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Hospitals in India still rely on handwritten medical records despite the availability of Electronic Medical Records (EMR), complicating statistical analysis and record retrieval. Handwritten records pose a unique challenge, requiring specialized data for training models to recognize medications and their recommendation patterns. While traditional handwriting recognition approaches employ 2-D LSTMs, recent studies have explored using Multimodal Large Language Models (MLLMs) for OCR tasks. Building on this approach, we focus on extracting medication names and dosages from simulated medical records. Our methodology MIRAGE (Multimodal Identification and Recognition of Annotations in indian GEneral prescriptions) involves fine-tuning the QWEN VL, LLaVA 1.6 and Idefics2 models on 743,118 high resolution simulated medical record images-fully annotated from 1,133 doctors across India. Our approach achieves 82% accuracy in extracting medication names and dosages., Comment: 5 pages, 9 figures, 3 tables, submitted to ISBI 2025

We numerically study the distribution of the lowest eigenvalue of finite many-boson systems with $k$-body interactions modeled by Bosonic Embedded Gaussian Orthogonal [BEGOE($k$)] and Unitary [BEGUE($k$)] random matrix Ensembles. Following the recently published result that the $q$-normal describes the smooth form of the eigenvalue density of the $k$-body embedded ensembles, the first four moments of the distribution of lowest eigenvalues have been analyzed as a function of the $q$ parameter, with $q \sim 1$ for $k = 1$ and $q = 0$ for $k = m$; $m$ being the number of bosons. Analytics are difficult as we are dealing with highly correlated variables, however we provide ansatzs for centroids and variances of these distributions. These match very well with the numerical results obtained. Our results show the distribution exhibits a smooth transition from Gaussian like for $q$ close to 1 to a modified Gumbel like for intermediate values of $q$ to the well-known Tracy-Widom distribution for $q=0$. It should be emphasized that this is a new result which numerically demonstrates that the distribution of the lowest eigenvalue of finite many-boson systems with $k$-body interactions exhibits a smooth transition from Gaussian like (for $q$ close to 1) to a modified Gumbel like (for intermediate values of $q$) to the well-known Tracy-Widom distribution (for $q=0$). In addition, we have also studied the distribution of normalized spacing between the lowest and next lowest eigenvalues and it is seen that this distribution exhibits a transition from Wigner's surmise (for $k=1$) to Poisson (for intermediate $k$ values with $k \le m/2$) to Wigner's surmise (starting from $k = m/2$ to $k = m$) with decreasing $q$ value. Thus, the spacings at the spectrum edge behave differently from the spacings inside the spectrum bulk., Comment: 24 pages, 10 figures

Applications of the proxy-$SU(3)$ model of Bonatsos and collaborators to nuclei in A=60-90 region introduces proxy-$SU(4)$ symmetry. Shell model spaces with single particle (sp) orbits $^1p_{3/2}$, $^1p_{1/2}$, $^0f_{5/2}$ and $^0g_{9/2}$ are essential for these nuclei and also protons and neutrons in this region occupy the same sp orbits. With this and applying the "proxy scheme", the $^0g_{9/2}$ changes to $^0f_{7/2}$ giving the SGA $U(40) \supset [U(10) \supset G \supset SO(3)] \otimes [SU(4) \supset SU_S(2) \otimes SU_T(2)]$. With $G=SU(3)$, we have the proxy-$SU(3)$ model. It is easy to see that proxy-$SU(3)$ symmetry implies goodness of the $SU(4)$ symmetry appearing above, i.e. proxy-$SU(4)$ symmetry. Shell model calculations pointing out the need for $^0g_{9/2}$ orbit, ground state masses, shape changes and shape co-existence in A=60-90 region and GT distributions clearly show the importance of proxy-$SU(4)$ in this mass region. Besides presenting this evidence, new proxy schemes with $G=SU(5)$, $SO(6)$ and $SO(10)$ that are generated by good proxy-$SU(4)$ symmetry are described in some detail. An important feature is that the four proxy symmetries $SU(3)$, $SO(6)$, $SU(5)$ and $SO(10)$ appear twice., Comment: Based on the talk given by the first author (VKBK) in SDANCA-23 held in Sofia (Bulgaria) during September 21-23, 2023

Large-scale shell-model calculations have been performed for the study of two neutrino double-beta ($2\nu\beta\beta$) decay in $^{82}$Se, $^{94}$Zr, $^{108}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te, $^{136}$Xe, and $^{150}$Nd. We have employed JUN45 interaction to calculate the nuclear matrix element (NME) for $2\nu\beta\beta$ decay in $^{82}$Se. In the case of $^{94}$Zr, the glekpn effective interaction is used. For $^{108}$Cd, we have used a realistic effective interaction derived through the G-matrix approach. In the case of $^{124}$Sn, $^{128,130}$Te and $^{136}$Xe, the sn100pn effective interaction is employed. For $^{150}$Nd, we have used KHHE effective interaction based on holes in a $^{208}$Pb core. We have extracted the half-lives of these nuclei for the $2\nu\beta\beta$ decay with the help of calculated NME. Our results are consistent with the available experimental half-lives. The variation of cumulative $2\nu\beta\beta$ NME with respect to the excitation energy of the intermediate $1^+$ states is also shown, and in all cases, it is ensured that their values are almost saturated. In the present work we have calculated more intermediate $1^+$ states as much as possible in comparison to results available in the literature., Comment: 17 pages, 2 figures, 2 tables

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 in constructing this ensemble, called EGUE($k:\mathbf{\pi} \mathbf{\nu}$), is that the $\mathbf{\pi}$ fermions ($m_1$ in number) occupy $N_1$ number of degenerate single particle (sp) states and similarly $\mathbf{\nu}$ fermions ($m_2$ in number) in $N_2$ number of degenerate sp states. The Hamiltonian is assumed to be $k$-body preserving $(m_1,m_2)$. Formulas with finite $(N_1,N_2)$ corrections and asymptotic limit formulas both show that the eigenvalue density takes $q$-normal form with the $q$ parameter defined by the fourth moment. The EGUE($k:\mathbf{\pi} \mathbf{\nu}$) formalism and results are extended to two species boson systems. Results in this work show that the $q$-normal form of the eigenvalue density established only recently for identical fermion and boson systems extends to two species fermion and boson systems., Comment: 21 pages, 3 figures, version accepted for publication in J. Stat. Mech. (2023)

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 years back. Two-point correlation function in eigenvalues of a random matrix ensemble is the ensemble average of the product of the density of eigenvalues at two eigenvalues say $E$ and $E^\prime$. Fluctuation measures such as the number variance and Dyson-Mehta $\Delta_3$ statistic are defined by the two-point function and so also the variance of the level motion in the ensemble. Recently, it is recognized that for the embedded ensembles with $k$-body interactions the one-point function (ensemble averaged density of eigenvalues) follows the so called $q$-normal distribution. With this, the eigenvalue density can be expanded by starting with the $q$-normal form and using the associated $q$-Hermite polynomials $He_\zeta(x|q)$. Covariances $\overline{S_\zeta S_{\zeta^\prime}}$ (overline representing ensemble average) of the expansion coefficients $S_\zeta$ with $\zeta \ge 1$ here determine the two-point function as they are a linear combination of the bivariate moments $\Sigma_{PQ}$ of the two-point function. Besides describing all these, in this paper derived are formulas for the bivariate moments $\Sigma_{PQ}$ with $P+Q \le 8$, of the two-point correlation function, for the embedded Gaussian unitary ensembles with $k$-body interactions [EGUE($k$)] as appropriate for systems with $m$ fermions in $N$ single particle states. Used for obtaining the formulas is the $SU(N)$ Wigner-Racah algebra. These formulas with finite $N$ corrections are used to derive formulas for the covariances $\overline{S_\zeta S_{\zeta^\prime}}$ in the asymptotic limit., Comment: 37 pages, 1 table, added some new formulas

Statistical nuclear spectroscopy (also called spectral distribution method), introduced by J.B. French in late 60's and developed in detail in the later years by his group and many other groups, is based on the Gaussian forms for the state (eigenvalue) and transition strength densities in shell model spaces with their extension to partial densities defined over shell model subspaces. The Gaussian forms have their basis in embedded random matrix ensembles with nuclear Hamiltonians consisting of a mean-field one-body part and a residual two-body part. However, following the recent random matrix results for the so called Sachdev-Ye-Kitaev model due to Verbaaarschot et al, embedded random matrix ensembles with $k$-body interactions are re-examined and it is shown that the density of states, transition strength densities and strength functions (partial densities) in fact follow more closely the $q$-normal distribution (the parameter $q$ is related to the fourth moment of these distributions with $q=1$ giving Gaussian and $q=0$ giving semi-circle form). The $q$-normal has the important property that it is bounded for $0 \le q < 1$. The $q$-normal (also its bivariate and general multi-variate extensions) and the associated $q$-Hermite polynomials are studied for their properties by Bryc, Szabowski and others [P.J. Szabowski, Electronic Journal of Probability {\bf 15}, 1296 (2010)]. Following these, in the present article developed is statistical nuclear spectroscopy based on $q$-normal (univariate and bivariate) distributions and the associated $q$-Hermite polynomials. In particular, formulation is presented for nuclear level densities, shell model orbit occupancies, transition strengths (for electromagnetic and $\beta$ and double $\beta$-decay type operators) and strength sums., Comment: 31 pages, 4 figures. Ann. Phys. (N. Y.), Available online 29 September 2022

Realistic nuclear structure calculations are presented for the event rates due to coherent elastic neutrino-nucleus scattering (CE$\nu$NS), assuming neutrinos from pion-decay at-rest, from nuclear reactors and from Earth's interior. We focus on the currently interesting Germanium isotopes, $^{70,73,76}$Ge, which constitute detector materials of the recently planned CE$\nu$NS experiments. We study in addition the potential use of $^{64,70}$Zn and $^{28}$Si isotopes as promising CE$\nu$NS detectors. From nuclear physics perspectives, recently, calculations have been carried out within the framework of the deformed shell-model (DSM), based on realistic nuclear forces, and assessed on the reproducibility of spectroscopic nuclear properties. The high confidence level acquired by their agreement with experimental results and by their comparison with other mostly phenomenological calculations encouraged the use of DSM to extract predictions for the CE$\nu$NS event rates of the above isotopes. Our detailed estimation of the nuclear physics aspects of the recently observed neutral current coherent neutrino-nucleus scattering may shed light on unravelling the still remaining uncertainties for the CE$\nu$NS process within and beyond the Standard Model., Comment: 13 pages, 1 table, 6 figures. V2: References added, discussion on the h.o. parameter expanded, matches the published version

With nucleons occupying several shell model $j$ orbits, the isovector pair creation operator $A^1_\mu$ (creates a two particle state with angular momentum $J=0$ and isospin $T=1$) is no longer unique. Choosing it to be a sum of single-$j$ isovector pair creation operators each with a phase, there will be multiple pair $SO(5)$ algebras with isospin; with $r$ number of $j$ orbits, there will be $2^{r-1}$ $SO(5)$ algebras each with a corresponding complementary $Sp(2\Omega)$ algebra [$2\Omega = \sum_j (2j+1)$] that gives seniority and reduced isospin quantum numbers. Three applications of multiple $SO(5)$ algebras are presented demonstrating the usefulness of considering $SO(5)$ pairing algebras with general sign factors., Comment: 10 pages, 1 table, 1 figure, to appear in Bulgarian Journal of Physics

Shell model and interacting boson model spaces admit multiple $SU^{(\alpha)}(3)$ algebras generating the same rotational spectra but different $E2$ decay properties, depending on the phases ${\alpha}$ in the quadrupole generator. In the ground ($g$) $K=0^+$ bands in nuclei this is demonstrated recently using systems with nucleons in a single oscillator shell [Kota, Sahu and Srivastava, Bulg. J. Phys. {\bf 46}, 313 (2019); Eur. Phys. J. Special Topics {\bf 229}, 2389 (2020)]. Going beyond these preliminary studies, results are presented here for $E2$ decay properties of $\beta$ and $\gamma$ bands members, as generated by multiple $SU(3)$ algebras, using $sdg$IBM and $sdgi$IBM examples. In addition, results are presented for the $E2$ and $M1$ decay properties of the levels of the $1^+$ scissors band in heavy nuclei using $sdg$IBM-2 and $sdgi$IBM-2. The scissors $1^+$ band properties are also studied using a shell model example with six protons in $(pf)$ shell and twelve neutrons in $(sdg)$ shell. These results establish that: (i) with multiple $SU(3)$ algebras, it is possible to have rotational bands with very weak $E2$ strengths among the levels where normally one expects strong strengths; (ii) $E2$ decay of the levels of $\beta$ and $\gamma$ bands to the ground band are quite different for some of the $SU^{(\alpha)}(3)$ algebras with strong dependence on ${\alpha}$; (iii) it is possible to have the scissors $1^+$ band with the $E2$ and $M1$ decay of the low-lying levels of this band to the $g$ band are strong or weak depending on $\alpha$., Comment: 6 tables, 4 figures

For finite quantum many-particle systems modeled with say $m$ fermions in $N$ single particle states and interacting with $k$-body interactions ($k \leq m$), the wavefunction structure is studied using random matrix theory. Hamiltonian for the system is chosen to be $H=H_0(t) + \lambda V(k)$ with the unperturbed $H_0(t)$ Hamiltonian being a $t$-body operator and $V(k)$ a $k$-body operator with interaction strength $\lambda$. Representing $H_0(t)$ and $V(k)$ by independent Gaussian orthogonal ensembles (GOE) of random matrices in $t$ and $k$ fermion spaces respectively, first four moments, in $m$-fermion spaces, of the strength functions $F_\kappa(E)$ are derived; strength functions contain all the information about wavefunction structure. With $E$ denoting the $H$ energies or eigenvalues and $\kappa$ denoting unperturbed basis states with energy $E_\kappa$, the $F_\kappa(E)$ give the spreading of the $\kappa$ states over the eigenstates $E$. It is shown that the first four moments of $F_\kappa(E)$ are essentially same as that of the conditional $q$-normal distribution given in: P.J. Szabowski, Electronic Journal of Probability {\bf 15}, 1296 (2010). This naturally gives asymmetry in $F_\kappa(E)$ with respect to $E$ as $E_\kappa$ increases and also the peak value changes with $E_\kappa$. Thus, the wavefunction structure in quantum many-fermion systems with $k$-body interactions follows in general the conditional $q$-normal distribution., Comment: 23 pages, 3 figures

Detection rates for the elastic and inelastic scattering of weakly interacting massive particles (WIMP) off $^{23}$Na are calculated within the framework of Deformed Shell Model (DSM) based on Hartree-Fock states. First the spectroscopic properties like energy spectra and magnetic moments are calculated and compared with experiment. Following the good agreement for these, DSM wave functions are used for obtaining elastic and inelastic spin structure functions, nuclear structure coefficients etc. for the WIMP-$^{23}$Na scattering. Then, the event rates are also calculated with a given set of supersymmetric parameters. In the same manner, using DSM wavefunctions, nuclear structure coefficients and event rates for elastic scattering of WIMP from $^{40}$Ar are also obtained. These results for event rates and also for annual modulation will be useful for the upcoming and future WIMP detection experiments involving detectors with $^{23}$Na and $^{40}$Ar., Comment: arXiv admin note: substantial text overlap with arXiv:2004.04055, arXiv:1706.08112

With nucleons occupying an oscillator shell $\eta$, there are $2^{\eta/2}$ number of $SU(3)$ algebras; $\eta/2$ is the integer part of $\eta/2$. 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.

The event rates for WIMP-nucleus and neutrino-nucleus scattering processes, expected to be detected in ton-scale rare-event detectors, are investigated. We focus on nuclear isotopes that correspond to the target nuclei of current and future experiments looking for WIMP- and neutrino-nucleus events. The nuclear structure calculations, performed in the context of the deformed shell model, are based on Hartree-Fock intrinsic states with angular momentum projection and band mixing for both the elastic and the inelastic channels. Our predictions in the high-recoil-energy tail show that detectable distortions of the measured/expected signal may be interpreted through the inclusion of the non-negligible incoherent channels, Comment: 34 pages, 13 figures, 3 tables. V2: matches published version in PRC

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 $\rho$ 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., Comment: 19 pages, 3 figures, 3 tables

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., Comment: Submitted version of the manuscript

Motivated by the recent observation of coherent elastic neutrino-nucleus scattering (CE$\nu $NS) at the COHERENT experiment, our goal is to explore its potential in probing important nuclear structure parameters. We show that the recent COHERENT data offers unique opportunities to investigate the neutron nuclear form factor. Our present calculations are based on the deformed Shell Model (DSM) method which leads to a better fit of the recent CE$\nu $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., Comment: 13 pages, 5 figures, 2 tables; v2: minor corrections, version to appear in PLB

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 $\eta$. 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., Comment: 27 pages, 2 figures, 7 tables

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) $(\lambda_H, \mu_H)$. For nucleons in an oscillator shell $\eta$, with ${\cal N}=(\eta +1)(\eta +2)/2$, 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 $(\lambda_H, \mu_H)$ in any given irrep $\{f\}$ of $U({\cal N})$. Results are provided for $(\lambda_H, \mu_H)$ irreps for $\eta$ 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., Comment: 12 pages, 4 tables

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 $\gamma_2$ 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., Comment: 21 pages, 7 figures, 2 tables

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$\nu$NS), an important source of background to dark matter searches, is extensively calculated. The impact of new contributions to CE$\nu$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., Comment: 16 pages, 12 figures, 3 Tables; 1 figure and 1 table added; references added; matches published version

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., Comment: 19 pages, 3 figures

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., Comment: 9 pages, 7 figures and 3 tables: Accepted for Publication in Journal of Physics G: Nuclear and Particle Physics

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, $S_+=\sum_j \alpha_j S_+(j); \alpha_j=\pm 1$. 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 $S_0=(\hat{n} -\Omega)/2$ operators; $\hat{n}$ is number operator and $\Omega=[\sum_j (2j+1)]/2$. There are now multiple pairing quasi-spin $SU(2)$ algebras. Also, the $\alpha_j$'s and the generators of the corresponding generalized seniority generating sympletic algebras $Sp(2\Omega)$ in $U(2\Omega) \supset Sp(2\Omega)$ have one-to-one correspondence. Using these, derived are the special seniority selection rules for electromagnetic transitions. A particular choice for $\alpha_j$'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 $SO(2\Omega)$ in $U(2\Omega) \supset SO(2\Omega)$. The different $SO(2\Omega)$ algebras here will be important in the study of quantum phase transitions and order-chaos transitions in nuclei., Comment: 25 pages, 3 figure

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.

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., Comment: 7 pages, 6 figures

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 ($\lambda$). It is shown that, in the region (defined by $\lambda>\lambda_c$) after the onset of Poisson to GOE transition in energy levels, the strength functions exhibit Breit-Wigner to Gaussian transition for $\lambda>\lambda_{F_k}>\lambda_c$. Further, analyzing information entropy and participation ratio, it is established that there is a region defined by $\lambda\sim\lambda_t$ where the system exhibits thermalization. The $F$-spin dependence of the transition markers $\lambda_{F_k}$ and $\lambda_t$ follow from the propagator for the spectral variances. These results, well tested near the center of the spectrum and extend to the region within $\pm2\sigma$ to $\pm3\sigma$ from the center ($\sigma^2$ 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., Comment: 11 pages, 6 figures, Contribution to the Special Issue "Many-Body Localization" in Annalen der Physik

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., Comment: 12 pages, 3 figures and one table; Article for the invited talk (by R Sahu) given in the 35th International Workshop on "Nuclear Theory" held at Rila Mountains (Sofia, Bulgaria) during June 26 to July 2nd, 2016

Statistical spectral distribution method based on shell model and random matrix theory is developed for calculating neutrinoless double beta decay nuclear transition matrix elements. First results obtained for $^{82}$Se and $^{76}$Ge using the spectral method are close to the available shell model results., Comment: Article for the invited talk (by VKBK) given in the 35th International Workshop on "Nuclear Theory" held at Rila Mountains (Sofia, Bulgaria) during June 26 to July 2nd, 2016

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., Comment: 16 pages, 6 figures, Accepted for publication in Journal of Statistical Mechanics (2016)

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., Comment: 65 pages, 5 figures, 4 tables; some sections of the paper overlap considerably with the arXiv papers 1106.0395, 1411.6391 and 1501.07670

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., Comment: submitted for publication in the proceedings of the XVI International Conference on Symmetry Methods in Physics (SYMPHYS-XVI) held at JINR, Dubna (Moscow region, Russia) during 13-18 October 2014

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 $0\nu$ and $2\nu$ 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., Comment: 5 figures

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 Schr\"odinger 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., Comment: 28 pages, 7 figures; used software available at http://ultracold.org

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., Comment: J. Phys.: Conf. Ser. in press (Proceedings of the 30th International Colloquium on `Group Theoretical Methods in Physics' held at Ghent University, Belgium, during 14-18 July 2014)

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., Comment: enlarged version, 30 pages, 10 figures

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., Comment: 9 pages, 4 figures

We present a TCAD compatible multiscale model of phonon-assisted band-to-band tunneling (BTBT) in semiconductors, that incorporates the non-parabolic nature of complex bands within the bandgap of the material. This model is shown capture the measured current-voltage data in silicon, for current transport along the $[100]$, $[110]$ and $[111]$ directions. Our model will be useful to predict band-to-band tunneling phenomena to quantify on and off currents in Tunnel FETs and in small geometry MOSFETs and FINFETs.

Complex bands $\vec{k}^{\perp}(E)$ in a semiconductor crystal, along a general direction $\vec{n}$, can be computed by casting Schr\"odinger's equation as a generalized polynomial eigenvalue problem. When working with primitive lattice vectors, the order of this eigenvalue problem can grow large for arbitrary $\vec{n}$. It is however possible to always choose a set of non-primitive lattice vectors such that the eigenvalue problem is restricted to be quadratic. The complex bands so obtained need to be unfolded onto the primitive Brillouin zone. In this paper, we present a unified method to unfold real and complex bands. Our method ensures that the measure associated with the projections of the non-primary wavefunction onto all candidate primary wavefunctions is invariant with respect to the energy $E$.

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 $H_\lambda = (H_0+\lambda V)/\sqrt{1+\lambda^2}$ interpolating Poisson ($\lambda=0$) and GOE ($\lambda \rightarrow \infty$) we have analyzed the transition curves for $\langle r\rangle$ and $\langle \tilde{r}\rangle$ as $\lambda$ 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 $\Lambda \sim \lambda^2\,d$, i.e. the $\langle r\rangle$ vs $\lambda$ (similarly for $\langle \tilde{r}\rangle$ vs $\lambda$) curves for different $d$'s merge to a single curve when this is considered as a function of $\Lambda$. 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., Comment: 9 Pages, 5 figures

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 $\Sigma^2(L)$, and the Dyson-Mehta $\Delta_3-$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.

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., Comment: 7 pages, 10 figures

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 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., Comment: 22 pages, 6 figures