Nonlinear Classical Dynamics described by a Density Matrix in the Classical Limit

• URL: http://arxiv.org/abs/2512.05423v1
• Date: Fri, 05 Dec 2025 04:42:01 GMT
• Title: Nonlinear Classical Dynamics described by a Density Matrix in the Classical Limit
• Authors: Gaspar Gonzalez, Angelo Plastino, Andrés Kowalski,
• Abstract summary: We examine the classical limit of a fairly general nonlinear semiclassical hybrid system within a MaxEnt framework.<n>We demonstrate that the classical limit is characterized by a pure density matrix representing a single state, which reproduces the dynamics of its classical analogue.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine the classical limit of a fairly general nonlinear semiclassical hybrid system within a MaxEnt framework. The consistency of the hybrid dynamics requires algebraic constraints on quantum operators and smoothness conditions for the classical variables. Analytically, we demonstrate that the classical limit is characterized by a pure density matrix representing a single state, which reproduces the dynamics of its classical analogue. To illustrate the methodology, we revisit and synthesize two previously studied examples.

Related papers

• Bound states and decay dynamics in $N$-level Friedrichs model with factorizable interactions [12.15434198600518]
  We derive analytical expressions for the bound states and the dynamical evolution within this single-excitation Friedrichs model.<n>We apply our framework to an atomic chain embedded in a photonic crystal waveguide, uncovering a rich variety of decay dynamics.
  arXiv  Detail & Related papers  (2025-12-19T03:37:36Z)
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics [28.13921029707672]
  We employ a comprehensive toolbox of state-of-the-art numerical approaches to classically simulate the dynamics of the two-dimensional transverse field Ising model.<n>Our work connects classical simulability to different regimes associated with quantum dynamics in Rydberg arrays.
  arXiv  Detail & Related papers  (2025-11-24T17:39:29Z)
• Classically Prepared, Quantumly Evolved: Hybrid Algorithm for Molecular Spectra [41.99844472131922]
  We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems.<n>The method combines classical preparation of a perturbed ground state with short-time quantum evolution of product states sampled from it.
  arXiv  Detail & Related papers  (2025-10-28T19:27:12Z)
• Classical-quantum oscillators as diffusive processes in phase space [0.0]
  We show that for any initial state, the dynamics flows to a unique (non-equilibrium) steady state, which we compute explicitly.<n>We make use of a useful mapping between hybrid and classical diffusive dynamics, which we characterise in detail in the master equation formalism.
  arXiv  Detail & Related papers  (2025-10-08T18:01:02Z)
• Exploring the nonclassical dynamics of the "classical" Schr\"odinger equation [0.0]
  We explore the nonlinear effects induced by subtracting a term proportional to Bohm's quantum potential to the usual Schr"odinger equation. We find an analytical explanation to why the dynamics in the nonlinear "classical" regime is still strongly nonclassical.
  arXiv  Detail & Related papers  (2023-12-05T18:59:50Z)
• Convergence of Dynamics on Inductive Systems of Banach Spaces [68.8204255655161]
  Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. We present a flexible modeling tool for the limit of theories: soft inductive limits constituting a generalization of inductive limits of Banach spaces.
  arXiv  Detail & Related papers  (2023-06-28T09:52:20Z)
• A healthier semi-classical dynamics [0.0]
  We study the back-reaction of quantum systems onto classical ones.<n>We take the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space.
  arXiv  Detail & Related papers  (2022-08-24T18:04:14Z)
• 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)
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain [21.24186888129542]
  We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
  arXiv  Detail & Related papers  (2020-10-14T16:46:11Z)
• Pure-state density matrix that competently describes classical chaos [0.0]
  We work with reference to a well-known semiclassical model, in which quantum degrees of freedom interact with classical ones. We show that, in the classical limit, it is possible to represent classical results by means a pure-state density matrix.
  arXiv  Detail & Related papers  (2020-07-29T02:48:38Z)
• Hybrid filtering for a class of nonlinear quantum systems subject to classical stochastic disturbances [11.170233682435303]
  A hybrid quantum-classical filtering problem, where a qubit system is disturbed by a classical process, is investigated. The strategy is to model the classical disturbance by using an optical cavity. Relations between classical disturbances and the cavity analog system are analyzed. A master equation for the qubit-cavity hybrid system is given, based on which estimates for the state of the cavity system and the classical signal are obtained.
  arXiv  Detail & Related papers  (2020-04-06T06:37:47Z)

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.