On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation

• URL: http://arxiv.org/abs/2109.14540v5
• Date: Mon, 13 Jun 2022 14:09:39 GMT
• Title: On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
• Authors: Francisco M. Fern\'andez
• Abstract summary: We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a Hermitian, positive-definite, diagonal operator.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a Hermitian, positive-definite, diagonal operator. We show that there is an important difference between open boundary conditions and periodic ones. We illustrate the theoretical results by means of two simple, widely used, models.

Related papers

• Abstract ladder operators for non self-adjoint Hamiltonians, with applications [0.0]
  We consider in many details what happens if the Hamiltonian of the system is not self-adjoint. In the second part of the paper we discuss two different examples of our framework: pseudo-quons and a deformed generalized Heisenberg algebra.
  arXiv  Detail & Related papers  (2024-06-30T08:12:25Z)
• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Theory of mobility edge and non-ergodic extended phase in coupled random matrices [18.60614534900842]
  The mobility edge, as a central concept in disordered models for localization-delocalization transitions, has rarely been discussed in the context of random matrix theory. We show that their overlapped spectra and un-overlapped spectra exhibit totally different scaling behaviors, which can be used to construct tunable mobility edges. Our model provides a general framework to realize the mobility edges and non-ergodic phases in a controllable way in RMT.
  arXiv  Detail & Related papers  (2023-11-15T01:43:37Z)
• Matrix Completion from General Deterministic Sampling Patterns [28.116011361245224]
  We establish theoretical guarantee for the exact and approximate low-rank matrix completion problems. We show that the algorithm can be successful as the observation graph is well-connected and has similar node degrees.
  arXiv  Detail & Related papers  (2023-06-04T07:01:31Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Algebraic analysis of non-Hermitian quadratic Hamiltonians [0.0]
  We study a general one-mode non-Hermitian quadratic Hamiltonian that does not exhibit $mathcalPT$-symmetry.
  arXiv  Detail & Related papers  (2022-09-28T14:58:16Z)
• Extremely broken generalized $\mathcal{PT}$ symmetry [0.0]
  We discuss some simple H"uckel-like matrix representations of non-Hermitian operators with antiunitary symmetries. One of them exhibits extremely broken antiunitary symmetry because of the degeneracy of the operator in the Hermitian limit.
  arXiv  Detail & Related papers  (2022-06-22T13:38:40Z)
• Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space [0.0]
  We study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta. We analyze the energy spectrum of some simple models by constructing and studying the representation spaces of the unitary irreducible representations.
  arXiv  Detail & Related papers  (2022-05-02T13:20:52Z)
• Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space [62.997667081978825]
  We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. We extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces.
  arXiv  Detail & Related papers  (2022-02-09T19:14:13Z)
• Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices [0.0]
  A general strategy is provided to identify the most general metric for diagonalizable pseudo-Hermitian and anti-pseudo-Hermitian Hamilton operators. A permutation of the eigen-values of the Hamilton operator in the process of its diagonalization influences the metric.
  arXiv  Detail & Related papers  (2021-02-14T21:15:10Z)
• Dissipative flow equations [62.997667081978825]
  We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
  arXiv  Detail & Related papers  (2020-07-23T14:47:17Z)

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.