Related papers: Random matrix ensembles with random interactions: …
Recently Pluhar and Weidenmueller [Ann. Phys. (N.Y.) Vol 297, 344 (2002)] showed that the eigenvectors of the matrix of second moments of embedded Gaussian unitary ensemble of random matrices generated by k-body interactions (EGUE(k)) for m…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…
For $m$ number of bosons, carrying spin ($S$=1) degree of freedom, in $\Omega$ number of single particle orbitals, each triply degenerate, we introduce and analyze embedded Gaussian orthogonal ensemble of random matrices generated by random…
Following the earlier studies on embedded unitary ensembles generated by random two-body interactions [EGUE(2)] with spin SU(2) and spin-isospin SU(4) symmetries, developed is a general formulation, for deriving lower order moments of the…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
In finite many-body quantum systems such as nuclei, atoms, mesoscopic systems like quantum dots and small metallic grains, interacting spin systems modeling quantum computing core and BEC, the interparticle interactions are essentially…
For $m$ number of bosons, carrying spin ($\cs=\spin$) degree of freedom, in $\Omega$ number of single particle orbitals, each doubly degenerate, we introduce and analyze embedded Gaussian orthogonal ensemble of random matrices generated by…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
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…
The random matrix ensembles (RME), especially Gaussian RME and Ginibre RME, are applied to nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart…
A new class of Random Matrix Ensembles is introduced. The Gaussian orthogonal, unitary, and symplectic ensembles GOE, GUE, and GSE, of random matrices are analogous to the classical Gibbs ensemble governed by Boltzmann's distribution in the…
We extend the recent study of the k-body embedded Gaussian ensembles by Benet et al. (Phys. Rev. Lett. 87 (2001) 101601-1 and Ann. Phys. 292 (2001) 67) and by Asaga et al. (cond-mat/0107363 and cond-mat/ 0107364). We show that central…
One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-$\pi$] generated by a random two-body interaction (modeled by GOE in two particle spaces) in the presence of a mean-field, for spinless…
Embedded random matrix ensembles with $k$-body interactions are well established to be appropriate for many quantum systems. For these ensemble the two point correlation function is not yet derived though these ensembles are introduced 50…
Eigenvalue density generated by embedded Gaussian unitary ensemble with $k$-body interactions for two species (say $\mathbf{\pi}$ and $\mathbf{\nu}$) fermion systems is investigated by deriving formulas for the lowest six moments. Assumed…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
The embedded ensembles were introduced by Mon and French as physically more plausible stochastic models of many--body systems governed by one--and two--body interactions than provided by standard random--matrix theory. We review several…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…