Phase-locking in dynamical systems and quantum mechanics

• URL: http://arxiv.org/abs/2504.20181v1
• Date: Mon, 28 Apr 2025 18:33:06 GMT
• Title: Phase-locking in dynamical systems and quantum mechanics
• Authors: Artem Alexandrov, Alexey Glutsyuk, Alexander Gorsky,
• Abstract summary: We discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation.<n>The structure of phase-locking domains in the dynamical system on torus is mapped into the band-gap structure of the Hill equation.
• Score: 41.94295877935867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this study, we discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrodinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the band-gap structure of the Hill equation. For the parametric oscillator, we provide the relation between the non-adiabatic Hannay angle and the Poincare rotation number of the corresponding dynamical system. In terms of quantum mechanics, the integer rotation number is connected to the quantization number via the Milne quantization approach and exact WKB. Using recent results concerning the exact WKB approach in quantum mechanics, we discuss the possible non-perturbative effects in the dynamical systems on the torus and for parametric oscillator. The semiclassical WKB is interpreted in the framework of a slow-fast dynamical system. The link between the classification of the coadjoint Virasoro orbits and the Hill equation yields a classification of the phase-locking domains in the parameter space in terms of the classification of Virasoro orbits. Our picture is supported by numerical simulations for the model of the Josephson junction and Mathieu equation.

Related papers

• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators [37.69303106863453]
  We study the onset of ground-state and excited-state quantum phase transitions in KPOs.<n>We identify the critical points associated with quantum phase transitions and analyze their influence on the energy spectrum and tunneling dynamics.<n>Our findings provide insights into the engineering of robust quantum states, quantum dynamics control, and onset of quantum phase transitions with implications for critical quantum sensing.
  arXiv  Detail & Related papers  (2025-04-21T18:00:19Z)
• Machine Learning-Enhanced Characterisation of Structured Spectral Densities: Leveraging the Reaction Coordinate Mapping [41.94295877935867]
  Spectral densities encode essential information about system-environment interactions in open-quantum systems. We leverage machine learning techniques to reconstruct key environmental features using the reaction coordinate mapping. For a dissipative spin-boson model with a structured spectral density expressed as a sum of Lorentzian peaks, we demonstrate that the time evolution of a system observable can be used by a neural network to classify the spectral density as comprising one, two, or three Lorentzian peaks.
  arXiv  Detail & Related papers  (2025-01-13T17:02:04Z)
• Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
  We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
  arXiv  Detail & Related papers  (2024-10-31T14:36:38Z)
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer [0.0]
  We provide quantum circuits to perform ground and excited states calculations. We benchmark our approach on a chain with L=6 sites and periodic boundary conditions.
  arXiv  Detail & Related papers  (2024-10-10T10:19:02Z)
• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Attractive-repulsive interaction in coupled quantum oscillators [14.37149160708975]
  We find an interesting symmetry-breaking transition from quantum limit cycle oscillation to quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from quantum homogeneous to inhomogeneous steady state. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analogue in the classical domain.
  arXiv  Detail & Related papers  (2024-08-23T10:45:19Z)
• Transient dynamical phase diagram of the spin-boson model [0.0]
  We investigate the real-time dynamics of the sub-Ohmic spin-boson model using the numerically exact inchworm quantum Monte Carlo algorithm.<n>We show that the dynamical phase diagram thus obtained differs from the equilibrium phase diagram in both the values of critical couplings and the associated values of the critical exponent.
  arXiv  Detail & Related papers  (2024-02-28T18:52:23Z)
• Decoherence time in quantum harmonic oscillators as quantum memory systems [0.7252027234425334]
  This paper is concerned with open quantum harmonic oscillators (OQHOs) described by linear quantum differential equations. In a more realistic case of system-environment coupling, we define a memory decoherence horizon as a typical time for a mean-square deviation of the system variables. We consider the decoherence time over the energy and coupling matrix of the OQHO as a memory system in its storage phase and obtain a condition under which the zero Hamiltonian delivers a suboptimal solution.
  arXiv  Detail & Related papers  (2023-10-26T08:29:42Z)
• Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems [5.50622466592942]
  We develop a comprehensive framework for studying biorthogonal dynamical quantum phase transitions in non-Hermitian systems. We discover that the periodicity of biorthogonal dynamical quantum phase transitions depends on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.
  arXiv  Detail & Related papers  (2023-07-06T13:54:47Z)
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits [0.0]
  We identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. We show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic, sparse circuits.
  arXiv  Detail & Related papers  (2023-04-19T17:37:10Z)
• Chiral current in Floquet cavity-magnonics [0.0]
  Floquet engineering can induce complex collective behaviour and interesting synthetic gauge-field in quantum systems. We realize a chiral state-transfer in a cavity-magnonic system using a Floquet drive on frequencies of the magnon modes.
  arXiv  Detail & Related papers  (2022-06-20T02:33:14Z)

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.