Dr. Santosh Kumar | Department of Physics

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Dr. Santosh
Kumar
Associate Professor
Department of Physics
School of Natural Sciences (SNS)
santosh.kumar@snu.edu.in
A023K
Block-A, Shiv Nadar University
Greater Noida Uttar Pradesh
India
91-0120-7170100
Extn: 
266
Educational Qualifications 
2011
Ph. D.
Jawaharlal Nehru University, New Delhi
2005
M. Sc. Physics
Jawaharlal Nehru University, New Delhi
2002
B. Sc. Physics (Hons.)
Vinoba Bhave University, Hazaribagh, Jharkhand
Work Experience 
07/19 – Present
Associate Professor,
Department of Physics, School of Natural Sciences, Shiv Nadar University, Delhi-NCR
I currently work here
07/13
06/19
Assistant Professor,
Department of Physics, School of Natural Sciences, Shiv Nadar University, Delhi-NCR
07/11
06/13
Post-Doctoral Research Associate,
University of Duisburg-Essen,
Duisburg, Germany
Teaching & Research Interests: 

Research Interests: Our research is concerned with the investigation of statistical properties of complex and/or chaotic systems using Random Matrix Theory. The study covers topics as varied as quantum conductance in mesoscopic devices, entanglement in random pure states, transmission properties in microwave resonators, and performance of multiple antenna communication systems.

Research Areas 
Mathematical Modelling
Wireless Networks and IOT
Statistical Physics of Complex Systems
Courses Taught(Selected) 
Introduction to Physics I (PHY101)
Introduction to Physics II (PHY102)
Introduction to Mathematical Physics I (PHY203)
Introduction to Mathematical Physics II (PHY204)
Electronics I (PHY206)
Abridge course for Minor students (PHY207)
Classical Electrodynamics (PHY303)
Adv. topics in non-linear dyn (PHY548)
Prob, Stat, Mat Th.& App (PHY557)
Non-linear dynamics (PHY415)
Conferences (Select): 
  • Invited talk (online) in Nonlinear Dynamics Lecture Series/Rusa Lecture Series, Bharathidasan University, Tiruchirappalli (Februrary 2023)
  • Invited talk at the Conference on Nonlinear Systems and Dynamics (CNSD2022), IISER Pune (December 2022)
  • Invited talk at the Dynamics Day Delhi (DDD) XVI, Bennett University, Greater Noida (November 2022)
  • Invited talk (online) at the Indo-Mexican Workshop: Multivariate Analysis & Machine Learning in Econophysics, Brain Activity, Sociophysics, and more (June 2022)
  • Invited talk (online) at the Summer School on Quantum Information and Quantum Technology-2021, IISER Kolkata (June - July 2021)
  • Invited talk (online) at the University of Melbourne random matrix theory seminar (June 2020)
  • Invited for delivering Random Matrix Theory lectures in the workshop “Advances in Mathematical Sciences and Applications" at Dayalbagh Educational Institute, Agra, India (April 2019)
  • Invited for delivering Random Matrix Theory lectures at DST-SERB school on Nonlinear Dynamics, Guru Nanak Dev University, Amritsar, India (December 2018)
  • Invited speaker at the international workshop 'Sums and Products of Random Matrices', Bielefeld University, Bielefeld, Germany (August 2018)
  • Invited speaker at the international Workshop on Experimental and Theoretical Developments on Complex Quantum Systems, Lanzhou University, Lanzhou, China (July 2018)
  • Invited speaker at the international symposium ‘RMT, Time Series and Many-Body Systems’, Centro Internacional de Ciencias A. C.,Cuernavaca, Mexico (June 2017)
  • Invited speaker at Mini Symposium of the 10th Conference on Nonlinear Systems and Dynamics (CNSD-2016), IISER Kolkata, Kolkata, India (December 2016)
  • Invited speaker at the "4th International Conference on Complex Dynamical Systems & Applications", NIT Durgapur, India (February 2016)
  • Invited speaker at the "IX Brunel-Bielefeld Workshop on Random Matrix Theory", Bielefeld University, Bielefeld, Germany (December 2013)
  • Invited speaker at the Langeoog conference of the Collaborative Research Center SFB/TR12 “Symmetries and universality in mesoscopic systems", Langeoog, Germany (February 2013)
  • Invited speaker at the workshop on Quantum chaos and quantum information, IIT Madras, Chennai, India (July 2010)

Scholarly Activity

Journal Publications (accepted or published)

48. Signatures of spectral crossovers in the short- and long-range spectral correlations of a disordered spin-chain with Kramers degeneracy, D. Kundu, S. Kumar, and S. S. Gupta, Physical Review B 107, 094205 (2023).
DOI Link: https://doi.org/10.1103/PhysRevB.107.094205

47. Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance, A. Laha and S. Kumar, Physical Review E 107, 034206 (2023).
DOI Link: https://doi.org/10.1103/PhysRevE.107.034206

46. Statistics of conductance and shot noise power in chaotic mesoscopic cavities with one ideal and one nonideal lead, A. Dheer and S. Kumar, Physica B 639, 413939 (2022).
DOI Link: https://doi.org/10.1016/j.physb.2022.413939

45. Investigation of chemical space networks using graph measures and random matrix theory, M. Kothiyal, S. Kumar, and N. Sukumar, Journal of Mathematical Chemistry 60, 891 (2022).
DOI Link: https://doi.org/10.1007/s10910-022-01341-y

44. Differential recurrences for the distribution of the trace of the β-Jacobi ensemble, P. J. Forrester and S. Kumar, Physica D 434, 133220 (2022).
DOI Link: https://doi.org/10.1016/j.physd.2022.133220

43. Spectral crossovers and universality in quantum spin-chains coupled to random fields, D. Kundu, S. Kumar, and S. S. Gupta, Physical Review B 105, 014205 (2022).
DOI Link: https://doi.org/10.1103/PhysRevB.105.014205

42. Random density matrices: Analytical results for mean root fidelity and the mean-square Bures distance, A. Laha, A. Aggarwal, and S. Kumar, Physical Review A 104, 022438 (2021).
DOI Link: https://doi.org/10.1103/PhysRevA.104.022438

41. Computable structural formulas for the distribution of the β-Jacobi edge eigenvalues, P. J. Forrester and S. Kumar, The Ramanujan Journal (2021).
DOI Link: https://doi.org/10.1007/s11139-021-00493-w

40. Optical MIMO communication with unequal power allocation to channels, A. Laha and S. Kumar, Optik 244, 167533 (2021).
DOI Link: https://doi.org/10.1016/j.ijleo.2021.167533

39. Generation of Bures-Hall mixed states using coupled kicked tops, A. Sarkar and S. Kumar, Physical Review A 103, 032423 (2021).
DOI Link: https://doi.org/10.1103/PhysRevA.103.032423

38. Electronic transport in chaotic mesoscopic cavities: A Kwant and random matrix theory based exploration, R. S. Chandramouli, R. K. Srivastav, and S. Kumar, Chaos 30, 123120 (2020).
DOI Link: https://doi.org/10.1063/5.0026039

37. Spectral statistics for the difference of two Wishart matrices, S. Kumar and S. Sai Charan, Journal of Physics A: Mathematical and Theoretical 53, 505202 (2020).
DOI Link: https://doi.org/10.1088/1751-8121/abc3fe

36. Wishart and random density matrices: Analytical results for mean square Hilbert-Schmidt distance, S. Kumar, Physical Review A 102, 012405 (2020).
DOI Link: https://doi.org/10.1103/PhysRevA.102.012405

35. Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles, A. Sarkar, M. Kothiyal, and S. Kumar, Physical Review E 101, 012216 (2020).
DOI Link: https://doi.org/10.1103/PhysRevE.101.012216

34. Synergistic Effect of Singly Charged Oxygen Vacancies and Ligand-Field for Regulating Transport Properties of Resistive Switching Memories, D. Das, A. Barman, S. Kumar, A. Sinha, M. Gupta, R. Singhal, P. Johari, and A. Kanjilal, The Journal of Physical Chemistry C 123, 26812 (2019).
DOI Link: https://doi.org/10.1021/acs.jpcc.9b08078

33. Recursion scheme for the largest β-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport, P. J. Forrester and S. Kumar, Journal of Physics A: Mathematical and Theoretical (Letters) 52, 42LT02 (2019).
[Featured article]
DOI Link: https://doi.org/10.1088/1751-8121/ab433c

32. Exact Distributions for Bit Error Rate and Channel Capacity in Free Space Optical Communication, S. Kumar, R. K. Singh, and Karmeshu, IET Communications 13, 2966 (2019).
DOI Link: https://doi.org/10.1049/iet-com.2019.0314

31. Bures-Hall ensemble: spectral densities and average entropies, A. Sarkar and S. Kumar, Journal of Physics A: Mathematical and Theoretical 52, 295203 (2019).
[Featured article]
DOI Link: https://doi.org/10.1088/1751-8121/ab2675

30. Recursion for the smallest eigenvalue density of β-Wishart-Laguerre ensemble, S. Kumar, Journal of Statistical Physics 175, 126 (2019).
DOI Link: https://doi.org/10.1007/s10955-019-02245-z
Full-text view-only link: https://rdcu.be/bmtAs

29. Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions, S. Kumar, G. Kumar, R. S. Chandramouli, and S. Anand, Physical Review E 98, 063301 (2018).
DOI Link: https://doi.org/10.1103/PhysRevE.98.063301

28. Asymptotic Eigenvalue Density for the Quotient Ensemble of Wishart Matrices,  S. Kumar, G. F. Pivaro, Y. R. Yerrababu, G. Fraidenraich, D. A. Guimarães, and R. A. A. de Souza, IEEE Communications Letters 22, 2575 (2018).
DOI Link: https://doi.org/10.1109/LCOMM.2018.2877327

27. Comments on 'Cutset Bounds on the Capacity of MIMO Relay Channels', S. Kumar, G. F. Pivaro, and G. Fraidenraich, IEEE Access 6, 35129 (2018).
DOI Link: https://doi.org/10.1109/ACCESS.2018.2849640

26. The Probability That All Eigenvalues are Real for Products of Truncated Real Orthogonal Random Matrices, P. J. Forrester and S. Kumar, Journal of Theoretical Probability 31, 2056 (2018).
DOI Link:

25. Exact distribution of spacing ratios for random and localized states in quantum chaotic systems,  S. H. Tekur, S. Kumar, and M. S. Santhanam, Physical Review E 97, 062212 (2018).
DOI Link: https://doi.org/10.1103/PhysRevE.97.062212

24. How many eigenvalues of a product of truncated orthogonal matrices are real?,  P. J. Forrester, J. R. Ipsen, and S. Kumar, Experimental Mathematics (2018).
DOI Link: https://doi.org/10.1080/10586458.2018.1459962

23. A New Approximation for PDF of K Distribution: Analytical Study of QoS Parameters in Free Space Optical Communication,  R. K. Singh, S. Kumar, and Karmeshu, IET Communications 12, 1703 (2018).
DOI Link: https://dx.doi.org/10.1049/iet-com.2017.1388

22. Bit Error Probability for MMSE Receiver in GFDM Systems, D. C. Melgarejo, S. Kumar, G. Fraidenraich, and L. L. Mendes, IEEE Communications Letters 22, 942 (2018).
DOI Link: https://doi.org/10.1109/LCOMM.2018.2808475

21. Distribution of off-diagonal cross sections in quantum chaotic scattering: Exact results and data comparison, S. Kumar, B Dietz, T Guhr, and A Richter, Physical Review Letters 119, 244102 (2017).
[Editors' Suggestion]
DOI Link:

20. Relativistic nature of carriers: Origin of electron-hole conduction asymmetry in monolayer graphene, P. K. Srivastava, S. Arya, S. Kumar, and S. Ghosh, Physical Review B (Rapid Communications) 96, 241407(R) (2017).
DOI Link:

19. A Novel Approximation for K Distribution: Closed form BER using DPSK Modulation in Free Space Optical Communication, R. K. Singh, Karmeshu, and S. Kumar, IEEE Photonics Journal 9, 1 (2017).
DOI Link:

18. Smallest eigenvalue density for regular or fixed-trace complex Wishart–Laguerre ensemble and entanglement in coupled kicked tops, S. Kumar, B. Sambasivam, and S. Anand, Journal of Physics A: Mathematical and Theoretical 50, 345201 (2017).
DOI Link:

17. Approximate Sum Rate for Integer-Forcing Receiver, A. S. Guerreiro, G. Fraidenraich, and S. Kumar, IEEE Transactions on Communications 65, 4899 (2017).
DOI Link:

16. On the Exact and Approximate Eigenvalue Distribution for Sum of Wishart Matrices, G. F. Pivaro, S. Kumar, G. Fraidenraich, and C. F. Dias, IEEE Transactions on Vehicular Technology 66, 10537 (2017).
DOI Link:

15. On the Exact Distribution of Mutual Information of Two-user MIMO MAC Based on Quotient Distribution of Wishart Matrices, G. Pivaro, S. Kumar, G. Fraidenraich, EURASIP Journal on Wireless Communications and Networking 2017, 75 (2017).
DOI Link:

14. On the Ergodic Capacity of Distributed MIMO Antenna Systems, S. Kumar, Wireless Personal Communications 92, 381 (2017).
DOI Link:

13. The Correlated Jacobi and the Correlated Cauchy-Lorentz Ensembles, T. Wirtz, D. Waltner, M. Kieburg, S. Kumar, Journal of Statistical Physics 162, 495 (2016).
DOI Link:

12. Exact evaluations of some Meijer G-functions and probability of all eigenvalues real for the product of two Gaussian matrices, S. Kumar, Journal of Physics A: Mathematical and Theoretical 48, 445206 (2015).
DOI Link:
IOP Publisher's Pick - Interview:

11. Random matrix ensembles involving Gaussian Wigner and Wishart matrices, and biorthogonal structure, S. Kumar, Physical Review E 92, 032903 (2015).
DOI Link:

10. Eigenvalue Statistics for the Sum of Two Complex Wishart Matrices, S. Kumar, Europhysics Letters 107, 60002 (2014).
DOI Link:

9. Distributions of Off-Diagonal Scattering Matrix Elements: Exact Results, A. Nock, S. Kumar, H.-J. Sommers and T. Guhr, Annals of Physics 342, 103 (2014).
DOI Link:

8. Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering, S. Kumar, A. Nock, H.-J. Sommers, T. Guhr, B. Dietz, M. Miski-Oglu, A. Richter, and F. Schäfer, Physical Review Letters 111, 030403 (2013).
DOI Link:

7. Random Matrix Ensembles: Wang-Landau Algorithm for Spectral Densities, S. Kumar, Europhysics Letters. 101, 20002 (2013).
DOI Link:

6. Entanglement in Random Pure States: Spectral Density and Average von Neumann Entropy, S. Kumar and A. Pandey, Journal of Physics A: Mathematical and Theoretical 44, 445301 (2011).
DOI Link:

5. Skew-Orthogonal Polynomials and Crossover Ensembles of Random Matrices, S. Kumar and A. Pandey, Annals of Physics 326, 1877 (2011).
DOI Link:

4. Conductance Distributions in Chaotic Mesoscopic Cavities, S. Kumar and A. Pandey, Journal of Physics A: Mathematical and Theoretical 43, 285101 (2010).
DOI Link:

3. Random Matrix Model for Nakagami-Hoyt Fading, S. Kumar and A. Pandey, IEEE Transactions on Information Theory 56, 2360 (2010).
DOI Link:

2. Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues, S. Kumar and A. Pandey, Journal of Physics A: Mathematical and Theoretical 43, 085001 (2010).
DOI Link:

1. Universal Spectral Correlations in Orthogonal-Unitary and Symplectic-Unitary Crossover Ensembles of Random Matrices, S. Kumar and A. Pandey, Physical Review E 79, 026211 (2009).
DOI Link:

Conference Publications

Associative Memory on Small World Networks, Y. Gurbani, S. M. Kamil, and S. Kumar, AIP Conference Proceedings 2377, 040005 (2021)
DOI Link: https://doi.org/10.1063/5.0063386

Achievable Sum Rate and Outage Capacity of GFDM Systems with MMSE Receivers, D. Carrillo, S. Kumar, G. Fraidenraich, P. H. J. Nardelli, and D. B. da Costa, ICC 2020 - 2020 IEEE International Conference on Communications (ICC), pp. 1-6 (2020)
DOI Link: https://doi.org/10.1109/ICC40277.2020.9149450

Convergence of MassiveMIMO Frequency Selective Channels, G. Srikanth, V. K. Chakka, and S. Kumar, TENCON 2019 - 2019 IEEE Region 10 Conference (TENCON), pp. 1499-1503 (2019)
Web Link: https://ieeexplore.ieee.org/document/8929694

Laguerre unitary ensemble to Gaussian unitary ensemble crossover: Eigenvalue statistics, S. Kumar, Indian Academy of Sciences Conference Series 2 (1), 131 (2019)
Web Link: https://www.ias.ac.in/describe/article/conf/002/0019

Volume of metric balls in real Grassmann manifold with an application to frames, S. Kumar, R.-A. Pitaval, and L. Wei, IEEE International Symposium on Information Theory and Its Applications (ISITA) (2016).
Web Link:

Projects

DST-SERB Core Research Grant Funding

Project Title: Applications of structured random matrix models to some problems in classical and quantum information theories
Duration: 3 years (2023-2026)

 

DST-SERB Extra Mural Research Funding

Project Title: Investigation of Electronic Transport Properties in Mesoscopic Systems Using Random Matrix Theory
Duration: 3 years (2017-2020)

 

Opportunities for Undergraduate Research (OUR), SNU

OUR 2021-22
Title: Universality aspects of the adjacency matrix spectrum in multilayer networks
Student: Ananya SelapariSetti
This project was graded ‘very good’ by the OUR jury.

OUR 2019-20
Title: Spectral statistics of Dirac operator in quantum chromodynamics using random matrices
Student: Ajay Shanmuga S.

OUR 2018-19
Title: Classical and Quantum-mechanical explorations of a particle in a random potential
Student: S. Sai Charan
Chosen for award of distinction

OUR 2017-18
Title: Exploration of Quantum Chaotic Systems using Random Matrix Theory
Student: Suvendu Barik
This project was awarded the second prize by the OUR jury

Title: Free Probability approach for investigating density of states of disordered systems
Student: Yogeesh Reddy Yerrababu

OUR 2016-17
Title: Investigation of the Phase Transition in Self Gravitating Systems
Student: Girish Kumar
This project resulted in a publication:
S. Kumar, G. Kumar, R. S. Chandramouli, and S. Anand, Physical Review E 98, 063301 (2018).

OUR 2015-16
Title: Entanglement in Random Pure States: Statistics of Extreme Schmidt Eigenvalues
Student: Bharath Sambasivam
This project was graded ‘excellent’ and awarded the second prize by the OUR jury. It also resulted in a publication:
S. Kumar, B. Sambasivam, and S. Anand, Journal of Physics A: Mathematical and Theoretical 50, 345201 (2017).

OUR 2014-15
Title: Statistics of Green’s function in chaotic systems: A Supersymmetry approach Student: Tarun Tummuru
This project was graded ‘very good’ by the OUR jury.