710 research outputs found
Level Repulsion in Constrained Gaussian Random-Matrix Ensembles
Introducing sets of constraints, we define new classes of random-matrix
ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian
unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE.
We derive a sufficient condition for GUE-type level repulsion to persist in the
presence of constraints. For special classes of constraints, we extend this
approach to the orthogonal and to the symplectic ensembles. A generalized
Fourier theorem relates the spectral properties of the constraining ensembles
with those of the constrained ones. We find that in the DGUEs, level repulsion
always prevails at a sufficiently short distance and may be lifted only in the
limit of strictly enforced constraints.Comment: 20 pages, no figures. New section adde
Effect of phase relaxation on quantum superpositions in complex collisions
We study the effect of phase relaxation on coherent superpositions of
rotating clockwise and anticlockwise wave packets in the regime of strongly
overlapping resonances of the intermediate complex. Such highly excited
deformed complexes may be created in binary collisions of heavy ions, molecules
and atomic clusters. It is shown that phase relaxation leads to a reduction of
the interference fringes, thus mimicking the effect of decoherence. This
reduction is crucial for the determination of the phase--relaxation width from
the data on the excitation function oscillations in heavy--ion collisions and
bimolecular chemical reactions. The difference between the effects of phase
relaxation and decoherence is discussed.Comment: Extended revised version; 9 pages and 3 colour ps figure
Towards a common thread in Complexity: an accuracy-based approach
The complexity of a system, in general, makes it difficult to determine some
or almost all matrix elements of its operators. The lack of accuracy acts as a
source of randomness for the matrix elements which are also subjected to an
external potential due to existing system conditions. The fluctuation of
accuracy due to varying system-conditions leads to a diffusion of the matrix
elements. We show that, for the single well potentials, the diffusion can be
described by a common mathematical formulation where system information enters
through a single parameter. This further leads to a characterization of
physical properties by an infinite range of single parametric universality
classes
Scattering off an oscillating target: Basic mechanisms and their impact on cross sections
We investigate classical scattering off a harmonically oscillating target in
two spatial dimensions. The shape of the scatterer is assumed to have a
boundary which is locally convex at any point and does not support the presence
of any periodic orbits in the corresponding dynamics. As a simple example we
consider the scattering of a beam of non-interacting particles off a circular
hard scatterer. The performed analysis is focused on experimentally accessible
quantities, characterizing the system, like the differential cross sections in
the outgoing angle and velocity. Despite the absence of periodic orbits and
their manifolds in the dynamics, we show that the cross sections acquire rich
and multiple structure when the velocity of the particles in the beam becomes
of the same order of magnitude as the maximum velocity of the oscillating
target. The underlying dynamical pattern is uniquely determined by the phase of
the first collision between the beam particles and the scatterer and possesses
a universal profile, dictated by the manifolds of the parabolic orbits, which
can be understood both qualitatively as well as quantitatively in terms of
scattering off a hard wall. We discuss also the inverse problem concerning the
possibility to extract properties of the oscillating target from the
differential cross sections.Comment: 18 page
Time-resolved broadband analysis of slow-light propagation and superluminal transmission of electromagnetic waves in three-dimensional photonic crystals
A time-resolved analysis of the amplitude and phase of THz pulses propagating
through three-dimensional photonic crystals is presented. Single-cycle pulses
of THz radiation allow measurements over a wide frequency range, spanning more
than an octave below, at and above the bandgap of strongly dispersive photonic
crystals. Transmission data provide evidence for slow group velocities at the
photonic band edges and for superluminal transmission at frequencies in the
gap. Our experimental results are in good agreement with
finite-difference-time-domain simulations.Comment: 7 pages, 11 figure
Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
The embedded ensembles were introduced by Mon and French as physically more
plausible stochastic models of many--body systems governed by one--and
two--body interactions than provided by standard random--matrix theory. We
review several approaches aimed at determining the spectral density, the
spectral fluctuation properties, and the ergodic properties of these ensembles:
moments methods, numerical simulations, the replica trick, the eigenvector
decomposition of the matrix of second moments and supersymmetry, the binary
correlation approximation, and the study of correlations between matrix
elements.Comment: Final version. 29 pages, 4 ps figures, uses iopart.st
The relationship between mental toughness and cognitive control: evidence from the item-method directed forgetting task
Previous research by the authors found that mental toughness, as measured by the Mental Toughness Questionnaire 48 (MTQ48; Clough, P.J., Earle, K., & Sewell, D. [2002]. Mental toughness: the concept and its measurement. In I. Cockerill (Ed.), Solutions in sport psychology [pp. 32â43]. London: Thomson Publishing), was significantly associated with performance on the list-method directed forgetting task. The current study extends this finding to the item-method directed forgetting task in which the instruction to Remember or Forget is given after each item in the study list. A significant positive association was found between the correct recognition of Remember words and the emotional control subscale of the MTQ48. No significant associations were observed with other measures of mental toughness or personality. The findings are discussed in terms of the relationship between mental toughness and cognitive control
Macroscopic quantum superpositions in highly-excited strongly-interacting many-body systems
We demonstrate a break-down in the macroscopic (classical-like) dynamics of
wave-packets in complex microscopic and mesoscopic collisions. This break-down
manifests itself in coherent superpositions of the rotating clockwise and
anticlockwise wave-packets in the regime of strongly overlapping many-body
resonances of the highly-excited intermediate complex. These superpositions
involve many-body configurations so that their internal interactive
complexity dramatically exceeds all of those previously discussed and
experimentally realized. The interference fringes persist over a time-interval
much longer than the energy relaxation-redistribution time due to the
anomalously slow phase randomization (dephasing). Experimental verification of
the effect is proposed.Comment: Title changed, few changes in the abstract and in the main body of
the paper, and changes in the font size in the figure. Uses revTex4, 4 pages,
1 ps figur
Periodic Orbits and Escapes in Dynamical Systems
We study the periodic orbits and the escapes in two different dynamical
systems, namely (1) a classical system of two coupled oscillators, and (2) the
Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a
general relativistic system). We find their simple periodic orbits, their
characteristics and their stability. Then we find their ordered and chaotic
domains. As the energy goes beyond the escape energy, most chaotic orbits
escape. In the first case we consider escapes to infinity, while in the second
case we emphasize escapes to the central "bumpy" black hole. When the energy
reaches its escape value a particular family of periodic orbits reaches an
infinite period and then the family disappears (the orbit escapes). As this
family approaches termination it undergoes an infinity of equal period and
double period bifurcations at transitions from stability to instability and
vice versa. The bifurcating families continue to exist beyond the escape
energy. We study the forms of the phase space for various energies, and the
statistics of the chaotic and escaping orbits. The proportion of these orbits
increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical
Astronomy
Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space
We investigate the properties of eigenstates and local density of states
(LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical
correspondence in energy representation. To construct the classical
counterparts of LDOS and the structure of eigenstates (SES), the effects of the
boundary are first incorporated (via a canonical transformation) into an
effective potential, rendering the one-particle motion in the 2D rippled
billiard equivalent to that of two-interacting particles in 1D geometry. We
show that classical counterparts of SES and LDOS in the case of strong chaotic
motion reveal quite a good correspondence with the quantum quantities. We also
show that the main features of the SES and LDOS can be explained in terms of
the underlying classical dynamics, in particular of certain periodic orbits. On
the other hand, statistical properties of eigenstates and LDOS turn out to be
different from those prescribed by random matrix theory. We discuss the quantum
effects responsible for the non-ergodic character of the eigenstates and
individual LDOS that seem to be generic for this type of billiards with a large
number of transverse channels.Comment: 13 pages, 18 figure
- âŠ