Classical bifurcations and entanglement in smooth Hamiltonian system

We study entanglement in two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near a anti-pitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization that have been much studied in quantum chaos and elsewhere. We also point to an interesting near-degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay of localization and symmetry.Comment: 7 pages, 6 figure

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Quantum Chaos of a particle in a square well : Competing Length Scales and Dynamical Localization

The classical and quantum dynamics of a particle trapped in a one-dimensional infinite square well with a time periodic pulsed field is investigated. This is a two-parameter non-KAM generalization of the kicked rotor, which can be seen as the standard map of particles subjected to both smooth and hard potentials. The virtue of the generalization lies in the introduction of an extra parameter R which is the ratio of two length scales, namely the well width and the field wavelength. If R is a non-integer the dynamics is discontinuous and non-KAM. We have explored the role of R in controlling the localization properties of the eigenstates. In particular the connection between classical diffusion and localization is found to generalize reasonably well. In unbounded chaotic systems such as these, while the nearest neighbour spacing distribution of the eigenvalues is less sensitive to the nature of the classical dynamics, the distribution of participation ratios of the eigenstates proves to be a sensitive measure; in the chaotic regimes the latter being lognormal. We find that the tails of the well converged localized states are exponentially localized despite the discontinuous dynamics while the bulk part shows fluctuations that tend to be closer to Random Matrix Theory predictions. Time evolving states show considerable R dependence and tuning R to enhance classical diffusion can lead to significantly larger quantum diffusion for the same field strengths, an effect that is potentially observable in present day experiments.Comment: 29 pages (including 14 figures). Better quality of Figs. 1,3 & 9 can be obtained from author

Entanglement production in Quantized Chaotic Systems

Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, presence of chaos in the system produces more entanglement. However, coupling strength between two subsystems is also very important parameter for the entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed state entanglement production are qualitatively similar to the pure state entanglement production. We however still lack an analytical understanding of the mixed state entanglement production in chaotic systems.Comment: 16 pages, 5 figures. To appear in Pramana:Journal of Physic

Post-Stroke Brain Health Monitoring and Optimization: A Narrative Review

Significant advancements have been made in recent years in the acute treatment and secondary prevention of stroke. However, a large proportion of stroke survivors will go on to have enduring physical, cognitive, and psychological disabilities from suboptimal post-stroke brain health. Impaired brain health following stroke thus warrants increased attention from clinicians and researchers alike. In this narrative review based on an open timeframe search of the PubMed, Scopus, and Web of Science databases, we define post-stroke brain health and appraise the body of research focused on modifiable vascular, lifestyle, and psychosocial factors for optimizing post-stroke brain health. In addition, we make clinical recommendations for the monitoring and management of post-stroke brain health at major post-stroke transition points centered on four key intertwined domains: cognition, psychosocial health, physical functioning, and global vascular health. Finally, we discuss potential future work in the field of post-stroke brain health, including the use of remote monitoring and interventions, neuromodulation, multi-morbidity interventions, enriched environments, and the need to address inequities in post-stroke brain health. As post-stroke brain health is a relatively new, rapidly evolving, and broad clinical and research field, this narrative review aims to identify and summarize the evidence base to help clinicians and researchers tailor their own approach to integrating post-stroke brain health into their practices

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.Comment: 23 pages, REVTEX

Bipartite entanglement and localization of one-particle states

We study bipartite entanglement in a general one-particle state, and find that the linear entropy, quantifying the bipartite entanglement, is directly connected to the paricitpation ratio, charaterizing the state localization. The more extended the state is, the more entangled the state. We apply the general formalism to investigate ground-state and dynamical properties of entanglement in the one-dimensional Harper model.Comment: 4 pages and 3 figures. Version