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41.
M. Grifoni E. Paladino U. Weiss 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(4):719-729
The dynamics of the reduced density matrix of the driven dissipative two-state system is studied for a general diagonal/off-diagonal
initial state. We derive exact formal series expressions for the populations and coherences and show that they can be cast
into the form of coupled nonconvolutive exact master equations and integral relations. We show that neither the asymptotic
distributions, nor the transition temperature between coherent and incoherent motion, nor the dephasing rate and relaxation
rate towards the equilibrium state depend on the particular initial state chosen. However, in the underdamped regime, effects
of the particular initial preparation, e.g. in an off-diagonal state of the density matrix, strongly affect the transient dynamics. We find that an appropriately tuned external ac-field
can slow down decoherence and thus allow preparation effects to persist for longer times than in the absence of driving.
Received 23 October 1998 and Received in final form 26 February 1999 相似文献
42.
J.C. Gimel T. Nicolai D. Durand J.M. Teuler 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(1):91-97
Dynamic properties of Brownian particles immersed in a periodic potential with two barriers V1 and V2 (symmetric bistable potential) are studied by using the Fokker-Planck equation which we solve numerically by the matrix continued
fraction method. This study will therefore serve to demonstrate the influence of this form of potential, which is of great
interest for superionic conductors and for many other solid systems, on the diffusion process. Thus, we have calculated the
full width at half maximum (FWHM) ) of the quasi-elastic line of the dynamic structure factor, for a large range of values of the wave-vectors q. Our results show clearly that, by varying the ratio of the barriers strictly between and 1, the Fokker-Planck equation describes a diffusive process which has some characteristic of jump and
liquid-like regimes. While in the limit cases, i.e. when tends to or 1, the diffusion process can be described only by a simple jump motion. However, the jump-lengths corresponding
to each limit case are not equal. In general the change of the ratio is found to have a significant effect on the character
of the diffusive motion. We have also performed Fokker-Planck dynamics calculations of the diffusion coefficient in a bistable
potential. We have found a good agreement between numerical calculations and analytical approximation results obtained in
the high friction limit.
Received 25 May 1998 and Received in final form 15 November 1998 相似文献
43.
This paper studies the heavily trimmed sums (*)
[ns] + 1
[nt]
X
j
(n)
, where {X
j
(n)
}
j = 1
n
are the order statistics from independent random variables {X
1,...,X
n
} having a common distributionF. The main theorem gives the limiting process of (*) as a process oft. More smoothly trimmed sums like
j = 1
[nt]
J(j/n)X
j
(n)
are also discussed. 相似文献
44.
M. Celasco R. Eggenhöffner 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(4):415-419
A dynamical percolative model explaining the universality of 1/
f
γ
noise is reported. Exponents γ ranging from 0 to 2 are obtained under the hypothesis that noise originates from random switching events between two ON-OFF
states in elemental parts (switchers) of a physical system. The usual noise behaviour with γ very close to 1 in an arbitrarily wide frequency range is obtained assuming a statistical distribution of switcher relaxation
time τ proportional to τ
-1
, as in McWhorter's model. The impact of these results with respect to recent self-organised criticality models is discussed.
Received 6 November 2000 and Received in final form 22 May 2001 相似文献
45.
We consider a queueing network with two single-server stations and two types of customers. Customers of type A require service only at station 1 and customers of type B require service first at station 1 and then at station 2. Each server has a different general service time distribution, and each customer type has a different general interarrival time distribution. The problem is to find a dynamic sequencing policy at station 1 that minimizes the long-run average expected number of customers in the system.The scheduling problem is approximated by a dynamic control problem involving Brownian motion. A reformulation of this control problem is solved, and the solution is interpreted in terms of the queueing system in order to obtain an effective sequencing policy. Also, a pathwise lower bound (for any sequencing policy) is obtained for the total number of customers in the network. We show via simulation that the relative difference between the performance of the proposed policy and the pathwise lower bound becomes small as the load on the network is increased toward the heavy traffic limit. 相似文献
46.
Let X
t be a one-dimensional diffusion of the form dX
t=dB
t+(X
t)dt. Let Tbe a fixed positive number and let
be the diffusion process which is X
t conditioned so that X
0=X
T=x. If the drift is constant, i.e.,
, then the conditioned diffusion process
is a Brownian bridge. In this paper, we show the converse is false. There is a two parameter family of nonlinear drifts with this property. 相似文献
47.
We consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure. Uniqueness of the Gibbs measure for two cases is shown. Also the typical path behaviour, the degree of mixing and some further properties are derived. We use cluster expansion in the small coupling parameter. 相似文献
48.
利用Brown运动在H\"older 范数下关于$(r,p)$-容度的大偏差,证明了Brown运动增量在H\"older范数下关于$(r,p)$-容度的泛函极限定理. 相似文献
49.
本文利用白噪声分析的方法,讨论了分式布朗运动的局部时,即将其看作一个Hida分布.进一步,给出分式布朗运动的局部时的混沌分解以及局部时平方可积性. 相似文献
50.
Almost sure exponential stability of backward Euler-Maruyama discretizations for hybrid stochastic differential equations 总被引:1,自引:0,他引:1
Xuerong Mao Yi ShenAlison Gray 《Journal of Computational and Applied Mathematics》2011,235(5):1213-1226
This is a continuation of the first author’s earlier paper [1] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler-Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [1] is the global Lipschitz condition. However, we will show in this paper that without this global Lipschitz condition the EM method may not preserve the almost sure exponential stability. We will then show that the backward EM method can capture the almost sure exponential stability for a certain class of highly nonlinear hybrid SDEs. 相似文献