arXiv subjects

Dekel Shapira

Publications and source records attributed to Dekel Shapira.

5 recordsLinked to original sources

arXiv2022

Emergence of Sinai Physics in the stochastic motion of passive and active particles

A particle that is immersed in a uniform temperature bath performs Brownian diffusion, as discussed by Einstein. But Sinai has realized that in a "random environment" the diffusion is suppressed. Follow-up works have pointed out that in the presence of bias $f$ there are delocalization and sliding transitions, with threshold value $f_c$ that depends on the disorder strength. We discuss in a critical way the emergence of Sinai physics for both passive and active Brownian particles. Tight-binding and Fokker-Planck versions of the model are addressed on equal footing. We assume that the transition rates between sites are enhanced either due to a driving mechanism or due to self-propulsion mechanism that are induced by an irradiation source. Consequently, counter intuitively, the dynamics becomes sub-diffusive and the relaxation modes become over-damped. For a finite system, spontaneous delocalization may arise, due to residual bias that is induced by the irradiation.

cond-mat.stat-mech↗

arXiv2021

Breakdown of quantum-to-classical correspondence for diffusion in high temperature thermal environment

We re-consider the old problem of Brownian motion in homogeneous high-temperature thermal environment. The semiclassical theory implies that the diffusion coefficient does not depend on whether the thermal fluctuations are correlated in space or disordered. We show that the corresponding quantum analysis exhibits a remarkable breakdown of quantum-to-classical correspondence. Explicit results are found for a tight binding model, within the framework of an Ohmic master equation, where we distinguish between on-site and on-bond dissipators. The breakdown is second-order in the inverse temperature, and therefore, on the quantitative side, involves an inherent ambiguity that is related to the Ohmic approximation scheme.

cond-mat.stat-mech↗

arXiv2020

Quantum stochastic transport along chains

The spreading of a particle along a chain, and its relaxation, are central themes in statistical and quantum mechanics. One wonders what are the consequences of the interplay between coherent and stochastic transitions. This fundamental puzzle has not been addressed in the literature, though closely related themes were in the focus of the Physics literature throughout the last century, highlighting quantum versions of Brownian motion. Most recently this question has surfaced again in the context of photo-synthesis. Here we consider both an infinite tight-binding chain and a finite ring within the framework of an Ohmic master equation. With added disorder it becomes the quantum version of the Sinai-Derrida-Hatano-Nelson model, which features sliding and delocalization transitions. We highlight non-monotonic dependence of the current on the bias, and a counter-intuitive enhancement of the effective disorder due to coherent hopping.

cond-mat.stat-mech↗

arXiv2018

Localization due to topological stochastic disorder in active networks

An active network is a prototype model in non-equilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle, and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations; or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergent aspect is the topological stochastic disorder (TSD). It is implied by the non-uniformity of the illumination. In technical terms the TSD reflects the local non-zero circulations (affinities) of the stochastic transitions. This type of disorder, unlike non-homogeneous magnetic field, is non-hermitian, and can lead to the emergence of a complex relaxation spectrum. It is therefore dramatically distinct from the conservative Anderson-type or Sinai-type disorder. We discuss the consequences of having TSD. In particular we illuminate 3~different routes to under-damped relaxation, and show that localization plays a major role in the analysis. Implications of the bulk-edge correspondence principle are addressed too.

cond-mat.stat-mech↗

arXiv2017

The lognormal-like statistics of a stochastic squeeze process

We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate~$w$, and the angular diffusion coefficient~$D$. We carry out an exact analysis to determine the drift and the diffusion coefficient of $\log(r)$, where $r$ is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common "Quantum Zeno" approximation, the radial diffusion is not simply $D_r = (1/8)w^2/D$, but has a non-monotonic dependence on $w/D$. Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the $\log(r)$ distribution.

cond-mat.stat-mech↗