Hydrodynamic theory of scrambling in chaotic long-range interacting systems

• URL: http://arxiv.org/abs/2208.01649v1
• Date: Tue, 2 Aug 2022 18:00:00 GMT
• Title: Hydrodynamic theory of scrambling in chaotic long-range interacting systems
• Authors: Tianci Zhou, Andrew Y. Guo, Shenglong Xu, Xiao Chen, Brian Swingle
• Abstract summary: We study a problem using a model of coupled quantum dots with interactions decaying as $frac1ralpha$, where each dot hosts $N$ degrees of freedom. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings.
• Score: 4.63545587688238
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density; in the systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here we study this problem using a model of coupled quantum dots with interactions decaying as $\frac{1}{r^{\alpha}}$, where each dot hosts $N$ degrees of freedom. The large $N$ limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by $\frac{1}{N}$ corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings that we previously found for $N=1$ and generic finite $N$. In order to reproduce these scalings, the fractional index $\mu$ in the FKPP equation needs to be shifted from the na\"ive value of $\mu = 2\alpha - 1$ to a renormalized value $\mu = 2\alpha - 2$. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

Related papers

• Classical and Quantum Phase Transitions in Multiscale Media: Universality and Critical Exponents in the Fractional Ising Model [0.0]
  We show that for $q 1$ in the classical regime and $q 2$ in the quantum regime, fractional interactions allow phase transitions in one dimension. This work establishes fractional derivatives as a powerful tool for engineering critical behavior.
  arXiv  Detail & Related papers  (2025-01-23T23:21:00Z)
• Quantum chaos in the sparse SYK model [0.6144680854063939]
  The Sachdev-Ye-Kitaev (SYK) model is a system of $N$ Majorana fermions with random interactions and strongly chaotic dynamics. We study a sparsified version of the SYK model, in which interaction terms are deleted with probability $1-p$.
  arXiv  Detail & Related papers  (2024-03-20T18:00:02Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• New insights on the quantum-classical division in light of Collapse Models [63.942632088208505]
  We argue that the division between quantum and classical behaviors is analogous to the division of thermodynamic phases. A specific relationship between the collapse parameter $(lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams.
  arXiv  Detail & Related papers  (2022-10-19T14:51:21Z)
• Analyticity constraints bound the decay of the spectral form factor [0.0]
  Quantum chaos cannot develop faster than $lambda leq 2 pi/(hbar beta)$ for systems in thermal equilibrium. We show that similar constraints also bound the decay of the spectral form factor (SFF) The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.
  arXiv  Detail & Related papers  (2022-02-23T19:00:00Z)
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids [58.720142291102135]
  We advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids. We also uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL)
  arXiv  Detail & Related papers  (2021-10-12T18:00:00Z)
• Porter-Thomas fluctuations in complex quantum systems [0.0]
  We find that the coupling to the decay channels can change the effective number of degrees of freedom from $nu = 1$ to $nu = 2$. Our conclusions are based on a configuration-interaction Hamiltonian originally constructed to test the validity of transition-state theory.
  arXiv  Detail & Related papers  (2021-06-29T11:07:49Z)
• Mapping the charge-dyon system into the position-dependent effective mass background via Pauli equation [77.34726150561087]
  This work aims to reproduce a quantum system composed of a charged spin - $1/2$ fermion interacting with a dyon with an opposite electrical charge.
  arXiv  Detail & Related papers  (2020-11-01T14:38:34Z)
• Resilience of the superradiant phase against $\mathbf {A^2}$ effects in the quantum Rabi dimer [0.0]
  We study the quantum criticality of a two-site model combining quantum Rabi models with hopping interaction. We find that the model allows the appearance of a superradiant quantum phase transition (QPT) even in the presence of strong $mathbfA2$ terms. Our work provides a way to the study of phase transitions in presence of the $mathbfA2$ terms and offers the prospect of investigating quantum-criticality physics and quantum devices in many-body systems.
  arXiv  Detail & Related papers  (2020-03-03T04:14:13Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.