Power spectrum and form factor in random diagonal matrices and integrable billiards

• URL: http://arxiv.org/abs/2011.02210v1
• Date: Wed, 4 Nov 2020 10:18:05 GMT
• Title: Power spectrum and form factor in random diagonal matrices and integrable billiards
• Authors: Roman Riser and Eugene Kanzieper
• Abstract summary: We focus on a model of random diagonal matrices (RDM) We examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. We argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Triggered by a controversy surrounding a universal behaviour of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) -- that the power spectrum is merely determined by the spectral form factor -- breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.

Related papers

• Spectral form factor and energy correlations in banded random matrices [0.0]
  Banded random matrices were introduced as a more realistic alternative to full random matrices for describing the spectral statistics of heavy nuclei. We show that, despite the absence of short-range energy correlations, weak long-range energy correlations persist in the nonergodic phase of banded random matrices. We also show that the high-frequency behavior of the power spectrum of energy fluctuations can distinguish between the nonergodic and ergodic phases of the banded random matrices.
  arXiv  Detail & Related papers  (2025-02-04T19:00:06Z)
• Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity [0.0]
  We show that the brickwall model exhibits features consistent with random matrix theory across various ensembles. We also identify signatures of integrability at extreme values of the Dirichlet boundary condition parameter.
  arXiv  Detail & Related papers  (2024-12-16T19:12:59Z)
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
  We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-21T10:56:49Z)
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor [0.0]
  Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form factor. We study the partial spectral form factor in chaotic dual-unitary quantum circuits in the thermodynamic limit.
  arXiv  Detail & Related papers  (2024-07-29T12:02:24Z)
• Quantum chaos, integrability, and late times in the Krylov basis [0.8287206589886881]
  Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features are well described by Random Matrix Theory (RMT) We show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffices to produce the full long time behavior of general survival probabilities. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos.
  arXiv  Detail & Related papers  (2023-12-06T19:02:22Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• Spectral determinant of the two-photon quantum Rabi model [0.0]
  We show that only the G-function proposed by Chen et al. in 2012 exhibits an explicitly known pole structure which dictates the approach to the collapse point. We derive this function rigorously employing the $mathbbZ_4$-symmetry of the model and show that its zeros correspond to the complete regular spectrum.
  arXiv  Detail & Related papers  (2022-06-06T11:43:18Z)
• Spectral density reconstruction with Chebyshev polynomials [77.34726150561087]
  We show how to perform controllable reconstructions of a finite energy resolution with rigorous error estimates. This paves the way for future applications in nuclear and condensed matter physics.
  arXiv  Detail & Related papers  (2021-10-05T15:16:13Z)
• Fano Resonances in Quantum Transport with Vibrations [50.591267188664666]
  Quantum mechanical scattering continuum states coupled to a scatterer with a discrete spectrum gives rise to Fano resonances. We consider scatterers that possess internal vibrational degrees of freedom in addition to discrete states.
  arXiv  Detail & Related papers  (2021-08-07T12:13:59Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)

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.