Michal Macek

Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei

Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.

Coulomb analogy for non-Hermitian degeneracies near quantum phase transitions.

Degeneracies near the real axis in a complex-extended parameter space of a Hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.

Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. I. Level dynamics

We investigate the evolution of quantal spectra and the corresponding wave functions along the [O(6)-U(5)] superset of O(5) transition of the interacting boson model. The model is integrable in this regime, and its ground state passes through a second-order structural phase transition. We show that the whole spectrum as a function of the Hamiltonian control parameter as well as structures of all excited states exhibit rather organized and correlated behaviors, which provide deeper insight into the nature of this transitional path.

Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. II. Classical trajectories

We continue our previous study of level dynamics in the [O(6)-U(5)] superset of O(5) transition of the interacting boson model [Phys. Rev. C 73, 014306 (2006)] by using the semiclassical theory of spectral fluctuations. We find classical monodromy, related to a singular bundle of orbits with infinite period at energy E=0, and bifurcations of numerous periodic orbits for E>0. The spectrum of allowed ratios of periods associated with {beta} and {gamma} vibrations exhibits an abrupt change around zero energy. These findings explain anomalous bunching of quantum states in the E{approx_equal}0 region, which is responsible for the redistribution of levels between O(6) and U(5) multiplets.

Evolution of order and chaos across a first-order quantum phase transition

Abstract We study the evolution of the dynamics across a generic first-order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robustly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective rotational terms on this intricate interplay of order and chaos is investigated.

Regularity and chaos at critical points of first-order quantum phase transitions

We study the interplay between regular and chaotic dynamics at the critical point of a generic first-order quantum phase transition in an interacting boson model of nuclei. A classical analysis reveals a distinct behavior of the coexisting phases in a broad energy range. The dynamics is completely regular in the deformed phase and, simultaneously, strongly chaotic in the spherical phase. A quantum analysis of the spectra separates the regular states from the irregular ones, assigns them to particular phases, and discloses persisting regular rotational bands in the deformed region.

Chaotic dynamics in collective models of nuclei

We present results of an extensive analysis of classical and quantum signatures of chaos in the geometric collective model (GCM) and the interacting boson model (IBM) of nuclei. Apart from comparing the regular fraction of the classical phase space and the Brody parameter for the nearest neighbor spacing distribution in the quantum case, we also adopt (i) the Peres lattices allowing one to distinguish ordered and disordered parts of spectra and to reveal main ordering principles of quantum states, (ii) the geometrical method to determine the position where the transition from order to chaos occurs, and (iii) we look for the 1/fα power law in the power spectrum of energy level fluctuations. The Peres method demonstrates the adiabatic separation of collective rotations in the IBM.

Regular and Chaotic Collective Modes in Nuclei

Atomic nuclei constitute an exemplary realization of chaotic dynamics in the quantum domain. These dense clouds of strongly interacting particles were at the dawn of the field of physics called quantum chaos [1, 2]. In the 1980s, when its fundamentals were formulated, the field might be seen just as an exotic branch of quantum mechanics, but the present rapid growth of “quantum technologies” gives it a more practical potential.

Order and chaos in the geometric collective model

We investigate collective vibrations and rotations of atomic nuclei from the classical viewpoint within the geometric collective model. We quantify the proportion of regular and chaotic orbits in the phase space, observing very complex behavior of its dependence on the model control parameters, energy, and angular momentum.

COEXISTENCE OF ORDER AND CHAOS AT CRITICAL POINTS OF FIRST-ORDER QUANTUM PHASE TRANSITIONS IN NUCLEI

We study the interplay between ordered and chaotic dynamics at the critical point of a generic first-order quantum phase transition in the interacting boson model of nuclei. Classical and quantum analyses reveal a distinct behavior of the coexisting phases. While the dynamics in the deformed phase is robustly regular, the spherical phase shows strongly chaotic behavior in the same energy intervals. The effect of collective rotations on the dynamics is investigated.