Related papers: Bost-Connes systems for local fields of characteri…
We investigate the universal dissipationless dynamics of Gaussian continuous-variable systems in the presence of a band-gapped bosonic environment. Our results show that environmental band gaps can induce localized modes, which give rise to…
This paper introduces results for characteristically near Stein-Weiss groups inherent in vector fields in the complex plane $\mathbb{C}$. Near groups are discerned in the context of characteristic nearness approximation spaces (cNASs). A…
We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. In particular, we show that local-global principles hold for such zero-cycles…
Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two dimensional model of bosons with correlated-hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without…
For stochastic processes leading to condensation, the condensate, once it is formed, performs an ergodic stationary-state motion over the system. We analyse this motion, and especially its characteristic time, for zero-range processes. The…
A generalized particle system interacting with a massless Bose field is investigated. We assume regularity conditions for the commutation relations of the interaction and annihilation operators. It is proven that if the ground state exists,…
Asymptotic states in field theories containing non-local kinetic terms are analyzed using the canonical method, naturally defined in Minkowski space. We apply our results to study the asymptotic states of a non-local Maxwell-Chern-Simons…
To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate…
We construct a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explict class field theory for such fields. This system…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
We present results on Bose-Einstein condensation (BEC) on general compact quantum graphs, i.e., one-dimensional systems with a (potentially) complex topology. We first investigate non-interacting many-particle systems and provide a complete…
We consider a Bose-Einstein condensate, which is confined in a very tight toroidal/annular trap, in the presence of a potential, which breaks the axial symmetry of the Hamiltonian. We investigate the stationary states of the condensate,…
The complex-field zeros of the Random Energy Model are analytically determined. For T<T_c they are distributed in the whole complex plane with a density that decays very fast with the real component of H. For T>T_c a region is found which…
We formulate a classical fields method for description of relativistic interacting bosonic particles at nonzero temperatures. The method relays on the assumption that at low temperatures the Bose field can be described by a c-number…
Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in…
The theory of non-interacting Bose gases is supplemented by a numerical quantum field description with a two-dimensional non-local order parameter that allows the modeling of wave-like atomic correlations and interference effects in the…
It is shown for the Bose-Einstein condensate of cold atomic system that the new unperturbed Hamiltonian, which includes not only the first and second powers of the zero mode operators but also the higher ones, determines a unique and…
The present contribution explores phase transitions that occur in the ground state (GS) of spin-1 Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) under the action of gradient magnetic fields. By solving the corresponding…
The report reviews the problem of topological coherent modes, which are nonlinear collective states of Bose-condensed atoms. Such modes can be generated by means of alternating external fields, whose frequencies are in resonance with the…
Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in \emph{Phys.…