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Quasispin models in quantum physics
Zymin, Andrii ; Stránský, Pavel (advisor) ; Kloc, Michal (referee)
Title: Quasispin models in quantum physics Author: Andrii Zymin Department: Institute of Particle and Nuclear Physics Supervisor: Mgr. Pavel Stránský, Ph.D., Institute of Particle and Nuclear Physics Abstract: The use of symmetries in quantum physics helps in a deeper understanding of physical systems and simplifies numerical calculations. This thesis studies models based on the SU(2) algebra, which, in spite of their apparent simplicity, show rather rich behavior and describe a wide spectrum of physical phenomena. We review various realizations of the SU(2) algebra (namely the spin, boson, and fermion realization) and present the most general quantum hamiltonian with one- and two-body interactions, constructed from the SU(2) generators. We perform the classical limit of the hamiltonian and show a numerical study of several particular examples. Keywords: dynamical symmetries, Lipkin model, su(2) algebra, quasispin
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Precursors of phase transitions in quantum systems
Dvořák, Martin ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
In this diploma thesis precursors of quantum phase transitions in finite many-body systems are studied. The main attention is paid to the mechanism, how nonanalytic behaviour of the ground state is generated for certain critical values of real control parameters. It is shown that nonanalytic behaviour of energy levels and eigenstates is closely connected with exceptional points of the hamiltonian, which are points in control parameter space extended into a complex domain where at least two eigenvalues and corresponding eigenvectors coincide. Differences in the distribution of exceptional points in the complex plane of control parameter for the first and second order phase transitions and also evolutions of the position of exceptional points with increasing particle number are discussed.
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Quasispin models in quantum physics
Zymin, Andrii ; Stránský, Pavel (advisor) ; Kloc, Michal (referee)
Title: Quasispin models in quantum physics Author: Andrii Zymin Department: Institute of Particle and Nuclear Physics Supervisor: Mgr. Pavel Stránský, Ph.D., Institute of Particle and Nuclear Physics Abstract: The use of symmetries in quantum physics helps in a deeper understanding of physical systems and simplifies numerical calculations. This thesis studies models based on the SU(2) algebra, which, in spite of their apparent simplicity, show rather rich behavior and describe a wide spectrum of physical phenomena. We review various realizations of the SU(2) algebra (namely the spin, boson, and fermion realization) and present the most general quantum hamiltonian with one- and two-body interactions, constructed from the SU(2) generators. We perform the classical limit of the hamiltonian and show a numerical study of several particular examples. Keywords: dynamical symmetries, Lipkin model, su(2) algebra, quasispin
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Dynamics of externally driven quantum systems
Dolejší, Jakub ; Cejnar, Pavel (advisor) ; Stránský, Pavel (referee)
Dynamics of externally driven quantum systems Jakub Dolejší Abstract We present the concept of an excited-state quantum phase transition and analyse its influence on the non-equilibrium dynamics after a quantum quench in the Lipkin model. We show that if the energy distribution of the initial state after the quench is centred at the critical energy, the survival probability of the initial state evolves in an anomalous way. Keywords Quantum phase transitions, Excited-state quantum phase transitions, Quantum quenches, Lipkin model 1
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Precursors of phase transitions in quantum systems
Dvořák, Martin ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
In this diploma thesis precursors of quantum phase transitions in finite many-body systems are studied. The main attention is paid to the mechanism, how nonanalytic behaviour of the ground state is generated for certain critical values of real control parameters. It is shown that nonanalytic behaviour of energy levels and eigenstates is closely connected with exceptional points of the hamiltonian, which are points in control parameter space extended into a complex domain where at least two eigenvalues and corresponding eigenvectors coincide. Differences in the distribution of exceptional points in the complex plane of control parameter for the first and second order phase transitions and also evolutions of the position of exceptional points with increasing particle number are discussed.
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