Related papers: A Tight-Binding Approach to Overdamped Brownian Mo…
We derive the effective one-dimensional Schrodinger-Pauli equation for electrons constrained to move on a space curve. The electrons are confined using a double thin-wall quantization procedure with adiabatic separation of fast and slow…
A decimation method is applied to the tight binding model describing the two dimensional electron gas with next nearest neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum…
A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M and the gas is…
We develop a comprehensive theory for the effective dynamics of Bloch electrons based on symmetry. We begin with a scheme to systematically derive the irreducible representations (IRs) characterizing the Bloch functions. Starting from a…
Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, non-linear feedback control. Specifically, the particle is subject to a force derived from…
Elastic metamaterials may exhibit band gaps at wavelengths far exceeding feature sizes. This is attributed to local resonances of embedded or branching substructures. In branched configurations, such as a pillared plate, waves propagating…
We present a non-standard Hubbard model applicable to arbitrary single-particle potential profiles and inter-particle interactions. Our approach involves a novel treatment of Wannier functions, free from the ambiguities of conventional…
Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point…
This paper proposes a universal microscopic model for the shallow confinement regime of single-electron tunneling devices. We consider particle escape from a quantum well generically emerging as a bifurcation in a smooth electrostatic…
Starting from a microscopic model of self-propelled hard spheres we use tools of non-equilibrium statistical mechanics and the kinetic theory of hard spheres to derive a Smoluchowski equation for interacting Active Brownian particles. We…
We investigate the statistical properties of an over-damped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is…
This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…
We explore dissipative quantum tunnelling, a phenomenon central to various physical and chemical processes, using a double-well potential model. This paper aims to bridge gaps in understanding the crossover from thermal activation to…
Based on the dynamical quantization method we derive a quantum phase-space non-Markovian Smoluchowski equation describing the non-inertial Brownian motion of a harmonic oscillator immersed in a generic environment. In the long-time regime…
We construct almost invariant subspaces and the corresponding effective Hamiltonian for magnetic Bloch bands. We also discuss the question of the dynamics related to the effective Hamiltonian. We assume that the magnetic and electric…
We present a systematic expansion of Kramers equation in the high friction limit. The latter is expanded within an operator continued fraction scheme. The relevant operators include both temporal and spatial derivatives and a covariant…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
In this work we develop and apply a path integral formulation for the microscopic degrees of freedom obeying stochastic differential equations to an active Brownian particle (ABP) trapped in a harmonic potential. The formalism allows to…
This work sets the exact equations for the quasiclassical response function and susceptibility of a Brownian particle immersed in a bath of quantum harmonic oscillators driving by nonlinear harmonic potentials. A delta force perturbation…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…