Measures of Systems of Oscillators and Properties of Trajectories

• URL: http://arxiv.org/abs/2506.18093v1
• Date: Sun, 22 Jun 2025 16:38:29 GMT
• Title: Measures of Systems of Oscillators and Properties of Trajectories
• Authors: Vsevolod Sakbaev, Igor Volovich,
• Abstract summary: Properties of trajectories of systems of harmonic oscillators equipped with a point, absolutely continuous or singular measure are considered.<n>For infinite-dimensional linear flows of a countable system of oscillators there is a new type of trajectories that is not periodic.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Properties of trajectories of systems of harmonic oscillators equipped with a point, absolutely continuous or singular measure are considered in this paper. Linear flow of an infinite system of oscillators on an infinite dimensional tori in the phase space are studied. It was shown in [28] that for infinite-dimensional linear flows of a countable system of oscillators there is a new type of trajectories that is not periodic and has no transitive projection on any 4-dimensional symplectic subspace. A trajectory with this property is absent in the finite-dimensional case, it is not typical for a countably system of oscillators and it is typical for a continual one. We show that any point of a non-degenerated invariant torus is non-wandering point of the flow of a countable system of harmonic oscillators. But a point of a non-degenerated invariant torus of a flow of continual system of harmonic oscillator with absolutely continuous measure is wandering point. For the continual system of oscillators with a singular measure we obtain sufficient conditions on measure and torus for absence of transitive trajectory and non-wandering points.

Related papers

• The Quantum Foucault Modes [0.0]
  We consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving.<n>We show that the resulting set of Wigner-space trajectories of an initial coherent state is identical to the set of real-space trajectories of the classical Foucault pendulum.
  arXiv  Detail & Related papers  (2025-07-24T13:57:56Z)
• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs)<n>We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations.<n> Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• Anomalous transport in U(1)-symmetric quantum circuits [41.94295877935867]
  Investigation of discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple function of the magnetization profile. From this quantity we extract transport exponents, revealing behaviors across the phase diagram consistent with localized, diffusive, and - most interestingly for a disordered system - superdiffusive regimes.
  arXiv  Detail & Related papers  (2024-11-21T17:56:26Z)
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry [49.1574468325115]
  We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics.<n>We study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models, and (b) when these symmetries emerge locally around stationary states.
  arXiv  Detail & Related papers  (2024-11-19T02:15:59Z)
• Gapless Floquet topology [40.2428948628001]
  We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
  arXiv  Detail & Related papers  (2024-11-04T19:05:28Z)
• Driven transitions between megastable quantized orbits [0.0]
  We show quasilinear increasing amplitude of the megastable spectrum of quantized quasicircular orbits.<n>We rationalize this effect based on the basins of different limit cycles in phase space.
  arXiv  Detail & Related papers  (2024-06-06T09:40:57Z)
• Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response [0.0]
  This work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator. Two non-linear terms break the rotational phase space symmetry, Wigner distribution of quantum mechanical limit cycle state is not rotationally symmetric. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue.
  arXiv  Detail & Related papers  (2024-01-08T11:19:51Z)
• Measuring quantum geometric tensor of non-Abelian system in superconducting circuits [21.82634956452952]
  We use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. We reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.
  arXiv  Detail & Related papers  (2022-09-26T01:08:39Z)
• 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)
• Nonlinear interferometry beyond classical limit facilitated by cyclic dynamics [18.236929748580867]
  We present an approach that is broadly applicable to cyclic systems for implementing nonlinear interferometry without invoking time reversal. We implement such a 'closed-loop' nonlinear interferometer and achieve a metrological gain of $3.87_-0.95+0.91$ decibels over the classical limit for a total of 26500 atoms.
  arXiv  Detail & Related papers  (2021-11-01T09:41:34Z)
• New type of self-oscillating systems [0.0]
  An absence of equilibrium in a bosonic oscillator is discussed as a tool to create a non-stationary memory storage. The connection between such a system and the well-known nonlinear self-oscillating systems is demonstrated.
  arXiv  Detail & Related papers  (2021-05-11T07:29:07Z)
• Signatures of quantum chaos transition in short spin chains [0.0]
  The study of the long-time oscillations of the out-of-time-ordered correlator (OTOC) appears as a versatile tool, that can be adapted to the case of systems with a small number of degrees of freedom. We show that the systematic of the OTOC oscillations describes well, in a chain with only 4 spins, the integra-to-chaos transition inherited from the infinite chain.
  arXiv  Detail & Related papers  (2020-04-29T19:13:58Z)

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.