Michel Bauer (Saclay), Krzysztof Gawędzki (Lyon), François Huveneers (Paris), Jean-Marc Luck (Saclay), Mazyar Mirrahimi (Paris), Yan Pautrat (Orsay), Tomaž Prosen (Ljubljana),

Michel Bauer (Saclay): Equilibrium Fluctuations in Maximally Noisy Extended Quantum Systems. pdf

Quantum systems subject to external noise exhibit in general statistical as well as quantum fluctuations. Though much relevant information is already contained in the behavior of the statistical average of the density matrix (leading in the Markovian setting to Lindblad type equations), it is of importance to understand the full statistical distribution, for instance via a study of moments.
In this talk I will present a very simple example of a one-dimensional quantum system coupled to external noise. Though the time evolution of the system is unitary, I shall review how it arises in a natural way as the strong noise limit of a dissipative quantum spin chain. Then I will explain how the statistical fluctuations of certain quantum averages can be computed in detail, due to the fact that the effect of noise on the corresponding observables is maximal. The famous Harish-Chandra-Itzykson-Zuber formula plays a crucial, yet a priori unexpected, role in our analysis.

Krzysztof Gawędzki (Lyon): Full Counting Statistics of heat transfers in nonequilibrium Conformal Field Theory.

I shall discuss an exact formula for the statistics of heat transfers in simple non-equilibrium states of 1+1 dimensional CFT. The formula is obtained using the "conformal welding" of surfaces technique.

François Huveneers (Paris): The many-body localization transition. pdf

The dynamics of disordered quantum materials may be non-ergodic if the interaction among the quantum degrees of freedom is weak: Any transport of the conserved quantities is suppressed, and there is no thermalization. This state of matter has been dubbed the many-body localized phase. However, when the interaction strength becomes larger, it is expected that ergodicity is restored. In this talk, I will discuss the transition towards the ergodic phase and exhibit the mechanism for thermalization.

Jean-Marc Luck (Saclay): Selected topics on the dynamics of quantum walkers. pdf

Quantum walks are commonly used as a tool to implement algorithms in quantum information theory. They are also relevant to investigate the dynamics of various systems in the quantum coherent regime, such as ultra-cold atoms. A quantum walker propagates ballistically and its wavefunction exhibits sharp ballistic fronts. This is to be contrasted with the diffusive scaling and the rather dull Gaussian probability profile of a classical random walker. Most physical properties of quantum walkers are qualitatively different from those of classical ones. We shall give a few examples, focussing on continuous-time quantum walkers on the one-dimensional chain. A quantum walker can easily avoid a static trap, so that it survives forever with non-zero probability, at variance with a classical random walker. Bound states formed by two or more interacting quantum walkers, either fermionic or bosonic, also spread ballistically. Their wavefunction generically exhibits many internal fronts in the center-of-mass coordinate, besides the two extremal ones. A special instance of a many-body fermionic bound state dubbed the quantum centipedes can be analyzed via a mapping onto an integrable spin chain. Its spreading velocity remains non-zero even when the number of fermions becomes infinitely large. The return probability of several non-interacting quantum walkers to their global initial state falls off as a power law in time, whose exponent is different from the classical one and depends on details of the initial state and of the dynamics. These results have been obtained in collaboration with Paul Krapivsky and Kirone Mallick.

Mazyar Mirrahimi (Paris): A hardware-efficient and scalable approach to fault-tolerant quantum computation.

I overview a series of recent theoretical proposals, and preliminary experimental developments, to enable a hardware-efficient paradigm for quantum error correction. These proposals are based on two main ingredients: 1- encoding of information in the so-called Schrödinger cat states of microwave radiation in a superconducting resonator, 2- application of dissipation/reservoir engineering methods to stabilize a manifold of quantum states where the information is encoded.

Yan Pautrat (Orsay): Landauer's Principle in Repeated Interaction Systems.

We study Landauer's principle for repeated interaction systems consisting of a reference quantum system S in contact with an environment E made of a chain of independent quantum probes. The system S interacts with each probe sequentially, and the Landauer principle relates the energy variation of E and the decrease of entropy of S. We consider the adiabatic regime where the chain contains T probes and displays variations of order 1/T between the successive probes. We consider refinements of the Landauer bound at the level of the full statistics (FS) associated with a two-time measurement protocol. Our results rely on a non-unitary adiabatic theorem and and an analysis of the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps. This is joint work with Eric Hanson, Alain Joye and Renaud Raquépas.

Tomaž Prosen (Ljubljana): Exact Spectral Form Factor and Entanglement Spreading in a Minimal Model of Many-Body Quantum Chaos

I will discuss the concept of self-duality in periodically driven (Floquet) quantum Ising spin 1/2 chains which allows for some non-trivial exact computations, despite manifest non-integrability of the model. For example, I will outline a rigorous proof of random matrix spectral form factors in the model and universal entanglement spreading which saturates the minimal cut bounds.