Structure of wavefunctions in (1+2)-body random matrix ensembles

Abstrtact: Random matrix ensembles defined by a mean-field one-body plus a chaos generating random two-body interaction (called embedded ensembles of (1+2)-body interactions) predict for wavefunctions, in the chaotic domain, an essentially one parameter Gaussian forms for the energy dependence of the number of principal components NPC and the localization length {\boldmath l}_H (defined by information entropy), which are two important measures of chaos in finite interacting many particle systems. Numerical embedded ensemble calculations and nuclear shell model results, for NPC and {\boldmath l}_H, are compared with the theory. These analysis clearly point out that for realistic finite interacting many particle systems, in the chaotic domain, wavefunction structure is given by (1+2)-body embedded random matrix ensembles.Comment: 20 pages, 3 figures (1a-c, 2a-b, 3a-c), prepared for the invited talk given in the international conference on `Perspectives in Theoretical Physics', held at Physical Research Laboratory, Ahmedabad during January 8-12, 200

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 $\Omega$ 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 figure

MODELLING WAVES: INTEGRATING TECHNOLOGY WITH MODELLING AND INQUIRY IN AN UNDERGRADUATE PHYSICS EXPERIMENT

This project focuses on the novel idea of integration of technologies with inquiry skills and modelling (Crook & Sharma, 2013; Cornish et al., 2019; Gilbert, 2004) and associates these with students’ cognitive engagement, behavioural engagement and emotional engagement (Muller, Sharma & Reimann, 2008; Kota, Cornish & Sharma, 2019). Using design-based research methodology, we integrated technology and inquiry to design an experiment on ‘modelling waves on a rope’, a standard topic in first-year undergraduate physics. Furthermore, we investigated how students engaged with the new experiment? It had three features; (1) qualitative description and kinaesthetic feel of waves being created on ropes, (2) taking measurements using video analysis software, and (3) a whole class comparison of experimental and theoretical values using a pre-designed EXCEL spreadsheet. The experiment was trialled in two tutor training sessions, and the final version was implemented in first year physics labs in 2018 and 2019. We used a survey (Barrie et al., 2015) that measures student experiences in labs by evaluating: how technology was integrated, how much inquiry skills are developed, and how well the students understand the modelling. We also collected observational notes and student logbooks and conducted interviews. Tutors were also surveyed. The sample size includes 406 students and 24 tutors. Findings show that students engaged in a hands-on experiment by creating waves on a rope, in using technology for data analysis and in developing ICT skills, and in understanding modelling using EXCEL spreadsheets. The experiment also fostered teamwork and required investment of an appropriate level of mental effort demonstrating that the experiment did engage students in a meaningful manner. The integration of digital technologies with ‘modelling waves on a rope’ resulted in higher overall enjoyment of the experiment and increased student engagement. REFERENCES Barrie, S. C., Bucat, R. B., Buntine, M. A., Burke da Silva, K., Crisp, G. T., George, A. V., & Yeung, A. (2015). Development, evaluation and use of a student experience survey in undergraduate science laboratories: The Advancing Science by Enhancing Learning in the Laboratory Student Laboratory Learning Experience Survey. International Journal of Science Education, 37(11), 1795-1814. Cornish, S., Yeung, A., Kable, S. H., Orgill, M., & Sharma, M. D. (2019). Using teacher voices to develop the ASELL Schools professional development workshops. Teaching Science, 65(1), 4. Crook, S. J. & Sharma, M. D. (2013). Bloom-ing heck! The activities of Australian science teachers and students two years into a 1:1 laptop program across 14 high schools. International Journal of Innovation in Science and Mathematics Education, 21(1), 54-69. Gilbert, J. K. (2004). Models and modelling: Routes to more authentic science education. International Journal of Science and Mathematics Education, 2(2), 115–130. Kota, S. D., Cornish, S, & Sharma, M. D. (2019); Switched on! Student and teacher engagement in an electricity practical, Physics Education, 54(1), 1-9. Muller, D. A., Sharma, M. D., & Reimann P 2008 Raising cognitive load with linear multimedia to promote conceptual change, Science Education, 92, 278–296

O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits with O(12) algebra which break F-spin but preserves the quantum number M_F. The generators of O(12) are derived and the quantum number `v' of O(12) for a given boson number N is determined by identifying the corresponding quasi-spin algebra. The O(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With the O(12) algebra identified, complete classification of pnIBM symmetry limits with good M_F is established.Comment: 22 pages, 1 figur

Constraining nuclear physics parameters with current and future COHERENT data

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 PL

RIS-NOMA integrated low-complexity transceiver architecture: Sum rate and energy efficiency perspective

This paper aims to explore reconfigurable intelligent surface (RIS) integration in a millimeter wave (mmWave) communication system with low-complexity transceiver architecture under imperfect CSI assumption. Towards this, we propose a RIS-aided system with a fully analog (FA) architecture at the base station. However, to overcome the disadvantage of single-user transmission due to the single RF-chain, we employ NOMA. For such a system, we formulate sum rate (SR) and energy efficiency (EE) maximization problems to obtain the joint transmit beamformer, RIS phase shift matrix, and power allocation solutions under minimum rate constraint. We first tackle the fractional objectives of both problems by reformulating the SR and EE maximization problems into equivalent quadratic forms using the quadratic transform. On the other hand, we employ successive convex approximation and the semi-definite relaxation technique to handle the non-convex minimum rate and unit modulus constraint of the RIS phase shifts, respectively. Next, we propose an alternating optimization-based algorithm that iterates over the transmit beamformer, power allocation, and RIS phase shift subproblems. Further, we also show that the quadratic reformulation is equivalent to the WMSE-based reformulation for the case of SR maximization problem. Our numerical results show that the proposed RIS-NOMA integrated FA architecture system outperforms the optimally configured fully digital architecture in terms of SR at low SNR and EE for a wide range of SNR while still maintaining low hardware complexity and cost. Finally, we present the numerical performance analysis of the RIS-NOMA integrated low-complexity system for various system configuration parameters