Picture: Cutting-edge Finnish engineering from two centuries. Left: a VR Class Hv1 4-6-0 steam locomotive, which was built by
Oy Tampella Ab in Turku. Right: a quantum heat device that was fabricated and operated in the Pico group at Aalto University.
PHYS-E0542 - Special Course in Theoretical Physics V (Open Quantum Systems and Quantum Thermodynamics).
5 ECTS points
Lecturer: Kay Brandner (firstname.lastname@example.org)
Exercise tutor: Paul Menczel (email@example.com)
Please feel free to contact us with any inquiries concerning the course.
Heat engines convert thermal energy into useful work. A steam engine, for example, uses the pressure of a hot fluid to produce mechanical motion. Design and optimisation of such machines require a thorough understanding of the basic rules that govern their performance. More than 200 years ago, this need was the driving force behind the emergence of classical thermodynamics, a universal theory that has ever since enabled engineers to devise more and more powerful trains, cars and airplanes.
During the past two decades, a new era has begun for thermal machines, in which scientists are exploring miniaturization as a novel design principle.This development has recently led to landmark experiments showing that the working fluid of piston engines can indeed be reduced to tiny objects like an atom or even a single quantum spin. This new generation of engines can be equipped with features that no classical engineer could have imagined; quantum phenomena like coherence, entanglement and the measurement-induced collapse of wave functions change the characteristics of thermodynamic processes, enable new mechanisms of energy conversion with no classical counterpart and might even make it possible to overcome the fundamental performance limits of macroscopic devices. The search for strategies to describe these new features and utilise them for practical applications is the quest of quantum thermodynamics and the central topic of our course.
We will approach the world of quantum engines in two major steps. In part I of our course (lectures 1-6), we will, after a brief review of the basic rules of quantum mechanics, introduce the quantum-jump method and the Lindblad equation as powerful tools to describe the dynamics of open quantum systems. Using practical examples, we will then learn how these methods make it possible to describe the crucial phenomena of decoherence and dissipation.
During part II of the course (lectures 7-12), we will work through the key principles of quantum thermodynamics. Using the tools introduced in part I, we will formulate the laws of thermodynamics for quantum systems far from equilibrium, learn how to model finite-time engine and refrigeration cycles in the quantum regime and discuss fundamental differences with classical thermodynamic processes. Closing the gap to quantum engineering, in the last two lectures, we will meet the machinery of dynamical control theory and show how it can be used to optimise the performance of quantum devices.
After each lecture, we will give out an exercise sheet that should encourage you to develop your own thoughts by applying the concepts presented in the lectures to practical and research-related problems. Most of the exercise sheets will also guide you through a specific landmark paper that had a crucial impact on the development of its field. The exercises should be solved at home and will be discussed during the exercise classes accompanying the lectures. Every week, we will ask you to hand in your solutions for specified problems in written form two days before the respective exercise session. Group work will be most welcome.
After this course, you will:
- Be able to work with the quantum-jump and Lindblad methods to describe open quantum systems.
- Understand the crucial role of decoherence and dissipation for quantum technologies.
- Be familiar with the rules of quantum thermodynamics and the most important paradigms of this theory.
- Have the essential tools to develop and analyse models for quantum thermal machines.
- Understand the basic strategies of optimal control theory and know how to use them for quantum device optimisation.
- Be familiar with selected landmark papers that paved the way for modern quantum technologies.
Course structure and workload:
Part I (29.10.2018-12.12.2018) + Part II (07.01.2019-15.02.2019)
- 12 2h-lectures (Mondays, 12:00-14:00, Otakaari 1 M203)
- 12 2h-exercise-classes (Wednesdays,12:00-14:00, Otakaari 1 M203)
- 12 exercise sheets (homework) with written and discussion part
Our course is aimed at master's-level and early PhD students, who are familiar with quantum mechanics and classical thermodynamics. Some knowledge about statistical physics is helpful but not required.
Evaluation of our course is based on homeworks, exercise classes and a written exam. If you hand in all written homeworks and contribute actively to the exercise sessions, you collect enough points to pass the course. Your final grades will largely be determined by the written exam.
Materials and further reading:
Lecture notes, exercise sheets and the papers that will be discussed in the exercises will be provided under the sections Lecture notes and Exercise sheets (accessible for Aalto users). This material will be sufficient to work through our course. For enthusiasts who would like to get more background information, we can recommend the following literature.
- H.-P. Breuer and F. Petruccione The Theory of Open Quantum Systems (Oxford University Press, 2002). A comprehensive introduction into the topic with many worked out examples and applications.
- Á. Rivas and S. F. Huelga Open Quantum Systems - An Introduction (SpringerBriefs in Physics, 2012). A brief and concise overview on the mathematical aspects of open quantum systems.
- M. W. Zemansky and R. H. Dittman Heat and Thermodynamics (The McGraw-Hill Companies, Inc., 1997). A thorough and approachable introduction on classical thermodynamics with many applications to classical engine cycles.
- S. Vinjanampathy and J. Anders Quantum Thermodynamics, Contemp. Phys. 57, 545 (2016). A well-written and concise overview on basic principles and current developments in the field.