共查询到20条相似文献,搜索用时 15 毫秒
1.
V. S. Kirchanov 《Theoretical and Mathematical Physics》2006,148(2):1117-1122
For quantum systems with linear dissipation, we obtain the representation of the Linblad equation in the canonical form via
Hermitian operators. Based on this representation, we derive equations for the entropy density and for the statistical projection
operator. We consider the quantum harmonic oscillator with linear dissipation as an example.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 288–294, August, 2006.
An erratum to this article is available at . 相似文献
2.
A. M. Chebotarev 《Mathematical Notes》2002,71(3-4):408-427
We prove that a quantum stochastic differential equation is the interaction representation of the Cauchy problem for the Schrödinger equation with Hamiltonian given by a certain operator restricted by a boundary condition. If the deficiency index of the boundary-value problem is trivial, then the corresponding quantum stochastic differential equation has a unique unitary solution. Therefore, by the deficiency index of a quantum stochastic differential equation we mean the deficiency index of the related symmetric boundary-value problem.In this paper, conditions sufficient for the essential self-adjointness of the symmetric boundary-value problem are obtained. These conditions are closely related to nonexplosion conditions for the pair of master Markov equations that we canonically assign to the quantum stochastic differential equation. 相似文献
3.
本文研究一类由分数布朗运动驱动的一维倒向随机微分方程解的存在性与唯一性问题,在假设其生成元满足关于y Lipschitz连续,但关于z一致连续的条件下,通过应用分数布朗运动的Tanaka公式以及拟条件期望在一定条件下满足的单调性质,得到倒向随机微分方程的解的一个不等式估计,应用Gronwall不等式得到了一个关于这类方程的解的存在性与唯一性结果,推广了一些经典结果以及生成元满足一致Lipschitz条件下的由分数布朗运动驱动的倒向随机微分方程解的结果. 相似文献
4.
A. M. Sinev 《Theoretical and Mathematical Physics》2009,158(3):377-390
We consider a solvable problem describing the dynamics of a quantum oscillator interacting with an electromagnetic field,
a classical force, and a heat bath. We propose a general method for solving Markovian master equations, the method of quantum
trajectories. We construct the stochastic evolution operator involving the stochastic analogue of the Baker-Hausdorff formula
and calculate the system density matrix for an arbitrary initial state. As a physical application, we evaluate the influence
of the environment at a finite temperature on the accuracy of measuring a weak classical force by the interference method.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 444–459, March, 2009. 相似文献
5.
6.
Yazdan Shirvany Mohsen Hayati Rostam Moradian 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2132-2145
We present a method to solve boundary value problems using artificial neural networks (ANN). A trial solution of the differential equation is written as a feed-forward neural network containing adjustable parameters (the weights and biases). From the differential equation and its boundary conditions we prepare the energy function which is used in the back-propagation method with momentum term to update the network parameters. We improved energy function of ANN which is derived from Schrodinger equation and the boundary conditions. With this improvement of energy function we can use unsupervised training method in the ANN for solving the equation. Unsupervised training aims to minimize a non-negative energy function. We used the ANN method to solve Schrodinger equation for few quantum systems. Eigenfunctions and energy eigenvalues are calculated. Our numerical results are in agreement with their corresponding analytical solution and show the efficiency of ANN method for solving eigenvalue problems. 相似文献
7.
Yinghan Zhang 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(3):415-427
In this paper, we consider the stochastic elastic equation driven by a cylindrical fractional Brownian motion. The regularities of the solution to the linear stochastic problem corresponding to the stochastic elastic equation are proved. Then, we obtain the existence of the solution using the Picard iteration. 相似文献
8.
V. S. Kirchanov 《Theoretical and Mathematical Physics》2008,156(3):1347-1355
We develop a formalism for describing quantum dissipative systems in statistical mechanics based on the quantum Renyi entropy.
We derive the quantum Renyi distribution from the principle of maximum quantum Renyi entropy and differentiate this distribution
(the temperature density matrix) with respect to the inverse temperature to obtain the Bloch equation. We then use the Feynman
path integral with a modified Mensky functional to obtain a Lindblad-type equation. From this equation using projection operators,
we derive the integro-differential equation for the reduced temperature statistical operator, an analogue of the Zwanzig equation
in statistical mechanics, and find its formal solution in the form of a series in the class of summable functions.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 444–453, September, 2008. 相似文献
9.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(2):1098-1105
This paper extends the concept of limiting phase trajectories (LPT) to systems with dissipation. The Duffing oscillator with linear dissipation and periodic excitation is studied. Under condition of 1:1 resonance, we obtain an approximate analytic solution describing two stages of motion: at the first stage the trajectory is close to the non-dissipative LPT, while at the second stage the trajectory approaches stationary oscillations near the steady state. 相似文献
10.
In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the It5 type set-valued stochastic differential equation. 相似文献
11.
《随机分析与应用》2013,31(5):1097-1114
12.
We construct a new explicit solution of the stochastic Schrödinger equation describing a quantum model of the interferometric detector of gravitational waves. For the evolution of this quantum model, we estimate autocorrelation functions of the detected signal and perturbations created by the measuring device. We discuss the influence of the characteristics of the measuring procedure on optimal choice of the length of the moving window which is used to estimate the frequency of gravitational waves by the method of correlation functions. 相似文献
13.
Evolution Equations for Markov Cocycles Obtained by Second Quantization in the Symplectic Fock Space
G. G. Amosov 《Theoretical and Mathematical Physics》2006,146(1):152-157
We derive a quantum stochastic differential equation satisfied by the unitary Markov cocycles obtained for a model situation
during second quantization in the symmetric Fock space.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 186–192, January, 2006. 相似文献
14.
本文是文[1~4]的继续和升华.(1)在本文中,我们根据互补性原理,建立了耗散力学.它是与量子力学相对应的一种耗散理论.可以用这种理论来统一地处理非平衡态热力学和粘滞流体动力学问题,并可以用它来处理量子力学中各种耗散和不可逆的问题.耗散力学的基本方程是与Schr?dinger方程或Dirac方程相对应的一类本征值方程;(2)在本文中,我们将一些基本的非线性耗散型方程,特别是作为宏观非平衡态热力学和粘滞流体动力学基本方程的Navier-Stokes方程,统一地归结为耗散力学基本方程的可积性条件,从而为利用散射反演方法求它们的精确解扫平了道路. 相似文献
15.
Guolian Wang Ming Zeng Boling Guo 《Journal of Mathematical Analysis and Applications》2010,371(1):210-222
In this paper, we consider the stochastic Burgers' equation driven by a genuine cylindrical fractional Brownian motion with Hurst parameter . We first prove the regularities of the solution to the linear stochastic problem corresponding to the stochastic Burgers' equation. Then we obtain the local and global existence and uniqueness results for the stochastic Burgers' equation. 相似文献
16.
Said Hamadène 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(4):632-649
In this paper, we establish a new existence and uniqueness result of a continuous viscosity solution for integro-partial differential equation (IPDE in short). The novelty is that we relax the so-called monotonicity assumption on the driver which is classically assumed in the literature of viscosity solutions of equation with non-local terms. Our method strongly relies on the link between IPDEs and backward stochastic differential equations with jumps for which we already know that the solution exists and is unique for general drivers. In the second part of the paper, we deal with the IPDE with obstacle and we obtain similar results. 相似文献
17.
The Stratonovich version of non-commutative stochastic calculus is introduced and shown to be equivalent to the Itô version developed by Hudson and Parthasarathy [1]. The conversion from Stratonovich to Itô version is shown to be implemented by a stochastic form of Wick's theorem: that is, involving the normal ordering of time-dependent noise fields. It is shown for a model of a quantum mechanical system coupled to a Bosonic field in a Gaussian state that under suitable scaling limits, in particular the weak coupling limit (for linear interactions) and low density limit (for scattering interactions), the limit form of the dynamical equation of motion is most naturally described as a quantum stochastic differential equation of Stratonovich form. We then convert the limit dynamical equations from Stratonovich to Itô form. Thermal Stratonovich noises are also presented. 相似文献
18.
Comment on “New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”
Nikolai A. Kudryashov Pavel N. RyabovDmitry I. Sinelshchikov 《Journal of Computational and Applied Mathematics》2011,235(15):4513-4515
In this comment we analyze the paper [Abdelhalim Ebaid, S.M. Khaled, New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity, J. Comput. Appl. Math. 235 (2011) 1984-1992]. Using the traveling wave, Ebaid and Khaled have found “new types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”. We demonstrate that the authors studied the well-known nonlinear ordinary differential equation with the well-known general solution. We illustrate that Ebaid and Khaled have looked for some exact solution for the reduction of the nonlinear Schrodinger equation taking the general solution of the same equation into account. 相似文献
19.
Denis Bell 《Journal of Functional Analysis》2005,218(1):130-149
We obtain divergence theorems on the solution space of an elliptic stochastic differential equation defined on a smooth compact finite-dimensional manifold M. The resulting divergences are expressed in terms of the Ricci curvature of M with respect to a natural metric on M induced by the stochastic differential equation. The proofs of the main theorems are based on the lifting method of Malliavin together with a fundamental idea of Driver. 相似文献
20.
Nonlinear Schroedinger equation arises in many physical problems. There are many works in which properties of the solution are studied. In this paper we use fully discrete Fourier spectral method to get an approximation solution of nonlinear weakly dissipative Schroedinger equation with quintic term. We give a large-time error estimate and obtain the existence of the approximate attractor A N^k. 相似文献