Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator

• URL: http://arxiv.org/abs/2210.01134v2
• Date: Wed, 02 Oct 2024 10:23:10 GMT
• Title: Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator
• Authors: Sayantan Choudhury, Suman Dey, Rakshit Mandish Gharat, Saptarshi Mandal, Nilesh Pandey,
• Abstract summary: We study the time-dependent behaviour of quantum correlations of a system governed by out-of-equilibrium dynamics. Next, we study a specific case, where the system exhibits chaotic behaviour by computing the quantum Lyapunov from the time-dependent behaviour of OTOC.
• Score: 0.0
• License:
• Abstract: In this work, we study the time-dependent behaviour of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger-Keldysh formalism in presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstates and continuous energy eigenvalues. Using the expression for the eigenstates, we further derive the most general expression for the generating function as well as the out-of-time-ordered correlators (OTOC) for the given system using this formalism. Further, considering the time-dependent coupling and frequency of the quantum inverted oscillator characterized by quench parameters, we comment on the dynamical behaviour, specifically the early, intermediate and late time-dependent features of the OTOC for the quenched quantum inverted oscillator. Next, we study a specific case, where the system of inverted oscillator exhibits chaotic behaviour by computing the quantum Lyapunov exponent from the time-dependent behaviour of OTOC in presence of the given quench profile.

Related papers

• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics [0.0]
  We reformulated the path integral to develop an explicit expression for the propagator. This formalism is applied to specific cases, including a Dunkl-harmonic oscillator with time-dependent mass and frequency.
  arXiv  Detail & Related papers  (2024-10-27T17:53:08Z)
• Quantum-Classical Correspondence in a Quartic Oscillator -- Corrections to Frequency and Bounds for Periodic Motion [0.0]
  We take a comparative look at the behavior of quantum and classical quartic anharmonic oscillators. The associated equation of motion allows us to compute the classical frequency of the oscillation order by order. We derive a bound for periodicity of such oscillations in both the classical and quantum cases.
  arXiv  Detail & Related papers  (2024-10-13T04:30:39Z)
• Hysteresis and Self-Oscillations in an Artificial Memristive Quantum Neuron [79.16635054977068]
  We study an artificial neuron circuit containing a quantum memristor in the presence of relaxation and dephasing. We demonstrate that this physical principle enables hysteretic behavior of the current-voltage characteristics of the quantum device.
  arXiv  Detail & Related papers  (2024-05-01T16:47:23Z)
• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Initial value formulation of a quantum damped harmonic oscillator [0.18416014644193066]
  We study the initial state-dependence, decoherence, and thermalization of a quantum damped harmonic oscillator. We find that the dynamics must include a non-vanishing noise term to yield physical results for the purity. We briefly consider time-nonlocal dissipation as well, to show that the fluctuation-dissipation relation is satisfied for a specific choice of dissipation kernels.
  arXiv  Detail & Related papers  (2023-03-08T19:03:12Z)
• Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics [0.0]
  We show that an equivalent transformation can be performed for classical systems in the context of Koopman von-Neumann (KvN) dynamics. We further extend this mapping to dissipative evolutions in both the quantum and classical cases, and show that this mapping imparts an identical time-dependent scaling on the dissipation parameters for both types of dynamics.
  arXiv  Detail & Related papers  (2022-07-19T18:59:01Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Dynamics of entropy and information of time-dependent quantum systems: exact results [0.0]
  Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. We show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic fields, the increase of the entropy and dynamics of the Fisher information can be directly described and related. We detail the behavior of quantum quenches for the case of mutually non-interacting non-relativistic fermions in a harmonic trap.
  arXiv  Detail & Related papers  (2021-08-02T15:22:32Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)

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.