TOPICS

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 years, 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, which could eventually  overcome the limitations of their classical counterparts.

Our aim is to explore the fundamental principles that govern the dynamics and performance of quantum thermal devices far from equilibrium. We are 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, we are searching for new strategies to exploit quantum phenomena in order to enhance the power, efficiency and operational precision of thermal machines.

Thermodynamics of Ballistic Transport. In macroscopic systems at high temperature, transport is a stochastic process, where particles undergo ceaseless collisions that randomly change their velocity and direction of motion. Reducing the temperature of a conductor increases the average distance that a particle can travel between two collisions. Ballistic, or coherent, transport sets in when this mean free path becomes comparable to the dimensions of the sample. In this regime the trans-fer of particles through the system is governed by the reversible laws of Hamiltonian or quantum mechanics while irreversible processes occur in external reservoirs.

 

Scattering theory provides an elegant method and physically transparent to describe the thermodynamics of ballistic conductors. As a key result, this approach leads to a direct link between the microscopic properties of the sample and thermodynamic observables like electric currents and entropy production. Here, we use this theoretical framework to investigate the interplay between dissipation, quantum and thermal fluctuations in small-scale conductors and to explore the basic principles that govern the performance and precision of current-driven nano-devices such as thermoelectric generators and refrigerators.

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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 this line of research, we are 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 behaviour 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 a goal of our research.

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