372 research outputs found
Disordered mesoscopic systems with interactions: induced two-body ensembles and the Hartree-Fock approach
We introduce a generic approach to study interaction effects in diffusive or
chaotic quantum dots in the Coulomb blockade regime. The randomness of the
single-particle wave functions induces randomness in the two-body interaction
matrix elements. We classify the possible induced two-body ensembles, both in
the presence and absence of spin degrees of freedom. The ensembles depend on
the underlying space-time symmetries as well as on features of the two-body
interaction. Confining ourselves to spinless electrons, we then use the
Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF
wave functions for many realizations of the ensemble. We study the statistical
properties of the resulting one-body HF ensemble for a fixed number of
electrons. In particular, we determine the statistics of the interaction matrix
elements in the HF basis, of the HF single-particle energies (including the HF
gap between the last occupied and the first empty HF level), and of the HF
single-particle wave functions. We also study the addition of electrons, and in
particular the distribution of the distance between successive conductance
peaks and of the conductance peak heights.Comment: 25 pages, 16 figure
Statistical Fluctuations of Electromagnetic Transition Intensities in pf-Shell Nuclei
We study the fluctuation properties of E2 and M1 transition intensities among
T=0,1 states of A = 60 nuclei in the framework of the interacting shell model,
using a realistic effective interaction for pf-shell nuclei with a Ni56 as a
core. It is found that the B(E2) distributions are well described by the
Gaussian orthogonal ensemble of random matrices (Porter-Thomas distribution)
independently of the isobaric quantum number T_z. However, the statistics of
the B(M1) transitions is sensitive to T_z: T_z=1 nuclei exhibit a Porter-Thomas
distribution, while a significant deviation from the GOE statistics is observed
for self-conjugate nuclei (T_z=0).Comment: 8 pages, latex, 3 figures (ps format
Recent developments in the shell model Monte Carlo approach to nuclei
The shell model Monte Carlo (SMMC) approach provides a powerful method for
the microscopic calculation of statistical and collective nuclear properties in
model spaces that are many orders of magnitude larger than those that can be
treated by conventional methods. We discuss recent applications of the method
to describe the emergence of collectivity in the framework of the
configuration-interaction shell model and the crossover from vibrational to
rotational collectivity in families of rare-earth nuclei. We have calculated
state densities of these rare-earth nuclei and find their collective
enhancement factors to be correlated with the pairing and shape phase
transitions. We also discuss an accurate method to calculate the ground-state
energy of odd-even and odd-odd nuclei, circumventing the sign problem that
originates in the projection on an odd number of particles. We have applied
this method to calculate pairing gaps in families of isotopes in the iron
region.Comment: 7 pages, 5 figures, Proceedings of Horizons of Innovative Theories,
Experiments, and Supercomputing in Nuclear Physics (HITES 2012
Statistical Fluctuations of Electromagnetic Transition Intensities and Electromagnetic Moments in pf-Shell Nuclei
We study the fluctuation properties of electromagnetic
transition intensities and electromagnetic moments in nuclei within
the framework of the interacting shell model, using a realistic effective
interaction for
-shell nuclei with a Ni core. The distributions of the transition
intensities and of the electromagnetic moments are well described by the
Gaussian orthogonal ensemble of random matrices. In particular, the transition
intensity distributions follow a Porter-Thomas distribution. When diagonal
matrix elements (i.e., moments) are included in the analysis of transition
intensities, we find that the distributions remain Porter-Thomas except for the
isoscalar . The latter deviation is explained in terms of the structure of
the isoscalar operator.Comment: 11 pages, 4 figure
Spin-orbit interaction in quantum dots in the presence of exchange correlations
We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive
quantum dot in the presence of exchange correlations. Spin-orbit scattering
breaks spin rotation invariance, and in the crossover regime between different
symmetries of the spin-orbit coupling, the problem has no closed solution. A
conventional choice of a many-particle basis in a numerical diagonalization is
the set of Slater determinants built from the single-particle eigenstates of
the one-body Hamiltonian (including the spin-orbit terms). We develop a
different approach based on the use of a good-spin many-particle basis that is
composed of the eigenstates of the universal Hamiltonian in the absence of
spin-orbit scattering. We introduce a complete labelling of this good-spin
basis and use angular momentum algebra to calculate in closed form the matrix
elements of the spin-orbit interaction in this basis. Spin properties, such as
the ground-state spin distribution and the spin excitation function, are easily
calculated in this basis.Comment: 14 pages, 3 figure
Generalized Morse and Poschl-Teller potentials : The connection via Schrodinger equation
We present here a systematic and unified treatment to connect the Schrodinger
equation corresponding to generalized Morse and Poschl-Teller potentials. We
then show that the wave functions and generalized potentials are linked through
the Fourier and Hankel transforms, respectively.Comment: 17 pages, 0 figure
Exact Dynamical and Partial Symmetries
We discuss a hierarchy of broken symmetries with special emphasis on partial
dynamical symmetries (PDS). The latter correspond to a situation in which a
non-invariant Hamiltonian accommodates a subset of solvable eigenstates with
good symmetry, while other eigenstates are mixed. We present an algorithm for
constructing Hamiltonians with this property and demonstrate the relevance of
the PDS notion to nuclear spectroscopy, to quantum phase transitions and to
mixed systems with coexisting regularity and chaos.Comment: 10 pages, 5 figures, Proc. GROUP28: The XXVIII Int. Colloquium on
Group-Theoretical Methods in Physics, July 26-30, 2010, Newcastle upon Tyne,
U
Scaling Properties of the Giant Dipole Resonance Width in Hot Rotating nuclei
We study the systematics of the giant dipole resonance width in hot
rotating nuclei as a function of temperature , spin and mass . We
compare available experimental results with theoretical calculations that
include thermal shape fluctuations in nuclei ranging from A=45 to A=208. Using
the appropriate scaled variables, we find a simple phenomenological function
which approximates the global behavior of the giant dipole
resonance width in the liquid drop model. We reanalyze recent experimental and
theoretical results for the resonance width in Sn isotopes and Pb.Comment: LaTeX, 4 pages with 4 figures (to appear in Phys. Rev. Lett.
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