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Stark resonances for random potentials of Anderson type. (English) Zbl 0955.47044

The paper is devoted to the study of the spectral properties of the Hamiltonian of an electron moving in a random potential and subject to an exterior constant electric field. \(H_\omega(F)= -{d^2\over dx^2}+ \sigma\omega_ju_j(x- j)+ F(x)\), \((F>0)\) on \({\mathcal H}= L^2(R)\). The atomic potentials \(U_j\) re supposed to be negative and vanishing at \(\infty\). The coupling constants \(\omega_j\) are independent random variables. A resonance is defined as a pole of some matrix elements of the resolvent operator. The investigation makes use of the analytical distortion method (Hunziker). The authors prove the existence of resonances with a width exponentially small with respect to the intensity of the field.

MSC:

47N50 Applications of operator theory in the physical sciences
81V70 Many-body theory; quantum Hall effect
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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