arXiv subjects
Publications and source records attributed to A. Leviatan.
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of first-order with an arbitrary barrier.
Properties of quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Special emphasis is paid to the dynamics at the critical-point of a general first-order phase transition.
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states corresponding to two degenerate minima in the energy surface separated by an arbitrary barrier. Explicit expressions are derived for wave functions and observables at the critical-point.
X(5) is a paradigm for the structure at the critical point of a particular first-order phase transition for which the intrinsic energy surface has two degenerate minima separated by a low barrier. For a finite system, we show that the dynamics at such a critical point can be described by an effective deformation determined by minimizing the energy surface after projection onto angular momentum zero, and combined with two-level mixing. Wave functions of a particular analytic form are used to derive estimates for energies and quadrupole rates at the critical point.
Relativistic symmetries of the Dirac Hamiltonian with a mixture of spherically symmetric Lorentz scalar and vector potentials, are examined from the point of view of supersymmetric quantum mechanics. The cases considered include the Coulomb, pseudospin and spin limits relevant, respectively, to atoms, nuclei and hadrons.
Shell-model states involving several pseudospin doublets and ``intruder'' levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
We show that the Dirac equation in 3+1 dimensions gives rise to supersymmetric patterns when the scalar and vector potentials are (i) Coulombic with arbitrary strengths or (ii) when their sum or difference is a constant, leading to relativistic pseudospin and spin symmetries. The conserved quantities and the common intertwining relation responsible for such patterns are discussed.
Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints.
We introduce the notion of a partial dynamical symmetry for which a prescribed symmetry is neither exact nor completely broken. We survey the different types of partial dynamical symmetries and present empirical examples in each category.
We consider properties of critical points in the interacting boson model, corresponding to flat-bottomed potentials as encountered in a second-order phase transition between spherical and deformed $γ$-unstable nuclei. We show that intrinsic states with an effective $β$-deformation reproduce the dynamics of the underlying non-rigid shapes. The effective deformation can be determined from the the global minimum of the energy surface after projection onto the appropriate symmetry. States of fixed $N$ and good O(5) symmetry projected from these intrinsic states provide good analytic estimates to the exact eigenstates, energies and quadrupole transition rates at the critical point.
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can describe the dynamics at the critical point. This effective deformation is determined by minimizing the energy surface after projection onto the appropriate symmetries. We derive analytic expressions for energies and quadrupole rates which provide good estimates for these observables at the critical point.
Explicit forms of IBM Hamiltonians with a generalized partial dynamical O(6) symmetry are presented and compared with empirical data in $^{162}$Dy.
We introduce the notion of a generalized partial dynamical symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in $^{162}$Dy.
A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed-symmetry states is considered within the proton-neutron interacting boson model of even-even nuclei. Analytic expressions for the dominant terms in the B(M1) transition rates from the first and second $2^+$ states are derived in the U(5) and SO(6) dynamic symmetry limits of the model, and the applicability of a sum rule approach is examined at and in-between these limits. Lastly, the sum rule is applied to the new data on mixed-symmetry states of 94Mo and a quadrupole d-boson ratio $nd(0^+_1)/nd(2^+_2) \approx 0.6$ is obtained in a largely parameter-independent way
We review recent developments that show that pseudospin symmetry is an approximate relativistic symmetry of the Dirac Hamiltonian with realistic nuclear mean field potentials.
We show that a natural explanation for characteristic features (angular momentum and radial quantum numbers) of pseudospin doublets and intruder levels in nuclei can be obtained by combining the relativistic attributes of pseudospin symmetry with known properties of Dirac bound states.
The identification of pseudospin symmetry as a relativistic symmetry of the Dirac Hamiltonian is used to explain the structure of radial nodes occurring in pseudospin doublets and to illuminate the special status of nodeless intruder states in nuclei.
Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.