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, $d$. The critical exponent $\nu$ controlling the divergence of the localization length at the transition is found to be $\nu = {1 \over 2}+ {1 \over {d-2}}$. 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.

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 $k = k_c$. For $k > k_c$ 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 $k \approx k_c$ 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 $\propto t^{2/3}$. 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 $D$ 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