Quantum critical effects in the spectrum of excited states
| Thesis title in Czech: | Kvantové kritické efekty ve spektru excitovaných stavů |
|---|---|
| Thesis title in English: | Quantum critical effects in the spectrum of excited states |
| Key words: | Příprava kvantového stavu|Kvantové fázové přechody v základním i excitovanýc|Adiabatická perturbační teorie|Lipkin-Meshkov-Glickův model|Optimální dráha |
| English key words: | Quantum state preparation|Ground-state and excited-state quantum phase trans|Adiabatic perturbation theory|Lipkin-Meshkov-Glick model|Optimal path |
| Academic year of topic announcement: | 2018/2019 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| 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: | 17.07.2019 |
| Date of assignment: | 17.07.2019 |
| Confirmed by Study dept. on: | 02.10.2019 |
| Date and time of defence: | 20.06.2025 10:00 |
| Date of electronic submission: | 10.04.2025 |
| Date of submission of printed version: | 10.04.2025 |
| Date of proceeded defence: | 20.06.2025 |
| Opponents: | Mgr. Michal Macek, Ph.D. |
| prof. Armando Relano | |
| Advisors: | doc. Mgr. Pavel Stránský, Ph.D. |
| Guidelines |
| The work belongs to the framework of theoretical quantum physics of non-relativistic systems. It is focused on so called Excited-State Quantum Phase Transitions (ESQPTs), which represent a generalization of the ground-state Quantum Phase Transitions (QPTs) to the excited domain. The ESQPTs were identified - so far mostly on the theoretical level, but in some cases also experimentally - in the collective dynamics of numerous quantum many body systems, like atomic nuclei, molecules, quantum optical systems, D-dimensional crystals etc.
The student will perform theoretical analyses related to specific realizations of the ESQPT phenomenon in selected models of quantum many-body systems. One class of the models that can be investigated is represented by various algebraic models of collective dynamics in spatially localized quantum systems, another one by models of collective excitations in spatially extended lattice systems. The ESQPT effects will be studied from the spectroscopic perspective, i.e., in properties like level density as a function of energy, level flow with varying control parameter, expectation values of various observables in individual eigenstates etc. The study can then proceed to various dynamical and/or thermodynamical aspects of ESQPTs, like anomalous responses related to various kinds of driven dynamics (adiabatic versus diabatic driving) or differences between canonical and microcanonical thermodynamical descriptions. The research in these directions will be adapted to actual results and challenges that will appear during the solution. |
| References |
| [1] Understanding Quantum Phase Transitions, edited by L.D. Carr (CRC press, Boca Raton, 2011)
[2] F. Iachello, Lie Algebras and Applications, Lecture Notes in Physics 891, 2nd edition (Springer, Heidelberg, 2014) [3] T. Brandes, Phys. Rep. 408, 315 (2005) [4] M. Kastner, Rev. Mod. Phys. 80, 167 (2008) [5] P. Cejnar and J. Jolie, Prog. Part. Nucl. Phys. 62, 210 (2009) [6] P. Cejnar, P. Stránský, Phys. Scr. 91, 083006 (2016) [7] M. A. Caprio, P. Cejnar and F. Iachello, Ann. Phys.(N.Y.) 323, 1106 (2008) [8] P. Stránský, M. Macek and P. Cejnar, Ann. Phys. (N.Y.) 345, 73 (2014) [9] P. Stránský, M. Macek, A. Leviatan and P. Cejnar, Ann. Phys. (N.Y.) 356, 57 (2015) [10] F. Iachello, B. Dietz, M. Miski-Oglu and A. Richter, Phys. Rev. B 91, 214307 (2015) [11] M. Kloc, P. Stránský and P. Cejnar, Ann. Phys. (N.Y.) 382, 85 (2017) [12] M. Kloc, P. Stránský and P. Cejnar, Phys. Rev. A 98, 013836 (2018) |
| Preliminary scope of work in English |
| The work belongs to the framework of theoretical quantum physics of non-relativistic systems. It is focused on so called Excited-State Quantum Phase Transitions (ESQPTs), which represent a generalization of the ground-state Quantum Phase Transitions (QPTs) to the excited domain. The ESQPTs were identified - so far mostly on the theoretical level, but in some cases also experimentally - in the collective dynamics of numerous quantum many body systems, like atomic nuclei, molecules, quantum optical systems, D-dimensional crystals etc. |