Qualification: 
Ph.D, MPhil, MSc, BSc
m_dharani@blr.amrita.edu
Phone: 
9916497200

Dr. M. Dharani currently serves as Assistant Professor (Sr. Gr.) at the Department of Physics, School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru campus. Her areas of research include Quantum Physics, Condensed Matter Physics and Biophysics. She has successfully defended her Ph.D. thesis titled “Investigation on Threshold Conditions, Bound States, Band Structure and Transmission by Periodic Delta Potentials” at Amrita Vishwa Vidyapeetham, Coimbatore.

Education

  • 2017: Ph. D.
    Amrita Vishwa Vidyapeetham
  • 2003: M. Phil.
    Bharathiar University
  • 2001: M. Sc.
    Bharathiar University
  • 1999: B. Sc.
    Bharathiar University

Professional Appointments

Year Affiliation
2010 - Present Assistant Professor (Sr. Gr.), School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru
2006 - 2010 Assistant Professor, School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru
2003-2006 Lecturer, CMS College of Science, Coimbatore

Publications

Publication Type: Journal Article

Year of Publication Title

2019

M. Dharani, Sahu, B., and Shastry, C. S., “Selective suppression of eigenstates with an absorptive delta potential in one and three dimensional potential scattering”, Physica B: Condensed Matter, vol. 557, pp. 95-98, 2019.[Abstract]


We demonstrate that the manifestation of a subset of the resonances generated by twin symmetric delta potential barrier in one dimension can be effectively suppressed by introducing an absorptive delta potential in between keeping the rest of resonance structure practically unaffected. Similar results are also valid in s–wave scattering. An explanation of this feature is provided.

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2018

M. Dharani and Shastry, C. S., “Structure of the transmission peaks in bands generated by attractive Dirac comb potentials”, Materials Today: Proceedings, vol. 5, pp. 16214-16219, 2018.[Abstract]


We study the pattern of bands generated by the transmission coefficient for transmission across N equispaced attractive Dirac comb potentials each having strength parameter V. The nature of the first band is found to be different from all higher bands and requires careful analysis. The number of peaks in the first band is found to depend on the bound states generated by N attractive delta potential, whereas in all other higher bands the number of peak is found to depend on the number of gaps between the adjacent delta terms. We illustrate these results for various values of N and V.

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2017

M. Dharani and Shastry, C. S., “Model study of transmission across N periodically placed ionic molecules in one dimension”, AIP Conference Proceedings, vol. 1832, p. 110038, 2017.[Abstract]


The conditions for occurrence of threshold bound states for orderly placed set of N ionic molecules in one dimension and their relation with the corresponding transmission coefficient as a function of energy are studied by simulating the same by N alternating pairs of attractive and repulsive delta potential. It is demonstrated that the number of peaks in the first band of transmission coefficient is N-Nb where Nb signifies the number of bound states in the system. The nature of distribution of peaks in higher bands is also explored.

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2017

M. Dharani and Shastry, C. S., “Investigation of bound states and transmission across orderly arranged pairs of attractive and repulsive delta potentials”, Physica B: Condensed Matter, vol. 516, pp. 27-31, 2017.[Abstract]


The pattern of bands generated by the transmission coefficient T for transmission across N ionic molecules in one dimension simulated by N alternating pairs of attractive and repulsive delta potential is studied by exploring its relation with the conditions for the occurence of threshold bound state. The number of peaks in the first band of T is found to be the difference between N and the number of negative energy bound states generated by this potential. Further we systematically study the nature of distribution of peaks in higher bands as a function of potential strength and distance parameters and compare it with the results obtained in our earlier works.

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2016

M. Dharani and Shastry, C. S., “Band structures in transmission coefficients generated by Dirac comb potentials”, Physica B: Condensed Matter, vol. 500, pp. 66-76, 2016.[Abstract]


Using the threshold conditions and bound state energies investigated earlier by us as a critical input we systematically study the nature of band formation in the transmission coefficient generated by Dirac comb potentials having equispaced (i) attractive, (ii) repulsive and (iii) alternating attractive and repulsive delta terms having same strength and confined within a fixed range. We find that positions of the peaks of transmission coefficient generated by a combination of one attractive and one repulsive delta terms having same strength and separated by gap a is independent of the potential strength and coincide with the energy eigenvalues of 1D box of range a. We further study analytically and numerically the transmission across Dirac comb potentials containing two or three delta terms and these results are useful in the analysis of the transmission in the general case. In the case of Dirac comb potentials containing Na attractive delta terms we find that the nature of the first band and higher bands of the transmission coefficient are different, and if such a potential generates Nb number of bound states, the first band in the transmission coefficient generated by the potential has NT1=Na−Nb peaks. In the case of higher bands generated by delta comb potential having N delta terms each band has N−1 peaks. Further we systematically study the behavior of band gaps and band spread as a function of potential strength and number of terms in the Dirac comb. The results obtained by us provide a relation between bound state spectrum, number of delta terms in the Dirac comb and the band pattern which can be explored for potential applications.

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2016

M. Dharani and Shastry, C. S., “Threshold conditions, energy spectrum and bands generated by locally periodic Dirac comb potentials”, Physica B: Condensed Matter, vol. 481, pp. 104–117, 2016.[Abstract]


We derive expressions for polynomials governing the threshold conditions for different types of locally periodic Dirac comb potentials comprising of attractive and combination of attractive and repulsive delta potential terms confined symmetrically inside a one dimensional box of fixed length. The roots of these polynomials specify the conditions on the potential parameters in order to generate threshold energy bound states. The mathematical and numerical methods used by us were first formulated in our earlier works and it is also very briefly summarized in this paper. We report a number of mathematical results pertaining to the threshold conditions and these are useful in controlling the number of negative energy states as desired. We further demonstrate the correlation between the distribution of roots of these polynomials and negative energy eigenvalues. Using these results as basis, we investigate the energy bands in the positive energy spectrum for the above specified Dirac comb potentials and also for the corresponding repulsive case. In the case of attractive Dirac comb the base energy of the each band excluding the first band coincides with specific eigenvalue of the confining box whereas in the repulsive case it coincides with the band top. We deduce systematic correlation between band gaps, band spreads and box eigenvalues and explain the physical reason for the vanishing of band pattern at higher energies. In the case of Dirac comb comprising of orderly arranged attractive and repulsive delta potentials, specific box eigenvalues occur in the middle of each band excluding the first band. From our study we find that by controlling the number and strength parameters of delta terms in the Dirac comb and the size of confining box it is possible to generate desired types of band formations. We believe the results from our systematic analysis are useful and relevant in the study of various one dimensional systems of physical interest in areas like nanoscience.

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2014

M. Dharani, Sahu, B., and Shastry, C. S., “Threshold conditions and bound states for locally periodic delta potentials”, vol. 12, no. 10, pp. 755 - 766, 2014.[Abstract]


We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = gn, n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D1(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D1(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D1(N, g). A similar study is presented for case (b). Using the properties of D1(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of gnas a function of n and several interesting features of the energy spectrum for different values of g and N are also described.

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2013

M. Dharani, Sahu, Bb, and Shastry, C. Sc, “Conditions governing the generalisation of threshold bound states by N attractive delta potentials in one and three dimensions”, Central European Journal of Physics, vol. 11, pp. 995-1005, 2013.[Abstract]


This paper proves that for N attractive delta function potentials the number of bound states (Nb) satisfies 1 ≤ N b ≤ N in one dimension (1D), and is 0 ≤ N b ≤ N in three dimensions (3D). Algebraic equations are obtained to evaluate the bound states generated by N attractive delta potentials. In particular, in the case of N attractive delta function potentials having same separation a between adjacent wells and having the same strength λV, the parameter g=λVa governs the number of bound states. For a given N in the range 1-7, both in 1D and 3D cases the numerical values of gn, where n=1,2,..N are obtained. When g=gn, Nb ≤ n where Nb includes one threshold energy bound state. Furthermore, gn are the roots of the Nth order polynomial equations with integer coefficients. Based on our numerical calculations up to N=40, even when N becomes large, 0 ≤ g n ≤ 4 and (Formula presented.) and this result is expected to be generally valid. Thus, for g > 4 there will be no threshold or zero energy bound state, and if g≈ 2 for a given large N, the number of bound states will be approximately N/2. The empirical formula gn = 4/[1+exp((N 0 - n)/β)] gives a good description of the variation of gn as a function of n. This formula is useful in estimating the number of bound states for any N and g both in 1D and 3D cases. © 2013 Versita Warsaw and Springer-Verlag Wien.

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Publication Type: Conference Paper

Year of Publication Title

2016

M. Dharani and Shastry, C. Sb, “Interesting features of transmission across locally periodic delta potentials”, in AIP Conference Proceedings, 2016, vol. 1731.[Abstract]


We study the theory of transmission of electrons through N delta potential barriers as well as wells. Some of the interesting features like the correlation between resonance peak positions and box states, number of peaks in transmission band and bound states are analyzed for locally periodic attractive, repulsive and pair of attractive and repulsive potentials. © 2016 Author(s).

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2012

M. Dharani, Shastry, C. S., Sahu, B., and Dr. Mahadevan S., “Selective suppression of Eigen states with an absorptive delta potential”, in Proceedings of the DAE-BRNS symposium on nuclear physics. V. 57, 2012.[Abstract]


Delta function potentials are used to explain short range elastic impurities and nature of the spectrum generated by the delta function potential embedded in a box and to construct model atomic systems interacting with the electromagnetic fields leading to multi photon absorption and ionization process. Similar study can be carried out in a nuclear system to analyze different properties of radioactive ions. The resonances generated when particle traverses across two delta potentials in one-dimension (ID) are studied. In this contribution, a novel feature is demonstrated that an absorptive delta potential suitably placed within a potential pocket can be used to selectively manipulate and suppress the resonances generated by the pocket

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Publication Type: Conference Proceedings

Year of Publication Title

2015

M. Dharani, Shastry, C. S., Bhattacharyya, D., Chitra, R., and Sahoo, N. K., “Threshold conditions and bands in attractive Dirac comb”, AIP Conference Proceedings. AIP Publishing, 2015.[Abstract]


Taking into account the threshold conditions for the generation of bound states by an attractive delta comb in one dimension, we describe the band structure generated by the same when confined to a box demonstrating the correlation between the potential strength, band width and band gap.

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2012

K. Aditya, M. Dharani, Prema, P., Dr. Mahadevan S., and Shastry, C. S., “Calculation of Q values and Half lives of $\alpha$-decay for A= 152-181 using S-Matrix method”, Proceedings of the DAE-BRNS Symposium on Nuclear Physics, vol. 44. 2012.[Abstract]


The success in the description of half lives and Q-values of Super heavy elements (SHE) using the microscopic alpha daughter nucleus potential and S-Matrix method (SM) prompted us to extend the analysis to the nuclei in the rare earth regions with A=152-181. We have reported in 2010, the results of the half lives and Q-values for the nuclei A=152-181 using WKB method. In this paper we report the results obtained using the more accurate S-Matrix method. The microscopic alpha nucleus potential is generated in the double folding model (τρρ-approximation) using relativistic mean field (RMF) densities along with density dependent M3Ynucleon-nucleon interaction. This potential is then used in the SM method to calculate both Q-values and decay half lives

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Courses Taught

  • Engineering Physics
  • Engineering Physics lab
  • Physics of Semiconductors
  • Electrical Engineering Materials
  • Lasers and its Applications
  • Material Science
  • Nuclear Energy: Principles and Application
  • Advanced Mathematical Physics
  • Advanced Quantum Physics
  • Biology for Engineers

Student Guidance

Postgraduate Students
Sl. No. Name of the Student Topic Status – Ongoing/Completed Year of Completion
1. M. Praveen Quantum Physics Ongoing  
2. Sundararagavan K. S. Quantum Physics Ongoing  
3. Nivetha N. K. Quantum Physics Ongoing  
4. Surya Ramachandran Special Features of Transmission, Reflection and Absorption Across an Emissive Complex Potential Completed April 2019
Research Scholars
1. Geetha Rani Madhuri Fluid Flow Visualisation using Machine Learning Ongoing