Feshbach-Schur RG for the Anderson Model

Duration: 51 mins 11 secs

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Description:	Imbrie, J Friday 26th October 2018 - 14:30 to 15:30


Created:	2018-10-29 10:38
Collection:	Scaling limits, rough paths, quantum field theory
Publisher:	Isaac Newton Institute
Copyright:	Imbrie, J
Language:	eng (English)


Abstract:	Consider the localization problem for the Anderson model of a quantum particle moving in a random potential. We develop a renormalization-group framework based on a sequence of Feshbach-Schur maps. Each map produces an effective Hamiltonian on a lower-dimensional space by localizing modes in space and in energy. Randomness in ever-larger neighborhoods produces nontrivial eigenvalue movement and separates eigenvalues, making the next step of the RG possible. We discuss a particularly challenging case where the disorder has a discrete distribution.

Abstract:

Consider the localization problem for the Anderson model of a quantum particle moving in a random potential. We develop a renormalization-group framework based on a sequence of Feshbach-Schur maps. Each map produces an effective Hamiltonian on a lower-dimensional space by localizing modes in space and in energy. Randomness in ever-larger neighborhoods produces nontrivial eigenvalue movement and separates eigenvalues, making the next step of the RG possible. We discuss a particularly challenging case where the disorder has a discrete distribution.

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