Sommerfeld Theory Colloquium (ASC)

Sommerfeld Theory Colloquium, The decay of a false vacuum of unbroken B-L, the difference of baryon and lepton number, is an intriguing and testable mechanism to gen- erate the initial conditions of the hot early universe. If B-L is broken at the grand unification scale, the false vacuum phase yields hybrid inflation, ending in tachyonic preheating. The dynamics of the B-L breaking Higgs field and thermal processes produce an abundance of heavy neutrinos whose decays generate entropy, baryon asymmetry and dark matter.

Sommerfeld Theory Colloquium, This lecture is aimed at a rather broad audience including under- graduates. It will discuss scaling arguments, what they can achieve (Kolmogorov’s -5/3 law, etc.) and what they miss (fractals, Etc).

Sommerfeld Theory Colloquium, Lorentz non-invariance in quantum field theory is reconsidered as well as its interplay with gravity, string theory, diffeomorphism invariance and changing reference frames. We clarify these issues, and argue that Lorentz violation is always an environmental effect. We provide a holographic view of the breaking, and its connection to Horava- Lifshitz type of gravitational theories. We also argue that dissipation is always a signal of Lorentz violation. We provide calculations of dissipation at strong coupling.

Sommerfeld Theory Colloquium, Reflection positivity is a useful tool in statistical mechanics and con- densed matter physics. A recent application is to the determination of the possible distortions of the hexagonal graphene lattice. Other applications, such as to potential theory, the flux-phase problem, Peierls instability and stripe formation, will also be given.

Sommerfeld Theory Colloquium, Much of condensed matter physics is concerned with understanding how different kinds of order emerge from interactions between a large number of simple constituents. In ordered phases such as crystals, magnets, and superfluids, the order is understood through ”symme- try breaking”: in a crystal, for example, the continuous symmetries of space under rotations and translations are not reflected in the ground state. A major discovery of the 1980s was that electrons confined to two dimensions and in a strong magnetic field exhibit a completely different, ”topological” type of order that underlies the quantum Hall effect.

In the past few years, we have learned that topological order also occurs in some three-dimensional materials, dubbed ”topological in- sulators”, in zero magnetic field. Spin-orbit coupling, an intrinsic property of all solids, drives the formation of the topological state. This talk will explain what topological order means, how topologi- cal were predicted and discovered, and how they realize the ”axion electrodynamics” studied by particle physicists in the 1980s. Some possible applications of these new materials are discussed in closing.

Sommerfeld Theory Colloquium, Conformal interfaces are the long-distance limits of domain walls. They play a role in condensed-matter physics, and could be also rel- evant for theories of gravity. I will review some recently-developed techniques for analyzing their properties, and will discuss their pos- sible applications.

Sommerfeld Theory Colloquium, In collisions of ultra-intense laser-pulse with relativistic electrons as well as in ultra relativistic heavy ion collisions at RHIC and at LHC it is possible to probe critical acceleration a=mc^3/hbar. The behavior of a particle undergoing critical acceleration challenges the limits of the current understanding of basic interactions: little is known about this physics frontier; both classical and quantum physics will need further development in order to be able to address this newly accessible area of physics. The problem of critical acceleration is closely connected to strong field particle production, Mach's Principle, Unruh and Hawking radiation.

Sommerfeld Theory Colloquium, In this lecture I propose to discuss some issues concerning the founda- tions of quantum mechanics and its interplay with space-time physics. I start by clarifying the distinction between ’realistic theories’ and ’probabilistic theories’ of Nature and sketch how the latter can often be viewed as ’deformations’ of the former. I then briefly recall some of the intriguing features of atomistic Quantum Mechanics, which belongs to the second class of theories. I attempt to describe, in con- ceptual terms, what it is that Quantum Mechanics predicts about Nature when appropriate experiments are done. I try to sketch some implications of this discussion for our views of space and time. I will conclude by sketching some recent results on the ’effective quantum dynamics’ of Open Systems, in particular on ’Quantum Brownian Motion’.

Sommerfeld Theory Colloquium, The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-body

problem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is in

many cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Complete

factorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. I

will give examples how one can apply this powerful theoretical concept in experiment.

A detailed study of non-translation invariant correlation functions reveals that the pre-thermalized state a system of

two 1-dimensional quantum gas relaxes to after a splitting quench [1], is described by a generalized Gibbs ensemble

[2]. This is verified through phase correlations up to 10th order.

Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon /

massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize

[3]. This allowed us to characterize the essential features of the model solely from our experimental measurements:

detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states the

quasi-particles live in. The experiment thus provides a comprehensive insight into the components needed to solve a

non-trivial quantum field theory.

Our examples establish a general method to analyse quantum systems through experiments. It thus represents a

crucial ingredient towards the implementation and verification of quantum simulators.

Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg).

Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 and

the EU: ERC-AdG QuantumRelax

[1] M. Gring et al., Science, 337, 1318 (2012);

[2] T. Langen et al., Science 348 207-211 (2015).

[3] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126

Quantum Criticality, High Tc Superconductivity and the AdS/CFT Correspondence of String Theory , The central mystery in quantum matter is the general nature of mat- ter formed from fermions. The methods of many body quantum physics fail and one can only rely on the phenomenological Fermi- liquid and BCS theories. However, in heavy fermion systems and cuprates one deals with non Fermi-liquid quantum critical metals, and to understand the superconductivity one needs to understand these normal states first. Remarkably, it might well be that the mathematics of string theory is capable of describing such states of fermion matter. The AdS/CFT correspondence translates this problem into an equivalent general-relativity problem involving the propagation of classical fields in an Anti-de-Sitter space-time with a black hole in its center. This development started with the demon- stration that AdS/CFT predicts correctly the low viscosity of the quark-gluon plasma of the Brookhaven heavy ion collider. In 2007 it was realized that it could have relevance to high Tc superconductors but only last year the focus shifted to the way AdS/CFT processes fermions, creating much excitement: it appears that both emergent heavy Fermi-liquids and non Fermi-liquids can be gravitationally encoded, as well as holographic superconductors having suggestive traits in common with the real life high Tc variety.