Dynamika a kritické chování parametricky závislých kvantových systémů
| Thesis title in Czech: | Dynamika a kritické chování parametricky závislých kvantových systémů |
|---|---|
| Thesis title in English: | Dynamics and critical behavior of parameter-dependent quantum systems |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | dissertation |
| Thesis language: | čeština |
| Department: | Institute of Particle and Nuclear Physics (32-UCJF) |
| Supervisor: | prof. RNDr. Pavel Cejnar, Dr., DSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 02.08.2022 |
| Date of assignment: | 02.08.2022 |
| Confirmed by Study dept. on: | 19.09.2022 |
| Advisors: | doc. Mgr. Pavel Stránský, Ph.D. |
| Guidelines |
| The student will investigate various theoretical approches to quantum systems depending on external control parameters [1,2]. The analyses will focus mostly on specific many-body systems with a finite number of degrees of freedom which show signatures of quantum criticality, particularly the ground-state and/or excited-state quantum phase transitions [3,4].
The geometric approach to parameter-dependent quantum systems [5,6] and its role in the dynamics will be investigated. Manifestations of quantum critical effects will be analyzed in static properties (density of energy eigenstates, expectation values of observables...) [4] and in the response of the system to various kinds of external driving (diabatic, adiabatic, counterdiabatic...) [7,8], with potential applications to the design of maximum-fidelity quantum state preparation protocols [9]. The work can be extended to periodically driven systems, scattering systems with continuous energy spectra and/or to open systems with decoherence and thermalization [10]. The research in these directions will be adapted to actual results and challenges that will appear during the solution. |
| References |
| [1] T. Brandes, Physics Reports 408 (2005) 315
[2] C. Gardiner, P. Zoller: The Quantum World of Ultra-Cold Atoms and Light, Books I, II and III (Imperial College Press, London, 2014, 2015, 2016) [3] Understanding Quantum Phase Transitions, edited by L.D. Carr (CRC press, Boca Raton, 2011) [4] P. Cejnar, P. Stránský, M. Macek, M. Kloc, Journal of Physics A: Mathematical and Theoretical 54 (2021) 133001 [5] Geometric Phases in Physics, edited by A. Shapre and F. Wilczek (World Scientific, Singapore, 1990) [6] M. Kolodrubetz, D. Sels, P. Mehta, A. Polkovnikov, Physics Reports 697 (2017) 1 [7] A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Reviews of Modern Physics 83 (2011) 863 [8] M.V. Berry, Journal of Physics A: Mathematical and Theoretical 42 (2009) 365303 [9] M. Bukov, D. Sels, A. Polkovnikov, Physical Review X 9 (2019) 011034 [10] Thermodynamics in the Quantum Regime, edited by F. Binder, L.A. Correa, C. Gogolin, J. Anders and G. Adesso G (Springer, Berlin, 2019) |
| Preliminary scope of work in English |
| This Ph.D. work is focused on a connection of two active areas of theoretical research in quantum many-body physics: (a) the investigation of general dynamics of complex quantum systems out of equilibrium and (b) the study of quantum phase transitions for the ground and excited states. Recent rapid progress in the design of laboratory quantum simulators makes an increasing amount of theoretical predictions available to experimental tests and opens routes to their future applications. |