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E. Barkai

Publications and source records attributed to E. Barkai.

46 records · Page 3Linked to original sources
arXiv2006

Occupation Time Statistics in the Quenched Trap Model

We investigate the distribution of occupation times for a particle undergoing a random walk among random energy traps and in the presence of a deterministic potential field $U^{\rm det}(x)$. When the distribution of energy traps is exponential with a width $T_g$ we find that the occupation time statistics behaves according to (i) the canonical Boltzmann theory when $T>T_g$, (ii) while for $T<T_g$ they are distributed according to the Lamperti distribution with the asymmetry of the distribution determined by the Boltzmann factor $\exp(-U^{\rm det}(x)/T_g)$ with $T_g$ and not $T$ being the effective temperature. We explain how our results describe occupation times in other systems with quenched disorder, when the underlying partition function of the problem is a random variable distributed according to Lévy statistics.

cond-mat.stat-mech↗
arXiv2004

Coherent Destruction of Photon Emission from a Single Molecule Source: A Renormalization Group Approach

The photon emission from a single molecule driven simultaneously by a laser and a slow electric radio frequency (rf) field is studied. We use a non-Hermitian Hamiltonian approach which accounts for the radiative decay of a two level system modeling a single molecule source. We apply the renormalization group method for differential equations to obtain long time solution of the corresponding Schrdinger equation, which allows us to calculate the average waiting time for the first photon emission. Then, we analyze the conditions for suppression and enhancement of photon emission in this dissipative two-level system. In particular we derive a transcendental equation, which yields the non-trivial rf field control parameters, for which enhancement and suppression of photon emission occurs. For finite values of radiative decay rate an abrupt transition from the molecule's localization in its ground state to delocalization is found for certain critical values of the rf field parameters. Our results are shown to be in agreement with the available experiments [Ch. Brunel et al, Phys. Rev. Lett. 81, 2679 (1998)].

cond-mat.other↗
arXiv2004

Coherent Destruction of Photon Emission from a Single Molecule Source

The behavior of a single molecule driven simultaneously by a laser and by an electric radio frequency field is investigated using a non-Hermitian Hamiltonian approach. Employing the renormalization group method for differential equations we calculate the average waiting time for the first photon emission event to occur, and determine the conditions for the suppression and enhancement of photon emission. An abrupt transition from localization-like behavior to delocalization behavior is found.

quant-ph↗
arXiv2003

Lévy Statistics for Random Single--Molecule Line Shapes in a Glass

We demonstrate that the statistical behavior of random line shapes of single tetra-tert-butylterrylene chromophores embedded in an amorphous polyisobutylene matrix at T=2 K, is described by Lévy statistics as predicted theoretically by Barkai, Silbey, and Zumofen [{\em Phys. Rev. Lett.} {\bf 84} 5339 (2000)]. This behavior is a manifestation of the long range interaction between two level systems in the glass and the single molecule. A universal amplitude ratio is investigated which shows that the standard tunneling model assumptions are compatible with the experimental data.

cond-mat.stat-mech↗
arXiv2002

Aging in a Chaotic System

We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks, introduced previously to model diffusion in glasses.

cond-mat.stat-mech↗
arXiv2000

One-Dimensional Stochastic Lévy-Lorentz Gas

We introduce a Lévy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers $\{ξ_i \}$ are independent random variables identically distributed according to the probability density function $μ(ξ)\sim ξ^{-(1 + γ)}$. We show that under certain conditions the mean square displacement of the particle obeys $ \ge C t^{3 - γ}$ for $1 < γ< 2$. This behavior is compatible with a renewal Lévy walk scheme. We discuss the importance of rare events in the proper characterization of the diffusion process.

cond-mat.stat-mech↗
arXiv2000

Fractional Kramers Equation

We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external non-linear force field. For the force free case the velocity damping follows the Mittag-Leffler relaxation and the diffusion is enhanced. The equation obeys the generalized Einstein relation, and its stationary solution is the Boltzmann distribution. Our results are compared to previous results on enhanced Lévy type of diffusion derived from stochastic collision models.

cond-mat.stat-mech↗
arXiv2000

Transforming Gaussian diffusion into fractional a generalized law of large numbers approach

The fractional Fokker-Planck equation (FFPE) [R. Metzler, E. Barkai, J. Klafter, Phys. Rev. Lett., 82, 3563 (1999)] describes an anomalous sub diffusive behavior of a particle in an external force field. In this paper we present the solution of the FFPE in terms of an integral transformation. The transformation maps the solution of ordinary Fokker-Planck equation onto the solution of the FFPE. We investigate in detail the force free particle and the particle in uniform and harmonic fields. The meaning of the transformation is explained based on the asymptotic solution of the continuous time random walk (CTRW). We also find an exact solution of the CTRW and compare the CTRW result with the integral solution of the FFPE for the force free case.

cond-mat.stat-mech↗