Quantum Theory on All Scales

Lectures

Long Courses

• Connected Components of the Space of Gapped Ground States

  Martin Fraas (UC Davis)

  These lectures discuss the classification of gapped quantum phases from an analytic viewpoint. The central question is when two systems can be connected by a continuous path of gapped Hamiltonians, placing the emphasis on the connected components of the space of gapped ground states rather than on topological invariants. I will outline the basic analytic framework for constructing such paths and illustrate it in selected examples. I will also discuss open questions and conjectures.

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• Approach to Equilibrium for translationally invariant lattice fermionic and quantum spin systems

  Vojkan Jaksic (Milano)

  The phenomena of the macroscopic world are irreversible: heat flows from hot to cold, entropy increases, and isolated systems approach equilibrium. Explaining these phenomena from the time-reversible laws of classical and quantum mechanics has been one of the central problems of statistical mechanics since the works of Maxwell and Boltzmann. The lectures will discuss this problem from the perspective of modern mathematical physics and focus on what has recently been called the “Minus First Law” of thermodynamics: an isolated macroscopic system, left to itself, evolves toward thermal equilibrium.
  
  The lectures will present a research program devoted to the mathematical theory of approach to equilibrium in infinitely extended classical and quantum systems. The main emphasis will be on translation-invariant quantum spin and fermionic systems. We will discuss both the kinematical thermodynamic formalism — Gibbs and KMS states, variational principles, entropy, phases, and constants of motion — and the corresponding dynamical formalism describing irreversible relaxation toward equilibrium.
  
  A central theme will be the relation between entropy increase, conservation laws, locality, and scattering. We will explain why finite systems cannot exhibit genuine thermalization, how infinitely extended systems allow irreversible behavior through escape of correlations to infinity, and how equilibration is related to restoration of locality in the large-time limit. Integrable and non-integrable quantum spin systems, including Ising, XY, and XYZ models, will serve as the main examples and sources of open problems.
  
  The lectures will include recent results, conjectures, and open problems concerning dynamical Gibbs variational principles, weak Gibbsianity, constants of motion, dephasing, and thermalization in many-body quantum systems. TBA

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• Renormalization group and quantum transport

  Marcello Porta (SISSA)

  TBA

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• Facets of quantum glasses

  Simone Warzel (TUM)

  TBA

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• Many-body quantum systems: mean-field regime and beyond

  Chiara Saffirio (U Basel & Freiburg)

  TBA

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• Quantum Information and Gravity

  Stefan Hollands (U Leipzig)

  These lectures provide an exposition to a circle of ideas at the interface between high energy physics and gravity that involve directly or indirectly ideas about entropy and quantum information. Emphasis is in particular on the connection to operator algebras. My exposition will be informal for the most part, assuming a knowledge of the standard formalism of quantum theory, basic quantum field theory, and basic notions related to entropy as would be taught in a standard course on statistical physics, but no prior knowledge of operator algebra theory. My aim is to introduce some methods and notions from operator algebras that can be useful also for someone with only a casual interest in the technicalities of the subject. In particular, I want to highlight recent advances related to Bekenstein-type bounds, the quantum null energy condition, and modular theory of von Neumann algebras.

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