Related papers: Matrix oscillator and Calogero-type models
We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model (E(5/12)) to describe odd nuclei at the critical point in the transition from the spherical to $\gamma$-unstable behaviour. In the model, a…
In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is achieved by constructing the appropriate point…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory, for the case when the…
A nonlinear model of the scalar field with a coupling between the field and its gradient is developed. It is shown, that such model is suitable for the description of phase transition accompanied by formation of spatial inhomogeneous…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $…
A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary…
We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
In quantum mechanics the time operator $\Theta$ satisfies the commutation relation $[\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$. The time operator associated with a given Hamiltonian…
We propose a generalized matrix-valued synchronization model which can be regarded as matrix generalization of the classical Winfree model to the special orthogonal group, and we provide several sufficient frameworks leading to the emergent…
We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an…
Allowing for the inclusion of the parity operator, it is possible to construct an oscillator model whose Hamiltonian admits an EXACT square root, which is different from the conventional approach based on creation and annihilation…
This paper presents a comprehensive description of the coordinate rings and Poisson brackets associated with the fourth Calogero-Moser space and invariant commuting pairs of matrices of size four. As an application, we compute their…
The Hamiltonian symmetry reduction of the geodesics system on a symmetric space of negative curvature by the maximal compact subgroup of the isometry group is investigated at an arbitrary value of the momentum map. Restricting to regular…
In this paper we investigate the one-dimensional harmonic oscillator with a singular perturbation concentrated in one point. We describe all possible selfadjoint realizations and we show that for certain conditions on the perturbation…
We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
The effective many-body Hamiltonian which describes vacuum oscillations and self interactions of neutrinos in a two flavor mixing scheme under the single angle approximation has the same dynamical symmetries as the well known BCS pairing…