Spea­kers

Tristan Benoist (Toulouse)

Daniel Burgarth (Erlangen)

Marilena Ligabo (Bari)

Melchior Wirth (Leipzig)

Registration is free but mandatory. Please use the following website:

https://indico.uni-paderborn.de/event/174/

There is a limited amount of financial support, please apply before September 4th.

If you would like to give a contributed talk, please let us also know until September 4th via the registration tool.

Tristan Benoist: Introduction to repeated quantum measurements and quantum trajectories

Repeated indirect measurements are ubiquitous in quantum optics experiments. Their mathematical formulation is based on quantum instruments and they give rise to both dynamical systems of measurement outcomes and Markov processes on states called quantum trajectories. In these lectures I will introduce the quantum instrument formalism and define the dynamical system describing measurement outcomes and the induced quantum trajectories. I will then present recent results on their ergodic and asymptotic behavior. In particular, for quantum trajectories, I will focus on the phenomenon of purification.

Daniel Burgarth: Quantum control - steering finite and infinite dimensional quantum systems

Quantum control is an interdisciplinary area between engineering, physics and mathematics. While much of physics and mathematics aims to solve differential equations, engineers often start with the desired solution and work backwards to find a suitable differential equation. In the context of quantum mechanics, this amounts to using the Schrödinger equation or master equations to engineer quantum gates and states. For finite dimensional systems, there is a nice Lie-algebraic theory which I will introduce. For infinite dimensional systems, some interesting partial results are known, and I will give a selection of these, driven by recent research.

Marilena Ligabò: Self-adjoint operators and boundary conditions in quantum mechanics

Self-adjoint operators play a fundamental role in quantum mechanics, both as mathematical representatives of observables and as generators of unitary dynamics. For differential operators, however, self-adjointness is not determined by the differential expression alone: the choice of domain, and in particular of suitable boundary conditions, is an essential part of the problem.
These lectures will provide an introduction to the theory of self-adjoint extensions of symmetric operators, starting from the classical abstract approach of von Neumann and then moving, in the case of differential operators, to a more concrete description in terms of boundary conditions. Particular attention will be devoted to different parametrizations of self-adjoint extensions and admissible boundary conditions. 
The general theory will be illustrated through representative examples from quantum mechanics and spectral theory. Applications may include Schrödinger-type operators, Laplacians on bounded domains, singular interactions, quantum graph and related models in which different self-adjoint realizations correspond to different physical boundary conditions or coupling mechanisms.

Melchior Wirth: Quantum Markov Semigroups and Their Generators

Quantum Markov semigroups (QMS) describe the time time evolution of open quantum systems in regimes when memory effects can be neglected. For such systems, the evolution is governed by the master equation ρ̇_t=Lρ_t and the superoperator L is called the generator of the QMS. In these lectures, I will discuss which superoperators occur as generators of QMS both in finite and infinite dimensions. Of particular interest is the case when the open system is coupled to an environment in equilibrium, which is captured by a detailed balance condition.  I will present a class of mathematical models of detailed balance conditions and discuss how they are reflected in the generator.