Spectrum statistics in the integrable Lieb-Liniger model
- URL: http://arxiv.org/abs/2105.02967v1
- Date: Wed, 5 May 2021 05:07:08 GMT
- Title: Spectrum statistics in the integrable Lieb-Liniger model
- Authors: Samy Mailoud Sekkouri, Felix Izrailev, Fausto Borgonovi
- Abstract summary: We show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum.
On the other hand, when studying long-range correlations between energy levels, we found strong deviations from the predictions given by a Poisson process.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We address the old and widely debated question of the statistical properties
of integrable quantum systems, through the analysis of the paradigmatic
Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons
allows for the rigorous determination of energy spectra via the Bethe ansatz
approach and our interest is understanding whether Poisson statistics is a
characteristic feature of this model. Using both analytical and numerical
studies we show that the properties of spectra strongly depend on whether the
analysis is done for a full energy spectrum or for a single subset with fixed
total momentum. We show that the Poisson distribution of spacing between
nearest-neighbor energies can occur only for a set of energy levels with fixed
total momentum, for neither too large nor too weak interaction strength, and
for sufficiently high energy. On the other hand, when studying long-range
correlations between energy levels, we found strong deviations from the
predictions given by a Poisson process.
Related papers
- 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) - Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra [0.0]
We use a generalized tanh shaped hyperbolic potential to investigate bound state solutions of the Dirac equation.
Results indicate that the energy eigenvalues are strongly correlated with the potential parameters.
Using this potential to model mass spectra of charmonium and bottomonium, we show that results for the calculated quark mass spectra align closely with experimentally observed values.
arXiv Detail & Related papers (2024-09-23T20:40:59Z) - Accurate Analytic Model for the Energy Spectrum of the Anharmonic Oscillator [0.0]
In this work, we extend our results to the calculation of the full energy spectrum.
The energy levels found are accurate for all couplings and principal quantum numbers considered here.
arXiv Detail & Related papers (2024-08-02T09:54:27Z) - Spectral chaos bounds from scaling theory of maximally efficient
quantum-dynamical scrambling [49.1574468325115]
A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient.
We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics.
We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
arXiv Detail & Related papers (2023-10-17T15:41:50Z) - The Entanglement of Elastic and Inelastic Scattering [0.0]
A new measure of entanglement, the scattering entropy, is suggested.
The amount of entanglement is found to track with the strength of the inelastic interaction.
An analysis of high-energy $pp$ scattering data shows that entanglement is near maximum for lab energies greater than about 1 GeV.
arXiv Detail & Related papers (2023-06-26T16:02:26Z) - Statistical Efficiency of Score Matching: The View from Isoperimetry [96.65637602827942]
We show a tight connection between statistical efficiency of score matching and the isoperimetric properties of the distribution being estimated.
We formalize these results both in the sample regime and in the finite regime.
arXiv Detail & Related papers (2022-10-03T06:09:01Z) - Statistical Properties of the Entropy from Ordinal Patterns [55.551675080361335]
Knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class of time series models would allow statistical tests that are unavailable to date.
We characterize the distribution of the empirical Shannon's Entropy for any model under which the true normalized Entropy is neither zero nor one.
We present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's Entropy.
arXiv Detail & Related papers (2022-09-15T23:55:58Z) - Relaxation of non-integrable systems and correlation functions [0.0]
We investigate early-time equilibration rates of observables in closed many-body quantum systems.
We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical.
Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians.
arXiv Detail & Related papers (2021-12-17T12:34:34Z) - The relevant excitations for the one-body function in the Lieb-Liniger
model [0.0]
We study the ground state one-body correlation function in the Lieb-Liniger model.
In the spectral representation, correlations are built from contributions stemming from different excited states of the model.
We conjecture that relevant excitations take form similar to two-spinon states known from XXZ spin chain.
arXiv Detail & Related papers (2021-04-21T12:22:42Z) - Exact thermal properties of free-fermionic spin chains [68.8204255655161]
We focus on spin chain models that admit a description in terms of free fermions.
Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
arXiv Detail & Related papers (2021-03-30T13:15:44Z) - Fast approximations in the homogeneous Ising model for use in scene
analysis [61.0951285821105]
We provide accurate approximations that make it possible to numerically calculate quantities needed in inference.
We show that our approximation formulae are scalable and unfazed by the size of the Markov Random Field.
The practical import of our approximation formulae is illustrated in performing Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment, and also in likelihood ratio testing for anisotropy in the spatial patterns of yearly increases in pistachio tree yields.
arXiv Detail & Related papers (2017-12-06T14:24:34Z)
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.