arXiv subjects

V. K. B. Kota

Publications and source records attributed to V. K. B. Kota.

At least 55 records · Page 3Linked to original sources

arXiv2015

Many-body entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons

We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of $N=10$ interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schrödinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information entropy approaches the value predicted for the Gaussian orthogonal ensemble of random matrices and implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a non-trivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the build-up of correlations and loss of coherence in the system. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. Our results are the first ones obtained for thermalization of finite quantum systems using an optimized time-dependent and genuinely many-body basis set.

cond-mat.quant-gas↗

arXiv2015

Random Matrix Theory for Transition Strength Densities in Finite Quantum Systems: Results from Embedded Unitary Ensembles

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 and interacting via $k$-body interactions, we have EGUE($k$) and the embedding algebra is $U(N)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (same initial and final systems), nuclear beta and double beta decay (different initial and final systems), particle addition to/removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities, we have derived formulas for lower order bivariate moments of the strength densities generated by a variety of transition operators. For a spinless fermion system, using EGUE($k$) representation for Hamiltonian and an independent EGUE($t$) representation for transition operator, finite-$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. Moments formulas are also derived for transition operator that removes $k_0$ number of particles from $m$ fermion system. Numerical results obtained using the exact formulas for two-body ($k=2$) Hamiltonians (in some examples for $k=3,4$) and the asymptotic formulas clearly establish that in general the smoothed form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.

quant-ph↗

arXiv2015

Deformed shell model results for neutrinoless double beta decay of nuclei in A=60-90 region

Nuclear transition matrix elements (NTME) for the neutrinoless double beta decay of $^{70}$Zn, $^{80}$Se and $^{82}$Se nuclei are calculated within the framework of the deformed shell model based on Hartree-Fock states. For $^{70}$Zn, jj44b interaction in $^{2}p_{3/2}$, $^{1}f_{5/2}$, $^{2}p_{1/2}$ and $^{1}g_{9/2}$ space with $^{56}$Ni as the core is employed. However, for $^{80}$Se and $^{82}$Se nuclei, a modified Kuo interaction with the above core and model space are employed. Most of our calculations in this region were performed with this effective interaction. However, jj44b interaction has been found to be better for $^{70}$Zn. The above model space was used in many recent shell model and interacting boson model calculations for nuclei in this region. After ensuring that DSM gives good description of the spectroscopic properties of low-lying levels in these three nuclei considered, the NTME are calculated. The deduced half-lives with these NTME, assuming neutrino mass is 1 eV, are $1.1 \times 10^{26}$ yr, $2.3 \times 10^{27}$ yr and $2.2 \times 10^{24}$ yr for $^{70}$Zn, $^{80}$Se and $^{82}$Se, respectively.

nucl-th↗

arXiv2015

Random Matrix Theory with U(N) Racah Algebra for Transition Strengths

For finite quantum many-particle systems, a given system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Working towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have started a program to derive formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. In this paper results are presented for a transition operator that removes $k_0$ number of particle by considering $m$ spinless fermions in $N$ single particle states. The Hamiltonian that is $k$-body is represented by EGUE($k$) [embedded Gaussian unitary ensemble of $k$-body interactions] and similarly the transition operator by an appropriate independent EGUE. Employing the embedding $U(N)$ algebra, finite-$N$ formulas for moments up to order four are derived and they show that in general the smoothed (with respect to energy) bivariate transition strength densities take bivariate Gaussian form. Extension of these results to particle addition operator and beta decay type operators are discussed.

math-ph↗

arXiv2015

Shape effects on double beta decay of $^{70}$Zn and $^{150}$Nd in deformed shell model

Using deformed shell model based on Hartree-Fock intrinsic states with $^{70}$Zn as an example and employing two realistic effective interactions, namely jj44b that produces deformed shape and JUN45 that generates spherical shape, it is demonstrated that the $0ν$ and $2ν$ nuclear transition matrix elements for double beta decay will reduce considerably as we go from spherical shapes to deformed shapes. This result is further substantiated by using $^{150}$Nd as another example.

nucl-th↗

arXiv2015

Shell model and deformed shell model spectroscopy of $^{62}$Ga

In the present work we have reported comprehensive analysis of recently available experimental data [H.M. David et al., Phys. Lett. B {\bf 726}, 665 (2013)] for high-spin states up to $17^+$ with $T=0$ in the odd-odd $N=Z$ nucleus $^{62}$Ga using shell model calculations within the full $f_{5/2}pg_{9/2}$ model space and deformed shell model based on Hartee-Fock intrinsic states in the same space. The calculations have been performed using jj44b effective interaction developed recently by B.A. Brown and A.F. Lisetskiy for this model space. The results obtained with the two models are similar and they are in reasonable agreement with experimental data. In addition to the $T=0$ and $T=1$ energy bands, band crossings and electromagnetic transition probabilities, we have also calculated the pairing energy in shell model and all these compare well with the available theoretical results.

nucl-th↗

arXiv2014

Group Theory for Embedded Random Matrix Ensembles

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 particle states and interacting with say $k$-body interactions, we have EGUE($k$) [embedded GUE of $k$-body interactions) with GUE embedding and the embedding algebra is $U(N)$. In this paper, using EGUE($k$) representation for a Hamiltonian that is $k$-body and an independent EGUE($t$) representation for a transition operator that is $t$-body and employing the embedding $U(N)$ algebra, finite-$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities (transition strengths multiplied by the density of states at the initial and final energies). In the asymptotic limit, these formulas reduce to those derived for the EGOE version and establish that in general bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extension of these results for other types of transition operators and EGUE ensembles with further symmetries are discussed.

math-ph↗

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↗

arXiv2014

Level spacing statistics and spectral correlations in the diffuse van der Waals clusters

We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbour level spacing distribution $P(s)$, the level number variance $Σ^2(L)$, and the Dyson-Mehta $Δ_3-$statistics for various cluster sizes. For large clusters we find that although the Bohigas-Giannoni-Schmit (BGS) conjecture seems to be valid, it does not exhibit true signatures of quantum chaos. However contrasting conjecture of Berry and Tabor is observed with smaller cluster size. For small number of bosons, we observe the existence of large number of quasi-degenerate states in low-lying excitation which exhibits the Shnirelman peak in $P(s)$ distribution. We also find a narrow region of intermediate spectrum which can be described by semi-Poisson statistics whereas the higher levels are regular and exhibit Poisson statistics. These observations are further supported by the analysis of the distribution of the ratio of consecutive level spacings $P(r)$ which is independent of unfolding procedure and thereby provides a tool for more transparent comparison with experimental findings than $P(s)$. Thus our detail numerical study clearly shows that the van der Waals clusters become more correlated with the increase in cluster size.

quant-ph↗

arXiv2013

Probability Distribution of the Ratio of Consecutive Level Spacings in Interacting Particle Systems

We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between the numerical results and the recently derived analytic form for the distribution and other related quantities is found to be close. This establishes conclusively that local level fluctuations generated by embedded ensembles follow the results of classical Gaussian ensembles.

nlin.CD↗

arXiv2012

Thermalization in one- plus two-body ensembles for dense interacting boson systems

Employing one plus two-body random matrix ensembles for bosons, temperature and entropy are calculated, using different definitions, as a function of the two-body interaction strength λfor a system with 10 bosons (m=10) in five single particle levels (N=5). It is found that in a region λ\sim λ_t, different definitions give essentially same values for temperature and entropy, thus defining a thermalization region. Also, (m,N) dependence of λ_t has been derived. It is seen that λ_t is much larger than the λvalues where level fluctuations change from Poisson to GOE and strength functions change from Breit-Wigner to Gaussian.

nlin.CD↗

arXiv2012

Energy level statistics of interacting trapped bosons

It is an well established fact that statistical properties of energy level spectra are the most efficient tool to characterize nonintegrable quantum systems. The study of statistical properties and spectral fluctuation in the interacting many boson systems have developed a new interest in this direction. Specially we are interested in the weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from the collective to single particle nature with the increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson like fluctuations due to the existence of external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are in the 3D confined harmonic potential. We study the nearest neighbour spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that increase in number of energy levels for repulsive BEC induces a transition from a Wigner like form displaying level repulsion to Poisson distribution for P(s). It does not follow the GOE prediction. For repulsive interaction, the lower levels are correlated and manifest level repulsion. For intermediate levels P (s) shows mixed statistic which clearly signifies the existence of two energy scales: external trap and interatomic interaction. Whereas for very high levels the trapping potential dominates, genarating Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shrielman like peak near s=0 which signifies the presence of large number of quasi-degenerate states.

cond-mat.quant-gas↗

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↗

arXiv2012

Embedded Gaussian Unitary Ensembles with $U(Ω) \otimes SU(r)$ Embedding generated by Random Two-body Interactions with $SU(r)$ Symmetry

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 one- and two-point correlation functions in eigenvalues, that is valid for any EGUE(2) and BEGUE(2) ('B' stands for bosons) with $U(Ω) \otimes SU(r)$ embedding and with two-body interactions preserving $SU(r)$ symmetry. Using this formulation with $r=1$, we recover the results derived by Asaga et al [Ann. Phys. (N.Y.) 297, 344 (2002)] for spinless boson systems. Going further, new results are obtained for $r=2$ (this corresponds to two species boson systems) and $r=3$ (this corresponds to spin 1 boson systems).

math-ph↗

arXiv2012

Spectral fluctuation and $\frac{1}{f^α}$ noise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by $\frac{1}{f^α}$ noise with $1\leqα\leq 2$. The system of interacting trapped bosons is inhomogeneous and a complex system. The presence of external harmonic trap makes it more interesting as in the atomic trap the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of collective nature and high-lying excitations are of single particle nature. We observe that for few bosons, $P(s)$ distribution shows the Shnirelman peak which exhibits a large number of quasi-degenerate states. For large number of bosons the low-lying levels are strongly affected by the interatomic interaction and the corresponding level fluctuation shows a transition to Wigner with increase in particle number. It does not follow GOE (Gaussian Orthogonal Ensemble) Random Matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that $\frac{1}{f^α}$ noise is ubiquitous in nature.

cond-mat.quant-gas↗

arXiv2011

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 specially 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, like 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 originated 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 quasi complete 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.

cond-mat.stat-mech↗

arXiv2011

Spectral distribution method for neutrinoless double-beta decay nuclear transition matrix elements: Binary correlation results

Neutrinoless double-beta decay nuclear transition matrix elements are generated by an effective two-body transition operator and it consists of Gamow-Teller like and Fermi like (also tensor) operators. Spectral distribution method for the corresponding transition strengths (squares of the transition matrix elements) involves convolution of the transition strength density generated by the non-interacting particle part of the Hamiltonian with a spreading function generated by the two-body part of the Hamiltonian. Extending the binary correlation theory for spinless embedded $k$-body ensembles to ensembles with proton-neutron degrees of freedom, we establish that the spreading function is a bivariate Gaussian for transition operators $\co(k_\co)$ that change $k_\co$ number of neutrons to $k_\co$ number of protons. Towards this end, we have derived the formulas for the fourth-order cumulants of the spreading function and calculated their values for some heavy nuclei; they are found to vary from $\sim -0.4$ to -0.1. Also for nuclei from $^{76}$Ge to $^{238}$U, the bivariate correlation coefficient is found to vary from $\sim 0.6 - 0.8$ and these values can be used as a starting point for calculating nuclear transition matrix elements using the spectral distribution method.

nucl-th↗

arXiv2011

Shell-model results in $fp$ and ${fpg_{9/2}}$ spaces for $^{61,63,65}$Co isotopes

Low-lying spectra and several high-spin states of odd--even $^{61,63,65}$Co isotopes are calculated in two different shell-model spaces. First set of calculations have been carried out in ${fp}$ shell valence space (full $fp$ space for $^{63,65}$Co and a truncated one for $^{61}$Co) using two recently derived ${fp}$ shell interactions, namely GXPF1A and KB3G, with $^{40}$Ca as core. Similarly, the second set of calculations have been performed in ${fpg_{9/2}}$ valence space using an ${fpg}$ effective interaction due to Sorlin {\it et al}., with $^{48}$Ca as core and imposing a truncation. It is seen that the results of GXPF1A and KB3G are reasonable for $^{61,63}$Co. For $^{65}$Co, shell-model results show that the ${fpg}$ interaction adopted in the study is inadequate and also point out that it is necessary to include orbitals higher than $1g_{9/2}$ for neutron-rich Co isotopes.

nucl-th↗