Related papers: Quantum lattice gases and their invariants
Using the concept of diffused vorticity and the formalism of rotational hydrodynamics we calculate the eigenmodes of a harmonically trapped Bose-Einstein condensate containing an array of quantized vortices. We predict the occurrence of a…
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for…
We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one…
From the theory of quantum $LC$ circuits with discrete charge, and {\em semiclassical} considerations, we obtain approximate energy eigenvalues, depending on the parameter $q_e^2/h$. Next, we include electrical resistance for the quantum…
We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change.…
It is well known that, Klein paradox is one of the most exotic and counterintuitive consequences of quantum theory. Nevertheless, many discussions about the Klein paradox are based upon single-particle Dirac equation in quantum mechanics…
We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a superimposed harmonic potential by analyzing the effective one-dimensional Bose-Hubbard Hamiltonian of the system. In order to have a reliable…
We show several novel aspects in the exact non-equilibrium dynamics of quantum double dark-soliton states in the Lieb-Liniger model for the one-dimensional Bose gas with repulsive interactions. We also show an exact finite-size scaling of…
The number state method is used to study soliton bands for three anharmonic quantum lattices: i) The discrete nonlinear Schr\"{o}dinger equation, ii) The Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these systems is…
It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
The formulation and resolution of integrable lattice statistical models in a quantum group covariant way is the subject of this review. The Bethe Ansatz turns to be remarkably useful to implement quantum group symmetries and to provide…
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast,…
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat…
Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas…
I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation)…
In this work we study the quantum Toda lattice, developing the asymptotic Bethe ansatz method first used by Sutherland. Despite its known limitations we find, on comparing with Gutzwiller's exact method, that it works well in this…
We analyze the eigenstates of a two-dimensional lattice with additional harmonic confinement in the presence of an artificial magnetic field. While the softness of the confinement makes a distinction between bulk and edge states difficult,…