Related papers: Quantum and classical complexity in coupled maps
There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the…
We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen…
We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well known measure of complexity in classical systems and which is valid for both pure and mixed states…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
We analyze the behaviour of two quantum dynamical entropies in connection with the classical limit. Using strongly chaotic classical dynamical systems as models (Arnold Cat Maps and Sawtooth Maps), we also propose a discretization procedure…
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos,…
We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant $\hbar_{eff}\equiv\beta$ and coupling to the environment, $\Gamma$. We study this using stochastic…
We study the behavior of an open quantum system, with an $N$--dimensional space of states, whose density matrix evolves according to a non--unitary map defined in two steps: A unitary step, where the system evolves with an evolution…
We study the dynamical generation of entanglement for a two-body interacting system, starting from a separable coherent state. We show analytically that in the quasiclassical regime the entanglement growth rate can be simply computed by…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
We investigate the separability properties of quantum states described by an extended Werner density matrix, where the classical component exhibits statistical dependence. By generalizing the classical part to allow correlations, we…
Can certain degrees of freedom of a closed physical system, described by a time-independent Hamiltonian, become more and more classical as they evolve from some state? This question is important because our universe seems to have done just…
We study the baker's map and its Walsh quantization, as a toy model of a quantized chaotic system. We focus on localization properties of eigenstates, in the semiclassical regime. Simple counterexamples show that quantum unique ergodicity…
We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct and investigate a family of the corresponding quantum maps.…
This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems in the short wavelength limit. We formulate and attempt to answer three fundamental questions: (i) What drives a dynamical quantum system to…
In this paper we describe two new computational operators, called complex entropic form (CEF) and generalized complex entropic form (GEF), for pattern characterization of spatially extended systems. Besides of being a measure of regularity,…
This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex…
Operator growth, or operator spreading, describes the process where a "simple" operator acquires increasing complexity under the Heisenberg time evolution of a chaotic dynamics, therefore has been a key concept in the study of quantum chaos…
We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with a tendency towards double welled potentials using model coupled harmonic diabatic potential-energy surfaces. The von Neumann entropy…