Complex Scaling Method applied to the study of the Swanson Hamiltonian in the broken PT-symmetry phase

• URL: http://arxiv.org/abs/2405.04599v2
• Date: Fri, 14 Jun 2024 12:21:04 GMT
• Title: Complex Scaling Method applied to the study of the Swanson Hamiltonian in the broken PT-symmetry phase
• Authors: Viviano Fernández, Romina Ramírez, Marta Reboiro,
• Abstract summary: We study the non-PT symmetry phase of the Swanson Hamiltonian in the framework of the Complex Scaling Method. We apply the formalism of the response function to analyse the time evolution of different initial wave packages.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we study the non-PT symmetry phase of the Swanson Hamiltonian in the framework of the Complex Scaling Method. By constructing a bi-orthogonality relation, we apply the formalism of the response function to analyse the time evolution of different initial wave packages. The Wigner Functions and mean value of operators are evaluated as a function of time. We analyse in detail the time evolution in the neighbourhood of Exceptional Points. We derive a continuity equation for the system. We compare the results obtained using the Complex Scaling Method to the ones obtained by working in a Rigged Hilbert Space.

Related papers

• On Hagedorn wavepackets associated with different Gaussians [0.0]
  Wavepackets formed by superpositions of Hagedorn functions have been successfully used to solve the Schr"odinger equation. For evaluating typical observables, such as position or kinetic energy, it is sufficient to consider orthonormal Hagedorn functions with a single Gaussian center.
  arXiv  Detail & Related papers  (2024-05-13T16:15:08Z)
• Towards Efficient Time Stepping for Numerical Shape Correspondence [55.2480439325792]
  Methods based on partial differential equations (PDEs) have been established, encompassing e.g. the classic heat kernel signature. We consider here several time stepping schemes. The goal of this investigation is to assess, if one may identify a useful property of methods for time integration for the shape analysis context.
  arXiv  Detail & Related papers  (2023-12-21T13:40:03Z)
• Complexity in two-point measurement schemes [0.0]
  We show that the probability distribution associated with the change of an observable in a two-point measurement protocol with a perturbation can be written as an auto-correlation function. We probe how the evolved state spreads in the corresponding conjugate space. We show that the complexity saturates for large values of the parameter only when the pre-quench Hamiltonian is chaotic.
  arXiv  Detail & Related papers  (2023-11-14T04:00:31Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• Better Regularization for Sequential Decision Spaces: Fast Convergence Rates for Nash, Correlated, and Team Equilibria [121.36609493711292]
  We study the application of iterative first-order methods to the problem of computing equilibria of large-scale two-player extensive-form games. By instantiating first-order methods with our regularizers, we develop the first accelerated first-order methods for computing correlated equilibra and ex-ante coordinated team equilibria.
  arXiv  Detail & Related papers  (2021-05-27T06:10:24Z)
• Entanglement dynamics of coupled oscillators from Gaussian states [0.0]
  We explore the dynamics of entanglement of an isolated quantum system consisting of two time-dependent, coupled harmonic oscillators. We use a numerical method that relies on the estimation of the system's Wigner representation by a specific Gaussian function. Also, we analyze how the entropy of entanglement change as a function of time.
  arXiv  Detail & Related papers  (2021-04-26T03:37:09Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)
• Symplectic Gaussian Process Regression of Hamiltonian Flow Maps [0.8029049649310213]
  We present an approach to construct appropriate and efficient emulators for Hamiltonian flow maps. Intended future applications are long-term tracing of fast charged particles in accelerators and magnetic plasma confinement.
  arXiv  Detail & Related papers  (2020-09-11T17:56:35Z)
• $\mathcal{PT}$-symmetry in compact phase space for a linear Hamiltonian [0.0]
  We study the time evolution of a PT-symmetric, non-Hermitian quantum system for which the associated phase space is compact. We analyze how the non-Hermitian part of the Hamiltonian affects the time evolution of two archetypical quantum states, coherent and Dicke states.
  arXiv  Detail & Related papers  (2020-07-30T20:38:00Z)

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.