Related papers: Dynamics of some piecewise smooth Fermi-Ulam Model…
The Stoner model predicts that a two-component Fermi gas at increasing repulsive interactions undergoes a ferromagnetic transition. Using the random-phase approximation we study the dynamical properties of the interacting Fermi gas. For an…
We consider the electric conductivity in normal metals in presence of a strong magnetic field. It is assumed here that the Fermi surface of a metal has rather complicated form such that different types of quasiclassical electron…
States of thermal equilibrium of an infinite system of interacting particles in a Euclidean space are studied. The particles bear 'unbounded' spins with a given symmetric a priori distribution. The interaction between the particles is…
Recent experiments have observed hints of hydrodynamic electron flow in a number of materials, not all of which have an isotropic Fermi surface. We revisit these experiments in $\mathrm{PdCoO}_2$, a quasi-two-dimensional material whose…
All possible symmetry-determined nonlinear normal modes (also called by simple periodic orbits, one-mode solutions etc.) in both hard and soft Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying their stability in…
We prove two results on the algebraic dynamics of billiards in generic algebraic curves of degree $d \geq 2$. First, the dynamical degree grows quadratically in $d$; second, the set of complex periodic points has measure 0, implying the…
When a 2D superconductor is subjected to a strong in-plane magnetic field, Zeeman polarization of the Fermi surface can give rise to inhomogeneous FFLO order with a spatially modulated gap. Further increase of the magnetic field eventually…
We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…
Recently, there has been an increasing interest on nonautonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map $F$ results in statistical behaviour close to that of $F$. We show this fact in…
The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is,…
The Kondo-Heisenberg model is used for a microscopic demonstration of existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a…
We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite size domains are formed which show orientational order. Domain formation leads to a substantial slowing down…
We prove that for a dynamical system on an algebraic variety over $\overline{\mathbb{Q}}$ generated by finitely many unramified endomorphisms, it is decidable whether a given point has a finite orbit. This is achieved by establishing an…
We prove that for some manifolds $M$ the set of robustly transitive partially hyperbolic diffeomorphisms of $M$ with one-dimensional nonhyperbolic centre direction contains a $C^1$-open and dense subset of diffeomorphisms with nonhyperbolic…
We investigate the periodically driven dynamics of many-body systems, either classical or quantum, finite-dimensional or mean-field, displaying an unbounded phase-space. Using the lattice $\phi^4$ model and the $p$-spin spherical model as…
We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
We introduce and study a model of time-dependent billiard systems with billiard boundaries undergoing infinitesimal wiggling motions. The so-called quivering billiard is simple to simulate, straightforward to analyze, and is a faithful…
We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau--Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain…
In metals, low-energy effective theories are characterized by a set of coupling functions. Among them, the angle-dependent Fermi momentum specifies the size and shape of Fermi surface. Since the Fermi momentum grows incessantly under the…