Related papers: Integrable quantum St\"ackel systems
We study the family of quantum integrable systems that arise from separating the Schr\"odinger equation in all 6 separable orthogonal coordinates on the 3 sphere: ellipsoidal, prolate, oblate, Lam\'{e}, spherical and cylindrical. On the one…
There are two fundamental problems studied by the theory of hamiltonian integrable systems: integration of equations of motion, and construction of action-angle variables. The third problem, however, should be added to the list: separation…
In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integrals of motion (I_0=H,I_1,I_2). Our main result, formulated and…
We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start from two functions on a one-dimensional phase space, a natural…
This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…
We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of ($\omega, \mathscr{H}$) structures. They are symplectic manifolds endowed with a compatible Haantjes algebra…
The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and the quantum cases are treated separately, emphasizing both…
In this article we investigate stationary cKdV systems and prove that every $N$-field stationary cKdV system can be written, after a careful reparametrization of jet variables, as a classical separable St\"ackel system on $N+1$ different…
Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes,…
We study the fate of interacting quantum systems which are periodically driven by switching back and forth between two integrable Hamiltonians. This provides an unconventional and tunable way of breaking integrability, in the sense that the…
A method for deriving superintegrable Hamiltonians with a spin orbital interaction is presented. The method is applied to obtain a new superintegrable system in Euclidean space $\mathbb{E}_3$ with the following properties. It describes a…
A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson's BM model, which is a process of eigenvalues of hermitian matrix-valued diffusion process in the Gaussian unitary…
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…
In the present paper we extend the multiparameter coupling constant metamorphosis, also known as the generalized St\"ackel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This…
We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant…
We investigate dynamics of semi-quantal spin systems in which quantum bits are attached to classically and possibly stochastically moving classical particles. The interaction between the quantum bits takes place when the respective…
We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail.
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…