Confined systems associated with the discrete Meixner polynomials

• URL: http://arxiv.org/abs/2003.14238v1
• Date: Mon, 30 Mar 2020 00:40:01 GMT
• Title: Confined systems associated with the discrete Meixner polynomials
• Authors: A. D. Alhaidari and T. J. Taiwo
• Abstract summary: We study quantum systems totally confined in space and associated with the discrete Meixners. We derive their corresponding potential functions, and plot some of their bound states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we study quantum systems totally confined in space and associated with the discrete Meixner polynomials. We present several examples of such systems, derive their corresponding potential functions, and plot some of their bound states.

Related papers

• Polynomial representation for multipartite entanglement of resonating valence bond ladders [0.0]
  A resonating valence bond (RVB) state of a lattice of quantum systems is a potential resource for quantum computing and communicating devices. We develop a representation of multipartite quantum states to prove that RVB states on ladder lattices possess genuine multipartite entanglement. The multipartite entanglement of doped RVB states and RVB states that are superposed with varying dimer for singlet coverings of ladder lattices can both be detected by using this technique.
  arXiv  Detail & Related papers  (2023-02-18T16:54:13Z)
• An Exponential Separation Between Quantum Query Complexity and the Polynomial Degree [79.43134049617873]
  In this paper, we demonstrate an exponential separation between exact degree and approximate quantum query for a partial function. For an alphabet size, we have a constant versus separation complexity.
  arXiv  Detail & Related papers  (2023-01-22T22:08:28Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• Supersymmetry and Shape Invariance of exceptional orthogonal polynomials [0.0]
  We express the differential equations for the Jacobi and the Laguerre exceptional orthogonals (EOP) as the eigenvalue equations. We show that the underlying shape invariance is responsible for the solubility of the differential equations associated with these systems.
  arXiv  Detail & Related papers  (2022-06-08T13:54:42Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Universal patterns in multifrequency-driven dissipative systems [0.0]
  We derive generic properties which follow from discrete time-translation symmetry of each driving component in dissipative systems. We propose possible implementations with quantum optical settings.
  arXiv  Detail & Related papers  (2022-01-21T12:25:31Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Probing many-body quantum chaos with quantum simulators [0.0]
  spectral form factors (SFF) and partial spectral form factors (PSFFs) provide insights into energy eigenstate statistics of many-body systems. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models. Our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment.
  arXiv  Detail & Related papers  (2021-06-29T16:00:09Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)
• Construction of potential functions associated with a given energy spectrum [0.0]
  We present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy spectrum. In this work, we study the class of problems with a mix of continuous and discrete energy spectrum that are associated with the continuous dual Hahn.
  arXiv  Detail & Related papers  (2020-02-05T14:30:26Z)

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.