9,112 research outputs found
Loschmidt echoes in two-body random matrix ensembles
Fidelity decay is studied for quantum many-body systems with a dominant
independent particle Hamiltonian resulting e.g. from a mean field theory with a
weak two-body interaction. The diagonal terms of the interaction are included
in the unperturbed Hamiltonian, while the off-diagonal terms constitute the
perturbation that distorts the echo. We give the linear response solution for
this problem in a random matrix framework. While the ensemble average shows no
surprising behavior, we find that the typical ensemble member as represented by
the median displays a very slow fidelity decay known as ``freeze''. Numerical
calculations confirm this result and show, that the ground state even on
average displays the freeze. This may contribute to explanation of the
``unreasonable'' success of mean field theories.Comment: 9 pages, 5 figures (6 eps files), RevTex; v2: slight modifications
following referees' suggestion
1/f noise in the Two-Body Random Ensemble
We show that the spectral fluctuations of the Two-Body Random Ensemble (TBRE)
exhibit 1/f noise. This result supports a recent conjecture stating that
chaotic quantum systems are characterized by 1/f noise in their energy level
fluctuations. After suitable individual averaging, we also study the
distribution of the exponent \alpha in the 1/f^{\alpha} noise for the
individual members of the ensemble. Almost all the exponents lie inside a
narrow interval around \alpha=1 suggesting that also individual members exhibit
1/f noise, provided they are individually unfoldedComment: 4 pages, 3 figures, Accepted for publication in Phys. Rev.
Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions
Using a fermionic renormalization group approach we analyse a model where the
electrons diffusing on a quantum dot interact via Fermi-liquid interactions.
Describing the single-particle states by Random Matrix Theory, we find that
interactions can induce phase transitions (or crossovers for finite systems) to
regimes where fluctuations and collective effects dominate at low energies.
Implications for experiments and numerical work on quantum dots are discussed.Comment: 4 pages, 1 figure; version to appear in Phys Rev Letter
Shell model study of the pairing correlations
A systematic study of the pairing correlations as a function of temperature
and angular momentum has been performed in the sd-shell region using the
spherical shell model approach. The pairing correlations have been derived for
even-even, even-odd and odd-odd systems near N=Z and also for the asymmetric
case of N=Z+4. The results indicate that the pairing content and the behavior
of pair correlations is similar in even-even and odd-mass nuclei. For odd-odd
N=Z system, angular momentum I=0 state is an isospin, t=1 neutron-proton paired
configuration. Further, these t=1 correlations are shown to be dramatically
reduced for the asymmetric case of N=Z+4. The shell model results obtained are
qualitatively explained within a simplified degenerate model
Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit
We show that problem of interacting electrons in a quantum dot with chaotic
boundary conditions is solvable in the large-g limit, where g is the
dimensionless conductance of the dot. The critical point of the
theory (whose location and exponent are known exactly) that separates strong
and weak-coupling phases also controls a wider fan-shaped region in the
coupling-1/g plane, just as a quantum critical point controls the fan in at
T>0. The weak-coupling phase is governed by the Universal Hamiltonian and the
strong-coupling phase is a disordered version of the Pomeranchuk transition in
a clean Fermi liquid. Predictions are made in the various regimes for the
Coulomb Blockade peak spacing distributions and Fock-space delocalization
(reflected in the quasiparticle width and ground state wavefunction).Comment: 4 pages, 2 figure
Statistical Theory of Parity Nonconservation in Compound Nuclei
We present the first application of statistical spectroscopy to study the
root-mean-square value of the parity nonconserving (PNC) interaction matrix
element M determined experimentally by scattering longitudinally polarized
neutrons from compound nuclei. Our effective PNC interaction consists of a
standard two-body meson-exchange piece and a doorway term to account for
spin-flip excitations. Strength functions are calculated using realistic
single-particle energies and a residual strong interaction adjusted to fit the
experimental density of states for the targets, ^{238} U for A\sim 230 and
^{104,105,106,108} Pd for A\sim 100. Using the standard Desplanques, Donoghue,
and Holstein estimates of the weak PNC meson-nucleon coupling constants, we
find that M is about a factor of 3 smaller than the experimental value for
^{238} U and about a factor of 1.7 smaller for Pd. The significance of this
result for refining the empirical determination of the weak coupling constants
is discussed.Comment: Latex file, no Fig
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