相关论文: Exact diagonalization of the truncated Bogoliubov …
In a gas of $N$ weakly interacting bosons \cite{Bogo1, Bogo2}, a truncated canonic Hamiltonian $\widetilde{h}_c$ follows from dropping all the interaction terms between free bosons with momentum $\hbar\mathbf{k}\ne\mathbf{0}$. Bogoliubov…
In a gas of $N$ interacting bosons, the Hamiltonian $H_c$, obtained by dropping all the interaction terms between free bosons with moment $\hbar\mathbf{k}\ne\mathbf{0}$, is diagonalized exactly. The resulting eigenstates…
As is well-known, in the conventional formulation of Bogoliubov's theory of an interacting Bose gas, the Hamiltonian $\hat{H}$ is written as a decoupled sum of contributions from different momenta of the form $\hat{H} = \sum_{k\neq…
The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used…
As is well-known, in Bogoliubov's theory of an interacting Bose gas the ground state of the Hamiltonian $\hat{H}=\sum_{\bf k\neq 0}\hat{H}_{\bf k}$ is found by diagonalizing each of the Hamiltonians $\hat{H}_{\bf k}$ corresponding to a…
We provide a general method for constructing bosonic Bogoliubov transformations that diagonalize a general class of quadratic Hamiltonians. These Hamiltonians describe the pair interaction models. Bogoliubov transformations are constructed…
We consider bosonic atoms that rotate in an anharmonic trapping potential. Using numerical diagonalization of the Hamiltonian, we identify the various phases of the gas as the rotational frequency of the trap and the coupling between the…
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated…
We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the…
Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Enstein Condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the…
We describe interacting bosons at low temperature in spatially correlated random potentials. By a Bogoliubov expansion around the deformed mean-field condensate, the fundamental Hamiltonian for elementary excitations is derived, achieving…
We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of…
On top of the mean-field analysis of a Bose-Einstein condensate, one typically applies the Bogoliubov theory to analyze quantum fluctuations of the excited modes. Therefore, one has to diagonalize the Bogoliubov Hamiltonian in a symplectic…
Bosonic quadratic Hamiltonians, often called Bogoliubov Hamiltonians, play an important role in the theory of many-boson systems where they arise in a natural way as an approximation to the full many-body problem. In this note we would like…
We investigate a system of $N$ spinless bosons confined in quasi-two-dimensional harmonic trap with repulsive two-body finite-range Gaussian interaction potential of large $s$-wave scattering length. Exact diagonalization of the Hamiltonian…
We study, using the Bogolyubov approximation, the thermodynamic behaviour of a superstable Bose system whose energy operator in the second-quantized form contains a nonlinear expression in the occupation numbers operators. We prove that for…
In the Bogoliubov theory a condensate initially prepared in its ground state described by stationary Bogoliubov vacuum and later perturbed by a time-dependent potential or interaction strength evolves into a time-dependent excited state…
In this paper, we study the homogeneous one-dimensional bosonic gas interacting via a repulsive contact potential by using the improved Gaussian approximation. We obtain the gapless excitation spectrum of Bogoliubov mode. Our result is in…
Recent experiments with trapped alkali atoms have drawn enormous interest to the theoretical studies concerning Bose-Einstein condensation. The purpose of this paper is to review one of the approaches to study bosonic matter at zero…
Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a non-analytic cusp in the wave function. Here we develop a transcorrelated approach where the cusp is treated exactly and folded…