shortcomings of the conventional theory of quantum Markov processes pointed out by Talkner are analyzed. It is shown that a frequently used quantum regression hypothesis is not correct, in general. A new generalized master equation determining the relaxation to equilibrium is derived by means of time-dependent projection operator techniques. It is shown that this master equation also determines the time evolution of equilibrium correlations and response functions. The Markovian approximation is discussed, and a new type of Markovian limit, the Brownian motion limit, is introduced besides the weak coupling limit. The shortcomings of the conventional approach are resolved by deriving new formulae for the time evolution of the correlation and response functions of a quantum Markov process. The symmetries of the process are emphasized, and it is shown how the fluctuation-dissipation theorem and the detailed balance symmetry emerge from the master equation approach.  相似文献   

3.
A theory is presented to take into account internal fluctuations in the study of stochastically driven systems. Internal fluctuations are modeled by a master equation in which external noise is introduced. External noise is modeled by a two-state Markov process. A unified theory of internal and external fluctuations is described in terms of an effective integrodifferential master equation or its equivalent generating function representation. Two examples for which exact analytical results can be obtained are presented. A discussion of the white noise limit of the theory is also given.  相似文献   

4.
A nonperturbative many electron theory of atom resonance ionization and ion resonance neutralization at a metal surface is presented. Particular attention is paid to the problem of the ion yield in SIMS experiments. Using a time dependent equation of motion method, the ionization probability is computed as a function of the velocity of secondary ions and the form of the dependence is sensitive to the detailed shape of the virtual level. For a lorentzian line shape the ionization probability is linear with the velocity for small velocities.  相似文献   

5.
Michio Tokuyama 《Physica A》1980,102(3):399-430
A new method of finding nonlinear Langevin type equations of motion for relevant macrovariables and the corresponding master equation for systems far from thermal equilibrium is presented by generalizing the time-convolutionless formalism proposed previously for equilibrium hamiltoian systems by Tokuyama and Mori. The Langevin type equation consists of a fluctuating force, and the nonlinear drift coefficients which are always identical to those of the master equation. A simple formula which relates the drift coefficients to the time correlation of the fluctuating forces is derived. This is a generalization of the fluctuation-dissipation theorem of the second kind in equilibrium systems and is valid not only for transport phenomena due to internal fluctuations but also for transport phenomena due to externally-driven fluctuations. A new cumulant expansion of the master equation is also obtained. The conditions under which a Langevin and a Fokker-Planck equation of a generalized type for non-equilibrium open systems can be derived are clarified.The theory is illustrated by studying hydrodynamic fluctuations near the Rayleigh-Bénard instability. The effects of two kinds of fluctuations, internal fluctuations of irrelevant macrovariables and external (thermal) noises, on the convective instability are investigated. A stochastic Ginzburg-Landau type equation for the order parameter and the corresponding nonlinear Fokker-Planck equation are derived.  相似文献   

6.
By application of a projection operator technique we derive a formally exact generalization of the nonlinear mean field master equation introduced recently for the study of local fluctuations in a reacting medium. Our starting point is a phenomenological cell master equation. The results of our theory are applicable to the theory of a fluctuating hydrodynamic reacting system. The mean field equation is placed on a firm theoretical foundation by showing it to be the lowest order approximation in an expansion in the dimensionality of the physical space keeping the product of the number of nearest neighbors (an increasing function of dimensionality) and the typical diffusion coefficient constant. A more accurate nonlinear master equation that allows for the correlation and fluctuations in the environment of a given volume element is derived in the form of an augmented mean field equation.Work supported in part by a grant from the National Science Foundation.  相似文献   

7.
In a recent paper a master equation describing the quasi-incoherent motion of Frenkel excitons in molecular crystals has been derived within the Haken-Strobl model for the coupled coherent and incoherent motion of Frenkel excitons. Starting from this master equation and using only the translational symmetry of the crystal lattice, for crystals with one molecule in the unit cell a diffusion equation is derived. For crystals with several molecules in the unit cell instead of a diffusion equation one obtains a set of diffusion-like equations. These equations are solved explicitly for the case of two molecules in the unit cell and asymptotic expressions are discussed. It is shown that this asymptotic behaviour is again described by a diffusion equation.  相似文献   

8.
The theory of the mean first passage time is developed for a general discrete non-Markov process whose time evolution is governed by a generalized master equation. The mean first passage time is determined by an adjoint matrix + in a form analogous to the Fokker Planck case. The theory is illustrated by two examples: A one-dimensional unit step non-Markov process and a non-Markov process with two-step transitions. Explicit expressions for the mean first passage time are derived.  相似文献   

9.
张素侠  陈纬庭 《物理学报》2018,67(6):60201-060201
研究选取合适的准坐标简化完整系统Boltzmann-Hamel方程的问题.基于流形上的标架场理论,指出了定常构形空间中的准速度与标架场的联系,并从几何不变性的角度上导出了完整系统的Boltzmann-Hamel方程.证明了对于任意广义力为零的均匀构形空间、广义力不为零的零曲率构形空间,Boltzmann-Hamel方程均可以化简为可积分的形式,同时给出具体的简化方法并举例说明本方法的适用性.本文方法为寻找运动方程的解析解提供了一条新途径.  相似文献   

10.
We develop a time-dependent theory of heavy-ion collisions which consistently treats the relative and the intrinsic motions by coupled equations derived from the many-body von Neumann equation. The structure of the equations determining the mean trajectory and the fluctuations of the relative motion is the same as that of the corresponding equations in the known linear response theory. The present theory differs, however, from the linear response theory, in that it presumes neither weak coupling between the relative motion and the intrinsic excitations, nor the canonical distribution function for the density operator of the intrinsic motions. We apply the theory especially to deep inelastic collisions, where the relative motion couples to intrinsic excitations through a stochastic hamiltonian. Based on the stochastic assumption, we study the properties of the Green functions that take into account the higher order effects of the coupling hamiltonian. We then discuss, in particular, the effects of the Green functions on the time evolution of the intrinsic state, which is described in terms of a coarse-grained master equation, the friction tensor and fluctuation dissipation theorems.  相似文献   

11.
The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.  相似文献   

12.
R. Görtz 《Physica A》1978,90(2):360-363
We start with a given deterministic equation of motion for a set of macrovariables. Suppose that we can construct a corresponding master equation which has the following properties. In the limit of large systems the deterministic equation can be derived from the master equation for not too long times and the steady-state probability distribution is the exponential of an extensive quantity. Then, using a theorem concerning the solutions of master equations, we can show that the solutions of the deterministic equations evolve into the direction of a nondecreasing steady-state probability.  相似文献   

13.
李强法 《物理学报》1980,29(11):1405-1415
本文给出了确定任意纵剖面形状的缓变波导开放谐振腔内各模式谐振频率的普遍关系式。探讨了腔内各谐振模式场的纵向分布函数的求解方法。具体地分析了鼓形腔和双圆锥腔,分别推导了这两种开放腔各模式的固有谐振频率公式以及场的纵向分布函数。理论分析与实验结果甚为一致。  相似文献   

14.
罗晓华 《物理学报》2014,63(1):17302-017302
假设超晶格量子阱是一个形状任意的周期势阱,电子在超晶格中的运动问题可视为周期场中的运动问题.在量子力学的框架内,从Schr dinger方程和它的一般解出发,利用Bloch理论和传输矩阵方法导出了系统的色散方程;在抛物线近似下,讨论了超晶格量子阱的电子跃迁.结果表明,辐射能量位于红外、远红外或太赫兹波段.  相似文献   

15.
A method is presented, which allows the exact elimination of the projection operator from the kernel of the Nakajima-Zwanzig generalized master equation without using perturbational expansions. Expressions for kernels of generalized master equations using several frequently occuring types of projection operators are derived explicitly. The application of this method for the exact derivation of generalized master equations describing the coherent and the coupled coherent and incoherent exciton motion is proposed. As another application, the derivation of the Smoluchowski equation is suggested.  相似文献   

16.
The planar equations of motion for a tapered fly line subjected to tension, bending, aerodynamic drag, and weight are derived. The resulting theory describes the large non-linear deformation of the line as it forms a propagating loop during fly casting. A cast is initiated by the motion of the tip of the fly rod that represents the boundary condition at one end of the fly line. At the opposite end, the boundary condition describes the equations of motion of a small attached fly (point mass with air drag). An efficient numerical algorithm is reviewed that captures the initiation and propagation of a non-linear wave that describes the loop. The algorithm is composed of three major steps. First, the non-linear initial-boundary-value problem is transformed into a two-point boundary-value problem, using finite differencing in time. The resulting non-linear boundary-value problem is linearized and then transformed into an initial-value problem in space. Example results are provided that illustrate how an overhead cast develops from initial conditions describing a perfectly laid out back cast. The numerical solutions are used to explore the influence of two sample effects in fly casting, namely, the drag created by the attached fly and the shape of the rod tip path.  相似文献   

17.
H. Kono  A.R. Ziv  S.H. Lin 《Surface science》1983,134(3):614-638
The band shape of electronic spectra for a diatomic molecule adsorbed on a surface is studied using the adiabatic approximation. In this approximation, the Schrödinger equation for the total system is separated into those for electronic motion, intramolecular vibration, and low frequency motions (e.g., hindered molecular rotation and lattice vibration). Our theory is applied to the system of an admolecule on the (001) surface of fcc monatomic crystals. We determine the line shape of a vibronic transition for both chemisorption and physisorption cases. In chemisorption cases, a side band due to the low frequency motions can appear in the line shape of a vibronic transition. On the other hand, in physisorption cases, the line shape is a single peak. Moreover, we suggest theoretically a new experimental technique for exciting adsorbed molecules; for this purpose, we derive equations giving the cross sections for the electronic excitation of admolecules by using ion impact at grazing incidence. The admolecules can be excited by this method; the subsequent light emission can give information on the orientation of the admolecule on the surface and on the admolecule-surface species interaction.  相似文献   

18.
Starting from the Haken-Strobl-model for the coupled coherent and incoherent motion of Frenkel excitons, a master equation is derived describing the quasi-incoherent motion of these excitations. In contrast to previous derivations no use is made of special symmetries. Therefore this equation may also describe the energy transfer in materials with non-periodic structure, which play a role in biological systems. The master equation is solved for crystals with one and two molecules in the unit cell, and explicit expressions are given for the case of nearest neighbour interaction too. Furtheron, asymptotic forms of the solutions are discussed.  相似文献   

19.
The Liouville operator of the master equation is decomposed into a part describing the proper system and another operator describing the interaction of the proper system with a set of reservoirs. If the motion of the proper system is described by a Hamiltonian, the corresponding solutions of the density matrix equation are spanned by all conserved quantities and are thus highly degenerate. We demonstrate how this degeneracy may be lifted by applying some sort of perturbation theory for degenerate systems. If there is only one relevant conserved quantity and if the heatbaths connect the quantum numbers of this conserved quantity by nearest-neighbour steps, the solution of the problem can be found explicitly. Otherwise the solution of the original master equation is reduced to a much simpler master equation of orderN, whereN is the number of conserved quantities. An application to a new type of parametric processes in nonlinear optics is given.  相似文献   

20.
A theory of relaxation of metastable states close to the spinodal line is proposed. The statistics of the process is derived on the basis of the equation of motion of the phase transition parameter.  相似文献   

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