arXiv subjects

H. N. Deota

Publications and source records attributed to H. N. Deota.

3 recordsLinked to original sources

arXiv2021

Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles

The probability distribution of the closest neighbor and farther neighbor spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded GOE of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a $3 \times 3$ random matrix model and other related quantities by Srivastava et. al [{\it J. Phys. A: Math. Theor.} {\bf 52} 025101 (2019)]. This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.

cond-mat.stat-mech↗

arXiv2014

Poisson to GOE transition in the distribution of the ratio of consecutive level spacings

Probability distribution for the ratio ($r$) of consecutive level spacings of the eigenvalues of a Poisson (generating regular spectra) spectrum and that of a GOE random matrix ensemble are given recently. Going beyond these, for the ensemble generated by the Hamiltonian $H_λ= (H_0+λV)/\sqrt{1+λ^2}$ interpolating Poisson ($λ=0$) and GOE ($λ\rightarrow \infty$) we have analyzed the transition curves for $\langle r\rangle$ and $\langle \tilde{r}\rangle$ as $λ$ changes from $0$ to $\infty$; $\tilde{r} = min(r,1/r)$. Here, $V$ is a GOE ensemble of real symmetric $d \times d$ matrices and $H_0$ is a diagonal matrix with a Gaussian distribution (with mean equal to zero) for the diagonal matrix elements; spectral variance generated by $H_0$ is assumed to be same as the one generated by $V$. Varying $d$ from 300 to 1000, it is shown that the transition parameter is $Λ\sim λ^2\,d$, i.e. the $\langle r\rangle$ vs $λ$ (similarly for $\langle \tilde{r}\rangle$ vs $λ$) curves for different $d$'s merge to a single curve when this is considered as a function of $Λ$. Numerically, it is also found that this transition curve generates a mapping to a $3 \times 3$ Poisson to GOE random matrix ensemble. Example for Poisson to GOE transition from a one dimensional interacting spin-1/2 chain is presented.

cond-mat.stat-mech↗

arXiv2012

Random matrix ensemble with random two-body interactions in presence of a mean-field for spin one boson systems

For $m$ number of bosons, carrying spin ($S$=1) degree of freedom, in $Ω$ number of single particle orbitals, each triply degenerate, we introduce and analyze embedded Gaussian orthogonal ensemble of random matrices generated by random two-body interactions that are spin (S) scalar [BEGOE(2)-$S1$]. The embedding algebra is $U(3) \supset G \supset G1 \otimes SO(3)$ with SO(3) generating spin $S$. A method for constructing the ensembles in fixed-($m$, $S$) space has been developed. Numerical calculations show that the form of the fixed-($m$, $S$) density of states is close to Gaussian and level fluctuations follow GOE. Propagation formulas for the fixed-($m$, $S$) space energy centroids and spectral variances are derived for a general one plus two-body Hamiltonian preserving spin. In addition to these, we also introduce two different pairing symmetry algebras in the space defined by BEGOE(2)-$S1$ and the structure of ground states is studied for each paring symmetry.

nlin.CD↗