Integrable and superintegrable systems of cylindrical type in magnetic fields

• URL: http://arxiv.org/abs/2210.02393v1
• Date: Tue, 4 Oct 2022 12:46:39 GMT
• Title: Integrable and superintegrable systems of cylindrical type in magnetic fields
• Authors: Ond\v{r}ej Kub\r{u}
• Abstract summary: The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates. It turns out that all these systems have already been known and no other exist.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find all quadratically integrable systems of the cylindrical type. Among them we search for systems admitting additional integrals of motion. We find all systems with an additional first order integral both in classical and quantum mechanics. It turns out that all these systems have already been known and no other exist. We also find all systems with an additional integral of type $L^2+\ldots$, respectively $L_y p_y-L_x p_y+\ldots$, of which the majority is new to the literature. All found superintegrable systems admit the first order integral $L_z$ and we solve their Hamilton-Jacobi and Schr\"odinger equations by separation of variables in the cylindrical coordinates, for the first order systems in the Cartesian coordinates as well.

Related papers

• Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction [0.0]
  General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable.
  arXiv  Detail & Related papers  (2024-11-04T15:22:14Z)
• Typical entanglement entropy in systems with particle-number conservation [3.9617282900065853]
  We calculate the typical bipartite entanglement entropy $langle S_Arangle_N$ in systems containing indistinguishable particles of any kind. We provide evidence that our results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems.
  arXiv  Detail & Related papers  (2023-10-30T18:00:00Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Cylindrical first order superintegrability with complex magnetic fields [0.0]
  This article is a contribution to the study of superintegrable Hamiltonian systems with magnetic fields on the three-dimensional Euclidean space $mathbbE_3$ in quantum mechanics.
  arXiv  Detail & Related papers  (2022-12-08T08:39:51Z)
• Quantum cylindrical integrability in magnetic fields [0.0]
  We present the classification of quadratically integrable systems of the cylindrical type with magnetic fields in quantum mechanics. Two of the systems have both cylindrical integrals quadratic in momenta and are therefore not separable.
  arXiv  Detail & Related papers  (2022-10-07T11:40:24Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Quantum quasi-Lie systems: properties and applications [0.0]
  A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values. This work extends quasi-Lie schemes and quantum Lie systems to cope with $t$-dependent Schr"odinger equations.
  arXiv  Detail & Related papers  (2022-04-02T23:25:26Z)
• Classical analog of qubit logic based on a magnon Bose-Einstein condensate [52.77024349608834]
  We present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose-Einstein condensate. The macroscopic wavefunctions of these two condensates serve as orthonormal basis states that form a system being a classical counterpart of a single qubit.
  arXiv  Detail & Related papers  (2021-11-12T16:14:46Z)
• Reachable sets for two-level open quantum systems driven by coherent and incoherent controls [77.34726150561087]
  We study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls. For two coherent controls, the system is shown to be completely controllable in the set of all density matrices.
  arXiv  Detail & Related papers  (2021-09-09T16:14:23Z)
• Quantum simulation of $\phi^4$ theories in qudit systems [53.122045119395594]
  We discuss the implementation of quantum algorithms for lattice $Phi4$ theory on circuit quantum electrodynamics (cQED) system. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates.
  arXiv  Detail & Related papers  (2021-08-30T16:30:33Z)
• Multi-objective discovery of PDE systems using evolutionary approach [77.34726150561087]
  In the paper, a multi-objective co-evolution algorithm is described. The single equations within the system and the system itself are evolved simultaneously to obtain the system. In contrast to the single vector equation, a component-wise system is more suitable for expert interpretation and, therefore, for applications.
  arXiv  Detail & Related papers  (2021-03-11T15:37:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.