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

• 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)
• Full range spectral correlations and their spectral form factors in chaotic and integrable models [0.0]
  Correlations between the eigenenergies of a system's spectrum can be a defining feature of quantum chaos. We show how each spectral distance participates in building it -- the linear ramp cannot be formed by short-range energy correlations only. We illustrate our findings in the XXZ spin chain with disorder, which interpolates between chaotic and integrable behavior.
  arXiv  Detail & Related papers  (2023-11-15T19:00:01Z)
• 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)
• Spectral Analysis of Quantum Field Fluctuations in a Strongly Coupled Optomechanical System [0.0]
  The asymmetry between positive and negative frequency branches in the displacement spectrum traces out the spectral features of the quantum fluctuations in the cavity field. In our two-dimensional mechanical system the quantum back-action, generated by such vacuum fluctuations, is strongly suppressed in a narrow spectral region due to a destructive interference in the overall susceptibility.
  arXiv  Detail & Related papers  (2022-11-25T15:16:34Z)
• 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)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.