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17 papers · 1 filter
The Dynamics of the One-Dimensional Delta-Function Bose Gas
Craig A. Tracy, Harold Widom
We give a method to solve the time-dependent Schroedinger equation for a system of one-dimensional bosons interacting via a repulsive delta function potential. The method uses the…
Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
Bruno Nachtergaele, Hillel Raz, Benjamin Schlein +1
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum har…
Lieb-Robinson Bounds and the Exponential Clustering Theorem
Bruno Nachtergaele, Robert Sims
We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential c…
Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
Michael Aizenman, Robert Sims, Simone Warzel
We consider the Laplacian on a rooted metric tree graph with branching number and random edge lengths given by independent and identically distributed bounded variable…
Non-unitary minimal models, Bailey's lemma and N=1,2 superconformal algebras
Lipika Deka, Anne Schilling
Using the Bailey flow construction, we derive character identities for the N=1 superconformal models SM(p',2p+p') and SM(p',3p'-2p), and the N=2 superconformal model with central c…
Quantum Spin Systems
Bruno Nachtergaele
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formu…