Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin

• URL: http://arxiv.org/abs/2604.09900v1
• Date: Fri, 10 Apr 2026 20:53:29 GMT
• Title: Inequivalence of Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics for a single quantum spin
• Abstract summary: Two non-linear purity preserving master equations extend classical atomistic spin dynamics into the quantum regime.<n>We show that the equivalence breaks down even at the level of a single spin, provided $s geq 1$.<n>Although our results highlight fundamental differences in dissipation mechanisms encoded in these equations, the resulting trajectories remain qualitatively similar.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine the relation between the quantum Landau-Lifshitz equation ($q$-LL) [Phys. Rev. Lett. 110, 147201 (2013)] and quantum Landau-Lifshitz-Gilbert equation ($q$-LLG) [Phys. Rev. Lett. 133, 266704 (2024)]; two non-linear purity preserving master equations that extend classical atomistic spin dynamics into the quantum regime. While the classical LL and LLG counterparts for any number of spins are known to be equivalent, i.e., give identical spin trajectories up to a rescaling of the time parameter, the quantum formulations are equivalent only in certain cases, such as for pure states or for arbitrary single spin-$\frac{1}{2}$ states. Here, we demonstrate that this equivalence breaks down even at the level of a single spin, provided $s \geq 1$. Focusing on a spin-1 particle in an anisotropic crystal field, we show that the $q$-LL and $q$-LLG equations generate inequivalent time evolution. We introduce temporal rescaling misfits that quantify the inequivalence of the two types of dynamics. Although our results highlight fundamental differences in dissipation mechanisms encoded in these equations, the resulting trajectories remain qualitatively similar for this system.

Related papers

• Quantum vs. Classical Spin: A Comparative Study of Dipolar Spin Dynamics and the Onset of Chaos [41.99844472131922]
  We compare a direct solution of the Schrodinger equation for quantum spins with simulations of classical spins.<n>We find that while the overall patterns are qualitatively similar, significant discrepancies emerge at both short and long timescales.
  arXiv  Detail & Related papers  (2026-04-27T15:30:00Z)
• Comparison of the standard and dressed-picture master equations for the quantum Rabi model in the ultrastrong coupling regime [78.55450146498553]
  This chapter investigates the effects of relaxation and dephasing on the quantum Rabi model in the ultrastrong coupling regime.<n>It provides explicit formulas to implement and numerically solve the resulting nonunitary dynamics.
  arXiv  Detail & Related papers  (2026-04-10T01:22:07Z)
• Examination of classical simulations for Heisenberg-Langevin equations for spin-1/2 [0.0]
  A system of spins coupled to a bath is a traditional setup in open quantum systems.<n>Heisenberg's equation, the spin dynamics can be modeled by a set of first-order differential equations.<n>Classical generalized Langevin equations, involving non-Markovian damping and colored noise, are well understood.
  arXiv  Detail & Related papers  (2026-03-04T19:10:38Z)
• Average-case quantum complexity from glassiness [45.57609001239456]
  Glassiness -- a phenomenon in physics characterized by a rough free-energy landscape -- implies hardness for stable classical algorithms.<n>We prove that the standard notion of quantum glassiness based on replica symmetry breaking obstructs stable quantum algorithms for Gibbs sampling.
  arXiv  Detail & Related papers  (2025-10-09T17:37:33Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma.<n>This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles.<n>We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Certifying the quantumness of a nuclear spin qudit through its uniform precession [28.4073170440133]
  We certify the quantumness of exotic states of a nuclear spin through its uniform precession. The experiment is performed on a single spin-7/2 $123$Sb nucleus implanted in a silicon nanoelectronic device.
  arXiv  Detail & Related papers  (2024-10-10T06:20:41Z)
• Quantum analog of Landau-Lifshitz-Gilbert dynamics [0.0]
  The Landau-Lifshitz-Gilbert (LLG) and Landau-Lifshitz (LL) equations play an essential role for describing the dynamics of magnetization in solids.<n>Here, we propose a quantum LLG equation that inherently conserves purity of the quantum state.
  arXiv  Detail & Related papers  (2024-03-14T10:27:14Z)
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model [44.84660857803376]
  We study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The robustness of $pi$ pairings against longitudinal disorder may be useful for quantum information processing.
  arXiv  Detail & Related papers  (2024-01-09T20:37:48Z)
• Solomon equations for qubit and two-level systems: Insights into non-Poissonian quantum jumps [41.94295877935867]
  We measure and model the combined relaxation of a qubit coupled to a discrete two-level system(TLS) environment. If the TLSs are much longer-lived than the qubit, non-exponential relaxation and non-Poissonian quantum jumps can be observed.
  arXiv  Detail & Related papers  (2023-07-13T16:51:29Z)
• Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians [1.497411457359581]
  Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale.<n>We prove a version of this correspondence, bounding the error between the quantum and classical evolutions for any sufficiently regular Hamiltonian $H(x,p)$ and Lindblad functions $L_k(x,p)$.<n>In a shorter companion paper, we treat the special case of Hamiltonians that decompose into kinetic and potential energy with linear Lindblad operators.
  arXiv  Detail & Related papers  (2023-07-07T17:01:23Z)
• Quantum Spin Puddles and Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics [0.0]
  We show how a simple parameter sweep can dynamically project a family of initial product states into the constrained space. We analytically and numerically show that this method efficiently prepares a spin liquid in finite-sized regions. Our work opens up a new avenue in the study of non-equilibrium physics.
  arXiv  Detail & Related papers  (2022-11-02T18:00:01Z)
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories [0.0]
  We introduce a hybrid-Liouvillian superoperator capable of describing the passage from an NHH (when one postselects only those trajectories without quantum jumps) to a true Liouvillian including quantum jumps (without postselection) Our approach allows to intuitively relate the effects of postselection and finite-efficiency detectors.
  arXiv  Detail & Related papers  (2020-02-26T17:02:35Z)

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.