![]() ![]() These conditions define critical values of the nuclear interaction parameters at which a ground-state energy second-order phase transition occurs and the critical temperature at which a thermodynamic second-order phase transition occurs. Concise conditions are given for the occurrence of a second-order phase transition of either type. Thermodynamic phase transitions are determined by investigating how the minima of the potential Phi change as a function of changing nuclear temperature. Groundstate energy phase transitions are determined by investigating how the minima of the potential hc change as a function of changing nuclear interaction parameters. These potentials are constructed very simply from the pseudospin Hamiltonian. ![]() The values of Eg/N and F(beta)/N are obtained by computing the minimum value of associated potential functions hc and Phi. A simple algorithm is developed for computing Eg/N, F(beta)/N and S/N (entropy per nucleon) exactly in the N -> ∞ limit. In the limit of large numbers of nucleons these bounds become equal. #Boson x steam stage edit freeUpper and lower bounds on the ground-state energy per nucleon Eg/N and the free energy per nucleon F(beta)/N are constructed for nuclear systems described by pseudospin Hamiltonians. Effects of kinetic collective rotational terms, which mayĭisrupt this simple pattern, are considered. QDS characterization of the remaining regularity, appear to be robust The pattern of mixed but well-separated dynamics and the PDS or Partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), Symmetry analysis of their wave functions shows that they are associated with Regular subsets of states retain their identity amidst a complicatedĮnvironment of other states and both occur in the coexistence region. Spherical region, and regular SU(3)-like rotational bands extending to highĮnergies and angular momenta, in the deformed region. A quantumĪnalysis discloses a number of regular low-energy U(5)-like multiplets in the Traces the crossing of the two minima in the Landau potential. Of mixed but well-separated dynamics persists in the coexistence region and Robustly regular dynamics ascribed to the deformed minimum. ![]() H\'enon-Heiles type of chaotic dynamics ascribed to the spherical minimum and a A~classical analysis of the intrinsicĭynamics reveals a rich but simply-divided phase space structure with a The interacting boson model Hamiltonian employed,ĭescribes a QPT between spherical and deformed shapes, associated with its U(5)Īnd SU(3) dynamical symmetry limits. We present a comprehensive analysis of the emerging order and chaos andĮnduring symmetries, accompanying a generic (high-barrier) first-order quantum Measures of chaos, but for small number of bosons and states with angular Using classical measures of chaos, as well as with studies using statistical Study of chaos using statistical measures are consistent with previous studies The position of the arc of regularity was alsoįound to be stable in the limit of large boson numbers. The energy dependence of chaos is provided for the first time using Transition intensities of 0 states in the framework of the interacting boson Statistical measures of chaos are applied on the spectrum and the ![]() Using statistical measures with those of the study of chaos using classical Vicinity of the arc of regularity and link the results of the study of chaos Provide complete quantum chaotic dynamics at zero angular momentum in the Number of bosons renders additional studies of chaos possible, that can provideĪ direct comparison with similar classical studies of chaos. Statistical measures of chaos have long been used in the study of chaoticĭynamics in the framework of the interacting boson model. The features studied here are inherent in a great majority of interacting boson systems. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a nontrivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. The intrinsic Hamiltonian formalism with angular momentum fixed to L=0 is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. #Boson x steam stage edit seriesThe series of articles devoted to excited-state quantum phase transitions (ESQPTs) in systems with f=2 degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. ![]()
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