Related papers: Periodic orbits, localization in normal mode space…
It is reported that the numerical simulations of the Fermi-Pasta-Ulam problem were performed by a young lady, Mary Tsingou. After 50 years of omission, it is time for a proper recognition of her decisive contribution to the first ever…
This work is devoted to incorporating into QFT the notion that particles and hence the particle states should be localizable in space. It focuses on the case of the Dirac field in 1+1 dimensional flat spacetime, generalizing a recently…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
The problem of detecting specific features of microscopic dynamics in the macroscopic behavior of a many-degrees-of-freedom system is investigated by analyzing the position and momentum time series of a heavy impurity embedded in a chain of…
One possible solution of the cosmological constant problem involves a so-called $q$-field, which self-adjusts so as to give a vanishing gravitating vacuum energy density (cosmological constant) in equilibrium. We show that this $q$-field…
We study conversion of thermal energy to mechanical energy and vice versa in $\alpha$-Fermi-Pasta-Ulam-Tsingou~(FPUT) chain with spatially sinusoidal profile of initial temperature. We show analytically that coupling between macroscopic…
The Fermi-Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum…
A statistical approach to the description of the thermodynamic properties of the Fermi particle system occupying a half-space over a plane of finite size in a uniform external field is proposed. The number of particles per unit area is…
The Fermi surface in the state of cuprates is highly unusual because it appears to consist of disconnected segments called arcs. Their very existence challenges the traditional concept of a Fermi surface as closed contours of gapless…
Feynman's model of a quantum computer provides an example of a continuous-time quantum walk. Its clocking mechanism is an excitation of a basically linear chain of spins with occasional controlled jumps which allow for motion on a planar…
The de~Broglie--Bohm (pilot wave) formulation of quantum theory appears to be free from the conceptual problems specific to quantum mechanics (problem of measurement) and to quantum cosmology (problem of time). We discuss the issue of…
Using a system consisting of a freely falling cloud of cold cesium atoms periodically kicked by pulses from a vertical standing wave of laser light, we present the first experimental observation of high-order quantum accelerator modes. This…
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One…
This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator.…
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
We study a natural class of Fermi-Ulam Models that features good hyperbolicity properties and that we call dispersing Fermi-Ulam models. Using tools inspired by the theory of hyperbolic billiards we prove, under very mild complexity…
We calculate the collective modes of a partially polarized Fermi gas trapped in a spherically symmetric harmonic potential. We show that the breathing mode frequency exhibits non-monotonic dependence on polarization in the entire BCS-BEC…
We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining…
When a free Fermi gas on a lattice is subject to the action of a linear potential it does not drift away, as one would naively expect, but it remains spatially localized. Here we revisit this phenomenon, known as Stark localization, within…