The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature classical chaos. rate is expected to coincide with Lyapunov exponent. This quantum-classical correspondence corroborated for kicked rotor and stadium billiard, which are one-body chaotic systems. conjecture not yet validated realistic systems interactions. We make progress in this direction by studying OTOC Dicke model, where two-level atoms cooperatively interact quantized radiation...

Quantum chaos refers to signatures of classical found in the quantum domain. Recently, it has become common equate exponential behavior out-of-time order correlators (OTOCs) with chaos. The quantum-classical correspondence between OTOC growth and limit indeed been corroborated theoretically for some systems there are several projects do same experimentally. Dicke model, particular, which a regular chaotic regime, is currently under intense investigation by experiments trapped ions. We show,...

We study the nonintegrable Dicke model and its integrable approximation, Tavis-Cummings model, as functions of both coupling constant excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing density states in semiclassical limit comparing it with numerical results for case large Hilbert spaces, taking advantage efficient methods recently developed. Two different ESQPTs identified models, which signaled singularities states; one static ESQPT occurs any coupling,...

The nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, are studied as functions of both coupling constant excitation energy. present contribution extends analysis presented in previous paper by focusing on statistical properties quantum fluctuations energy spectrum their relation with excited-state phase transitions. These compared dynamics observed semiclassical versions models. presence chaos for different energies constants is exhibited, employing...

The relation between the onset of chaos and critical phenomena, like quantum phase transitions (QPTs) excited-state (ESQPTs), is analyzed for atom-field systems. While it has been speculated that hard associated with ESQPTs based in resonant case, off-resonant cases, a close look at vicinity QPTs resonance, show clearly both chaos, respond to different mechanisms. results are supported detailed numerical study dynamics semiclassical Hamiltonian Dicke model. appearance quantified calculating...

Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation these correlations comes in the form so-called correlation hole, which is a dip below saturation point survival probability's time evolution. In this work, we study hole spin-boson (Dicke) model, presents regime can be realized experiments ultracold atoms ion traps. We derive an...

The emergence of chaos in an atom-field system is studied employing both semiclassical and numerical quantum techniques, taking advantage the algebraic character Hamiltonian. A Hamiltonian obtained by considering expectation value Glauber (for field) Bloch atoms) coherent states. Regular chaotic regions are identified looking at Poincaré sections for different energies parameter values. An analytical expression energy density states integrating available phase space, which provides exact...

The quasienergy spectrum recently measured in experiments with a squeeze-driven superconducting Kerr oscillator showed good agreement the energy of its corresponding static effective Hamiltonian. also demonstrated that dynamics low-energy states can be explained same emergent model. exhibits real (avoided) level crossings for specific values Hamiltonian parameters, which then chosen to suppress (enhance) quantum tunneling. Here we analyze and model up high energies, should soon within...

Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space simplest nonintegrable atom-field system, Dicke model. A close correlation between classical Lyapunov exponents quantum Participation Ratio coherent states on eigenenergy basis is exhibited for different points space. It also shown that scales linearly with number atoms its square root ones.

The thermodynamical properties of a generalized Dicke model are calculated and related with the critical its energy spectrum, namely quantum phase transitions (QPT) excited state (ESQPT). thermal both in canonical microcanonical ensembles. latter deduction allows for an explicit description relation between spectrum properties. While isolated system subspaces different pseudo spin disconnected, whole is accesible, ensamble situation radically different. multiplicity lowest states each...

We compare the entire classical and quantum evolutions of Dicke model in its regular chaotic domains. This is a paradigmatic interacting spin-boson great experimental interest. By studying survival probabilities initial coherent states, we identify features long-time dynamics that are purely discuss their impact on equilibration times. show ratio between asymptotic values probability serves as metric to determine proximity separatrix regime distinguish two manifestations chaos: scarring...

Using the Wehrl entropy, we study delocalization in phase space of energy eigenstates vicinity avoided crossings Lipkin-Meshkov-Glick model. These crossings, appearing at intermediate energies a certain parameter region model, originate classically from pairs trajectories lying different phase-space regions which, contrary to low-energy regime, are not connected by discrete parity symmetry As coupling parameters varied, sudden increase entropy is observed for participating that close...

We present a detailed analysis of the connection between chaos and onset thermalization in spin-boson Dicke model. This system has well-defined classical limit with two degrees freedom, it presents both regular chaotic regions. Our studies eigenstate expectation values distributions off-diagonal elements number photons excited atoms validate diagonal hypothesis (ETH) region, thus ensuring thermalization. The validity ETH reflects structure eigenstates, which we corroborate using von Neumann...

Abstract As the name indicates, a periodic orbit is solution for dynamical system that repeats itself in time. In regular regime, orbits are stable, while chaotic they become unstable. The presence of unstable directly associated with phenomenon quantum scarring, which restricts degree delocalization eigenstates and leads to revivals dynamics. Here, we study Dicke model superradiant phase identify two sets fundamental orbits. This experimentally realizable atom–photon at low energies high...

We study dynamical signatures of quantum chaos in one the most relevant models many-body mechanics, Bose-Hubbard model, whose high degree symmetries yields a large number invariant subspaces and degenerate energy levels. The standard procedure to reveal requires classifying levels according their symmetries, which may be experimentally theoretically challenging. show that this classification is not necessary observe manifestations spectral correlations temporal evolution survival...

Measuring the degree of localization quantum states in phase space is essential for description dynamics and equilibration systems, but this topic far from being understood. There no unique way to measure localization, individual measures can reflect different aspects same state. Here we present a general scheme define spaces, which based on what call R\'enyi occupations, any be derived. We apply four-dimensional unbounded interacting spin-boson Dicke model. In particular, make detailed...

There is no unique way to quantify the degree of delocalization quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies portion classical phase space occupied by state. The based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&amp;#x03B1;</mml:mi></mml:math>-moments Husimi function and known as Rényi occupation order...

Adiabatic invariants for the non-integrable Dicke model are introduced. They shown to provide approximate second integrals of motion in energy region where system exhibits a regular dynamics. This low-energy region, present any set values Hamiltonian parameters is described both with semiclassical and full quantum analysis broad parameter space. Peres lattices this exhibit that many observables vary smoothly energy, along distinct lines which beg formal description. It demonstrated how...

Using coherent states as initial states, we investigate the quantum dynamics of Lipkin-Meshkov-Glick (LMG) and Dicke models in semi-classical limit. They are representative bounded systems with one- two-degrees freedom, respectively. The first model is integrable, while second one has both regular chaotic regimes. Our analysis based on survival probability. Within regime, energy distribution consists quasi-harmonic sub-sequences energies Gaussian weights. This allows for derivation...

A very approximate second integral of motion the Dicke model is identified within a broad region above ground state, and for wide range values external parameters.This integral, obtained from Born Oppenheimer approximation, classifies whole regular part spectrum in bands labelled by its corresponding eigenvalues.Results this approximation are compared with exact numerical diagonalization finite systems superradiant phase, obtaining remarkable accord.The validity our approach parameter space,...

Abstract In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to point of the available phase space after long time, filling it uniformly. Using Born’s rules connect quantum states with probabilities, one might then expect all in regime should uniformly distributed space. This simplified picture was shaken by discovery scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite that, widely accepted most models indeed...

The interaction of a quantized electromagnetic field in cavity with set two-level atoms inside it can be described algebraic Hamiltonians increasing complexity, from the Rabi to Dicke models. Their character allows, through use coherent states, semiclassical description phase space, where non-integrable model has regions associated regular and chaotic motion. appearance classical chaos quantified calculating largest Lyapunov exponent over whole available space for given energy. In quantum...

Quantum biology seeks to explain biological phenomena via quantum mechanisms, such as enzyme reaction rates tunnelling and photosynthesis energy efficiency coherent superposition of states. However, less effort has been devoted study the role mechanisms in evolution. In this paper, we used transcription factor networks with two four different phenotypes, classical random walks (CRW) (QW) compare network search behaviour at finding novel phenotypes between CRW QW. temporal scales comparable...

We derive the exact solution of a system N-level atoms in contact with Markovian reservoir. The resulting Liouvillian expressed vectorized basis is mapped to an SU(N) trigonometric Richardson–Gaudin model whose given by set non-linear coupled equations. For N = 2 (SU(2)) we recover (2019 Phys. Rev. Lett. 122 010401). then study SU(3) case for three-level atom systems and discuss properties steady state dissipative gaps finite as well thermodynamic limit.