Energy correlations for a random matrix model of disordered bosons

Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the physical system determines a probability measure with support on this cone. The present paper analyzes a discrete family of such measures of exponential type, and does so in an attempt to capture, by a simple random matrix model, some generic statistical features of the characteristic frequencies of disordered bosonic quasi-particle systems. The level correlation functions of the said measures are shown to be those of a determinantal process, and the kernel of the process is expressed as a sum of bi-orthogonal polynomials. While the correlations in the bulk scaling limit are in accord with sine-kernel or GUE universality, at the low-frequency end of the spectrum an unusual type of scaling behavior is found.Comment: 20 pages, 3 figures, references adde

Correlation of creep rate with microstructural changes during high temperature creep

Creep tests were conducted on Haynes 188 cobalt-base alloy and alpha titanium. The tests on Haynes 188 were conducted at 1600 F and 1800 F for stresses from 3 to 20 ksi, and the as-received, mill-annealed results were compared to specimens given 5%, 10%, and 15% room temperature prestrains and then annealed one hour at 1800 F. The tests on alpha titanium were performed at 7,250 and 10,000 psi at 500 C. One creep test was done at 527 C and 10,000 psi to provide information on kinetics. Results for annealed titanium were compared to specimens given 10% and 20% room temperature prestrains followed by 100 hours recovery at 550 C. Electron microscopy was used to relate dislocation and precipitate structure to the creep behavior of the two materials. The results on Haynes 188 alloy reveal that the time to reach 0.5% creep strain at 1600 F increases with increasing prestrain for exposure times less than 1,000 hours, the increase at 15% prestrain being more than a factor of ten

Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from the numerical solution of the infinity-replica symmetry breaking equations which are solved using a new pseudo-spectral code which allows for very accurate results. With this methods we are able to get more insight into the analytical properties of the solutions. We are also able to determine numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T --> 0} x_{max}(T) > 0.5.Comment: 15 pages, 11 figures, RevTeX 4.

Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model

The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz corresponds to require Becchi-Rouet-Stora-Tyutin supersymmetry. The complexity computed this way is the Legendre transform of the free energy averaged over the quenched disorder. The stability analysis shows that this complexity is inconsistent at any free energy level but the equilibirum one. The further problem of building a physically well defined solution not invariant under supersymmetry and predicting an extensive number of metastable states is also discussed.Comment: 19 pages, 13 figures. Some formulas added corrected, changes in discussion and conclusion, one figure adde

Entanglement of random vectors

We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size and for arbitrary bipartite splitting as an implicit function of index i.Comment: 8 page

Calculation of the unitary part of the Bures measure for N-level quantum systems

We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the sampling of random states through the generation of random unitary matrices