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63873-01 - Lecture: Quantum Thermodynamics (4 CP)
| Semester | spring semester 2025 |
| Course frequency | Every spring sem. |
| Lecturers | Patrick Potts (patrick.potts@unibas.ch, Assessor) |
| Content | The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. This lecture provides an introduction to the thermodynamics of small quantum systems. After illustrating how the laws of thermodynamics emerge from quantum theory we will discuss how open quantum systems can be modeled. We then consider models of quantum systems that are designed to perform a certain task, such as cooling or generating entanglement. Finally, we investigate how fluctuations can be taken into account in a thermodynamic description by extending the laws of thermodynamics. Preliminary Outline: I Introduction ----------------- I.1 Basic concepts lecture notes only I.2 Macroscopic thermodynamics I.3 Information theory II. Thermodynamic Equilibrium ----------------------------------------- II.1 Grand canonical ensemble - the Gibbs state II.1.1 Subsystem of closed system II.1.2 Jaynes' maximum entropy principle II.1.3 Global passivity II.2 Equivalence of ensembles in the thermodynamic limit III The Laws of Thermodynamics -------------------------------------------- III.1 The general scenario III.2 Entropy production III.3 The first law of thermodynamics III.4 The second law of thermodynamics III.5 The zeroth law of thermodynamics III.6 The third law of thermodynamics IV Markovian Master Equations ------------------------------------------ IV.1 Nakajima-Zwanzig superoperators IV.2 Born-Markov approximations IV.3 Example: equilibration of a quantum dot IV.4 Obtaining GKLS form IV.4.1 The secular approximation IV.4.2 The singular coupling limit IV.4.3 The unified GKLS master equation IV.5 Example: a quantum double dot IV.5.1 The secular approximation IV.5.2 The singular coupling limit V Quantum Thermal Machines ----------------------------------------- V.1 A quantum dot heat engine V.1.1 Solving the master equation V.1.2 The first law V.1.3 The second law V.1.4 Refrigeration V.2 Entanglement generator V.2.1 Entanglement V.2.2 The master equation V.3 Absorption refrigerator V.3.1 The master equation V.3.2 Figures of merit V.3.3 Perturbation theory V.3.4 Coherence enhanced cooling VI Fluctuations -------------------- VI.1 Fluctuation theorem for a closed system VI.1.1 The two-point measurement scheme VI.1.2 The backward experiment VI.1.3 Fluctuation theorems VI.2 Fluctuation theorem for the general scenario VI.2.1 Forward trajectories VI.2.2 Backward trajectories VI.2.3 Fluctuation theorems VI.3 Full counting statistics VI.3.1 Counting particles VI.3.2 Example: transport through a quantum dot VI.3.3 Counting heat and work VI.4 Thermodynamic uncertainty relations VI.4.1 Current & current noise VI.4.2 Application: heat engine |
| Learning objectives | Apply the laws of thermodynamics – Develop intuition for small quantum systems, a valuable tool for any physicist. Describe open quantum systems – Gain insight into quantum systems studied at the University of Basel, from quantum dots to optical cavities. Explore useful tasks – Learn how quantum systems enable cooling, work generation, and entanglement. Understand fluctuations – Discover how fluctuations can be useful and how thermodynamic laws extend to describe them. |
| Bibliography | Lecture notes available at: https://arxiv.org/abs/2406.19206 |
| Language of instruction | English |
| Use of digital media | No specific media used |
| Interval | Weekday | Time | Room |
|---|---|---|---|
| wöchentlich | Monday | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
Dates
| Date | Time | Room |
|---|---|---|
| Monday 17.02.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 24.02.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 03.03.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 10.03.2025 | 13.15-15.00 | Fasnachstferien |
| Monday 17.03.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 24.03.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 31.03.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 07.04.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 14.04.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 21.04.2025 | 13.15-15.00 | Ostern |
| Monday 28.04.2025 | 13.15-15.00 | --, -- |
| Monday 05.05.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 12.05.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 19.05.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Monday 26.05.2025 | 13.15-15.00 | Physik, Seminarzimmer 4.1 |
| Modules |
Module Specialisation: Physics (Master's Studies: Nanosciences) Module: Specialisation (Master's Studies: Physics) |
| Assessment format | continuous assessment |
| Assessment details | - Pass oral exam - Obtain half of the points in the exercises - Solve two exercises in class at the blackboard |
| Assessment registration/deregistration | Reg.: course registration, dereg: cancel course registration |
| Repeat examination | no repeat examination |
| Scale | 1-6 0,5 |
| Repeated registration | as often as necessary |
| Responsible faculty | Faculty of Science, studiendekanat-philnat@unibas.ch |
| Offered by | Departement Physik |