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- Michael Aizenman, Alex Elgart, SERGEI NABOKO, Jeffrey H. Schenker
- 2003

We study localization effects of disorder on the spectral and dynamical 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)

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including a… (More)

- Joseph E . Avron, Alex Elgart, Gian Michele Graf, Lorenzo Sadun
- Physical review letters
- 2001

We study adiabatic quantum pumps on time scales that are short relative to the cycle of the pump. In this regime the pump is characterized by the matrix of energy shift which we introduce as the dual to Wigner's time delay. The energy shift determines the charge transport, the dissipation, the noise, and the entropy production. We prove a general lower… (More)

We introduce a mathematical setup for charge transport in quantum pumps connected to a number of external leads. It is proved that under rather general assumption on the Hamiltonian describing the system, in the adiabatic limit, the current through the pump is given by a formula of Büttiker, Prêtre, and Thomas, relating it to the frozen S-matrix and its… (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)

Consider the 3D Anderson model with a zero mean and bounded i.i.d. random potential. Let λ be the coupling constant measuring the strength of the disorder, and σ(E) the self energy of the model at energy E. For any ǫ > 0 and sufficiently small λ, we derive almost sure localization in the band E ≤ −σ(0)−λ4−ǫ. In this energy region, we show that the typical… (More)

- Itamar Sela, James Aisenberg, Tsampikos Kottos, Alex Elgart, Doron J. Cohen
- Physical review. E, Statistical, nonlinear, and…
- 2010

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)

- E . Avron, Alex Elgart, Lorenzo Sadun
- 2007

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 t0 that does not depend on the functional form. It is only for a flat continuum that we get… (More)