2,405 research outputs found
Multifractality and intermediate statistics in quantum maps
We study multifractal properties of wave functions for a one-parameter family
of quantum maps displaying the whole range of spectral statistics intermediate
between integrable and chaotic statistics. We perform extensive numerical
computations and provide analytical arguments showing that the generalized
fractal dimensions are directly related to the parameter of the underlying
classical map, and thus to other properties such as spectral statistics. Our
results could be relevant for Anderson and quantum Hall transitions, where wave
functions also show multifractality.Comment: 4 pages, 4 figure
Application of serious games to sport, health and exercise
Use of interactive entertainment has been exponentially expanded since the last decade. Throughout this 10+ year evolution there has been a concern about turning entertainment properties into serious applications, a.k.a "Serious Games". In this article we present two set of Serious Game applications, an Environment Visualising game which focuses solely on applying serious games to elite Olympic sport and another set of serious games that incorporate an in house developed proprietary input system that can detect most of the human movements which focuses on applying serious games to health and exercise
Standing Up for Industry Standing in Environmental Regulatory Challenges
Article III of the U.S. Constitution limits courts to hearing only cases and controversies. To address this limitation, federal courts have developed the doctrine of standing, which requires a litigant to have suffered a cognizable injury in fact, which was caused by the challenged conduct and that will be redressable by a favorable outcome. Courts have struggled to balance these components and, in practice, different requirements have developed for meeting standing depending on the nature of the case and the type of party bringing suit. This Article explores the U.S. Court of Appeals for the District of Columbia Circuit’s recent decisions in Coalition for Responsible Regulation, Inc. v. EPA, Grocery Manufacturers Ass’n v. EPA, and Alliance of Automobile Manufacturers v. EPA. It argues that the D.C. Circuit’s findings in these cases—that industry petitioners lacked standing to sue—are the result of the court’s overly narrow analysis of EPA rulemakings as individual acts, without regard to the broader effect of the regulatory scheme of which the rulemakings are a part. In so doing, the D.C. Circuit has precluded industry petitioners from accounting for the practical financial harms they have suffered. The authors conclude that the consequence of this narrow review is a higher bar to establish standing for industry petitioners than for environmental plaintiffs. Ultimately, the D.C. Circuit’s decisions raise the specter that a regulatory program that has tangible impacts on a regulated industry will nonetheless be shielded from judicial review
Entanglement as a signature of quantum chaos
We explore the dynamics of entanglement in classically chaotic systems by
considering a multiqubit system that behaves collectively as a spin system
obeying the dynamics of the quantum kicked top. In the classical limit, the
kicked top exhibits both regular and chaotic dynamics depending on the strength
of the chaoticity parameter in the Hamiltonian. We show that the
entanglement of the multiqubit system, considered for both bipartite and
pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite
entanglement is enhanced in the chaotic region, pairwise entanglement is
suppressed. Furthermore, we define a time-averaged entangling power and show
that this entangling power changes markedly as moves the system from
being predominantly regular to being predominantly chaotic, thus sharply
identifying the edge of chaos. When this entangling power is averaged over
initial states, it yields a signature of global chaos. The qualitative behavior
of this global entangling power is similar to that of the classical Lyapunov
exponent.Comment: 8 pages, 8 figure
Distribution of the spacing between two adjacent avoided crossings
We consider the frequency at which avoided crossings appear in an energy
level structure when an external field is applied to a quantum chaotic system.
The distribution of the spacing in the parameter between two adjacent avoided
crossings is investigated. Using a random matrix model, we find that the
distribution of these spacings is well fitted by a power-law distribution for
small spacings. The powers are 2 and 3 for the Gaussian orthogonal ensemble and
Gaussian unitary ensemble, respectively. We also find that the distributions
decay exponentially for large spacings. The distributions in concrete quantum
chaotic systems agree with those of the random matrix model.Comment: 11 page
Splitting of Andreev levels in a Josephson junction by spin-orbit coupling
We consider the effect of spin-orbit coupling on the energy levels of a
single-channel Josephson junction below the superconducting gap. We investigate
quantitatively the level splitting arising from the combined effect of
spin-orbit coupling and the time-reversal symmetry breaking by the phase
difference between the superconductors. Using the scattering matrix approach we
establish a simple connection between the quantum mechanical time delay matrix
and the effective Hamiltonian for the level splitting. As an application we
calculate the distribution of level splittings for an ensemble of chaotic
Josephson junctions. The distribution falls off as a power law for large
splittings, unlike the exponentially decaying splitting distribution given by
the Wigner surmise -- which applies for normal chaotic quantum dots with
spin-orbit coupling in the case that the time-reversal symmetry breaking is due
to a magnetic field.Comment: 6 pages, 3 figure
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
Photocount statistics of chaotic lasers
We derive the photocount statistics of the radiation emitted from a chaotic laser resonator in the regime of single-mode lasing. Random spatial variations of the resonator eigenfunctions lead to strong mode-to-mode fluctuations of the laser emission. The distribution of the mean photocount over an ensemble of modes changes qualitatively at the lasing transition, and displays up to three peaks above the lasing threshold
Density of State in a Complex Random Matrix Theory with External Source
The density of state for a complex random matrix coupled to an
external deterministic source is considered for a finite N, and a compact
expression in an integral representation is obtained.Comment: 7 pages, late
Anomalous power law of quantum reversibility for classically regular dynamics
The Loschmidt Echo M(t) (defined as the squared overlap of wave packets
evolving with two slightly different Hamiltonians) is a measure of quantum
reversibility. We investigate its behavior for classically quasi-integrable
systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2
depending solely on the dimension d of the system. This power law decay is
faster than the result ~ t^{-d} for the decay of classical phase space
densities
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