Classical and Quantum Elliptical Billiards: Mixed Phase Space and Short Correlations in Singlets and Doublets

• URL: http://arxiv.org/abs/2301.04654v1
• Date: Wed, 11 Jan 2023 20:56:55 GMT
• Title: Classical and Quantum Elliptical Billiards: Mixed Phase Space and Short Correlations in Singlets and Doublets
• Authors: T. Ara\'ujo Lima and R. B. do Carmo
• Abstract summary: We present numerical results on classical and quantum properties in two bi-parametric families of Billiards. Our numerical calculations show evidence that the elliptical families can present a mixed classical phase space. We observed that as $rho_textc$ decreases, the $p(s)$'s tend to move away simultaneously from the GOE (singlets) and GUE (doublets) distributions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Billiards are flat cavities where a particle is free to move between elastic collisions with the boundary. In chaos theory these systems are simple prototypes, their conservative dynamics of a billiard may vary from regular to chaotic, depending only on the border. The results reported here seek to shed light on the quantization of classically chaotic systems. We present numerical results on classical and quantum properties in two bi-parametric families of Billiards, Elliptical Stadium Billiard (ESB) and Elliptical-$C_3$ Billiards (E-$C_3$B). Both are elliptical perturbations of chaotic billiards with originally circular sectors on their borders. Our numerical calculations show evidence that the elliptical families can present a mixed classical phase space, identified by a parameter $\rho_\text{c} < 1$, which we use to guide our analysis of quantum spectra. We explored the short correlations through nearest neighbor spacing distribution $p(s)$, which showed that in the mixed region of the classical phase space, $p(s)$ is well described by the Berry-Robnik-Brody (BRB) distributions for the ESB. In agreement with the expected from the so-called ergodic parameter $\alpha = t_\text{H}/t_\text{T}$, the ratio between the Heisenberg time and the classical diffusive-like transport time signals the possibility of quantum dynamical localization when $\alpha < 1$. For the E-$C_3$B family, the eigenstates can be split into singlets and doublets. BRB describes $p(s)$ for singlets as the previous family in the mixed region. However, the $p(s)$ for doublets are described by new distributions recently introduced in the literature but only tested in a few cases for $\rho_\text{c} < 1$. We observed that as $\rho_\text{c}$ decreases, the $p(s)$'s tend to move away simultaneously from the GOE (singlets) and GUE (doublets) distributions.

Related papers

• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• The $\hbar\to 0$ limit of open quantum systems with general Lindbladians: vanishing noise ensures classicality beyond the Ehrenfest time [1.497411457359581]
  Quantum and classical systems evolving under the same formal Hamiltonian $H$ may exhibit dramatically different behavior after the Ehrenfest timescale. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution.
  arXiv  Detail & Related papers  (2023-07-07T17:01:23Z)
• Nonlocality under Computational Assumptions [51.020610614131186]
  A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations. We show that there exist (efficient) local producing measurements that cannot be reproduced through randomness and quantum-time computation.
  arXiv  Detail & Related papers  (2023-03-03T16:53:30Z)
• Laboratory-frame tests of quantum entanglement in $H \to WW$ [0.0]
  Quantum entanglement between the two $W$ bosons resulting from the decay of a Higgs boson may be investigated in the dilepton channel $H to WW to ell nu ell nu$ The dilepton invariant mass distribution, already measured by the ATLAS and CMS Collaborations at the LHC, can be used to observe the quantum entanglement of the $WW$ pair.
  arXiv  Detail & Related papers  (2022-09-28T12:22:12Z)
• 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)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard [0.0]
  We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space. We show that the level repulsion exponent $beta$ is empirically a rational function of $alpha$, and the mean $langle A rangle$ as a function of $alpha$ is also well approximated by a rational function.
  arXiv  Detail & Related papers  (2021-04-23T15:33:26Z)
• The distribution of localization measures of chaotic eigenstates in the stadium billiard [0.0]
  The localization measures $A$ of localized chaotic eigenstates in the Poincar'e-Husimi representation. The dependence of the standard deviation $sigma$ on $alpha$ is analyzed, as well as on the spectral parameter $beta$.
  arXiv  Detail & Related papers  (2021-04-18T17:30:06Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)

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.