Adiabatic Gauge Potential as a Tool for Detecting Chaos in Classical Systems

• URL: http://arxiv.org/abs/2502.12046v1
• Date: Mon, 17 Feb 2025 17:13:38 GMT
• Title: Adiabatic Gauge Potential as a Tool for Detecting Chaos in Classical Systems
• Authors: Nachiket Karve, Nathan Rose, David Campbell,
• Abstract summary: We study the adiabatic gauge potential (AGP), an object that describes deformations of a quantum state under adiabatic variation of the Hamiltonian. We show how the time variance of the AGP over a trajectory probes the long-time correlations of a generic observable. We demonstrate that strongly and weakly chaotic regimes correspond to normal and anomalous diffusion, respectively.
• Score: 0.0
• License:
• Abstract: The interplay between chaos and thermalization in weakly non-integrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical systems. In this work, we study the adiabatic gauge potential (AGP), an object typically studied in quantum mechanics that describes deformations of a quantum state under adiabatic variation of the Hamiltonian, in classical Fermi-Pasta-Ulam-Tsingou (FPUT) and Toda models. We show how the time variance of the AGP over a trajectory probes the long-time correlations of a generic observable and can be used to distinguish among nearly integrable, weakly chaotic, and strongly chaotic regimes. We draw connections between the evolution of the AGP and diffusion and derive a fluctuation-dissipation relation that connects its variance to long-time correlations of the observable. Within this framework, we demonstrate that strongly and weakly chaotic regimes correspond to normal and anomalous diffusion, respectively. The latter gives rise to a marked increase in the variance as the time interval is increased, and this behavior serves as the basis for our probe of the onset times of chaos. Numerical results are presented for FPUT and Toda systems that highlight integrable, weakly chaotic, and strongly chaotic regimes. We conclude by commenting on the wide applicability of our method to a broader class of systems.

Related papers

• Time-dependent Neural Galerkin Method for Quantum Dynamics [42.81677042059531]
  We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. We showcase the method's effectiveness simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D. Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches.
  arXiv  Detail & Related papers  (2024-12-16T13:48:54Z)
• Observing Time-Dependent Energy Level Renormalisation in an Ultrastrongly Coupled Open System [37.69303106863453]
  We show how strong coupling and memory effects influence the energy levels of open quantum systems. Measurements reveal a time-dependent shift in the system's energy levels of up to 15% of the bare system frequency. Our findings provide direct evidence of dynamic energy level renormalisation in strongly coupled open quantum systems.
  arXiv  Detail & Related papers  (2024-08-28T16:40:55Z)
• Defining classical and quantum chaos through adiabatic transformations [0.0]
  We propose a formalism which defines chaos in both quantum and classical systems. The complexity of adiabatic transformations which preserve classical time-averaged trajectories serves as a measure of chaos.
  arXiv  Detail & Related papers  (2024-01-03T19:00:00Z)
• TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems [43.39754726042369]
  We propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE) It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics. Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method.
  arXiv  Detail & Related papers  (2023-10-10T08:52:16Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Diagnosing quantum chaos with out-of-time-ordered-correlator quasiprobability in the kicked-top model [0.6999740786886535]
  We consider a benchmark system, the kicked top model, which displays chaotic behaviour in the classical version. We introduce for this scope the quasi-probability distribution behind the out-of-time-ordered correlator (OTOC) We compare the behavior of the nonclassicality with entanglement measures, such as the tripartite mutual information of the Hamiltonian.
  arXiv  Detail & Related papers  (2022-01-20T13:46:17Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Probing quantum chaos in multipartite systems [4.771483851099131]
  We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics. We show that signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function. Global quantum chaos can be suppressed at strong coupling.
  arXiv  Detail & Related papers  (2021-11-24T13:06:25Z)
• Sensing quantum chaos through the non-unitary geometric phase [62.997667081978825]
  We propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system is sensed by studying the implications that the system produces in the long-time dynamics of a probe coupled to it.
  arXiv  Detail & Related papers  (2021-04-13T17:24:08Z)
• Entanglement revivals as a probe of scrambling in finite quantum systems [0.0]
  We show that for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size. While for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling.
  arXiv  Detail & Related papers  (2020-04-18T21:30:30Z)
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos [0.0]
  We show that the norm of the adiabatic gauge potential serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures.
  arXiv  Detail & Related papers  (2020-04-10T14:13:18Z)

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.