TY - ELEC
AU - Constanze Liaw
PY - 2019
TI - Rank-one perturbations and Anderson-type Hamiltonians
LA - eng
M3 - Moving Image
AB - A rank-one perturbation $A+K$ of an operator $A$ is one where the range of $K$ is just one-dimensional. Being rather restrictive, they form a small class of perturbations. Yet, rank-one perturbations are related to many deep questions. Here we focus on a relation with Anderson-type Hamiltonians. These are random perturbations which are obtained by taking a countable sum of rank-one perturbation, each weighted by a randomly chosen coupling constant. Such perturbations are non-compact almost surely. Under mild conditions, the essential parts of two realizations of an Anderson-type Hamiltonian are almost surely related by a rank one perturbation.
N2 - A rank-one perturbation $A+K$ of an operator $A$ is one where the range of $K$ is just one-dimensional. Being rather restrictive, they form a small class of perturbations. Yet, rank-one perturbations are related to many deep questions. Here we focus on a relation with Anderson-type Hamiltonians. These are random perturbations which are obtained by taking a countable sum of rank-one perturbation, each weighted by a randomly chosen coupling constant. Such perturbations are non-compact almost surely. Under mild conditions, the essential parts of two realizations of an Anderson-type Hamiltonian are almost surely related by a rank one perturbation.
UR - https://open.library.ubc.ca/collections/48630/items/1.0381038
ER - End of Reference