Sommerfeld Theory Colloquium (ASC)

Sommerfeld Theory Colloquium, I will describe the process of how to award Nobel Prizes and then give the history behind this year’s prize.

Sommerfeld Theory Colloquium, The physics of elementary particles is governed by symmetries. A particular symmetry stands out: the one between left and right, called parity. Its breaking in beta decay created a bombshell more than fifty years ago, and ultimately led to the creation of the Standard Model of particle interactions, whose final crowning confirmation is to be provided by the Large Hadron Collider (LHC) at CERN. The Standard Model is based on the premise of parity being broken al- ways, at all energies. I argue, on the contrary, that in nature left-right symmetry is fundamental, and that at high energies of the LHC one could actually see its restoration in full glory. I show how this would probe the nature of neutrino, through the spectacular signatures of lepton number violation.

Sommerfeld Theory Colloquium, Tremendous progresses have been achieved in the last decade in real- ising and manipulating stable and controllable quantum systems, and these made possible to experimentally study fundamental questions posed in the early days of quantum mechanics. We shall theoretical discuss recent cavity QED experiments on non-demolition quantum measurements. While they nicely illustrate postulates of quantum mechanics and the possibility to implement efficient quantum state manipulations, these experiments pose a few questions such as: What does it mean to observe a progressive wave function collapse in real time? How to describe it? What do we learn from them? Their analysis will allow us one hand to link these experiments to basics notions of probability or information theory, and on the other hand to touch upon notions of quantum noise. As an illustration, we shall look at quantum systems in contact with a heat bath subject to quan- tum transitions between energy levels upon absorption or emission of energy quanta. Isolating the two indispensable mechanisms in com- petition, we shall describe the main physical features of thermally activated quantum jumps.

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, Absolute temperature, that is the fundamental temperature scale in thermodynamics, is usually bound to be positive. Under special con- ditions, however, negative temperatures - where high-energy states are more occupied than low-energy states - are also possible. In this talk, I will present a negative temperature state for motional degrees of freedom: By tailoring the Bose-Hubbard Hamiltonian we exper- imentally created an attractively interacting ensemble of ultracold bosons, which is stable against collapse for arbitrary atom numbers. In this negative temperature state, the quasi-momentum distribu- tion develops sharp peaks at the upper band edge, revealing thermal equilibrium and bosonic coherence over several lattice sites. Nega- tive temperatures imply negative pressures and open up new param- eter regimes for cold atoms, enabling fundamentally new many-body states and counterintuitive effects such as Carnot engines above unity efficiency. In addition, this system enabled us to study the dynam- ics of the phase transition from Mott insulator to superfluid and to experimentally investigate how fast phase coherence can spread.

Sommerfeld Theory Colloquium

Sommerfeld Theory Colloquium

Sommerfeld Theory Colloquium, A single potential impurity can drastically change a low-temperature transport of strongly interacting particles in one dimension - a sys- tem which is known as the Luttinger liquid. An arbitrary weak backscattering of fermions from the impurity totally destroys their zero-temperature current while even a very strong backscattering of bosons makes no impact on their flow. On the other hand, a more complicated impurity (like a quantum dot or a double-barrier struc- ture with a resonant level) can preserve an ideal resonant conductance of fermions, or conversely lead (in a different geometry) to an ideal (i.e. infinite) resonant resistance. I emphasize the role of a so-called duality in these transport effects. The duality was related to the integrability of the Luttinger liquid with an impurity. I will show that - surprisingly - duality survives the addition of a non-local and retarded interaction (like electron-phonon) which almost certainly destroys the integrability.

Sommerfeld Theory Colloquium, The restricted three body problem has an intriguing dynamics. Glo- bal surfaces of section are a tool to reduce the study of the dynamics on a three dimensional energy hypersurface to the study of an area preserving map of a two dimensional surface. The existence of such a global surface of section is far from obvious. So far mostly per- turbative methods have been used to prove its existence. However, recently developed global tools originating from Gromov-Witten the- ory combined with the fact that energy hypersurfaces are of contact type can be applied to produce new global surfaces of section. In this talk I explain the restricted three body problem, the notion of a global surface of section and the new results we can obtain by bringing holomorphic curves and the contact form into play.

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.