Related papers: Exponential Fermi acceleration in general time-dep…
A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In…
We offer some theorems, mainly of finiteness, for certain patterns in elliptical billiards, related to periodic trajectories. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in…
The adiabatic charge transport is investigated in a two dimensional Landau model perturbed by a bounded potential at zero temperature. We show that if the Fermi level lies in a spectral gap then in the adiabatic limit the accumulated excess…
We study billiards in plane domains, with a perpendicular magnetic field and a potential. We give some results on periodic orbits, KAM tori and adiabatic invariants. We also prove the existence of bound states in a related scattering…
We investigate quantum revivals in the dynamics of an atom in an atomic Fermi accelerator. It is demonstrated that the external driving field influences the revival time significantly. Analytical expressions are presented which are based on…
We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field…
Berry phases have long been known to significantly alter the properties of periodic systems, resulting in anomalous terms in the semiclassical equations of motion describing wave-packet dynamics. In non-Hermitian systems, generalizations of…
We study the one-dimensional Fermi gas subject to dissipative reactions. The dynamics is governed by the quantum master equation, where the Hamiltonian describes coherent motion of the particles, while dissipation accounts for irreversible…
We consider a random walk in a stationary ergodic environment in $\mathbb Z$, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
Let $f: [0, +\infty) \to (0, +\infty)$ be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain $Q$ delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. Under certain…
We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…
The accelerated optical lattice has emerged as a valuable technique for the investigation of quantum transport physics and has found widespread application in quantum sensing, including atomic gravimeters and atomic gyroscopes. In our…
A time dependent variational approach is considered to derive the equations of movement for the $\lambda \phi^4$ model. The temporal evolution of the model is performed numerically in the frame of the Gaussian approximation in a lattice of…
A novel and readily understandable derivation of the Golden Rule of time dependent perturbation theory is presented. The derivation is based on adiabatic turning on of the perturbation as used, for instance, in some formal developments of…
We derive the general formula giving the Berry phase for an arbitrary spin, having both magnetic-dipole and electric-quadrupole couplings with external time-dependent fields. We assume that the effective E and B fields remain orthogonal…
We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin--Helmholtz, Rayleigh--Taylor, or Richtmyer--Meshkov instabilities, and plasma particles are continuously accelerated…
We study combinatorics of billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in d-dimensional Euclidean and pseudo-Euclidean spaces. Such partitions uniquely codify the sets of…