C. Aslangul

Time behavior of the correlation functions in a simple dissipative quantum model

The force and velocity correlation functions for a particle interacting with a bath are calculated within a model allowing for finite memory effects. The relevance of a Brownian picture is delineated in view of the respective behavior of these functions and appears fully inadequate below some cross-over temperature; then, the interplay between quantum and thermal fluctuations yields some long time tails on the same time scale for both correlation functions. The real space transient diffusion coefficient is found to exceed its asymptotic Einstein value for most times in that regime. The limiting case of an infinitely short memory time is also investigated and is seen to produce weak divergences on a time scale which is small as compared to the other characteristic times.

Quantum ohmic dissipation: Transition from coherent to incoherent dynamics

Abstract We investigate the real-time dynamics of a particle in a double well coupled to phonons with ohmic dissipation. We refine previous results about the T =0 symmetry breaking: the critical behaviour of the order parameter is displayed and the symmetry is shown to be only fully broken for infinite coupling.

Dynamical Exponents for One-Dimensional Random-Random Directed Walks

The dynamical exponents of the coordinate and of the mean square displacement are explicitly calculated in the case of a directed random walk on a one-dimensional random lattice. Moreover, it is shown that, in the dynamical phase where the coordinate increases slower thant, the latter is not a self-averaging quantity.

Exact results and self-averaging properties for random-random walks on a one-dimensional infinite lattice

We present new exact results for a one-dimensional asymmetric disordered hopping model. The lattice is taken infinite from the start and we do not resort to the periodization scheme used by Derrida. An explicit resummation allows for the calculation of the velocityV and the diffusion constantD (which are found to coincide with those given by Derrida) and for demonstrating thatV is indeed a self-averaging quantity; the same property is established forD in the limiting case of a directed walk.

Random walk in a one-dimensional random medium

Abstract The random walk of a particle in a one-dimensional random medium is examined by means of the equivalent transfer rates technique, in the discrete as well as in the continuous version of the model. The probability distributions of the (energy-dependent) equivalent transfer rates are found analytically, either by a matching procedure (in the discrete case) or exactly (in the continuous model). Both discrete and continuous models are shown to belong to the same universality class. The average probability of presence of the particle at its initial point is then computed. For a non-zero global bias, it decreases at large times according to a negative power-law with an exponent depending on disorder and bias; when there is no global bias (Sinais model) the decay at large times follows a logarithmic law.

Quantum ohmic dissipation: Particle on a one-dimensional periodic lattice

Abstract We investigate the dynamics of a particle on a periodic lattice, coupled to phonons with ohmic dissipation. At T = 0 a symmetry breaking appears, which corresponds to a transition between a localized and a delocalized regime. For T > 0 we recover a diffusive motion for which the diffusion coefficient is computed.

Quantum dissipation: Dynamics of a particle in a symmetric double well in the presence of non-ohmic friction

We investigate the equilibrium value and the approach to equilibrium of a particle in a symmetric double-well potential and subjected to dissipation, within the model of Caldeira and Leggett, Ann. Phys. (N.Y.) 149 (1983) 374, but without the ohmic assumption. For subohmic friction, the critical value of the coupling with the bath above which the particle localizes is found to be dependent on the ratio (tunnelling frequency)/(bandwidth of the bath); for an infinite bandwidth, the results given by Leggett et al., Rev. Mod. Phys. 59 (1987) 1, are recovered. For superohmic dissipation, the particle never localizes and its coordinate always goes to zero by following, at large times, a power law in time of the form t−ν; the exponent ν is shown to have a non-intuitive variation as a function of the non-ohmicity.

Quantum dynamics of a dissipative free particle

Abstract We present exact results for the long time dynamics of a quantum free particle interacting with a bath with a coupling ∼ω δ at low frequency. The mean square displacement is dominated by a kinematical term for δ t v with v

Dynamics of excitation in systems with a randomly modulated decay channel

We have investigated the kinetics of excitation in the frame of the conventional Pauli master equation for a molecular aggregate with a decay channel attached to one distinguished molecule (or site). As a principally new feature we assume the rate of probability flow through the decay channel to be a randomly modulated function of time. The modulation is described by a Markoff stochastic process and we do not invoke the white-noise assumption. An exact calculation is given for a broad family of stochastic processes which bridges (and includes) the asymmetric random telegraph signal and the Gaussian process. The general method is then applied in three physically relevant situations: one-molecule aggregate, cyclic-antenna system and infinite linear chain. In these models, we discuss the site-occupation probabilities, the aggregate-excitation function and the mean de-excitation time.

MICROSCOPIC DYNAMICAL EXPONENTS FOR RANDOM-RANDOM DIRECTED WALK ON A ONE-DIMENSIONAL LATTICE WITH QUENCHED DISORDER

We demonstrate that the dynamical exponent for the time dependence of the coordinate, previously found for an average over disorder, is already present in any realization of a given sample. This ergodicity comes from the existence of a scaling law for the probability distribution of the parameter defining the asymptotic dynamical regime. The self-averaging or non-self-averaging properties of the normal or anomalous phases are direct consequences of this result.