Quantum multifractality as a probe of phase space in the Dicke model.

We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it.

Chaos and Thermalization in the Spin-Boson Dicke Model.

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

Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach.

By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite-dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model in the chaotic energy regime, restricting its unbounded four-dimensional phase space to a classically chaotic energy shell. This effective dimension can be employed to characterize quantum phenomena in infinite-dimensional systems, such as localization and scarring.

Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions.

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

Quantum localization measures in phase space.

Measuring the degree of localization of quantum states in phase space is essential for the description of the dynamics and equilibration of quantum systems, but this topic is far from being understood. There is no unique way to measure localization, and individual measures can reflect different aspects of the same quantum state. Here we present a general scheme to define localization in measure spaces, which is based on what we call Rényi occupations, from which any measure of localization can be derived.

Ubiquitous quantum scarring does not prevent ergodicity.

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

Quantum aspects of evolution: a contribution towards evolutionary explorations of genotype networks via quantum walks.

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

Quantum chaos in a system with high degree of symmetries.

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

Positive quantum Lyapunov exponents in experimental systems with a regular classical limit.

Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally.

Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system.

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 of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps.

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems.

The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems.

Classical chaos in atom-field systems.

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

Delocalization and quantum chaos in atom-field systems.

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