Welcome to the course!
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.
Course name:
PHYS-E0542
- Special Course in Theoretical Physics V (Open Quantum Systems and Quantum Thermodynamics).
Credits:
5 ECTS points
Contact:
Lecturer: Kay Brandner (kay.brandner@aalto.fi)
Exercise tutor: Paul Menczel (paul.menczel@aalto.fi)
Please feel free to contact us with any inquiries concerning the course.
Invitation:
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.
Description:
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.
Learning outcomes:
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
Course level:
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:
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.