33 citations · 149 across the 15 of their papers we have counts for
5 papers · 1 filter
Spectral gaps for the Two-Species Product Vacua and Boundary States models on the -dimensional lattice
Michael Bishop
We study the two-species Product Vacua and Boundary States (PVBS) models on the integer lattice and prove the existence and non-existence of a spectral gap for all c…
Spectral Gap and Edge Excitations of -dimensional PVBS models on half-spaces
Michael Bishop, Bruno Nachtergaele, Amanda Young
We analyze a class of quantum spin models defined on half-spaces in the -dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector …
Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials
Michael Bishop, Vita Borovyk, Jan Wehr
This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schrödinger operators with a Bernoulli-distributed potential. The proof approximates the low…
Ground State Energy of Mean-field Model of Interacting Bosons in Bernoulli Potential
Michael Bishop, Jan Wehr
This paper explores a system of interacting `soft core' bosons in the Gross-Pitaevskii mean-field approximation in a random Bernoulli potential. First, a condition for delocalizati…
Ground State Energy of the One-Dimensional Discrete Random Schrödinger Operator with Bernoulli Potential
Michael Bishop, Jan Wehr
In this paper, we show the that the ground state energy of the one dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is controlled asymptotically as the sy…