914 research outputs found
Canonical formalism for simplicial gravity
We summarise a recently introduced general canonical formulation of discrete
systems which is fully equivalent to the covariant formalism. This framework
can handle varying phase space dimensions and is applied to simplicial gravity
in particular.Comment: 4 pages, 5 figures, based on a talk given at Loops '11 in Madrid, to
appear in Journal of Physics: Conference Series (JPCS
Spectral correlations in systems undergoing a transition from periodicity to disorder
We study the spectral statistics for extended yet finite quasi 1-d systems
which undergo a transition from periodicity to disorder. In particular we
compute the spectral two-point form factor, and the resulting expression
depends on the degree of disorder. It interpolates smoothly between the two
extreme limits -- the approach to Poissonian statistics in the (weakly)
disordered case, and the universal expressions derived for the periodic case.
The theoretical results agree very well with the spectral statistics obtained
numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late
Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics
We consider a quasi one-dimensional chain of N chaotic scattering elements
with periodic boundary conditions. The classical dynamics of this system is
dominated by diffusion. The quantum theory, on the other hand, depends
crucially on whether the chain is disordered or invariant under lattice
translations. In the disordered case, the spectrum is dominated by Anderson
localization whereas in the periodic case, the spectrum is arranged in bands.
We investigate the special features in the spectral statistics for a periodic
chain. For finite N, we define spectral form factors involving correlations
both for identical and non-identical Bloch numbers. The short-time regime is
treated within the semiclassical approximation, where the spectral form factor
can be expressed in terms of a coarse-grained classical propagator which obeys
a diffusion equation with periodic boundary conditions. In the long-time
regime, the form factor decays algebraically towards an asymptotic constant. In
the limit , we derive a universal scaling function for the form
factor. The theory is supported by numerical results for quasi one-dimensional
periodic chains of coupled Sinai billiards.Comment: 33 pages, REVTeX, 13 figures (eps
Quantum Chaos and Random Matrix Theory - Some New Results
New insight into the correspondence between Quantum Chaos and Random Matrix
Theory is gained by developing a semiclassical theory for the autocorrelation
function of spectral determinants. We study in particular the unitary operators
which are the quantum versions of area preserving maps. The relevant Random
Matrix ensembles are the Circular ensembles. The resulting semiclassical
expressions depend on the symmetry of the system with respect to time reversal,
and on a classical parameter where U is the classical 1-step
evolution operator. For system without time reversal symmetry, we are able to
reproduce the exact Random Matrix predictions in the limit . For
systems with time reversal symmetry we can reproduce only some of the features
of Random Matrix Theory. For both classes we obtain the leading corrections in
. The semiclassical theory for integrable systems is also developed,
resulting in expressions which reproduce the theory for the Poissonian ensemble
to leading order in the semiclassical limit.Comment: LaTeX, 16 pages, to appear in a special issue of Physica D with the
proceedings of the workshop on "Physics and Dynamics Between Chaos, Order,
and Noise", Berlin, 199
Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]
Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for
convergent series representations of both the real and the imaginary part of
the QED effective action; these derivations were based on correct intermediate
steps. In this comment, we argue that the physical significance of the
"logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86,
1947 (2001)] in comparison to the usual expression for the QED effective action
remains to be demonstrated. Further information on related subjects can be
found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update
Spectral Statistics in Chaotic Systems with Two Identical Connected Cells
Chaotic systems that decompose into two cells connected only by a narrow
channel exhibit characteristic deviations of their quantum spectral statistics
from the canonical random-matrix ensembles. The equilibration between the cells
introduces an additional classical time scale that is manifest also in the
spectral form factor. If the two cells are related by a spatial symmetry, the
spectrum shows doublets, reflected in the form factor as a positive peak around
the Heisenberg time. We combine a semiclassical analysis with an independent
random-matrix approach to the doublet splittings to obtain the form factor on
all time (energy) scales. Its only free parameter is the characteristic time of
exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho
Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
A nonperturbative theory is developed, aiming at an exact and efficient
evaluation of a general quantum system interacting with arbitrary bath
environment at any temperature and in the presence of arbitrary time-dependent
external fields. An exact hierarchical equations of motion formalism is
constructed on the basis of calculus-on-path-integral algorithm, via the
auxiliary influence generating functionals related to the interaction bath
correlation functions in a parametrization expansion form. The corresponding
continued-fraction Green's functions formalism for quantum dissipation is also
presented. Proposed further is the principle of residue correction, not just
for truncating the infinite hierarchy, but also for incorporating the small
residue dissipation that may arise from the practical difference between the
true and the parametrized bath correlation functions. The final
residue-corrected hierarchical equations of motion can therefore be used
practically for the evaluation of arbitrary dissipative quantum systems.Comment: 12 pages, submitted to PR
Exact quantum master equation for a molecular aggregate coupled to a harmonic bath
We consider a molecular aggregate consisting of identical monomers. Each
monomer comprises two electronic levels and a single harmonic mode. The
monomers interact with each other via dipole-dipole forces. The monomer
vibrational modes are bilinearly coupled to a bath of harmonic oscillators.
This is a prototypical model for the description of coherent exciton transport,
from quantum dots to photosynthetic antennae. We derive an exact quantum master
equation for such systems. Computationally, the master equation may be useful
for the testing of various approximations employed in theories of quantum
transport. Physically, it offers a plausible explanation of the origins of
long-lived coherent optical responses of molecular aggregates in dissipative
environments
Signature of Chaotic Diffusion in Band Spectra
We investigate the two-point correlations in the band spectra of spatially
periodic systems that exhibit chaotic diffusion in the classical limit. By
including level pairs pertaining to non-identical quasimomenta, we define form
factors with the winding number as a spatial argument. For times smaller than
the Heisenberg time, they are related to the full space-time dependence of the
classical diffusion propagator. They approach constant asymptotes via a regime,
reflecting quantal ballistic motion, where they decay by a factor proportional
to the number of unit cells. We derive a universal scaling function for the
long-time behaviour. Our results are substantiated by a numerical study of the
kicked rotor on a torus and a quasi-one-dimensional billiard chain.Comment: 8 pages, REVTeX, 5 figures (eps
Determination of Gross Sections for the Production of 7Be, 10Be and 22Na by High-Energy Protons
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