Related papers: Bose-Hubbard Hamiltonian from generalized commutat…
We introduce a new slave-boson mean-field theory which allows the investigation of general multi-band Hubbard models. Unlike earlier attempts of such a generalisation, in our approach the quantum-mechanical problem is exactly reformulated…
Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of…
This paper presents the theory of Bohr-Sommerfeld-Heisenberg quantization of a completely integrable Hamiltonian system in the context of geometric quantization. The theory is illustrated with several examples.
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
The goal of this paper is to find the quantization conditions of Bohr-Sommerfeld of k quantum Hamiltonians acting on the euclidian space of dimension n, depending on a small parameter h, and which commute to each other. That is we…
We study two extended Bose-Hubbard-type Hamiltonians representing bosonic networks restricted to the graph of a cube. For both Hamiltonians, we demonstrate that Bethe ansatz methods of solution can be employed after applying a canonical…
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is…
Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form…
We investigate the correlation properties in the steady state of driven-dissipative interacting bosonic systems in the quantum regime, as for example non-linear photonic cavities. Specifically, we consider the Bose-Hubbard model on a…
We develop a generalized harmonic-fluid approach, based on a regularization of the effective low-energy Luttinger-liquid Hamiltonian, for a one-dimensional Bose gas with repulsive contact interactions. The method enables us to compute the…
We show how multi-level BCS Hamiltonians of finite systems in the strong pairing interaction regime can be accurately approximated using multi-dimensional shifted harmonic oscillator Hamiltonians. In the Shifted Harmonic Approximation…
Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…
Excitations of small one-dimensional matter-wave solitons are considered within a framework of the attractive Bose-Hubbard model. The initial eigenstates of the system are found by exact diagonalization of the Bose-Hubbard Hamiltonian. We…
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 determine the ground-state properties of a gas of interacting bosonic atoms in a one-dimensional optical lattice. The system is modelled by the Bose-Hubbard Hamiltonian. We show how to apply the time-evolving block decimation method to…
A new approach to dissipative quantum systems modelled by a system plus environment Hamiltonian is presented. Using a continuous sequence of infinitesimal unitary transformations the small quantum system is decoupled from its…
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…
The spectrum of energy levels is computed for all available angular momentum and parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to match experimental data from the Higgs-W boson sector of the standard model. Several…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
Extended Bose-Hubbard models have been employed in the study of cold-atom systems with dipolar interactions. It is shown that, for a certain choice of the coupling parameters, there exists an integrable extended 3-site Bose-Hubbard model…