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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…
In the present paper it is shown that the interaction between oscillations of a double-well trappedcondensate and excited Josephson states corresponding to a large enough initial disbalance of the particle number generates their bound…
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…
The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are…
The effect of the uniform magnetic field on the electron in the spherically symmetric square-well potential is studied. A transcendental equation that determines the electron energy spectrum is derived. The approximate value of the lowest…
A microscopic description of the zero energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the…
We look for upper bounds of the relative energy difference of two pure quantum states with a fixed fidelity between them or upper bounds of the fidelity for a fixed relative energy difference. The results depend on the concrete families of…
The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error bounds to the computed energies have been available only as estimates. In this…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
A system of two charged particles in a harmonic trap with additional magnetic field is considered. The problem is reduced to a single-particle one in relative coordinates. The ground- and lowest excited-state energies and wave functions are…
We study the bound states of a Kronig Penney potential for a nonlinear one-dimensional Schroedinger equation. This potential consists of a large, but not necessarily infinite, number of equidistant delta-function wells. We show that the…
It is shown that random quantum spin systems with centered disorder satisfy correlation inequalities previously proved (arXiv:cond-mat/0612371) in the classical case. Consequences include monotone approach of pressure and ground state…
The purpose of this study is to calculate the entanglement measure for a bipartite system where the two subsystems interact via a central potential, and more importantly, to analyze the conceptual implication in the case of gravitational…
Typically in many-body systems the correlation energy, which is defined as the difference between the exact ground state energy and the mean-field solution, has been a measure of the system's total correlations. However, under the quantum…
Quantitative isoperimetric inequalities for anisotropic surface energies are shown where the isoperimetric deficit controls both the Fraenkel asymmetry and a measure of the oscillation of the boundary with respect to the boundary of the…
The dominance (preponderance) of the 0+ ground state for random interactions is shown to be a consequence of certain random interactions with chaotic features. These random interactions, called chaotic random interactions, impart a symmetry…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous…
We consider a non-linear Hartree energy for bosonic particles in a symmetric double-well potential. In the limit where the wells are fare apart and the potential barrier is high, we prove that the ground state and first excited state are…