14,557 research outputs found
Nearest-Neighbor Distributions and Tunneling Splittings in Interacting Many-Body Two-Level Boson Systems
We study the nearest-neighbor distributions of the -body embedded
ensembles of random matrices for bosons distributed over two-degenerate
single-particle states. This ensemble, as a function of , displays a
transition from harmonic oscillator behavior () to random matrix type
behavior (). We show that a large and robust quasi-degeneracy is present
for a wide interval of values of when the ensemble is time-reversal
invariant. These quasi-degenerate levels are Shnirelman doublets which appear
due to the integrability and time-reversal invariance of the underlying
classical systems. We present results related to the frequency in the spectrum
of these degenerate levels in terms of , and discuss the statistical
properties of the splittings of these doublets.Comment: 13 pages (double column), 7 figures some in color. The movies can be
obtained at http://link.aps.org/supplemental/10.1103/PhysRevE.81.03621
Fidelity decay in interacting two-level boson systems: Freezing and revivals
We study the fidelity decay in the -body embedded ensembles of random
matrices for bosons distributed in two single-particle states, considering the
reference or unperturbed Hamiltonian as the one-body terms and the diagonal
part of the -body embedded ensemble of random matrices, and the perturbation
as the residual off-diagonal part of the interaction. We calculate the
ensemble-averaged fidelity with respect to an initial random state within
linear response theory to second order on the perturbation strength, and
demonstrate that it displays the freeze of the fidelity. During the freeze, the
average fidelity exhibits periodic revivals at integer values of the Heisenberg
time . By selecting specific -body terms of the residual interaction,
we find that the periodicity of the revivals during the freeze of fidelity is
an integer fraction of , thus relating the period of the revivals with the
range of the interaction of the perturbing terms. Numerical calculations
confirm the analytical results
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