Related papers: A Tight-Binding Approach to Overdamped Brownian Mo…
We derive and solve analytically the non-Markovian master equation for harmonic quantum Brownian motion proving that, for weak system-reservoir couplings and high temperatures, it can be recast in the form of the master equation for a…
The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of…
Considerable progress has recently been made with geometrical approaches to understanding and controlling small out-of-equilibrium systems, but a mathematically rigorous foundation for these methods has been lacking. Towards this end, we…
We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
The conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of…
We study the effects of an intermittent harmonic potential of strength $\mu = \mu_0 \nu$ -- that switches on and off stochastically at a constant rate $\gamma$, on an overdamped Brownian particle with damping coefficient $\nu$. This can be…
In this work, we construct a Wannier tight-binding model for TaS$_2$ under a superlattice potential modulation, based on the Joint Automated Repository for Various Integrated Simulations database established by the U.S. National Institute…
We analyze the existence of Brownian motion tilted by a potential of full support on hyperbolic spaces $\mathbb{H}^d$. On compact spaces, it is classical that these path limits, called Q-processes, exist and can be directly defined using…
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly…
Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of…
We give a mathematical analysis of the periodic band inversion phenomenon observed by Tan--Devakul for an electron in a two-dimensional periodic potential coupled to a circularly polarized photon cavity mode. In the strong-coupling limit,…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
The interplay of chirality, self-propulsion, and spatial confinement generates striking non-equilibrium fluctuations whose higher-order statistics carry information about the dynamics and shape of the position distribution. Here, we present…
Consider a d-dimensional Brownian motion in a random potential defined by attaching a nonnegative and polynomially decaying potential around Poisson points. We introduce a repulsive interaction between the Brownian path and the Poisson…
We study the energy spectrum of tight-binding Hamiltonian for regular hyperbolic tilings. More specifically, we compute the density of states using the continued-fraction expansion of the Green function on finite-size systems with more than…
In the present paper, an expansion of the transition density of Hyperbolic Brownian motion with drift is given, which is potentially useful for pricing and hedging of options under stochastic volatility models. We work on a condition on the…
A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical…
Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends…
A perturbation theory scheme in terms of electron hopping, which is based on the Wick theorem for Hubbard operators, is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each…