Non-Hermitian Hamiltonian beyond PT-symmetry for time-dependant SU(1,1) and SU(2) systems -- exact solution and geometric phase in pseudo-invariant theory

• URL: http://arxiv.org/abs/2207.02477v2
• Date: Sun, 10 Jul 2022 07:24:50 GMT
• Title: Non-Hermitian Hamiltonian beyond PT-symmetry for time-dependant SU(1,1) and SU(2) systems -- exact solution and geometric phase in pseudo-invariant theory
• Authors: Nadjat Amaouche, Maroua Sekhri, Rahma Zerimeche, Maamache Mustapha and J.-Q. Liang
• Abstract summary: A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant. The analytical results are exactly in agreement with those of corresponding Hermitian Hamiltonians in the literature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate in this paper time-dependent non-Hermitian Hamiltonians, which consist respectively of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1)and SU(2)systems in a unified manner. Then, we derive the LR phase, which can be separated to the dynamic phase and the geometrical phase. The analytical results are exactly in agreement with those of corresponding Hermitian Hamiltonians in the literature.

Related papers

• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  The interplay between symmetry and topological properties plays a very important role in modern physics. How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Solving the homogeneous Bethe-Salpeter equation with a quantum annealer [34.173566188833156]
  The homogeneous Bethe-Salpeter equation (hBSE) was solved for the first time by using a D-Wave quantum annealer. A broad numerical analysis of the proposed algorithms was carried out using both the proprietary simulated-anneaing package and the D-Wave Advantage 4.1 system.
  arXiv  Detail & Related papers  (2024-06-26T18:12:53Z)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• On the {\eta} pseudo PT symmetry theory for non-Hermitian Hamiltonians: time-dependent systems [0.0]
  A non-Hermitian Hamiltonian H is related to its adjoint Hdag via the relation, Hdag=PTHPT. We propose a derivation of pseudo PT symmetry and eta -pseudo-Hermiticity simultaneously for the time dependent non-Hermitian Hamiltonians.
  arXiv  Detail & Related papers  (2023-08-26T09:57:33Z)
• On the $\mathcal{P}\mathcal{T}$-symmetric parametric amplifier [0.0]
  General time-dependent PT-symmetric parametric oscillators for unbroken parity and time reversal regimes are studied theoretically. We have demostrated the time variation of the Wigner distribution for the system consisting of two spatially separated ground state of the TD-parametric amplifier.
  arXiv  Detail & Related papers  (2023-05-20T19:45:22Z)
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States [23.215516392012184]
  We propose a new method to construct non-Hermitian many-body systems by generalizing the parent Hamiltonian method into non-Hermitian regimes. We demonstrate this method by constructing a non-Hermitian spin-$1$ model from the asymmetric Affleck-Kennedy-Lieb-Tasaki state.
  arXiv  Detail & Related papers  (2023-01-29T14:13:55Z)
• Variational Matrix Product State Approach for Non-Hermitian System Based on a Companion Hermitian Hamiltonian [15.165363050850857]
  We propose an algorithm for solving the ground state of a non-Hermitian system in the matrix product state (MPS) formalism. If the eigenvalues of the non-Hermitian system are known, the companion Hermitian Hamiltonian can be directly constructed and solved.
  arXiv  Detail & Related papers  (2022-10-26T17:00:28Z)
• Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system [1.4287758028119788]
  Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. The classical version of the non-Hermitian Hamiltonian becomes a complex function of canonical variables and time. With the change of position-momentum to angle-action variables it is revealed that the non-adiabatic Hannay's angle $Delta theta_H$ and Berry phase satisfy precisely the quantum-classical correspondence.
  arXiv  Detail & Related papers  (2022-09-03T10:29:29Z)
• Exact solutions for time-dependent complex symmetric potential well [0.0]
  We investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well. The problem is exactly solvable and the analytic expressions of the Schr"odinger wavefunctions are given in terms of the Airy function.
  arXiv  Detail & Related papers  (2022-06-09T16:18:02Z)
• $PT$-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven $SU(1,1)$ system [1.2712661944741168]
  We study the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU (1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schr"odinger equation.
  arXiv  Detail & Related papers  (2022-01-01T10:30:22Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)

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.