Kay Brandner

Thermodynamics of Quantum Devices. Classical thermodynamics was once developed as a phenomenological theory of work and heat to describe and optimize the operation cycles of macroscopic machines such as Otto engines or household refrigerators. In recent yeas, a new era has begun, in which miniaturization is explored as a novel design principle for thermal devices. Heat engines and refrigerators can now be implemented on atomistic scales, where the rules of classical mechanics no longer apply. In the quantum world, particles can occupy two places at the same time, tunnel through barriers and influence each other at a distance without interaction. These striking phenomena are manifestations of the quantum laws of motion. They enable the design of thermal devices with radically new features. These quantum machinces could eventually  overcome the limitations of their classical counterparts.

My aim is to explore the fundamental principles that govern the dynamics and performance of quantum thermal devices far from equilibrium. I am thereby interested in both the general theory and specific setups that can be experimentally realized through present-day quantum engineering. Combing methods from quantum thermodynamics, the theory of open quantum systems and dynamical control theory, I am searching for new strategies to exploit quantum phenomena in order to enhance the power, efficiency and operational precision of thermal machines.

Lee-Yang Zeros. Phase transitions like the condensation of a gas into a liquid at  a critical temperature are determined by large fluctuations of thermodynamic observables and an anomalous behavior of the free energy. More than half a century ago, Lee and Yang realized that these exceptional features can be understood from the complex values of the external control parameter, e.g. temperature, at which the partition function of a small system vanishes; in the thermodynamic limit, these Lee-Yang zeros approach the critical point on the real axis. Over the last decades, this groundbreaking idea has lead to a powerful theoretical framework that covers not only conventional but also non-equilibrium and dynamical phase transitions.

In my second line of research, I am investigating the laws that determine the trajectories of Lee-Yang zeros in the complex plane and their relation to physical quantities like the high-order cumulants of a stochastic process, which can be directly observed in experiments. Applying tools from large-deviation theory, we recently showed that the complex Lee-Yang zeros can be used to infer the behavior of a system in the thermodynamic limit from its fluctuations in the small-size regime. Further exploring the generality and consequences of this result, which suggests a quite remarkable duality between small and large systems, is currently a major goal.

PUBLICATIONS

2019