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V. K. B. Kota

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

At least 37 records · Page 2Linked to original sources
arXiv2020

Quadrupole properties of the eight $SU(3)$ algebras in $(sdgi)$ space

With nucleons occupying an oscillator shell $η$, there are $2^{η/2}$ number of $SU(3)$ algebras; $η/2$ is the integer part of $η/2$. Analyzing the first non trivial situation with four $SU(3)$ algebras in $(sdg)$ space, demonstrated recently is that they generate quite different quadrupole properties though they all generate the same spectrum. More complex situation is with eight $SU(3)$ algebras in $(sdgi)$ space. In the present work, quadrupole properties generated by these eight algebras are analyzed first using the more analytically tractable interacting boson model. In addition, shell model and the closely related deformed shell model are used with three examples of nucleons in $sdgi$ space. It is found that in general six of the $SU(3)$ algebras generate prolate shape and two oblate shape. Out of all these, one of the $SU(3)$ algebra generates quite small quadrupole moments for the low-lying states.

nucl-th↗
arXiv2020

Bivariate $q$-normal distribution for transition strengths distribution from many-particle random matrix ensembles generated by $k$-body interactions

Recently it is established, via lower order moments, that the univariate q-normal distribution, which is the weight function for $q$-Hermite polynomials, describes the ensemble averaged eigenvalue density from many-particle random matrix ensembles generated by $k$-body interactions [Manan Vyas and V.K.B. Kota, J. Stat. Mech. {\bf 2019}, 103103 (2019)]. These ensembles are generically called embedded ensembles of $k$-body interactions [EE($k$)] and their GOE and GUE versions are called EGOE($k$) and EGUE($k$) respectively. Going beyond this work, the lower order bivariate reduced moments of the transition strength densities, generated by EGOE($k$) [or EGUE($k$)] for the Hamiltonian and an independent EGOE($t$) for the transition operator ${\cal O}$ that is $t$-body, are used to establish that the ensemble averaged bivariate transition densities follow the bivariate $q$-normal distribution. Presented are also formulas for the bivariate correlation coefficient $ρ$ and the $q$ values as a function of the particle number $m$, number of single particle states $N$ that the particles are occupying and the body ranks $k$ and $t$ of $H$ and ${\cal O}$ respectively. Finally, using the bivariate $q$ normal form a formula for the chaos measure number of principal components (NPC) in the transition strengths from a state with energy $E$ is presented.

math-ph↗
arXiv2019

Constraining nuclear physics parameters with current and future COHERENT data

Motivated by the recent observation of coherent elastic neutrino-nucleus scattering (CE$ν$NS) at the COHERENT experiment, our goal is to explore its potential in probing important nuclear structure parameters. We show that the recent COHERENT data offers unique opportunities to investigate the neutron nuclear form factor. Our present calculations are based on the deformed Shell Model (DSM) method which leads to a better fit of the recent CE$ν$NS data, as compared to known phenomenological form factors such as the Helm-type, symmetrized Fermi and Klein-Nystrand. The attainable sensitivities and the prospects of improvement during the next phase of the COHERENT experiment are also considered and analyzed in the framework of two upgrade scenarios.

hep-ph↗
arXiv2019

Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions

We study the dynamics of dipolar bosons in an external harmonic trap. We monitor the time evolution of the occupation in the natural orbitals and normalized first- and second-order Glauber's correlation functions. We focus in particular on the relaxation dynamics of the Shannon entropy. Comparison with the corresponding results for contact interactions is presented. We observe significant effects coming from the presence of the non-local repulsive part of the interaction. The relaxation process is very fast for dipolar bosons with a clear signature of a truly saturated maximum entropy state. We also discuss the connection between the entropy production and the occurrence of correlations and loss of coherence in the system. We identify the long-time relaxed state as a many-body state retaining only diagonal correlations in the first-order correlation function and building up anti-bunching effect in the second-order correlation function.

cond-mat.quant-gas↗
arXiv2019

Quenched many-body quantum dynamics with $k$-body interactions using $q$-Hermite polynomials

In a $m$ particle quantum system, one can have $k=1,\,2,\,\ldots,\,m$ body interactions. The rank of interactions and the nature of particles (fermions or bosons) can strongly affect the dynamics of the system. To explore this in detail, we study quenched quantum dynamics in many particle systems varying rank of interactions, both for fermionic and bosonic particles. We represent the system Hamiltonian by Fermionic Embedded Gaussian Orthogonal Ensembles (FEGOE) and Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) respectively. We show that generating function for $q$-Hermite polynomials describes the semi-circle to Gaussian transition in spectral densities of FEGOE$(k)$ and BEGOE$(k)$ (also the Unitary variants FEGUE$(k)$ and BEGUE$(k)$) as a function of rank of interactions $k$. Importantly, numerical Fourier transform of generating function of $q$-Hermite polynomials explains the short-time decay of survival probability in FEGOE$(1+k)$ and BEGOE$(1+k)$. The parameter $q$ describing these properties is related to excess parameter $γ_2$ and we give a formula for FEGOE$(k)$, FEGUE$(k)$, BEGOE$(k)$ and BEGUE$(k)$. We illustrate that the dynamics strongly depends on the rank of interactions and nature of particles and these universal features may be relevant to modeling non-equilibrium quantum systems.

quant-ph↗
arXiv2019

Multiple $SU(3)$ algebras in shell model and \\ interacting boson model

Rotational $SU(3)$ algebraic symmetry continues to generate new results in the shell model (SM). Interestingly, it is possible to have multiple $SU(3)$ algebras for nucleons occupying an oscillator shell $η$. Several different aspects of the multiple $SU(3)$ algebras are investigated using shell model and also deformed shell model based on Hartree-Fock single particle states with nucleons in $sdg$ orbits giving four $SU(3)$ algebras. Results show that one of the $SU(3)$ algebra generates prolate shapes, one oblate shape and the other two also generate prolate shape but one of them gives quiet small quadrupole moments for low-lying levels. These are inferred by using the standard form for the electric quadrupole transition operator and using quadrupole moments and $B(E2)$ values in the ground $K=0^+$ band in three different examples. Multiple $SU(3)$ algebras extend to interacting boson model and using $sdg$IBM, the structure of the four $SU(3)$ algebras in this model are studied by coherent state analysis and asymptotic formulas for $E2$ matrix elements. The results from $sdg$IBM further support the conclusions from the $sdg$ shell model examples.

nucl-th↗
arXiv2018

Simple formula for leading $SU(3)$ irreducible representation for nucleons in an oscillator shell

Applications of rotational $SU(3)$ symmetry in nuclei, using Elliott's $SU(3)$ or pseudo-$SU(3)$ or proxy-$SU(3)$ model, often need just the lowest or leading $SU(3)$ irreducible representation (irrep) $(λ_H, μ_H)$. For nucleons in an oscillator shell $η$, with ${\cal N}=(η+1)(η+2)/2$, we have the algebra $U(r{\cal N}) \supset [U({\cal N}) \supset SU(3)] \otimes SU(r)$; $r=2$ when there are only valence protons or neutrons and $r=4$ for nucleons with isospin $T$. Presented in this paper is a simple general formula for the leading $SU(3)$ irrep $(λ_H, μ_H)$ in any given irrep $\{f\}$ of $U({\cal N})$. Results are provided for $(λ_H, μ_H)$ irreps for $η$ values of interest in nuclei and for this for all allowed particle numbers. These results clearly show that prolate shape dominates over oblate shape in the shell model $SU(3)$ description.

nucl-th↗
arXiv2018

Novel neutrino-floor and dark matter searches with deformed shell model calculations

Event detection rates for WIMP-nucleus interactions are calculated for $^{71}$Ga, $^{73}$Ge, $^{75}$As and $^{127}$I (direct dark matter detectors). The nuclear structure form factors, that are rather independent of the underlying beyond the Standard Model particle physics scenario assumed, are evaluated within the context of the deformed nuclear shell model (DSM) based on Hartree-Fock nuclear states. Along with the previously published DSM results for $^{73}$Ge, the neutrino-floor due to coherent elastic neutrino-nucleus scattering (CE$ν$NS), an important source of background to dark matter searches, is extensively calculated. The impact of new contributions to CE$ν$NS due to neutrino magnetic moments and $Z^\prime$ mediators at direct dark matter detection experiments is also examined and discussed. The results show that the neutrino-floor constitutes a crucial source of background events for multi-ton scale detectors with sub-keV capabilities.

hep-ph↗
arXiv2018

Lie Algebraic approach to molecular spectroscopy: Diatomic to polyatomic molecules

Interacting dipole ($p$) bosons along with scalar ($s$) bosons, based on the ideas drawn from the interacting boson model of atomic nuclei, led to the development of the vibron model based on $U(4)$ spectrum generating algebra for diatomic molecules. The $U(4) \supset SO(4) \supset SO(3)$ algebra generates rotation-vibration spectra. Extending this to two coupled $SO(4)$ algebras and three $SO(4)$ algebras describe triatomic and four-atomic molecules respectively. Similarly, appropriately coupled $U(2) \supset SO(2)$ algebras will describe the stretching vibrations, with proper point group symmetries, in polyatomic molecules. In addition, coupled $U(3)$ algebras describe coupled benders. The Lie algebraic approach to molecular spectroscopy is briefly described along with a list giving future directions and presented in three appendices results for: (i) $U(3)$ algebra for bending vibrations and coupled benders; (ii) symmetry mixing Hamiltonians generating regular spectra; (iii) partition functions for diatomic and triatomic molecules.

physics.chem-ph↗
arXiv2017

Shell model results for $T=1$ and $T=0$ bands in $^{66}$As

Results of a comprehensive shell model (SM) analyses, within the full $f_{5/2}pg_{9/2}$ model space, of the recently available experimental data [P. Ruotsalainen et al., Phy. Rec. C {88}, 024320 (2013)] with four $T=0$ bands and one $T=1$ band in the odd-odd $N=Z$ nucleus $^{66}$As are presented. The calculations are performed using jj44b effective interaction developed recently by B.A. Brown and A.F. Lisetskiy for this model space. For the lowest two $T=0$ bands and the $T=1$ band, the results are in reasonable agreement with experimental data and deformed shell model is used to identify their intrinsic structure. For the $T=1$ band, structural change at $8^+$ is predicted. For the third $9^+$ band with $T=0$, the shell model $B(E2)$ values and quadrupole moments (in addition to energies) are consistent with the interpretation in terms of aligned isoscalar $np$ pair in $g_{9/2}$ orbit coupled to the $^{64}$Ge ground band. Similarly, the $9^+$ level of band 4 and a close lying $5^+$ level are found to be isomeric states in the analysis. Finally, energies of the band 5 members calculated using shell model with both positive and negative parity show that the observed levels are most likely negative parity levels. The SM results with jj44b are also compared with the results obtained using JUN45 interaction.

nucl-th↗
arXiv2017

Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?

We perform a thorough analysis of the spectral statistics of experimental molecular resonances, of bosonic erbium $^{166}$Er and $^{168}$Er isotopes, produced as a function of magnetic field($B$) by Frisch et al. [Nature 507, (2014) 475], utilizing some recently derived surmises which interpolate between Poisson and GOE and without unfolding. Supplementing this with an analysis using unfolded spectrum, it is shown that the resonances are close to semi-Poisson distribution. There is an earlier claim of missing resonances by Molina et al. [Phys. Rev. E 92, (2015) 042906]. These two interpretations can be tested by more precise measurements in future experiments.

cond-mat.stat-mech↗
arXiv2017

Multiple multi-orbit pairing algebras in shell model and interacting boson models

In nuclei with valence nucleons are say identical nucleons and say these nucleons occupy several-$j$ orbits, then it is possible to consider pair creation operator $S_+$ to be a sum of the single-$j$ shell pair creation operators $S_+(j)$ with arbitrary phases, $S_+=\sum_j α_j S_+(j); α_j=\pm 1$. In this situation, it is possible to define multi-orbit or generalized seniority that corresponds to the quasi-spin $SU(2)$ algebra generated by $S_+$, $S_-=(S_+)^\dagger$ and $S_0=(\hat{n} -Ω)/2$ operators; $\hat{n}$ is number operator and $Ω=[\sum_j (2j+1)]/2$. There are now multiple pairing quasi-spin $SU(2)$ algebras. Also, the $α_j$'s and the generators of the corresponding generalized seniority generating sympletic algebras $Sp(2Ω)$ in $U(2Ω) \supset Sp(2Ω)$ have one-to-one correspondence. Using these, derived are the special seniority selection rules for electromagnetic transitions. A particular choice for $α_j$'s as advocated by Arvieu and Moszkowski (AM) in the past gives pairing Hamiltonians having maximum correlation with well known effective interactions. The various results derived for identical fermion systems are shown to extend to identical boson systems with the bosons occupying several-$\ell$ orbits as for example in $sd$, $sp$, $sdg$ and $sdpf$ IBM's. The quasi-spin algebra here is $SU(1,1)$ and the generalized seniority quantum number is generated by $SO(2Ω)$ in $U(2Ω) \supset SO(2Ω)$. The different $SO(2Ω)$ algebras here will be important in the study of quantum phase transitions and order-chaos transitions in nuclei.

nucl-th↗
arXiv2017

Deformed shell model study of event rates for WIMP- $^{73}$Ge scattering

The event detection rates for the WIMP (a dark matter candidate) are calculated with $^{73}$Ge as the detector. The calculations are performed within the deformed shell model (DSM) based on Hartree-Fock states. First the energy levels and magnetic moment for the ground state and two low lying positive parity states for this nucleus are calculated and compared with experiment. The agreement is quite satisfactory. Then the nuclear wave functions are used to investigate the elastic and inelastic scattering of WIMP from $^{73}$Ge. The nuclear structure factors which are independent of supersymmetric model are also calculated as a function of WIMP mass. The event rates are calculated for a given set of SUSY parameters. The calculation shows that $^{73}$Ge is a good detector for detecting dark matter.

nucl-th↗
arXiv2017

$^{35,37,39}$S isotopes in $sd-pf$ space : Shell-model interpretation

The structure of $^{35,37,39}$S isotopes is described by performing comprehensive shell model calculations with SDPF-U and SDPFMW interactions. Protons and neutrons are restricted to the $sd$-shell for $N < 20$, neutrons start to fill the $pf$-shell for $N > 20$. Natural parity states are described by only in-shell mixing, unnatural parity states with 1p-1h inter-shell neutron excitations. With SDPF-U interaction, reported are the results for natural parity states only because this interaction is not suitable for cross shell excitations. Calculated energy levels, electromagnetic properties and spectroscopic factors are in good agreement with the recently available experimental data.

nucl-th↗
arXiv2017

Localization-Delocalization Transitions in Bosonic Random Matrix Ensembles

Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one- plus two-body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis, considered are bosonic EGOE(1+2) for two-species boson systems with a fictitious ($F$) spin degree of freedom [called BEGOE(1+2)-$F$]. Numerical calculations are carried out as a function of the two-body interaction strength ($λ$). It is shown that, in the region (defined by $λ>λ_c$) after the onset of Poisson to GOE transition in energy levels, the strength functions exhibit Breit-Wigner to Gaussian transition for $λ>λ_{F_k}>λ_c$. Further, analyzing information entropy and participation ratio, it is established that there is a region defined by $λ\simλ_t$ where the system exhibits thermalization. The $F$-spin dependence of the transition markers $λ_{F_k}$ and $λ_t$ follow from the propagator for the spectral variances. These results, well tested near the center of the spectrum and extend to the region within $\pm2σ$ to $\pm3σ$ from the center ($σ^2$ is the spectral variance), establish universality of the transitions generated by embedded ensembles. In the second analysis, entanglement entropy is studied for spin-less BEGOE(1+2) ensemble and shown that the results generated are close to the recently reported results for a Bose-Hubbard model.

nlin.CD↗
arXiv2016

Deformed shell model study of heavy N=Z nuclei and dark matter detection

Deformed shell model (DSM) based on Hartree-Fock intrinsic states is applied to address two current problems of interest. Firstly, in the $f_{5/2}pg_{9/2}$ model space with jj44b effective interaction along with isospin projection, DSM is used to describe the structure of the recently observed low-lying $T=0$ and $T=1$ bands in the heavy odd-odd N=Z nucleus $^{66}$As. DSM results are close to the data and also to the shell model results. For the $T=1$ band, DSM predicts structural change at $8^+$ just as in the shell model. In addition, the lowest two $T=0$ bands are found to have quasi-deuteron structure above a $^{64}$Ge core and the $5^+$ and $9^+$ levels of the third $T=0$ band are found to be isomeric states. Secondly, in a first application of DSM to dark matter, detection rates for the lightest supersymmetric particle (a dark matter candidate) are calculated with $^{73}$Ge as the detector.

nucl-th↗
arXiv2016

Fidelity decay and entropy production in many-particle systems after random interaction quench

We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic(bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin $S$. The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving $S$ for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time ($t_{sat}$) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.

cond-mat.stat-mech↗