The Generalized Fibonacci Oscillator as an Open Quantum System

• URL: http://arxiv.org/abs/2202.02196v2
• Date: Wed, 11 May 2022 05:32:01 GMT
• Title: The Generalized Fibonacci Oscillator as an Open Quantum System
• Authors: Franco Fagnola, Chul Ki Ko, Hyun Jae Yoo
• Abstract summary: We consider an open quantum system with Hamiltonian $H_S$ whose spectrum is given by a generalized Fibonacci sequence weakly coupled to a Boson reservoir in equilibrium at inverse temperature $beta$. We find the generator of the reduced system evolution and explicitly compute the stationary state of the system, that turns out to be unique and faithful, in terms of parameters of the model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We consider an open quantum system with Hamiltonian $H_S$ whose spectrum is given by a generalized Fibonacci sequence weakly coupled to a Boson reservoir in equilibrium at inverse temperature $\beta$. We find the generator of the reduced system evolution and explicitly compute the stationary state of the system, that turns out to be unique and faithful, in terms of parameters of the model. If the system Hamiltonian is generic we show that convergence towards the invariant state is exponentially fast and compute explicitly the spectral gap for low temperatures, when quantum features of the system are more significant, under an additional assumption on the spectrum of $H_S$.

Related papers

• A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus [0.0]
  We argue that for uniformly accelerated open systems, the formalism must breakdown as we move from a Fock representation over the algebra of field observables over all Minkowski space to the restriction to the algebra of observables over a Rindler wedge. We derive the quantum limit for a uniformly accelerated detector and establish an open systems description of the relaxation to thermal equilibrium at the Unruh temperature.
  arXiv  Detail & Related papers  (2024-11-12T16:45:50Z)
• Quantum mereology and subsystems from the spectrum [0.0]
  We show that decomposing a system into subsystems is equivalent to decomposing a spectrum into other spectra. We argue that the number of subsystems can be inferred from the spectrum itself. In local models, this information is encoded in finite size corrections to the Gaussian density of states.
  arXiv  Detail & Related papers  (2024-09-02T17:42:16Z)
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [18.47824812164327]
  We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework. This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.
  arXiv  Detail & Related papers  (2024-08-06T14:53:40Z)
• Detecting Quantum Anomalies in Open Systems [0.0]
  We introduce a novel and experimentally feasible approach to detect quantum anomalies in open systems. We numerically demonstrate the unavoidable singular behavior of $exp(rmitheta Sz_rm tot)$ for half-integer spin chains.
  arXiv  Detail & Related papers  (2023-12-18T13:29:07Z)
• Theory of robust quantum many-body scars in long-range interacting systems [0.0]
  Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems. We show that long-range interacting quantum spin systems generically host robust QMBS. Our theory unveils the stability mechanism of such QMBS for arbitrary system size.
  arXiv  Detail & Related papers  (2023-09-21T22:00:40Z)
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches [0.0]
  We calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. Our analyses provide a deeper understanding on the role of quantum information quantities for the dynamics of emergent phenomena reminiscent to systems in high-energy physics.
  arXiv  Detail & Related papers  (2022-10-27T18:00:01Z)
• Entropy decay for Davies semigroups of a one dimensional quantum lattice [13.349045680843885]
  We show that the relative entropy between any evolved state and the equilibrium Gibbs state contracts exponentially fast with an exponent that scales logarithmically with the length of the chain. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.
  arXiv  Detail & Related papers  (2021-12-01T16:15:58Z)
• Rapid thermalization of spin chain commuting Hamiltonians [13.349045680843885]
  We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.
  arXiv  Detail & Related papers  (2021-12-01T16:08:10Z)
• Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti-$\mathcal{PT}$ symmetry [15.273168396747495]
  Non-Hermitian systems with parity-time reversal ($mathcalPT$) or anti-$mathcalPT$ symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. We implement a Floquet Hamiltonian of a single qubit with anti-$mathcalPT$ symmetry by periodically driving a dissipative quantum system of a single trapped ion.
  arXiv  Detail & Related papers  (2021-07-27T07:11:32Z)
• Expectation Synchronization Synthesis in Non-Markovian Open Quantum Systems [15.285806487845036]
  We investigate the problem of engineering synchronization in non-Markovian quantum systems. For two homogenous subsystems, synchronization can always be synthesized without designing direct Hamiltonian coupling. System parameters are explicitly designed to achieve quantum synchronization.
  arXiv  Detail & Related papers  (2021-01-04T08:46:25Z)
• Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving [0.0]
  We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We show that for the systems under consideration the generalised spectral form factor can be expressed in terms of dynamical correlation functions. This also provides a connection between the many-body Thouless time $tau_rm th$ -- the time at which the generalised spectral form factor starts following the random matrix theory prediction -- and the conservation laws of the system.
  arXiv  Detail & Related papers  (2020-10-23T15:54:55Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.