Dynamické projevy fázových přechodů v energetických a kvazienergetických spektrech kvantových systémů

• Název práce v češtině: Dynamické projevy fázových přechodů v energetických a kvazienergetických spektrech kvantových systémů
• Název v anglickém jazyce: Dynamical signatures of phase transitions in energy and quasienergy spectra of quantum systems
• Akademický rok vypsání: 2022/2023
• Typ práce: disertační práce
• Ústav: Ústav částicové a jaderné fyziky (32-UCJF)
• Vedoucí / školitel: prof. RNDr. Pavel Cejnar, Dr., DSc.
• Řešitel: skrytý - zadáno a potvrzeno stud. odd.
• Datum přihlášení: 16.09.2022
• Datum zadání: 16.09.2022
• Datum potvrzení stud. oddělením: 06.10.2022
• Konzultanti: Mgr. Pavel Stránský, Ph.D.

Zásady pro vypracování

The student will theoretically investigate various dynamic manifestations of spectral singularities connected with the Ground- and Excited-State Quantum Phase Transitions (GSQPTs and ESQPTs) [1,2,3,4]. The focus will be set to the singularities in discrete (continuous) energy spectra of bound (unbound) quantum systems with a finite number of degrees of freedom [5,6,7], as well as to the singularities in quasienergy spectra of quantum systems subject to an external periodic driving [8,9,10,11].

The GSQPT and ESQPT effects will be first identified in the density of (quasi)energy spectra and in the expectation values of some relevant observables. Then various dynamic signatures will be analyzed in quantum evolution induced by stationary, forward-driven or periodic-driven Hamiltonians. The study of closed (isolated) systems can be extended to open systems which due to interactions with external components (e.g. heat baths) show dissipation, thermalization and/or decoherence effects. Further physical insight can be reached through studying the (semi)classical analogs of the systems under investigation or using other approximation techniques.

The research in these directions will be adapted to actual results and challenges that will appear during the solution.

Seznam odborné literatury

[1] Understanding Quantum Phase Transitions, edited by L.D. Carr (CRC press, Boca Raton, 2011)
[2] P. Cejnar, P. Stránský, M. Macek, M. Kloc, Journal of Physics A: Mathematical and Theoretical 54 (2021) 133001
[3] V.M. Bastidas, P. Pérez-Fernández, M. Vogl, T. Brandes, Physical Review Letters 112 (2014) 140408
[4] P. Stránský, M. Šindelka, P. Cejnar, Physical Review A 103 (2021) 062207
[5] T. Brandes, Physics Reports 408 (2005) 315
[6] 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)
[7] N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge UK, 2011)
[8] S. Rahav, I. Gilary, S. Fishman, Physical Review A 68 (2003) 013820
[9] N. Goldman, J. Dalibard, Physical Review X 4 (2014) 031027
[10] M. Bukov, L. D'Alessio, A. Polkovnikov, Advances in Physics 64 (2015) 139
[11] F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 2010)

Předběžná náplň práce v anglickém jazyce

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.