arXiv subjects

Luis Benet

Publications and source records attributed to Luis Benet.

22 records · Page 2Linked to original sources

arXiv2010

Nearest-Neighbor Distributions and Tunneling Splittings in Interacting Many-Body Two-Level Boson Systems

We study the nearest-neighbor distributions of the $k$-body embedded ensembles of random matrices for $n$ bosons distributed over two-degenerate single-particle states. This ensemble, as a function of $k$, displays a transition from harmonic oscillator behavior ($k=1$) to random matrix type behavior ($k=n$). We show that a large and robust quasi-degeneracy is present for a wide interval of values of $k$ 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 $k$, and discuss the statistical properties of the splittings of these doublets.

nlin.CD↗

arXiv2007

Slow cross-symmetry phase relaxation in complex collisions

We discuss the effect of slow phase relaxation and the spin off-diagonal $S$-matrix correlations on the cross section energy oscillations and the time evolution of the highly excited intermediate systems formed in complex collisions. Such deformed intermediate complexes with strongly overlapping resonances can be formed in heavy ion collisions, bimolecular chemical reactions and atomic cluster collisions. The effects of quasiperiodic energy dependence of the cross sections, coherent rotation of the hyperdeformed $\simeq (3:1)$ intermediate complex, Schrödinger cat states and quantum-classical transition are studied for $^{24}$Mg+$^{28}$Si heavy ion scattering.

quant-ph↗

arXiv2001

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

We consider $m$ spinless Fermions in $l > m$ degenerate single-particle levels interacting via a $k$-body random interaction with Gaussian probability distribution and $k <= m$ in the limit $l$ to infinity (the embedded $k$-body random ensembles). We address the cases of orthogonal and unitary symmetry. We derive a novel eigenvalue expansion for the second moment of the Hilbert-space matrix elements of these ensembles. Using properties of the expansion and the supersymmetry technique, we show that for $2k > m$, the average spectrum has the shape of a semicircle, and the spectral fluctuations are of Wigner-Dyson type. Using a generalization of the binary correlation approximation, we show that for $k << m << l$, the spectral fluctuations are Poissonian. This is consistent with the case $k = 1$ which can be solved explicitly. We construct limiting ensembles which are either fully integrable or fully chaotic and show that the $k$-body random ensembles lie between these two extremes. Combining all these results we find that the spectral correlations for the embedded ensembles gradually change from Wigner-Dyson for $2k > m$ to Poissonian for $k << m << l$.

cond-mat↗

arXiv2001

Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices

Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and Gaussian shape. The transition also affects the spectral fluctuations which deviate from Wigner-Dyson form and become Poissonian in the limit $k << m << l$. Here $m$ is the number of Fermions and $l$ the number of degenerate single-particle states.

cond-mat↗