Related papers: Ground state for point particles interacting throu…
Motivated by the fundamental question of the fate of interacting bosons in flat bands, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This type of…
The massless Nelson model describes non-relativistic, spinless quantum particles interacting with a relativistic, massless, scalar quantum field. The interaction is linear in the field. We analyze the one particle sector. First, we…
Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4-5 decades ago. For…
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…
We consider the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate without external confinement. We first consider the unstable regime, where the nonlocal nonlinearity is neither positive nor radially symmetric and…
We calculate the zero point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta function type. We use zeta functional regularization and express the regularized ground…
We investigate a real scalar field whose dynamics is governed by a nonlinear wave equation. We show that classical description can be applied to a quantum system of many interacting bosons provided that some quantum ingredients are…
We construct a variational ground-state wave function of weakly interacting M-component Bose-Einstein condensates beyond the mean-field theory by incorporating the dynamical 3/2-body processes, where one of the two colliding particles drops…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
Motivated by the experiment of two-component Bose-Einstein condensates produced in magnetically trapped $^{87}Rb$, we study one dimensional Boson systems with repulsive $\delta$-function interaction in the presence of SU(2) intrinsic degree…
We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle…
We consider an interacting system of massless scalar and electromagnetic field, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is…
We study a two-dimensional Bose-Hubbard model at a zero temperature with random local potentials in the presence of either uniform or binary disorder. Many low-energy metastable configurations are found with virtually the same energy as the…
Recent experiments have realized ultra-cold gases in twisted-bilayer optical lattices. We show that interacting bosons in these lattices present a highly non-trivial ground-state physics resulting from the interplay between inter- and…
This paper explores a system of interacting `soft core' bosons in the Gross-Pitaevskii mean-field approximation in a random Bernoulli potential. First, a condition for delocalization of the ground state wave function is proved which depends…
Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows,…
We consider a phase field crystal modeling approach for binary mixtures of interacting active and passive particles. The approach allows to describe generic properties for such systems within a continuum model. We validate the approach by…
We prove basic theorems about the ground states of the S=1 Bose-Hubbard model. The results are quite universal and depend only on the coefficient U_2 of the spin-dependent interaction. We show that the ground state exhibits saturated…
We describe Bose-Einstein condensation of strongly interacting particles into a quantum state which is an excited single-particle state, but becomes the ground state as density increases because it minimizes the interaction energy compared…
The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular it is proved that it has non-extensive Bose-Einstein condensation, i.e., there is condensation without macroscopic occupation of…