Equilibrium frame reveals hidden PT symmetry of passive systems

• URL: http://arxiv.org/abs/2008.06532v3
• Date: Thu, 12 Aug 2021 18:01:31 GMT
• Title: Equilibrium frame reveals hidden PT symmetry of passive systems
• Authors: Grzegorz Chimczak and Anna Kowalewska-Kud{\l}aszyk and Ewelina Lange and Karol Bartkiewicz
• Abstract summary: We show that non-Hermitian Hamiltonians possess hidden PT symmetries. We also show that the number of eigenstates having the same value in an exceptional point is usually smaller in the initial frame than in the equilibrium frame.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which only loss is present and gain is absent, can also display exceptional points, just like PT-symmetric systems, and therefore are extensively investigated. We demonstrate that non-Hermitian Hamiltonians, which can be divided into a PT-symmetric term and a term commuting with the Hamiltonian, possess hidden PT symmetries. These symmetries become apparent in the equilibrium frame. We also show that the number of eigenstates having the same value in an exceptional point is usually smaller in the initial frame than in the equilibrium frame. This property is associated with the second part of the Hamiltonian.

Related papers

• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking [14.693424479293737]
  We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. We find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. We construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
  arXiv  Detail & Related papers  (2024-10-16T18:00:00Z)
• Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators [20.572965801171225]
  Recent developments have extended the discussion of symmetry and its breaking to mixed states. We propose the Wightman correlator as an alternative diagnostic tool.
  arXiv  Detail & Related papers  (2024-10-12T02:04:40Z)
• Study of quantum phase transition and entanglement in coupled top systems with standard and nonstandard symmetries under Floquet formalism [15.699822139827916]
  We study an effective time-independent Hamiltonian of a coupled kicked-top (CKT) system derived using the Van Vleck-based perturbation theory at the high-frequency driving limit under Floquet formalism. We study classical and quantum versions of this coupled top system for torsion-free and nonzero torsion cases.
  arXiv  Detail & Related papers  (2024-09-13T06:36:41Z)
• 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)
• Symmetry restoration and quantum Mpemba effect in symmetric random circuits [3.326868738829707]
  Entanglement asymmetry serves as a diagnostic tool for symmetry breaking and a proxy for thermalization. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits.
  arXiv  Detail & Related papers  (2024-03-13T12:20:03Z)
• A symmetry perspective of the Riemann zeros [0.9790236766474201]
  We show that unbroken supersymmetry is associated with the presence of non-trivial zeros of the zeta function. In other cases, supersymmetry is spontaneously broken and the ground state energy of the system is not zero. Our findings provide insights into a $SU(2)$ symmetry that arises within these systems, with the Hilbert space having a two-level structure.
  arXiv  Detail & Related papers  (2023-09-04T06:20:09Z)
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schr\"odinger equation with focusing saturable nonlinearity and PT-symmetric potential [13.844860643212105]
  We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schr"odinger (FNLS) equation. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. We explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons.
  arXiv  Detail & Related papers  (2022-10-01T13:18:22Z)
• Symmetry protected entanglement in random mixed states [0.0]
  We study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $mathbbZ_N$ and $U(1)$ symmetry groups.
  arXiv  Detail & Related papers  (2021-11-30T19:00:07Z)
• Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti-$\mathcal{PT}$ symmetry [15.273168396747495]
  Non-Hermitian systems with parity-time reversal ($mathcalPT$) or anti-$mathcalPT$ symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. We implement a Floquet Hamiltonian of a single qubit with anti-$mathcalPT$ symmetry by periodically driving a dissipative quantum system of a single trapped ion.
  arXiv  Detail & Related papers  (2021-07-27T07:11:32Z)
• Dynamical signatures of symmetry protected topology following symmetry breaking [0.0]
  We investigate topological signatures in the short-time non-equilibrium dynamics of symmetry protected topological (SPT) systems. We show numerically that both the pure state and ensemble signatures are remarkably robust.
  arXiv  Detail & Related papers  (2021-01-29T04:55:28Z)
• Latent symmetry induced degeneracies [0.0]
  We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-abelian latent symmetry group.
  arXiv  Detail & Related papers  (2020-11-26T17:37:30Z)

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.