Chaotic many-body quantum dynamics, spectral correlations, and energy diffusion

• URL: http://arxiv.org/abs/2510.02198v1
• Date: Thu, 02 Oct 2025 16:45:51 GMT
• Title: Chaotic many-body quantum dynamics, spectral correlations, and energy diffusion
• Authors: J. T. Chalker, Dominik Hahn,
• Abstract summary: We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions.<n>We show that energy dynamics is described by a classical master equation and is diffusive.<n>We present a numerical study of a spin-half chain, finding an early-time enhancement of the spectral form factor.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to much-studied quantum circuits, and is analytically tractable for large local Hilbert space dimension and weak intersite coupling. In this limit we show that energy dynamics is described by a classical master equation and is diffusive. We also show that the spectral form factor can be expressed exactly in terms of the solution to this master equation. For a two-site system we obtain closed-form expressions for both the two-point correlator of energy density and the spectral form factor, in essentially perfect agreement with numerical simulations. For an $L$-site system we show at late times how a linear ramp emerges in the spectral form factor, as universally expected from level repulsion in chaotic quantum systems. Conversely, at earlier times we identify two distinct mechanisms for an increase of the spectral form factor above its ramp value. One of these is associated with energy diffusion and is effective until the Thouless time, which varies as $L^2$. The other involves contributions like those that would appear if the system were composed of many uncoupled subsystems: they generate a large enhancement of the spectral form factor, and are suppressed on a timescale varying as $(\ln L)^2$. Besides being exact for the limit considered, we believe our approach provides the natural approximation even for small local Hilbert space dimension and strong intersite coupling. We present a numerical study of a spin-half chain, finding an early-time enhancement of the spectral form factor which is qualitatively similar to that in our solvable model.

Related papers

• Quantum dynamics in lattices in presence of bulk dephasing and a localized source [0.0]
  We study the dynamics of quantum systems subjected to a localized fermionic source in the presence of bulk dephasing.<n>Our detailed study reveals an interesting interplay between Hamiltonian dynamics and various environmentally induced mechanisms in open quantum systems.
  arXiv  Detail & Related papers  (2025-11-01T14:42:52Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Many-body quantum geometry in time-dependent quantum systems with emergent quantum field theory instantaneously [13.437981636279718]
  We study many-body quantum geometric effects in time-dependent system with emergent quantum integrable field theory instantaneously.<n>Our results unveil telltale quantum geometric signatures in time-dependent many-body systems, elucidating the intricate interplay between quantum geometry and dynamics.
  arXiv  Detail & Related papers  (2025-03-24T07:09:04Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos [0.0]
  We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos. We find that the saturation value of spread complexity post-peak depends not only on the spectral statistics of the Hamiltonian, but also on the specific state. We conjecture that the thermofield double state (TFD) is suitable for probing signatures of chaos in quantum many-body systems.
  arXiv  Detail & Related papers  (2024-05-18T10:54:50Z)
• Dynamics and Resonance Fluorescence from a Superconducting Artificial Atom Doubly Driven by Quantized and Classical Fields [11.961708412157757]
  Experimental demonstration of resonance fluorescence in a two-level superconducting artificial atom under two driving fields coupled to a detuned cavity. The device consists of a transmon qubit strongly coupled to a one-dimensional transmission line and a coplanar waveguide resonator.
  arXiv  Detail & Related papers  (2024-03-17T08:48:30Z)
• Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches [41.94295877935867]
  We study the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics.
  arXiv  Detail & Related papers  (2023-12-19T16:14:01Z)
• Boundary Chaos: Spectral Form Factor [0.0]
  Random matrix spectral correlations are a defining feature of quantum chaos. We study such correlations in a minimal model of chaotic many-body quantum dynamics. We find they coincide with random matrix theory, possibly after a non-zero Thouless time.
  arXiv  Detail & Related papers  (2023-12-14T11:28:43Z)
• Universal spectral correlations in interacting chaotic few-body quantum systems [0.0]
  We study correlations in terms of the spectral form factor and its moments in interacting chaotic few- and many-body systems. We find a universal transition from the non-interacting to the strongly interacting case, which can be described as a simple combination of these two limits.
  arXiv  Detail & Related papers  (2023-02-20T12:49:59Z)
• Spectral form factor in a minimal bosonic model of many-body quantum chaos [1.3793594968500609]
  We study spectral form factor in periodically-kicked bosonic chains. We numerically find a nontrivial systematic system-size dependence of the Thouless time.
  arXiv  Detail & Related papers  (2022-03-10T15:56:24Z)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)

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.