1,020 research outputs found
Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons
We investigate the shape of the spectrum and the spectral fluctuations of the
-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the
number of Bosons while both , the rank of the interaction,
and , the number of single-particle states, are kept fixed. We show that the
relative fluctuations of the low spectral moments do not vanish in this limit,
proving that the ensemble is non-ergodic. Numerical simulations yield spectra
which display a strong tendency towards picket-fence type. The wave functions
also deviate from canonical random-matrix behaviourComment: 7 pages, 5 figures, uses epl.cls (included
Wigner--Dyson statistics for a class of integrable models
We construct an ensemble of second--quantized Hamiltonians with two bosonic
degrees of freedom, whose members display with probability one GOE or GUE
statistics. Nevertheless, these Hamiltonians have a second integral of motion,
namely the boson number, and thus are integrable. To construct this ensemble we
use some ``reverse engineering'' starting from the fact that --bosons in a
two--level system with random interactions have an integrable classical limit
by the old Heisenberg association of boson operators to actions and angles. By
choosing an --body random interaction and degenerate levels we end up with
GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.Comment: 3 pages, 1 figur
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
On The Critical Casimir Interaction Between Anisotropic Inclusions On A Membrane
Using a lattice model and a versatile thermodynamic integration scheme, we study the critical Casimir interactions between inclusions embedded in a two-dimensional critical binary mixtures. For single-domain inclusions we demonstrate that the interactions are very long range, and their magnitudes strongly depend on the affinity of the inclusions with the species in the binary mixtures, ranging from repulsive when two inclusions have opposing affinities to attractive when they have the same affinities. When one of the inclusions has no preference for either of the species, we find negligible critical Casimir interactions. For multiple-domain inclusions, mimicking the observations that membrane proteins often have several domains with varying affinities to the surrounding lipid species, the presence of domains with opposing affinities does not cancel the interactions altogether. Instead we can observe both attractive and repulsive interactions depending on their relative orientations. With increasing number of domains per inclusion, the range and magnitude of the effective interactions decrease in a similar fashion to those of electrostatic multipoles. Finally, clusters formed by multiple-domain inclusions can result in an effective affinity patterning due to the anisotropic character of the Casimir interactions between the building blocks
Fluctuations of wave functions about their classical average
Quantum-classical correspondence for the average shape of eigenfunctions and
the local spectral density of states are well-known facts. In this paper, the
fluctuations that quantum mechanical wave functions present around the
classical value are discussed. A simple random matrix model leads to a Gaussian
distribution of the amplitudes. We compare this prediction with numerical
calculations in chaotic models of coupled quartic oscillators. The expectation
is broadly confirmed, but deviations due to scars are observed.Comment: 9 pages, 6 figures. Sent to J. Phys.
Effect of phase relaxation on quantum superpositions in complex collisions
We study the effect of phase relaxation on coherent superpositions of
rotating clockwise and anticlockwise wave packets in the regime of strongly
overlapping resonances of the intermediate complex. Such highly excited
deformed complexes may be created in binary collisions of heavy ions, molecules
and atomic clusters. It is shown that phase relaxation leads to a reduction of
the interference fringes, thus mimicking the effect of decoherence. This
reduction is crucial for the determination of the phase--relaxation width from
the data on the excitation function oscillations in heavy--ion collisions and
bimolecular chemical reactions. The difference between the effects of phase
relaxation and decoherence is discussed.Comment: Extended revised version; 9 pages and 3 colour ps figure
Level Repulsion in Constrained Gaussian Random-Matrix Ensembles
Introducing sets of constraints, we define new classes of random-matrix
ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian
unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE.
We derive a sufficient condition for GUE-type level repulsion to persist in the
presence of constraints. For special classes of constraints, we extend this
approach to the orthogonal and to the symplectic ensembles. A generalized
Fourier theorem relates the spectral properties of the constraining ensembles
with those of the constrained ones. We find that in the DGUEs, level repulsion
always prevails at a sufficiently short distance and may be lifted only in the
limit of strictly enforced constraints.Comment: 20 pages, no figures. New section adde
- âŠ