共查询到20条相似文献,搜索用时 15 毫秒
1.
A. V. Churkin 《Mathematical Notes》2005,78(5-6):867-873
In this paper, we construct an exact solution of the stochastic Schrodinger equation for a quantum oscillator with possible dissipation of energy taken into account. Using the explicit form of the solution, we calculate estimates for the characteristic damping time of free damped oscillations. In the case of forced oscillations, we obtain formulas for the Q-factor of the system and for the variance of the coordinate and momentum of a quantum oscillator with dissipation. We obtain the quantum analog of the classical diffusion equation and explicitly show that the equations of motion for the mean value of the momentum operator following from the solution of the stochastic Schrodinger equation play the role of the quantum Langevin equation describing Brownian motion under the action of a stochastic force. 相似文献
2.
V. V. Sargsyan Z. Kanokov G. G. Adamyan N. V. Antonenko 《Theoretical and Mathematical Physics》2008,156(3):1331-1346
Based on the non-Markovian quantum Langevin equations, we obtain time-dependent transport coefficients for an inverted oscillator
coupled linearly in the coordinate to a thermostat. We comparatively analyze the diffusion coefficients for harmonic and inverted
oscillators and study the role of quantum statistical effects in the passage through a parabolic barrier.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 425–443, September, 2008. 相似文献
3.
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
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Estimates of growth of the standard d-dimensional Brownian motion W(t) and its integral V(t) = t
0 W (s) ds are obtained, as t , and an application is discussed to the long time asymptotics of the solutions of the nonlinear stochastic equation of the quantum filtering theory. 相似文献
6.
We consider the problem of the dynamics of a Gaussian wave packet in a one-dimensional harmonic ocsillator interacting with
a bath. This problem arises in many chemical and biochemical applications related to the dynamics of chemical reactions. We
take the bath-oscillator interaction into account in the framework of the Redfield theory. We obtain closed expressions for
Redfield-tensor elements, which allows finding the explicit time dependence of the average vibrational energy. We show that
the energy loss rate is temperature-independent, is the same for all wave packets, and depends only on the spectral function
of the bath. We determine the degree of coherence of the vibrational motion as the trace of the density-matrix projection
on a coherently moving wave packet. We find an explicit expression for the initial coherence loss rate, which depends on the
wave packet width and is directly proportional to the intensity of the interaction with the bath. The minimum coherence loss
rate is observed for a “coherent” Gaussian wave packet whose width corresponds to the oscillator frequency. We calculate the
limiting value of the degree of coherence for large times and show that it is independent of the structural characteristics
of the bath and depends only on the parameters of the wave packet and on the temperature. It is possible that residual coherence
can be preserved at low temperatures.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 130–144, October, 2007. 相似文献
7.
Abstract In this article, we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equation involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary, in using the penalization method. We also give a characterization of the solution as the value function of an optimal stopping time problem. Then we give a probabilistic formula for the viscosity solution of an obstacle problem for PDEs with a nonlinear Neumann boundary condition. 相似文献
8.
This paper is devoted to the study of optimization of investment, consumption and proportional reinsurance for an insurer with option type payoff at the terminal time under the criterion of exponential utility maximization. The surplus process of the insurer and the financial risky asset process are assumed to be diffusion processes driven by Brownian motions which are non-Markovian in general. Very general constraints are imposed on the investment and the proportional reinsurance processes. Based on the martingale optimization principle, we use BSDE and BMO martingale techniques to derive the optimal strategy and the optimal value function. Some interesting particular cases are studied in which the explicit expressions for the optimal strategy are given by using the Malliavin calculus. 相似文献
9.
We present a new approach to a concept of a set-valued stochastic integral with respect to semimartingales. Such an integral, called set-valued stochastic up-trajectory integral, is compatible with the decomposition of the semimartingale. Some properties of this integral are stated. We show applicability of the new integral in set-valued stochastic integral equations driven by multidimensional semimartingales. The uniqueness theorem is presented. Then we extend the notion of the set-valued stochastic up-trajectory integral to definition of a fuzzy stochastic up-trajectory integral with respect to semimartingales. A result on uniqueness of a solution to fuzzy stochastic integral equations incorporating the new fuzzy stochastic up-trajectory integral driven by the multidimensional semimartingale is stated. 相似文献
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Prasenjit Das Debasis MukherjeeA.K. Sarkar 《Applied mathematics and computation》2011,218(6):2509-2515
Discrete and stochastic version of a susceptible-infective model system with nonlinear incidence rate is investigated. We observe that the discrete system converges to a unique equilibrium point for certain effective transmission rate of the disease and beyond which stability of the system is disturbed. Stochastic analysis suggests that the model system is globally asymptotically stable in probability for certain strengths of white noise. Numerical simulations are also performed to validate the results. 相似文献
12.
本文建立了油气田开采动态系统的随机微分方程数学模型,在对模型求解的基础上,给出了各状态变量的均值函数与方差函数的估计。 相似文献
13.
We develop necessary and sufficient conditions for the a.s. asymptotic stability of solutions of a scalar, non-linear stochastic equation with state-independent stochastic perturbations that fade in intensity. These conditions are formulated in terms of the intensity function: roughly speaking, we show that as long as the perturbations fade quicker than some identifiable critical rate, the stability of the underlying deterministic equation is unaffected. These results improve on those of Chan and Williams; for example, we remove the monotonicity requirement on the drift coefficient and relax it on the intensity of the stochastic perturbation. We also employ different analytic techniques. 相似文献
14.
提出并证明了一类常微分方程解的存在唯一性成立的一个充要条件,并给出了多项式形式增长函数的一列上界.最终将此结果应用到证明一类倒向随机微分方程的唯一解问题. 相似文献
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We prove existence of the horizontal lift to a line bundle of certain diffusion processes on some infinite-dimensional manifolds. We provide three classes of finite-dimensional manifolds for which the corresponding loop spaces have a line bundle and thus provide three classes of loop manifolds on which certain diffusion processes admit a horizontal lift. Applications to Quantum Field Theory are indicated. 相似文献
18.
The functional Ito formula, in the form df() = f( + d ) f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25. 相似文献
19.
We use the nonequilibrium Liouville equation to derive the master equation for the reduced statistical operator in a heat
bath represented by a many-particle environment. Focusing on the case of a weak system-bath coupling, we consider the Born-Markov
approximation of the master equation and compare the result to different approaches. The master equation is elaborated for
the special case of an atom as a reduced system in a plasma background. We find that the dynamical structure factor determines
the effect of the plasma on the reduced system. We consider the operator equation in the atomic eigenstate and in the phase-space
representation, which yields two limiting cases: quantum mechanical behavior similar to the isolated atom for the lower strongly
bound levels and a semiclassical one for highly excited Rydberg levels.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 31–62, January, 2008. 相似文献