Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

• URL: http://arxiv.org/abs/2009.03893v5
• Date: Wed, 15 Sep 2021 08:20:06 GMT
• Title: Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• Authors: Parth Bhargava, Sayantan Choudhury, Satyaki Chowdhury, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino
• Abstract summary: This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe. We use the $Out-of-Time Ordered correlation (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: $Circuit~ Complexity$, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe from the paradigm of two well known bouncing cosmological solutions viz. $Cosine~ hyperbolic$ and $Exponential$ models of scale factors. Besides $circuit~ complexity$, we use the $Out-of-Time~ Ordered~ correlation~ (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times. In particular, we use the techniques of well known two-mode squeezed state formalism in cosmological perturbation theory as a key ingredient for the purpose of our computation. To give an appropriate theoretical interpretation that is consistent with the observational perspective we use the scale factor and the number of e-foldings as a dynamical variable instead of conformal time for this computation. From this study, we found that the period of post bounce is the most interesting one. Though it may not be immediately visible, but an exponential rise can be seen in the $complexity$ once the post bounce feature is extrapolated to the present time scales. We also find within the very small acceptable error range a universal connecting relation between Complexity computed from two different kinds of cost functionals-$linearly~ weighted$ and $geodesic~ weighted$ with the OTOC. Furthermore, from the $complexity$ computation obtained from both the cosmological models and also using the well known MSS bound on quantum Lyapunov exponent, $\lambda\leq 2\pi/\beta$ for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at late time scale. Finally, we provide a rough estimation of the scrambling time in terms of the conformal time.

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 complexity and localization in random quantum circuits [0.0]
  We study complexity in random quantum circuits with and without measurements. For $N$ qubits without measurements, the saturation value scales as $2N-1$, and the saturation time scales as $2N$. We observe that complexity acts as a novel probe of Anderson localization and many-body localization.
  arXiv  Detail & Related papers  (2024-09-05T16:10:54Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Complexity enriched dynamical phases for fermions on graphs [17.70942538295701]
  We investigate entanglement and Krylov complexity for fermions on regular graphs. Our investigations unveil that while entanglement follows volume laws on both types of regular graphs with degree $d = 2$ and $d = 3$, the Krylov complexity exhibits distinctive behaviors. For interacting fermions, our theoretical analyses find the dimension scales as $Dsim 4Nalpha$ for regular graphs of $d = 2$ with $0.38leqalphaleq0.59$, whereas it scales as $Dsim 4N$ for $d = 3$.
  arXiv  Detail & Related papers  (2024-04-11T18:00:20Z)
• Projected state ensemble of a generic model of many-body quantum chaos [0.0]
  The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design.
  arXiv  Detail & Related papers  (2024-02-26T19:00:00Z)
• Krylov complexity of density matrix operators [0.0]
  Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) are gaining prominence. We investigate their interplay by considering the complexity of states represented by density matrix operators.
  arXiv  Detail & Related papers  (2024-02-14T19:01:02Z)
• Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
  monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
  arXiv  Detail & Related papers  (2022-07-28T17:58:59Z)
• On quantum algorithms for the Schr\"odinger equation in the semi-classical regime [27.175719898694073]
  We consider Schr"odinger's equation in the semi-classical regime. Such a Schr"odinger equation finds many applications, including in Born-Oppenheimer molecular dynamics and Ehrenfest dynamics.
  arXiv  Detail & Related papers  (2021-12-25T20:01:54Z)
• Causality Constraint on Circuit Complexity from $COSMOEFT$ [1.5643170704979468]
  We study the behaviour of the circuit complexity measures and entanglement entropy with respect to the scale factor and $c_s$. We find various interesting unexplored features within the window, $0.024leq c_sleq 1$, which is supported by both causality and cosmological observation.
  arXiv  Detail & Related papers  (2021-11-22T19:09:51Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)
• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory [0.0]
  The out-of-time correlation function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. We demonstrate a formalism using which for the first time we compute the Cosmological OTOC during the particle production during inflation and reheating.
  arXiv  Detail & Related papers  (2020-05-24T14:18:59Z)

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.