357 research outputs found
An Entire Spectral Determinant for Semiclassical Quantization
We show that the eigenvalues of the first order partial differential equation
derived by quasi-classical approximation of the Schr\"odinger equation can be
computed from the trace of a classical operator. The derived trace formula is
different from the Gutzwiller trace formula.Comment: 8 pages, latex, no figur
Entire Fredholm determinants for Evaluation of Semi-classical and Thermodynamical Spectra
Proofs that Fredholm determinants of transfer operators for hyperbolic flows
are entire can be extended to a large new class of multiplicative evolution
operators. We construct such operators both for the Gutzwiller semi-classical
quantum mechanics and for classical thermodynamic formalism, and introduce a
new functional determinant which is expected to be entire for Axiom A flows,
and whose zeros coincide with the zeros of the Gutzwiler-Voros zeta function.Comment: 4 pages, Revtex + one PS figure attached to the end of the text cut
before you run revtex
Crossover from Regular to Chaotic Behavior in the Conductance of Periodic Quantum Chains
The conductance of a waveguide containing finite number of periodically
placed identical point-like impurities is investigated. It has been calculated
as a function of both the impurity strength and the number of impurities using
the Landauer-B\"uttiker formula. In the case of few impurities the conductance
is proportional to the number of the open channels of the empty waveguide
and shows a regular staircase like behavior with step heights .
For large number of impurities the influence of the band structure of the
infinite periodic chain can be observed and the conductance is approximately
the number of energy bands (smaller than ) times the universal constant
. This lower value is reached exponentially with increasing number of
impurities. As the strength of the impurity is increased the system passes from
integrable to quantum-chaotic. The conductance, in units of , changes
from corresponding to the empty waveguide to corresponding to
chaotic or disordered system. It turnes out, that the conductance can be
expressed as where the parameter measures the chaoticity of
the system.Comment: 5 pages Revte
Scaling in Words on Twitter
Scaling properties of language are a useful tool for understanding generative
processes in texts. We investigate the scaling relations in citywise Twitter
corpora coming from the Metropolitan and Micropolitan Statistical Areas of the
United States. We observe a slightly superlinear urban scaling with the city
population for the total volume of the tweets and words created in a city. We
then find that a certain core vocabulary follows the scaling relationship of
that of the bulk text, but most words are sensitive to city size, exhibiting a
super- or a sublinear urban scaling. For both regimes we can offer a plausible
explanation based on the meaning of the words. We also show that the parameters
for Zipf's law and Heaps law differ on Twitter from that of other texts, and
that the exponent of Zipf's law changes with city size
Spectral Determinant Method for Interacting N-body Systems Including Impurities
A general expression for the Green's function of a system of particles
(bosons/fermions) interacting by contact potentials, including impurities with
Dirac-delta type potentials is derived. In one dimension for bosons from
our {\it spectral determinant method} the numerically calculated energy levels
agree very well with those obtained from the exact Bethe ansatz solutions while
they are an order of magnitude more accurate than those found by direct
diagonalization. For N=2 bosons the agreement is shown analytically. In the
case of N=2 interacting bosons and one impurity, the energy levels are
calculated numerically from the spectral determinant of the system. The
spectral determinant method is applied to an interacting fermion system
including an impurity to calculate the persistent current at the presence of
magnetic field.Comment: revtex, 19 pages, 4 figure
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