Historical and interpretative aspects of quantum mechanics: a physicists' naive approach

Many theoretical predictions derived from quantum mechanics have been confirmed experimentally during the last 80 years. However, interpretative aspects have long been subject to debate. Among them, the question of the existence of hidden variables is still open. We review these questions, paying special attention to historical aspects, and argue that one may definitively exclude local realism on the basis of present experimental outcomes. Other interpretations of Quantum Mechanics are nevertheless not excluded.Comment: 30 page

Scaling and universality in the aging kinetics of the two-dimensional clock model

We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $\chi (t,s)\simeq s^{-a_\chi}f(t/s)$, we find $a_\chi$ consistent with the value $a_\chi =0.28$ found in the two-dimensional Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures

Work fluctuations in quantum spin chains

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.Comment: 10 pages, 13 figure

Symmetry relation for multifractal spectra at random critical points

Random critical points are generically characterized by multifractal properties. In the field of Anderson localization, Mirlin, Fyodorov, Mildenberger and Evers [Phys. Rev. Lett 97, 046803 (2006)] have proposed that the singularity spectrum $f(\alpha)$ of eigenfunctions satisfies the exact symmetry $f(2d-\alpha)=f(\alpha)+d-\alpha$ at any Anderson transition. In the present paper, we analyse the physical origin of this symmetry in relation with the Gallavotti-Cohen fluctuation relations of large deviation functions that are well-known in the field of non-equilibrium dynamics: the multifractal spectrum of the disordered model corresponds to the large deviation function of the rescaling exponent $\gamma=(\alpha-d)$ along a renormalization trajectory in the effective time $t=\ln L$. We conclude that the symmetry discovered on the specific example of Anderson transitions should actually be satisfied at many other random critical points after an appropriate translation. For many-body random phase transitions, where the critical properties are usually analyzed in terms of the multifractal spectrum $H(a)$ and of the moments exponents X(N) of two-point correlation function [A. Ludwig, Nucl. Phys. B330, 639 (1990)], the symmetry becomes $H(2X(1) -a)= H(a) + a-X(1)$, or equivalently $\Delta(N)=\Delta(1-N)$ for the anomalous parts $\Delta(N) \equiv X(N)-NX(1)$. We present numerical tests in favor of this symmetry for the 2D random $Q-$state Potts model with various $Q$.Comment: 15 pages, 3 figures, v2=final versio

Fluctuation-dissipation ratios in the dynamics of self-assembly

We consider two seemingly very different self-assembly processes: formation of viral capsids, and crystallization of sticky discs. At low temperatures, assembly is ineffective, since there are many metastable disordered states, which are a source of kinetic frustration. We use fluctuation-dissipation ratios to extract information about the degree of this frustration. We show that our analysis is a useful indicator of the long term fate of the system, based on the early stages of assembly.Comment: 8 pages, 6 figure

Probability distributions of the work in the 2D-Ising model

Probability distributions of the magnetic work are computed for the 2D Ising model by means of Monte Carlo simulations. The system is first prepared at equilibrium for three temperatures below, at and above the critical point. A magnetic field is then applied and grown linearly at different rates. Probability distributions of the work are stored and free energy differences computed using the Jarzynski equality. Consistency is checked and the dynamics of the system is analyzed. Free energies and dissipated works are reproduced with simple models. The critical exponent $\delta$ is estimated in an usual manner.Comment: 12 pages, 6 figures. Comments are welcom

Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions

We study the dynamics of the q-state random bond Potts ferromagnet on the square lattice at its critical point by Monte Carlo simulations with single spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases, conventional, rather than activated, dynamics. We also look at the distribution of relaxation times among different samples, finding different results for the two q values. For q=3 the relative variance of the relaxation time tau at the critical point is finite. However, for q=24 this appears to diverge in the thermodynamic limit and it is ln(tau) which has a finite relative variance. We speculate that this difference occurs because the transition of the corresponding pure system is second order for q=3 but first order for q=24.Comment: 9 pages, 13 figures, final published versio