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We introduce and numerically study a long-range-interaction generalization of the one-dimensional Fermi-Pasta-Ulam (FPU) $\beta-$ model. The standard quartic interaction is generalized through a coupling constant that decays as $1/r^\alpha$…
Presented are several example quantum computing representations of quantum systems with a relativistic energy relation. Basic unitary representations of free Dirac particles and BCS superconductivity are given. Then, these are combined into…
In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models…
We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi-Pasta-Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the…
We consider the common problem setting of an elastic sphere impacting on a flexible beam. In contrast to previous studies, we analyze the modal energy distribution induced by the impact, having in mind the particular application of impact…
Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy.…
The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the…
Time-dependent Stark-Zeeman systems describe the motion of an electron attracted by a proton subject to a magnetic and a time-dependent electric field. For instance the study of the dynamics of a gateway around the moon which is subject to…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
We investigate numerically the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in the alpha and beta Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in…
The dynamics of energy relaxation in thermalized one- and two-dimensional arrays with nonlinear interactions depend in detail on the interactions and, in some cases, on dimensionality. We describe and explain these differences for arrays of…
We quantize the \beta-Fermi-Pasta-Ulam (FPU) model with nearest and next-nearest neighbour interactions using a number conserving approximation and a numerical exact diagonalization method. Our numerical mean field bi-phonon spectrum shows…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…
We consider a $\pi$-mode solution of the Fermi-Pasta-Ulam $\beta$ system. By perturbing it, we study the system as a function of the energy density from a regime where the solution is stable to a regime, where is unstable, first weakly and…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Anderson localization, i.e., destructive quantum interference of multiple-scattering paths, halts transport entirely. Contrarily, time-dependent random forces expedite transport via Fermi acceleration, proposed as a mechanism for…
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a novel approach using periodic orbit theory to analyze plasma turbulence, identifying fundamental structures…
The Fermi-polaron problem of a mobile impurity interacting with fermionic medium emerges in various contexts, ranging from the foundations of Landau's Fermi-liquid theory to electron-exciton interaction in semiconductors, to unusual…
We investigate the quantum breathing mode (monopole oscillation) of trapped fermionic particles with Coulomb and dipole interaction in one and two dimensions. This collective oscillation has been shown to reveal detailed information on the…