2,609 research outputs found
Semiclassical universality of parametric spectral correlations
We consider quantum systems with a chaotic classical limit that depend on an
external parameter, and study correlations between the spectra at different
parameter values. In particular, we consider the parametric spectral form
factor which depends on a scaled parameter difference . For
parameter variations that do not change the symmetry of the system we show by
using semiclassical periodic orbit expansions that the small expansion
of the form factor agrees with Random Matrix Theory for systems with and
without time reversal symmetry.Comment: 18 pages, no figure
Periodic-orbit theory of universal level correlations in quantum chaos
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate
universal behaviour of the two-point correlator of the density of levels for
quantum systems whose classical limit is fully chaotic. We go beyond previous
work in establishing the full correlator such that its Fourier transform, the
spectral form factor, is determined for all times, below and above the
Heisenberg time. We cover dynamics with and without time reversal invariance
(from the orthogonal and unitary symmetry classes). A key step in our reasoning
is to sum the periodic-orbit expansion in terms of a matrix integral, like the
one known from the sigma model of random-matrix theory.Comment: 44 pages, 11 figures, changed title; final version published in New
J. Phys. + additional appendices B-F not included in the journal versio
Exclusive processes in position space and the pion distribution amplitude
We suggest to carry out lattice calculations of current correlators in
position space, sandwiched between the vacuum and a hadron state (e.g. pion),
in order to access hadronic light-cone distribution amplitudes (DAs). In this
way the renormalization problem for composite lattice operators is avoided
altogether, and the connection to the DA is done using perturbation theory in
the continuum. As an example, the correlation function of two electromagnetic
currents is calculated to the next-to-next-to-leading order accuracy in
perturbation theory and including the twist-4 corrections. We argue that this
strategy is fully competitive with direct lattice measurements of the moments
of the DA, defined as matrix elements of local operators, and offers new
insight in the space-time picture of hard exclusive reactions.Comment: 15 pages, 10 figure
Universal spectral form factor for chaotic dynamics
We consider the semiclassical limit of the spectral form factor of
fully chaotic dynamics. Starting from the Gutzwiller type double sum over
classical periodic orbits we set out to recover the universal behavior
predicted by random-matrix theory, both for dynamics with and without time
reversal invariance. For times smaller than half the Heisenberg time
, we extend the previously known -expansion to
include the cubic term. Beyond confirming random-matrix behavior of individual
spectra, the virtue of that extension is that the ``diagrammatic rules'' come
in sight which determine the families of orbit pairs responsible for all orders
of the -expansion.Comment: 4 pages, 1 figur
Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2
The two-point correlation function of chaotic systems with spin 1/2 is
evaluated using periodic orbits. The spectral form factor for all times thus
becomes accessible. Equivalence with the predictions of random matrix theory
for the Gaussian symplectic ensemble is demonstrated. A duality between the
underlying generating functions of the orthogonal and symplectic symmetry
classes is semiclassically established
Semiclassical Theory for Parametric Correlation of Energy Levels
Parametric energy-level correlation describes the response of the
energy-level statistics to an external parameter such as the magnetic field.
Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the
parametric energy-level correlation depending on the magnetic field difference.
The small-time expansion of the spectral form factor is shown to be
in agreement with the prediction of parameter dependent random-matrix theory to
all orders in .Comment: 25 pages, no figur
Semiclassical expansion of parametric correlation functions of the quantum time delay
We derive semiclassical periodic orbit expansions for a correlation function
of the Wigner time delay. We consider the Fourier transform of the two-point
correlation function, the form factor , that depends on the
number of open channels , a non-symmetry breaking parameter , and a
symmetry breaking parameter . Several terms in the Taylor expansion about
, which depend on all parameters, are shown to be identical to those
obtained from Random Matrix Theory.Comment: 21 pages, no 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
Semiclassical Approach to Chaotic Quantum Transport
We describe a semiclassical method to calculate universal transport
properties of chaotic cavities. While the energy-averaged conductance turns out
governed by pairs of entrance-to-exit trajectories, the conductance variance,
shot noise and other related quantities require trajectory quadruplets; simple
diagrammatic rules allow to find the contributions of these pairs and
quadruplets. Both pure symmetry classes and the crossover due to an external
magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version
Baryonic Strangeness and Related Susceptibilities in QCD
The ratios of off-diagonal to diagonal conserved charge susceptibilities
e.g., chi_{BS}/chi_{S}, chi_{QS}/chi_{S}, related to the quark flavor
susceptibilities, have proven to be discerning probes of the flavor carrying
degrees of freedom in hot strongly interacting matter. Various constraining
relations between the different susceptibilities are derived based on the
Gell-Mann-Nishijima formula and the assumption of isospin symmetry. Using
generic models of deconfined matter and results form lattice QCD, it is
demonstrated that the flavor carrying degrees of freedom at a temperature above
1.5T_c are quark-like quasiparticles. A new observable related by isospin
symmetry to C_{BS} = -3chi_{BS}/chi_{S} and equal to it in the baryon free
regime is identified. This new observable, which is blind to neutral and
non-strange particles, carries the potential of being measured in relativistic
heavy-ion collisions.Comment: 12 pages, 5 figures, RevTex
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