2,453 research outputs found
Correlations between spectra with different symmetry: any chance to be observed?
A standard assumption in quantum chaology is the absence of correlation
between spectra pertaining to different symmetries. Doubts were raised about
this statement for several reasons, in particular, because in semiclassics
spectra of different symmetry are expressed in terms of the same set of
periodic orbits. We reexamine this question and find absence of correlation in
the universal regime. In the case of continuous symmetry the problem is reduced
to parametric correlation, and we expect correlations to be present up to a
certain time which is essentially classical but larger than the ballistic time
Transition from Gaussian-orthogonal to Gaussian-unitary ensemble in a microwave billiard with threefold symmetry
Recently it has been shown that time-reversal invariant systems with discrete
symmetries may display in certain irreducible subspaces spectral statistics
corresponding to the Gaussian unitary ensemble (GUE) rather than to the
expected orthogonal one (GOE). A Kramers type degeneracy is predicted in such
situations. We present results for a microwave billiard with a threefold
rotational symmetry and with the option to display or break a reflection
symmetry. This allows us to observe the change from GOE to GUE statistics for
one subset of levels. Since it was not possible to separate the three
subspectra reliably, the number variances for the superimposed spectra were
studied. The experimental results are compared with a theoretical and numerical
study considering the effects of level splitting and level loss
Phase shift experiments identifying Kramers doublets in a chaotic superconducting microwave billiard of threefold symmetry
The spectral properties of a two-dimensional microwave billiard showing
threefold symmetry have been studied with a new experimental technique. This
method is based on the behavior of the eigenmodes under variation of a phase
shift between two input channels, which strongly depends on the symmetries of
the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been
identified by a simple and purely experimental method. This set clearly shows
Gaussian unitary ensemble statistics, although the system is time-reversal
invariant.Comment: RevTex 4, 5 figure
Semiclassical approach to discrete symmetries in quantum chaos
We use semiclassical methods to evaluate the spectral two-point correlation
function of quantum chaotic systems with discrete geometrical symmetries. The
energy spectra of these systems can be divided into subspectra that are
associated to irreducible representations of the corresponding symmetry group.
We show that for (spinless) time reversal invariant systems the statistics
inside these subspectra depend on the type of irreducible representation. For
real representations the spectral statistics agree with those of the Gaussian
Orthogonal Ensemble (GOE) of Random Matrix Theory (RMT), whereas complex
representations correspond to the Gaussian Unitary Ensemble (GUE). For systems
without time reversal invariance all subspectra show GUE statistics. There are
no correlations between non-degenerate subspectra. Our techniques generalize
recent developments in the semiclassical approach to quantum chaos allowing one
to obtain full agreement with the two-point correlation function predicted by
RMT, including oscillatory contributions.Comment: 26 pages, 8 Figure
Playing relativistic billiards beyond graphene
The possibility of using hexagonal structures in general and graphene in
particular to emulate the Dirac equation is the basis of our considerations. We
show that Dirac oscillators with or without restmass can be emulated by
distorting a tight binding model on a hexagonal structure. In a quest to make a
toy model for such relativistic equations we first show that a hexagonal
lattice of attractive potential wells would be a good candidate. First we
consider the corresponding one-dimensional model giving rise to a
one-dimensional Dirac oscillator, and then construct explicitly the
deformations needed in the two-dimensional case. Finally we discuss, how such a
model can be implemented as an electromagnetic billiard using arrays of
dielectric resonators between two conducting plates that ensure evanescent
modes outside the resonators for transversal electric modes, and describe an
appropriate experimental setup.Comment: 23 pages, 8 figures. Submitted to NJ
Interactional positioning and narrative self-construction in the first session of psychodynamic-interpersonal psychotherapy
The purpose of this study is to identify possible session one indicators of end of treatment psychotherapy outcome using the framework of three types of interactional positioning; client’s self-positioning, client’s positioning between narrated self and different partners, and the positioning between client and therapist. Three successful cases of 8-session psychodynamic-interpersonal (PI) therapy were selected on the basis of client Beck Depression Inventory scores. One unsuccessful case was also selected against which identified patterns could be tested. The successful clients were more descriptive about their problems and demonstrated active rapport-building, while the therapist used positionings expressed by the client in order to explore the positionings developed between them during therapy. The unsuccessful case was characterized by lack of positive self-comment, minimization of agentic self-capacity, and empathy-disrupting narrative confusions. We conclude that the theory of interactional positioning has been useful in identifying patterns worth exploring as early indicators of success in PI therapy
Flavor and Charge Symmetry in the Parton Distributions of the Nucleon
Recent calculations of charge symmetry violation(CSV) in the valence quark
distributions of the nucleon have revealed that the dominant symmetry breaking
contribution comes from the mass associated with the spectator quark
system.Assuming that the change in the spectator mass can be treated
perturbatively, we derive a model independent expression for the shift in the
parton distributions of the nucleon. This result is used to derive a relation
between the charge and flavor asymmetric contributions to the valence quark
distributions in the proton, and to calculate CSV contributions to the nucleon
sea. The CSV contribution to the Gottfried sum rule is also estimated, and
found to be small
Effective Lagrangians and Chiral Random Matrix Theory
Recently, sum rules were derived for the inverse eigenvalues of the Dirac
operator. They were obtained in two different ways: i) starting from the
low-energy effective Lagrangian and ii) starting from a random matrix theory
with the symmetries of the Dirac operator. This suggests that the effective
theory can be obtained directly from the random matrix theory. Previously, this
was shown for three or more colors with fundamental fermions. In this paper we
construct the effective theory from a random matrix theory for two colors in
the fundamental representation and for an arbitrary number of colors in the
adjoint representation. We construct a fermionic partition function for
Majorana fermions in Euclidean space time. Their reality condition is
formulated in terms of complex conjugation of the second kind.Comment: 27 page
Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
We study statistical properties of the ensemble of large random
matrices whose entries decrease in a power-law fashion
. Mapping the problem onto a nonlinear
model with non-local interaction, we find a transition from localized
to extended states at . At this critical value of the system
exhibits multifractality and spectral statistics intermediate between the
Wigner-Dyson and Poisson one. These features are reminiscent of those typical
for the mobility edge of disordered conductors. We find a continuous set of
critical theories at , parametrized by the value of the coupling
constant of the model. At all states are expected to be
localized with integrable power-law tails. At the same time, for
the wave packet spreading at short time scale is superdiffusive: , which leads to a modification of the
Altshuler-Shklovskii behavior of the spectral correlation function. At
the statistical properties of eigenstates are similar to those
in a metallic sample in dimensions. Finally, the region
is equivalent to the corresponding Gaussian ensemble of random
matrices . The theoretical predictions are compared with results of
numerical simulations.Comment: 19 pages REVTEX, 4 figure
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