40,792 research outputs found
Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems
We investigate a 1D disordered Hamiltonian with a non analytical step-like
dispersion relation whose level statistics is exactly described by Semi-Poisson
statistics(SP). It is shown that this result is robust, namely, does not depend
neither on the microscopic details of the potential nor on a magnetic flux but
only on the type of non-analyticity. We also argue that a deterministic kicked
rotator with a non-analytical step-like potential has the same spectral
properties. Semi-Poisson statistics (SP), typical of pseudo-integrable
billiards, has been frequently claimed to describe critical statistics, namely,
the level statistics of a disordered system at the Anderson transition (AT).
However we provide convincing evidence they are indeed different: each of them
has its origin in a different type of classical singularities.Comment: typos corrected, 4 pages, 3 figure
A semiclassical theory of the Anderson transition
We study analytically the metal-insulator transition in a disordered
conductor by combining the self-consistent theory of localization with the one
parameter scaling theory. We provide explicit expressions of the critical
exponents and the critical disorder as a function of the spatial
dimensionality, . The critical exponent controlling the divergence of
the localization length at the transition is found to be . This result confirms that the upper critical dimension is
infinity. Level statistics are investigated in detail. We show that the two
level correlation function decays exponentially and the number variance is
linear with a slope which is an increasing function of the spatial
dimensionality.Comment: 4 pages, journal versio
Anderson transition in systems with chiral symmetry
Anderson localization is a universal quantum feature caused by destructive
interference. On the other hand chiral symmetry is a key ingredient in
different problems of theoretical physics: from nonperturbative QCD to highly
doped semiconductors. We investigate the interplay of these two phenomena in
the context of a three-dimensional disordered system. We show that chiral
symmetry induces an Anderson transition (AT) in the region close to the band
center. Typical properties at the AT such as multifractality and critical
statistics are quantitatively affected by this additional symmetry. The origin
of the AT has been traced back to the power-law decay of the eigenstates; this
feature may also be relevant in systems without chiral symmetry.Comment: RevTex4, 4 two-column pages, 3 .eps figures, updated references,
final version as published in Phys. Rev.
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The relationship of drug reimbursement with the price and the quality of pharmaceutical innovations
This paper studies the strategic interaction between pharmaceutical firms' pricing decisions and government agencies' reimbursement decisions which discriminate between patients by giving reimbursement rights to patients for whom the drug is most effective. We show that if the reimbursement decision preceeds the pricing decision, the agency only reimburses some patients if the private and public health benefits from the new drug diverge. That is, when (i) there are large externalities of consuming the drug and (ii) the difference in costs between the new drug and the alternative treatment is large. Alternatively, if the firm can commit to a price in advance of the reimbursement decision, we identify a strategic effect which implies that by committing to a high price ex ante, the firm can force a listing outcome and make the agency more willing to reimburse than in the absence of commitment
Anderson transition in a three dimensional kicked rotor
We investigate Anderson localization in a three dimensional (3d) kicked
rotor. By a finite size scaling analysis we have identified a mobility edge for
a certain value of the kicking strength . For dynamical
localization does not occur, all eigenstates are delocalized and the spectral
correlations are well described by Wigner-Dyson statistics. This can be
understood by mapping the kicked rotor problem onto a 3d Anderson model (AM)
where a band of metallic states exists for sufficiently weak disorder. Around
the critical region we have carried out a detailed study of the
level statistics and quantum diffusion. In agreement with the predictions of
the one parameter scaling theory (OPT) and with previous numerical simulations
of a 3d AM at the transition, the number variance is linear, level repulsion is
still observed and quantum diffusion is anomalous with . We note that in the 3d kicked rotor the dynamics is not random but
deterministic. In order to estimate the differences between these two
situations we have studied a 3d kicked rotor in which the kinetic term of the
associated evolution matrix is random. A detailed numerical comparison shows
that the differences between the two cases are relatively small. However in the
deterministic case only a small set of irrational periods was used. A
qualitative analysis of a much larger set suggests that the deviations between
the random and the deterministic kicked rotor can be important for certain
choices of periods. Contrary to intuition correlations in the deterministic
case can either suppress or enhance Anderson localization effects.Comment: 10 pages, 5 figure
Symmetry limit properties of a priori mixing amplitudes for non-leptonic and weak radiative decays of hyperons
We show that the so-called parity-conserving amplitudes predicted in the a
priori mixing scheme for non-leptonic and weak radiative decays of hyperons
vanish in the strong-flavor symmetry limit
A new special class of Petrov type D vacuum space-times in dimension five
Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to
five dimensions, we invariantly classify all Petrov type vacuum solutions
for which the Riemann tensor is isotropic in a plane orthogonal to a pair of
Weyl alligned null directionsComment: 4 pages, 1 table, no figures. Contribution to the proceedings of the
Spanish Relativity Meeting 2010 held in Granada (Spain
Strong and weak thermalization of infinite non-integrable quantum systems
When a non-integrable system evolves out of equilibrium for a long time,
local observables are expected to attain stationary expectation values,
independent of the details of the initial state. However, intriguing
experimental results with ultracold gases have shown no thermalization in
non-integrable settings, triggering an intense theoretical effort to decide the
question. Here we show that the phenomenology of thermalization in a quantum
system is much richer than its classical counterpart. Using a new numerical
technique, we identify two distinct thermalization regimes, strong and weak,
occurring for different initial states. Strong thermalization, intrinsically
quantum, happens when instantaneous local expectation values converge to the
thermal ones. Weak thermalization, well-known in classical systems, happens
when local expectation values converge to the thermal ones only after time
averaging. Remarkably, we find a third group of states showing no
thermalization, neither strong nor weak, to the time scales one can reliably
simulate.Comment: 12 pages, 21 figures, including additional materia
State selection in the noisy stabilized Kuramoto-Sivashinsky equation
In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with
additive uncorrelated stochastic noise. The Eckhaus stable band of the
deterministic equation collapses to a narrow region near the center of the
band. This is consistent with the behavior of the phase diffusion constants of
these states. Some connections to the phenomenon of state selection in driven
out of equilibrium systems are made.Comment: 8 pages, In version 3 we corrected minor/typo error
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