Quantum entropy and its use
Entropy is a central quantity in information theory, probability and physics. This spring school will focus on fundamental concepts and basic operational interpretations of entropy with a particular…
Localization Bounds for Multiparticle Systems
- M. Aizenman, S. Warzel
- Physics
- 19 September 2008
We consider the spectral and dynamical properties of quantum systems of n particles on the lattice $${\mathbb{Z}^d}$$ , of arbitrary dimension, with a Hamiltonian which in addition to the kinetic…
Random Operators: Disorder Effects on Quantum Spectra and Dynamics
- M. Aizenman, S. Warzel
- Mathematics
- 14 December 2015
* Introduction* General relations between spectra and dynamics* Ergodic operators and their self-averaging properties* Density of states bounds: Wegner estimate and Lifshitz tails* The relation of…
Multiparticle localization for disordered systems on continuous space via the fractional moment method
- Michael Fauser, S. Warzel
- Mathematics, Physics
- 24 February 2014
We investigate the spectral and dynamical localization of a quantum system of n particles on ℝd which are subject to a random potential and interact through a pair potential which may have infinite…
Low-Energy Fock-Space Localization for Attractive Hard-Core Particles in Disorder
We study a one-dimensional quantum system with an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential.…
On the ubiquity of the Cauchy distribution in spectral problems
- M. Aizenman, S. Warzel
- Mathematics
- 30 December 2013
We consider the distribution of the values at real points of random functions which belong to the Herglotz–Pick (HP) class of analytic mappings of the upper half plane into itself. It is shown that…
The Absolute Continuity of the Integrated Density¶of States for Magnetic Schrödinger Operators¶with Certain Unbounded Random Potentials
- T. Hupfer, H. Leschke, P. Müller, S. Warzel
- Mathematics
- 20 February 2001
Abstract:The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrödinger operator with magnetic…
Resonant delocalization for random Schr\"odinger operators on tree graphs
- M. Aizenman, S. Warzel
- Mathematics
- 5 April 2011
We analyse the spectral phase diagram of Schr\"odinger operators $ T +\lambda V$ on regular tree graphs, with $T$ the graph adjacency operator and $V$ a random potential given by iid random…
Stability of the Absolutely Continuous Spectrum of Random Schrödinger Operators on Tree Graphs
- M. Aizenman, Robert Sims, S. Warzel
- Mathematics
- 1 February 2005
The subject of this work is random Schrödinger operators on regular rooted tree graphs with stochastically homogeneous disorder. The operators are of the form Hλ(ω)=T+U+λV(ω) acting in ℓ2(), with T…
QUASI-CLASSICAL VERSUS NON-CLASSICAL SPECTRAL ASYMPTOTICS FOR MAGNETIC SCHRÖDINGER OPERATORS WITH DECREASING ELECTRIC POTENTIALS
We consider the Schrodinger operator H(V) on L2 (ℝ2) or L2(ℝ3) with constant magnetic field, and electric potential V which typically decays at infinity exponentially fast or has a compact support.…
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