Quantum chaos on the separatrix of the periodically perturbed Harper model

• URL: http://arxiv.org/abs/2412.14926v2
• Date: Tue, 24 Dec 2024 00:14:55 GMT
• Title: Quantum chaos on the separatrix of the periodically perturbed Harper model
• Authors: Alice C. Quillen, Abobakar Sediq Miakhel,
• Abstract summary: We explore the relation between a classical periodic Hamiltonian system and an associated discrete quantum system on a torus in phase space. We numerically compute eigenstates of the Floquet propagator for the associated quantum system. We derive a related expression for the associated quantum system from the averaged perturbation in the interaction representation evaluated at states with energy close to the separatrix.
• Score: 0.0
• License:
• Abstract: We explore the relation between a classical periodic Hamiltonian system and an associated discrete quantum system on a torus in phase space. The model is a sinusoidally perturbed Harper model and is similar to the sinusoidally perturbed pendulum. Separatrices connecting hyperbolic fixed points in the unperturbed classical system become chaotic under sinusoidal perturbation. We numerically compute eigenstates of the Floquet propagator for the associated quantum system. For each Floquet eigenstate we compute a Husimi distribution in phase space and an energy and energy dispersion from the expectation value of the unperturbed Hamiltonian operator. The Husimi distribution of each Floquet eigenstate resembles a classical orbit with a similar energy and similar energy dispersion. Chaotic orbits in the classical system are related to Floquet eigenstates that appear ergodic. For a hybrid regular and chaotic system, we use the energy dispersion to separate the Floquet eigenstates into ergodic and integrable subspaces. The distribution of quasi-energies in the ergodic subspace resembles that of a random matrix model. The width of a chaotic region in the classical system is estimated by integrating the perturbation along a separatrix orbit. We derive a related expression for the associated quantum system from the averaged perturbation in the interaction representation evaluated at states with energy close to the separatrix.

Related papers

• Dynamics of Topological Defects in a Rashba Spin-Orbit Coupled Bose-Einstein Condensate [14.50864620620941]
  We investigate the quench dynamics of a two-dimensional Rashba spin-orbit coupled Bose-Einstein condensate. During this quench, topological defects emerge in the form of vortices.
  arXiv  Detail & Related papers  (2024-12-25T09:31:42Z)
• Emergent Anomalous Hydrodynamics at Infinite Temperature in a Long-Range XXZ Model [14.297989605089663]
  We find anomalous hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. We quantify the degree of quantum chaos using the Kullback-Leibler divergence. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of non-integrable quantum many-body systems.
  arXiv  Detail & Related papers  (2024-03-26T17:50:04Z)
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model [0.0]
  We show that the randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions in single-particle systems is lifted into many-body space. We then identify the universality of both the cross-correlations and the Gaussian distribution of expansion coefficients as the signatures of chaotic eigenstates.
  arXiv  Detail & Related papers  (2024-03-15T09:26:17Z)
• Dispersive Non-reciprocity between a Qubit and a Cavity [24.911532779175175]
  We present an experimental study of a non-reciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity. We show that the qubit-cavity dynamics is well-described in a wide parameter regime by a simple non-reciprocal master-equation model.
  arXiv  Detail & Related papers  (2023-07-07T17:19:18Z)
• Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation [16.87034694915828]
  We revisit the dissipaton equation of motion theory and establish an equivalent dissipatons-embedded quantum master equation (DQME) The DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and thus the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.
  arXiv  Detail & Related papers  (2023-03-19T14:14:46Z)
• Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
  Signatures of localization have been observed in condensed matter and cold atomic systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
  arXiv  Detail & Related papers  (2023-03-13T12:45:25Z)
• Quasiparticles of Decoherence Processes in Open Quantum Many-Body Systems: Incoherentons [8.329456268842227]
  We find that hitherto unrecognized quasiparticles -- incoherentons -- describe a coherent-to-incoherent transition in eigenmodes of a Liouvillian superoperator. We demonstrate the existence of incoherentons in a lattice boson model subject to dephasing, and show that the quantum coherence gap closes when incoherentons are deconfined.
  arXiv  Detail & Related papers  (2022-11-28T01:35:49Z)
• Quantum coherence controls the nature of equilibration in coupled chaotic systems [0.0]
  Quantum coherence of the initial product states in the uncoupled eigenbasis can be viewed as a resource for equilibration and approach to thermalization. Results are given for four distinct perturbation strength regimes, the ultra-weak, weak, intermediate, and strong regimes. Maximally coherent initial states thermalize for any perturbation strength in spite of the fact that in the ultra-weak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like.
  arXiv  Detail & Related papers  (2022-04-15T17:33:44Z)
• Field-theoretical approach to open quantum systems and the Lindblad equation [0.0]
  We develop a field-theoretical approach to open quantum systems based on condensed-matter many-body methods. Applying a condensed-matter pole or, equivalently, a quasi-type approximation, equivalent to the usual assumption of a timescale separation, we derive a master equation of the Markov type.
  arXiv  Detail & Related papers  (2022-02-10T18:04:19Z)
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous [62.997667081978825]
  The impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom. The dynamics of this system is determined in closed analytical form. We observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior.
  arXiv  Detail & Related papers  (2021-11-23T20:25:57Z)
• Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath [0.0]
  This work addresses quantum adiabatic decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system-environment interaction Hamiltonian that represents a partition of non-interacting subsystems.
  arXiv  Detail & Related papers  (2019-12-30T16:39:38Z)

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.