non-Markovian Limit Research Articles

Quantum phase-space function formulation of reactive flux theory

On the basis of a coherent-state representation of the quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee et al., Phys. Rev. E 65, 021109 (2002); 66, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time-dependent quantum transmission coefficient—a quantum analog of the classical Kramers–Grote–Hynes coefficient in the spirit of Kohen and Tannor’s classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for the intermediate to strong damping regimes with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low-temperature regime.

Magnetotransport in the two-dimensional Lorentz model: non-markovian Grad limit of the BBGKY hierarchy

We consider the classical two-dimensional Lorentz model of non-interacting charged point particles acted upon by a perpendicular uniform magnetic field. Particles are elastically scattered by hard disks randomly distributed in the motion plane. Trajectories of gas particles between collisions are arcs of cyclotron circles. We consider the Grad limit of the corresponding BBGKY hierarchy. The Lorentz model in magnetic field provides an example where the Grad limit of the solution for the one-particle density cannot be found by formally applying the limit to evolution equations. The resulting non-markovian kinetic equation is shown to coincide with the generalization of the Boltzmann equation originally proposed upon intuitive arguments.

Examples of Convergence and Non-convergence of Markov Chains Conditioned Not To Die

In this paper we give two examples of evanescent Markov chains which exhibit unusual behaviour on conditioning to survive for large times. In the first example we show that the conditioned processes converge vaguely in the discrete topology to a limit with a finite lifetime, but converge weakly in the Martin topology to a non-Markovian limit. In the second example, although the family of conditioned laws are tight in the Martin topology, they possess multiple limit points so that weak convergence fails altogether.

Mode suppression in the non-Markovian limit by time-gated stimulated photon echo

It is demonstrated that enhanced mode suppression in stimulated photon echo experiments can be obtained by diagonal time gating of the echo. This technique is especially important when the optical dynamics of the system is non-Markovian. A two-mode Brownian oscillator model is used to analyze the effect of time gating on the stimulated photon echo. The method is demonstrated on a dye solution of DTTCI in ethylene glycol at room temperature. Experimentally, time gating of the echo is accomplished by means of femtosecond phase-locked heterodyne detected stimulated photon echo. The vibrational dynamics in this system are explored by conventional stimulated photon echo experiments. Especially stimulated photon echo-maximum shift measurements are found to be particularly useful.

Non-Markovian fluctuation limits of infinite particle systems

S′-valued Gaussian processes of a certain class are shown to have the semimartingale decomposition similar to that one given by the Ornstein-Uhlenbeck equation. There is given a simple sufficient condition for the family of fluctuations to be tight.The non–Markov property for this class of processes is investigated

Theory of non-Markovian exciton transport in a one dimensional lattice

We consider non-Markovian exciton transport in a one dimensional system with nearest neighbor interactions. Kubo’s stochastic Liouville equation (SLE) is used to derive a set of coupled equations of motion which are exact for a Poisson bath and which also should give a fairly accurate long time description for a Gaussian bath. The SLE is especially suitable for this problem since both cumulunt expansion and projection operator techniques encounter difficulties when the system is quantum mechanical, the stochastic off-diagonal coupling is strong, and the relaxation is non-Markovian. To elucidate the role of correlations in space and time, we consider two different models: (a) Both diagonal and off-diagonal fluctuations arise from the same bath. (b) All the fluctuations arise from uncorrelated baths. We find that model (a) always gives coherent exciton transport even at long times if the mean off-diagonal coupling J is nonzero. Model (b) gives diffusive behavior at long times, but the diffusion constant is very different in the non-Markovian limit from the prediction of Markovian or weak-coupling theories. In the Markovian limit, the expressions for the mean square displacement agree exactly with those of Haken and co-workers and of Grover and Silbey. Some interesting new features of non-Markovian transport are discussed.

Non-markovian theory of molecular relaxation. I. Vibrational relaxation and dephasing in condensed phases

The cumulant expansion is used to derive two formally different master equations for a two-level molecular system interacting with a bath, starting wit The two master equations reduce to the same form in the markovian limit for the bath (where its correlation time is much shorter than the relaxation pr A detailed comparison is made between the predictions of the two approaches which enables us to understand their range of validity and limitations. We apply the formalism to the vibrational relaxation and dephasing of a molecular impurity in a solid matrix and obtain a closed expression for the vib In contrast to the simple stochastic approaches we predict that the line shape in the non-markovian limit contains information regarding the interactio However, the fluctuations in the mean interaction energy of the two-level system with the bath, if correlated with the frequency modulation, result in