Gravitational backgrounds, such as black holes, AdS, de Sitter and inflationary universes, should be viewed as composite of N soft constituent gravitons. It then follows that such systems are close to quantum criticality of graviton Bose-gas to Bose-liquid transition. Generic properties of the ordinary metric description, including geodesic motion or particlecreation in the background metric, e...

We consider a semi-classical completely integrable system defined by a ~-pseudodifferential operator Ĥ on the torus T. In order to study perturbed operators of the form Ĥ + ~K̂ , where K̂ is an arbitrary pseudodifferential operator and κ > 0, we prove the conjugacy to a suitable normal form. This is then used to construct a large number of quasimodes.

This study introduces a new signal analysis method called SCSA, based on a semi-classical approach. The main idea in the SCSA is to interpret a pulseshaped signal as a potential of a Schrödinger operator and then to use the discrete spectrum of this operator for the analysis of the signal. We present some numerical examples and the first results obtained with this method on the analysis of arte...

Quantum transport properties of electron systems driven by strong electric fields are studied by mapping the Landau-Zener transition dynamics to a quantum walk on a semi-infinite one-dimensional lattice with a reflecting boundary, where the sites correspond to energy levels and the boundary the ground state. Quantum interference induces a distribution localized around the ground state, and a de...

We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudospectra and boundary conditions in the semi-classical limit. AMS subject classification numbers: 81Q20, 47Axx, 34Lxx.

The semi-Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end-point of the support of the censoring time is strictly less than the right end-point of the support of the semi-Markov kernel, the transition p...