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| Semester | spring semester 2023 |
| 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 I.1.1 Linear algebra I.1.2 The density matrix I.1.3 Second quantization I.2 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.2.1 Example: equilibration of a quantum dot IV.3 Obtaining GKLS form IV.3.1 The secular approximation IV.3.2 The singular coupling limit IV.3.3 The unified GKLS master equation IV.3.4 Example: a quantum double dot V Quantum Thermal Machines ----------------------------------------- V.1 A quantum dot heat engine V.1.1 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 VII Summary VIII Outlook |
| Language of instruction | English |
| Use of digital media | No specific media used |
| Interval | Weekday | Time | Room |
|---|---|---|---|
| wöchentlich | Monday | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| wöchentlich | Friday | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Date | Time | Room |
|---|---|---|
| Monday 20.02.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 24.02.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 27.02.2023 | 10.15-12.00 | Fasnachstferien |
| Friday 03.03.2023 | 10.15-12.00 | Fasnachstferien |
| Monday 06.03.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 10.03.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 13.03.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 17.03.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 20.03.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 24.03.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 27.03.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 31.03.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 03.04.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 07.04.2023 | 10.15-12.00 | Ostern |
| Monday 10.04.2023 | 10.15-12.00 | Ostern |
| Friday 14.04.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 17.04.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 21.04.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 24.04.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 28.04.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 01.05.2023 | 10.15-12.00 | Tag der Arbeit |
| Friday 05.05.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 08.05.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 12.05.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 15.05.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 19.05.2023 | 10.15-12.00 | Auffahrt |
| Monday 22.05.2023 | 10.15-12.00 | Physik, Alter Hörsaal 2, 1.22 |
| Friday 26.05.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Monday 29.05.2023 | 10.15-12.00 | Pfingstmontag |
| Friday 02.06.2023 | 10.15-12.00 | Physik, Seminarzimmer 3.12 |
| Modules |
Module Specialisation: Physics (Master's Studies: Nanosciences) Module: Specialisation (Master's Studies: Physics) |
| Assessment format | continuous assessment |
| 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 |