Related papers: Quantum integrable systems in three-dimensional ma…
This paper considers the physical realizability condition for multi-level quantum systems having polynomial Hamiltonian and multiplicative coupling with respect to several interacting boson fields. Specifically, it generalizes a recent…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…
Solving the quantum-mechanical many-body problem requires scalable computational approaches, which are rooted in a good understanding of the physics of correlated electronic systems. Interacting electrons in a magnetic field display a huge…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for three magnetic qubits with the exchange interaction, that takes place in…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…
Quantum mechanical systems with position dependent masses (PDM) admitting two parametric Lie symmetry groups are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a two parametric Lie group,…
We present all real quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables of the Schr\"odinger equation in polar coordinates, 2. They allow an…
We review some known results on the superintegrability of monopole systems in the three-dimensional (3D) Euclidean space and in the 3D generalized Taub-NUT spaces. We show that these results can be extended to certain curved backgrounds…
A study is presented of superintegrable quantum systems in two-dimensional Euclidean space $E_2$ allowing the separation of variables in Cartesian coordinates. In addition to the Hamiltonian $H$ and the second order integral of motion $X$,…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…