$PT$-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven $SU(1,1)$ system

• URL: http://arxiv.org/abs/2201.00158v1
• Date: Sat, 1 Jan 2022 10:30:22 GMT
• Title: $PT$-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven $SU(1,1)$ system
• Authors: Yan Gu, Xue-Min Bai, Xiao-Lei Hao, J. -Q. Liang
• Abstract summary: 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.
• Score: 1.2712661944741168
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study in this paper 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\"{o}dinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a $PT$-symmetric but non-unitary transformation operator. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adiabatic one in the slow time-variation limit. A non-unitary time-evolution operator is found analytically. As an consequence of the non-unitarity the ket ($|\psi (t)\rangle $) and bra ($\langle \psi (t)|$) states are not normalized each other. While the inner product of two states can be evaluated with the help of a metric operator. It is shown explicitly that the model can be realized by a periodically driven oscillator.

Related papers

• Study And Implementation of Unitary Gates in Quantum Computation Using Schrodinger Dynamics [0.0]
  This thesis explores the concept of realizing quantum gates using physical systems like atoms and oscillators perturbed by electric and magnetic fields. In all design procedures, the gates that appear are infinite-dimensional, with an interaction between the atom and the electromagnetic field modulated by a controllable function of time.
  arXiv  Detail & Related papers  (2024-08-30T06:08:35Z)
• Klein-Gordon oscillators and Bergman spaces [55.2480439325792]
  We consider classical and quantum dynamics of relativistic oscillator in Minkowski space $mathbbR3,1$. The general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic functions on the K"ahler-Einstein manifold $Z_6$.
  arXiv  Detail & Related papers  (2024-05-23T09:20:56Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions [0.0]
  unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a 1D-box system with physics controlled by time-dependent boundary conditions. Our key message is that contrary to the conventional beliefs and in spite of the unitarity of the evolution of the system, neither its "Heisenbergian Hamiltonian" $Sigma(t)$ nor its "Schr"odingerian Hamiltonian" $G(
  arXiv  Detail & Related papers  (2024-01-19T13:28:42Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models [0.0]
  This paper introduces and describes a set of constructive returns of the description to one of the correct and eligible physical Hilbert spaces $cal R_N(0)$. In the extreme of the theory the construction is currently well known and involves solely the inner product metric $Theta=Theta(H)$. At $j=N$ the inner-product metric remains trivial and only the Hamiltonian must be Hermitized, $H to mathfrakh = Omega,H,Omega-1=mathfrak
  arXiv  Detail & Related papers  (2022-12-07T20:10:58Z)
• 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)
• 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 [0.0]
  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.
  arXiv  Detail & Related papers  (2022-07-06T07:07:36Z)
• 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)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)

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.