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- MICHAEL AIZENMAN, ALEX ELGART, SERGEI NABOKO, JEFFREY H. SCHENKER
- 2003

We study localization effects of disorder on the spectral and dy-namical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are… (More)

We prove an adiabatic theorem for the ground state of the Dicke model in a slowly rotating magnetic field and show that for weak electron-photon coupling , the adiabatic time scale is close to the time scale of the corresponding two level system–without the quantized radiation field. There is a correction to this time scale which is the Lamb shift of the… (More)

Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We… (More)

We study the decay of a prepared state E0 into a continuum {Ek} in the case of non-Ohmic models. This means that the coupling is Vk,|proportional|Ek-E0s-1 with s not equal 1. We find that irrespective of model details there is a universal generalized Wigner time t0 that characterizes the decay of the survival probability P0(t). The generic decay behavior… (More)

We study the decay of a prepared state into non-flat continuum. We find that the survival probability P (t) might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a universal characteristic time t 0 that does not depend on the functional form. It is only for a flat continuum that we… (More)

The adiabatic theorem of Quantum Mechanics disregards the soft photons of QED. Why, then, is it so successful? To understand the role of soft photons we prove an adiabatic theorem for the ground state of a simple model Hamiltonians that allows soft photons. We show that for weak electron-photon coupling, the adiabatic time scale is close to the time scale… (More)

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