Adiabatic Theorems for Quantum Resonances

We study the adiabatic time evolution of quantum resonances over time scales which are small compared to the lifetime of the resonances. We consider three typical examples of resonances: The first one is that of shape resonances corresponding, for example, to the state of a quantum-mechanical particle in a potential well whose shape changes over time scales small compared to the escape time of the particle from the well. Our approach to studying the adiabatic evolution of shape resonances is based on a precise form of the time-energy uncertainty relation and the usual adiabatic theorem in quantum mechanics. The second example concerns resonances that appear as isolated complex eigenvalues of spectrally deformed Hamiltonians, such as those encountered in the N-body Stark effect. Our approach to study such resonances is based on the Balslev-Combes theory of dilatation-analytic Hamiltonians and an adiabatic theorem for nonnormal generators of time evolution. Our third example concerns resonances arising from eigenvalues embedded in the continuous spectrum when a perturbation is turned on, such as those encountered when a small system is coupled to an infinitely extended, dispersive medium. Our approach to this class of examples is based on an extension of adiabatic theorems without a spectral gap condition. We finally comment on resonance crossings, which can be studied using the last approach.     

Air-related mechanisms of noise generation by solid rubber tyres with cavities

There are four main air-related noise generation mechanisms at the tyre/road interface, which were all categorised more than 20 years ago. The first one is the so-called ‘air pumping’ mechanism. Two other air-related phenomena that occur when there are air movements near the contact patch of the tyre are ‘air resonant radiation’ and ‘pipe resonances’ which appear at the footprint of the tyre. In addition to these, there is a forth effect, which is mentioned in the literature, that is occurring due to turbulence effects of the air surrounding the spinning tyre. There has been less focus on the air-related mechanisms than on other types of tyre noise generation mechanisms. This paper attempts to add some detail to current understanding of the air-related noise generation at the tyre road interface and gives some further information on how to identify the differences due to these mechanisms. Specifically in the present paper, a solid rubber tyre running on a vehicle chassis dynamometer is used to study the first two mechanisms. This is done with emphasis on the time history of the recorded signal and not on the frequency spectrum, as is more commonly used. A comparison with existing theoretical models of these mechanisms reveals some of the strength and weaknesses of the current understanding of these phenomena.     

Reconstructing the relaxation dynamics induced by an unknown heat bath

In quantum state tomography, one potential source of error is uncontrolled contact of the system with a heat bath whose detailed properties are not known, and whose impact on the system moreover varies between different runs of the experiment. Precisely these variations provide a handle for reconstructing the system?s effective relaxation dynamics. I propose a pertinent estimation scheme which is based on a steepest-descent ansatz and maximum likelihood. After reconstructing the relaxation dynamics, the original quantum state of the system can be constrained to a curve in state space.     

Upper Bound on the Density of Ruelle Resonances for Anosov Flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (−i)V, called Ruelle resonances, close to the real axis and for large real parts.     

Characterization of a 20 kHz sonoreactor. Part II: analysis of chemical effects by classical and electrochemical methods

A new electrochemical redox probe has been investigated in order to characterize the local production of radicals during the cavitation events. The results have been compared with those obtained with Fe(CN)6(3-)/Fe(CN)6(4-) (electrochemical probe for local mechanical effects) and classical chemical methods such as iodide and Fricke dosimeters (chemical probes for global effects).     

Higher order QCD contributions to electron structure functions

We study deep inelastice ⁺ e ^? scattering with untagged throughgoing target electrons. The corresponding electron structure functions are not trivially related to photon structure functions. Both can be calculated in QCD perturbation theory but the first ones can be measured more easily. In studying next-to-leading log contributions to electron structure functions we find that the leading logQ ² approximation completely fails at present energies. This is due to different scales λ andm _e . A modified leading-log approximation is introduced. Higher order corrections to this approximation are small away fromx=0 or 1.     

Bosonization,topological solitons and fractional charges in two-dimensional quantum field theory

We further develop the quantization of topological solitons in two-dimensional quantum field theory in terms of Euclidean region functional integrals. Our approach is nonperturbative and mathematically rigorous. We apply it to construct physical states with fractional fermion number in models of interacting bosons and fermions without recurring to a semiclassical approximation. A related issue discussed in this paper is two-dimensional chiral bosonization.