20,197 research outputs found
Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited
The fluctuations exhibited by the cross-sections generated in a
compound-nucleus reaction or, more generally, in a quantum-chaotic scattering
process, when varying the excitation energy or another external parameter, are
characterized by the width Gamma_corr of the cross-section correlation
function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a
method for its determination by simply counting the number of maxima featured
by the cross sections as function of the parameter under consideration. They,
actually, stated that the product of the average number of maxima per unit
energy range and Gamma_corr is constant in the Ercison region of strongly
overlapping resonances. We use the analogy between the scattering formalism for
compound-nucleus reactions and for microwave resonators to test this method
experimentally with unprecedented accuracy using large data sets and propose an
analytical description for the regions of isolated and overlapping resonances
A Poincar\'e section for the general heavy rigid body
A general recipe is developed for the study of rigid body dynamics in terms
of Poincar\'e surfaces of section. A section condition is chosen which captures
every trajectory on a given energy surface. The possible topological types of
the corresponding surfaces of section are determined, and their 1:1 projection
to a conveniently defined torus is proposed for graphical rendering.Comment: 25 pages, 10 figure
Dynamical typicality for initial states with a preset measurement statistics of several commuting observables
We consider all pure or mixed states of a quantum many-body system which
exhibit the same, arbitrary but fixed measurement outcome statistics for
several commuting observables. Taking those states as initial conditions, which
are then propagated by the pertinent Schr\"odinger or von Neumann equation up
to some later time point, and invoking a few additional, fairly weak and
realistic assumptions, we show that most of them still entail very similar
expectation values for any given observable. This so-called dynamical
typicality property thus corroborates the widespread observation that a few
macroscopic features are sufficient to ensure the reproducibility of
experimental measurements despite many unknown and uncontrollable microscopic
details of the system. We also discuss and exemplify the usefulness of our
general analytical result as a powerful numerical tool
Phase--coherence Effects in Antidot Lattices: A Semiclassical Approach to Bulk Conductivity
We derive semiclassical expressions for the Kubo conductivity tensor. Within
our approach the oscillatory parts of the diagonal and Hall conductivity are
given as sums over contributions from classical periodic orbits in close
relation to Gutzwiller's trace formula for the density of states. Taking into
account the effects of weak disorder and temperature we reproduce recently
observed anomalous phase coherence oscillations in the conductivity of large
antidot arrays.Comment: 11 pages, 2 figures available under request, RevTe
Strongly hyperbolic Hamiltonian systems in numerical relativity: Formulation and symplectic integration
We consider two strongly hyperbolic Hamiltonian formulations of general
relativity and their numerical integration with a free and a partially
constrained symplectic integrator. In those formulations we use hyperbolic
drivers for the shift and in one case also for the densitized lapse. A system
where the densitized lapse is an external field allows to enforce the momentum
constraints in a holonomically constrained Hamiltonian system and to turn the
Hamilton constraint function from a weak to a strong invariant.
These schemes are tested in a perturbed Minkowski and the Schwarzschild
space-time. In those examples we find advantages of the strongly hyperbolic
formulations over the ADM system presented in [arXiv:0807.0734]. Furthermore we
observe stabilizing effects of the partially constrained evolution in
Schwarzschild space-time as long as the momentum constraints are enforced.Comment: This version clarifies some points concerning the interpretation of
the result
Improved bounds for the crossing numbers of K_m,n and K_n
It has been long--conjectured that the crossing number cr(K_m,n) of the
complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):=
floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing
conjecture states that the crossing number cr(K_n) of the complete graph K_n
equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In
this paper we show the following improved bounds on the asymptotic ratios of
these crossing numbers and their conjectured values:
(i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1);
(ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and
(iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83.
The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8,
respectively. These improved bounds are obtained as a consequence of the new
bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for
cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to
set up a quadratic program on 6! variables whose minimum p satisfies
cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic
optimization techniques combined with a bit of invariant theory of permutation
groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure
Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer Heisenberg antiferromagnets
Based on exact diagonalization data for finite quantum Heisenberg
antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and
analytical arguments we map low-energy degrees of freedom of the spin models in
a magnetic field on classical lattice-gas models. Further we use
transfer-matrix calculations and classical Monte Carlo simulations to give a
quantitative description of low-temperature thermodynamics of the quantum spin
models. The classical lattice-gas model yields an excellent description of the
quantum spin models up to quite large temperatures. The main peculiarity of the
considered frustrated bilayer is a phase transition which occurs at low
temperatures for a wide range of magnetic fields below the saturation magnetic
field and belongs to the two-dimensional Ising model universality class.Comment: 17 pages, 8 figure
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