Oscillations of neutrinos and mesons in quantum field theory

This report deals with the quantum field theory of particle oscillations in vacuum. We first review the various controversies regarding quantum-mechanical derivations of the oscillation formula, as well as the different field-theoretical approaches proposed to settle them. We then clear up the contradictions between the existing field-theoretical treatments by a thorough study of the external wave packet model. In particular, we show that the latter includes stationary models as a subcase. In addition, we explicitly compute decoherence terms, which destroy interferences, in order to prove that the coherence length can be increased without bound by more accurate energy measurements. We show that decoherence originates not only in the width and in the separation of wave packets, but also in their spreading through space-time. In this review, we neither assume the relativistic limit nor the stability of oscillating particles, so that the oscillation formula derived with field-theoretical methods can be applied not only to neutrinos but also to neutral K and B mesons. Finally, we discuss oscillations of correlated particles in the same framework.Comment: v2, 124 pages, 10 figures (7 more); updated review of the literature; complete derivation of the oscillation probability at short and large distance; more details on the influence of the spreading of the amplitude on decoherence; submitted to Physics Report

Interplay between localization and absorption in disordered waveguides

This work presents results of ab-initio simulations of continuous wave transport in disordered absorbing waveguides. Wave interference effects cause deviations from diffusive picture of wave transport and make the diffusion coefficient position- and absorption-dependent. As a consequence, the true limit of a zero diffusion coefficient is never reached in an absorbing random medium of infinite size, instead, the diffusion coefficient saturates at some finite constant value. Transition to this absorption-limited diffusion exhibits a universality which can be captured within the framework of the self-consistent theory (SCT) of localization. The results of this work (i) justify use of SCT in analyses of experiments in localized regime, provided that absorption is not weak; (ii) open the possibility of diffusive description of wave transport in the saturation regime even when localization effects are strong.Comment: 10 pages, 3 figure

Disorder and interference: localization phenomena

The specific problem we address in these lectures is the problem of transport and localization in disordered systems, when interference is present, as characteristic for waves, with a focus on realizations with ultracold atoms.Comment: Notes of a lecture delivered at the Les Houches School of Physics on "Ultracold gases and quantum information" 2009 in Singapore. v3: corrected mistakes, improved script for numerics, Chapter 9 in "Les Houches 2009 - Session XCI: Ultracold Gases and Quantum Information" edited by C. Miniatura et al. (Oxford University Press, 2011

Weak localization with nonlinear bosonic matter waves

We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions.Comment: 67 pages, 19 figure

Effect of nonlinearity on the dynamics of a particle in dc field-induced systems

Dynamics of a particle in a perfect chain with one nonlinear impurity and in a perfect nonlinear chain under the action of dc field is studied numerically. The nonlinearity appears due to the coupling of the electronic motion to optical oscillators which are treated in adiabatic approximation. We study for both the low and high values of field strength. Three different range of nonlinearity is obtained where the dynamics is different. In low and intermediate range of nonlinearity, it reduces the localization. In fact in the intermediate range subdiffusive behavior in the perfect nonlinear chain is obtained for a long time. In all the cases a critical value of nonlinear strength exists where self-trapping transition takes place. This critical value depends on the system and the field strength. Beyond the self-trapping transition nonlinearity enhances the localization.Comment: 9 pages, Revtex, 6 ps figures include

Wave propagation through a coherently amplifying random medium

We report a detailed and systematic numerical study of wave propagation through a coherently amplifying random one-dimensional medium. The coherent amplification is modeled by introducing a uniform imaginary part in the site energies of the disordered single-band tight binding Hamiltonian. Several distinct length scales (regimes), most of them new, are identified from the behavior of transmittance and reflectance as a function of the material parameters. We show that the transmittance is a non-self-averaging quantity with a well defined mean value. The stationary distribution of the super reflection differs qualitatively from the analytical results obtained within the random phase approximation in strong disorder and amplification regime. The study of the stationary distribution of the phase of the reflected wave reveals the reason for this discrepancy. The applicability of random phase approximation is discussed. We emphasize the dual role played by the lasing medium, as an amplifier as well as a reflector.Comment: 33 pages RevTex, 14 EPS figures included, Accepted for publication in IJMP-