V. K. B. Kota

Thermalization in the two-body random ensemble

Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos. By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space. We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable. As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems. When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators. Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.

Bivariate distributions in statistical spectroscopy studies: IV. Interacting particle Gamow-Teller strength densities and β-decay rates offp-shell nuclei for presupernova stars

AbstractA method to calculate temperature dependentβ-decay rates is developed by writing the expression for the rates explicitly in terms of bivariateGT strength densities (IOH(GT)) for a given hamiltonianH=h+V and state densities of the parent nucleus besides having the usual phase space factors. The theory developed in the preceding paper (III) for constructing NIP strength densities is applied for generatingIOh(GT) and thenIOH(GT) is constructed using the bivariate convolution formIOH(GT)=ΣSIO(GT)h,S⊗ρO(GT)V,S;BIV-G. The spreading bivariate Gaussian ρO(GT)V;BIV-G, forfp-shell nuclei, is constructed by assuming that the marginal centroids are zero, the marginal variances are same as the corresponding state density variances and fixing the bivariate correlation coefficient

Bivariate distributions in statistical spectroscopy studies: III. Non interacting particle strength densities for one-body transition operators

\bar \zeta

Bivariate distributions in statistical spectroscopy studies

using experimentalβ-decay half lifes. With the deduced values of

Random matrix structure of nuclear shell model Hamiltonian matrices and comparison with an atomic example

\bar \zeta