Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians

• URL: http://arxiv.org/abs/2212.14804v2
• Date: Mon, 2 Jan 2023 23:12:15 GMT
• Title: Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians
• Authors: Milan \v{S}indelka, Pavel Str\'ansk\'y, Pavel Cejnar
• Abstract summary: We study exceptional points (EPs) of a nonhermitian Hamiltonian $hatH(lambda,delta)$. We derive a self contained set of equations of motion for the trajectory $lambda_k(delta)$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study exceptional points (EPs) of a nonhermitian Hamiltonian $\hat{H}(\lambda,\delta)$ whose parameters $\lambda \in {\mathbb C}$ and $\delta \in {\mathbb R}$. As the real control parameter $\delta$ is varied, the $k$-th EP (or $k$-th cluster of simultaneously existing EPs) of $\hat{H}(\lambda,\delta)$ moves in the complex plane of $\lambda$ along a continuous trajectory, $\lambda_k(\delta)$. We derive a self contained set of equations of motion (EOM) for the trajectory $\lambda_k(\delta)$, while interpreting $\delta$ as the propagation time. Such EOM become of interest whenever one wishes to study the response of EPs to external perturbations or continuous parametric changes of the pertinent Hamiltonian. This is e.g.~the case of EPs emanating from hermitian curve crossings/degeneracies (which turn into avoided crossings/near-degeneracies when the Hamiltonian parameters are continuously varied). The presented EOM for EPs have not only their theoretical merits, they possess also a substantial practical relevance. Namely, the just presented approach can be regarded even as an efficient numerical method, useful for generating EPs for a broad class of complex quantum systems encountered in atomic, nuclear and condensed matter physics. Performance of such a method is tested here numerically on a simple yet nontrivial toy model.

Related papers

• The robustness of entanglement in non-Hermitian cavity optomechanical system even away from exceptional points [2.778721019132512]
  Quantum physics can be extended into the complex domain by considering non-Hermitian Hamiltonians that are $mathcalPT$-symmetric. We find that the sudden disappearance of entanglement can be mitigated at EPs (similar to $mathcalPT$-symmetric systems) but also show that the revival of entanglement is quite robust to thermal noise in a group of parameters away from the EPs.
  arXiv  Detail & Related papers  (2024-12-11T06:18:05Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Calculating response functions of coupled oscillators using quantum phase estimation [40.31060267062305]
  We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. Our proposed quantum algorithm operates in the standard $s-sparse, oracle-based query access model. We show that a simple adaptation of our algorithm solves the random glued-trees problem in time.
  arXiv  Detail & Related papers  (2024-05-14T15:28:37Z)
• Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives [50.24983453990065]
  This article is devoted to developing an approach for manipulating the von Neumann entropy $S(rho(t))$ of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy $S(rho(T))$; (b) steering $S(rho(T))$ to a given target value; (c) steering $S(rho(T))$ to a target value and satisfying the pointwise state constraint $S(
  arXiv  Detail & Related papers  (2024-05-10T10:01:10Z)
• Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\rm XY$ model with clock anisotropy [0.0]
  A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions driven by interactions. We show that when the $mathcalPT$ symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues.
  arXiv  Detail & Related papers  (2024-04-26T12:45:16Z)
• Hamiltonian simulation for low-energy states with optimal time dependence [45.02537589779136]
  We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. We present a quantum algorithm that uses $O(tsqrtlambdaGamma + sqrtlambda/Gammalog (1/epsilon))$ queries to the block-encoding for any $Gamma$.
  arXiv  Detail & Related papers  (2024-04-04T17:58:01Z)
• 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)
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits [0.0]
  We develop the linear response theory formulation suitable for application to various pHH systems. We apply our results to two textitPT-symmetric non-Hermitian quantum systems.
  arXiv  Detail & Related papers  (2022-06-18T10:05:30Z)
• On quantum algorithms for the Schr\"odinger equation in the semi-classical regime [27.175719898694073]
  We consider Schr"odinger's equation in the semi-classical regime. Such a Schr"odinger equation finds many applications, including in Born-Oppenheimer molecular dynamics and Ehrenfest dynamics.
  arXiv  Detail & Related papers  (2021-12-25T20:01:54Z)
• $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
  Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-15T17:08:33Z)
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility [1.7205106391379026]
  The fidelity susceptibility has been used to detect quantum phase transitions in the Hermitian quantum many-body systems. Here the fidelity susceptibility $chi$ is generalized to non-Hermitian quantum systems by taking the geometric structure of the Hilbert space into consideration. As examples, we investigate the simplest $mathcalPT$ symmetric $2times2$ Hamiltonian with a single tuning parameter and the non-Hermitian Su-Schriffer-Heeger model.
  arXiv  Detail & Related papers  (2020-09-15T13:21:24Z)

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.