## Faculty at School of Natural Sciences

### Santosh Kumar

Associate Professor

School of Natural Sciences

##### Contact Information

- Email: [email protected]
- Number: 91-120-7170100
- Number: Extn: 266

Random Matrix Theory and Its Applications, Quantum Chaos, Statistical Physics of Complex Systems, Mathematical Physics

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- 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

- 07/19 - Present Associate Professor, Department of Physics, School of Natural Sciences, Shiv Nadar Institution of Eminence, Delhi-NCR
- 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

- Outstanding Research Award, Circle of Excellence Awards, SNU (2021)
- OUR Supervision Award, Circle of Excellence Awards, SNU (2021)
- CSIR Senior Research Fellow (2007 - 2010)
- CSIR Junior Research Fellow (2005 - 2007)
- Qualified Graduate Aptitude Test in Engineering (GATE) in Physics in 2005
- Gold Medalist of the M.Sc. 2003-2005 batch at JNU, New Delhi

- D. Kundu,
**S. Kumar**, and S. S. Gupta, Signatures of spectral crossovers in the short- and long-range spectral correlations of a disordered spin-chain with Kramers degeneracy, Physical Review B 107, 094205 (2023). - A. Laha and
**S. Kumar**, Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance, Physical Review E 107, 034206 (2023) - A. Dheer and
**S. Kumar**, Statistics of conductance and shot noise power in chaotic mesoscopic cavities with one ideal and one nonideal lead, Physica B 639, 413939 (2022). - M. Kothiyal,
**S. Kumar**, and N. Sukumar, Investigation of chemical space networks using graph measures and random matrix theory, Journal of Mathematical Chemistry 60, 891 (2022). - P. J. Forrester and
**S. Kumar**, Differential recurrences for the distribution of the trace of the β-Jacobi ensemble, Physica D 434, 133220 (2022). - D. Kundu,
**S. Kumar**, and S. S. Gupta, Spectral crossovers and universality in quantum spin-chains coupled to random fields, Physical Review B 105, 014205 (2022). - A. Laha, A. Aggarwal, and
**S. Kumar**, Random density matrices: Analytical results for mean root fidelity and the mean-square Bures distance, Physical Review A 104, 022438 (2021). - P. J. Forrester and
**S. Kumar**, Computable structural formulas for the distribution of the β-Jacobi edge eigenvalues, The Ramanujan Journal (2021). - A. Laha and
**S. Kumar**, Optical MIMO communication with unequal power allocation to channels, Optik 244, 167533 (2021). - A. Sarkar and
**S. Kumar**, Generation of Bures-Hall mixed states using coupled kicked tops, Physical Review A 103, 032423 (2021). - R. S. Chandramouli, R. K. Srivastav, and
**S. Kumar**, Electronic transport in chaotic mesoscopic cavities: A Kwant and random matrix theory based exploration, Chaos 30, 123120 (2020). **S. Kumar**and S. Sai Charan, Spectral statistics for the difference of two Wishart matrices, Journal of Physics A: Mathematical and Theoretical 53, 505202 (2020).**S. Kumar**, Wishart and random density matrices: Analytical results for mean square Hilbert-Schmidt distance, Physical Review A 102, 012405 (2020).- A. Sarkar, M. Kothiyal, and
**S. Kumar**, Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles, Physical Review E 101, 012216 (2020). - D. Das, A. Barman,
**S. Kumar**, A. Sinha, M. Gupta, R. Singhal, P. Johari, and A. Kanjilal, Synergistic Effect of Singly Charged Oxygen Vacancies and Ligand-Field for Regulating Transport Properties of Resistive Switching Memories, The Journal of Physical Chemistry C 123, 26812 (2019). - P. J. Forrester and
**S. Kumar**, Recursion scheme for the largest β-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport, Journal of Physics A: Mathematical and Theoretical (Letters) 52, 42LT02 (2019). **S. Kumar**, R. K. Singh, and Karmeshu, Exact Distributions for Bit Error Rate and Channel Capacity in Free Space Optical Communication, IET Communications 13, 2966 (2019).- A. Sarkar and
**S. Kumar**, Bures-Hall ensemble: spectral densities and average entropies, Journal of Physics A: Mathematical and Theoretical 52, 295203 (2019). **S. Kumar**, Recursion for the smallest eigenvalue density of β-Wishart-Laguerre ensemble, Journal of Statistical Physics 175, 126 (2019).**S. Kumar**, G. Kumar, R. S. Chandramouli, and S. Anand, Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions, Physical Review E 98, 063301 (2018).**S. Kumar**, G. F. Pivaro, Y. R. Yerrababu, G. Fraidenraich, D. A. Guimarães, and R. A. A. de Souza, Asymptotic Eigenvalue Density for the Quotient Ensemble of Wishart Matrices, IEEE Communications Letters 22, 2575 (2018).**S. Kumar**, G. F. Pivaro, and G. Fraidenraich, Comments on 'Cutset Bounds on the Capacity of MIMO Relay Channels', IEEE Access 6, 35129 (2018).- P. J. Forrester and
**S. Kumar**, The Probability That All Eigenvalues are Real for Products of Truncated Real Orthogonal Random Matrices, Journal of Theoretical Probability 31, 2056 (2018). - S. H. Tekur,
**S. Kumar**, and M. S. Santhanam, Exact distribution of spacing ratios for random and localized states in quantum chaotic systems, Physical Review E 97, 062212 (2018). - P. J. Forrester, J. R. Ipsen, and
**S. Kumar**, How many eigenvalues of a product of truncated orthogonal matrices are real?, Experimental Mathematics (2018). - R. K. Singh,
**S. Kumar**, and Karmeshu, A New Approximation for PDF of K Distribution: Analytical Study of QoS Parameters in Free Space Optical Communication, IET Communications 12, 1703 (2018). - D. C. Melgarejo,
**S. Kumar**, G. Fraidenraich, and L. L. Mendes, Bit Error Probability for MMSE Receiver in GFDM Systems, IEEE Communications Letters 22, 942 (2018). **S. Kumar**, B Dietz, T Guhr, and A Richter, Distribution of off-diagonal cross sections in quantum chaotic scattering: Exact results and data comparison, Physical Review Letters 119, 244102 (2017).- P. K. Srivastava, S. Arya,
**S. Kumar**, and S. Ghosh, Relativistic nature of carriers: Origin of electron-hole conduction asymmetry in monolayer graphene, Physical Review B (Rapid Communications) 96, 241407(R) (2017). - R. K. Singh, Karmeshu, and
**S. Kumar**, A Novel Approximation for K Distribution: Closed form BER using DPSK Modulation in Free Space Optical Communication, IEEE Photonics Journal 9, 1 (2017). **S. Kumar**, B. Sambasivam, and S. Anand, Smallest eigenvalue density for regular or fixed-trace complex Wishart–Laguerre ensemble and entanglement in coupled kicked tops, Journal of Physics A: Mathematical and Theoretical 50, 345201 (2017).- A. S. Guerreiro, G. Fraidenraich, and
**S. Kumar**, Approximate Sum Rate for Integer-Forcing Receiver, IEEE Transactions on Communications 65, 4899 (2017). **S. Kumar**, G. Fraidenraich, and C. F. Dias, On the Exact and Approximate Eigenvalue Distribution for Sum of Wishart Matrices, G. F. Pivaro, IEEE Transactions on Vehicular Technology 66, 10537 (2017).- G. Pivaro,
**S. Kumar**, G. Fraidenraich, On the Exact Distribution of Mutual Information of Two-user MIMO MAC Based on Quotient Distribution of Wishart Matrices, EURASIP Journal on Wireless Communications and Networking 2017, 75 (2017). **S. Kumar**, On the Ergodic Capacity of Distributed MIMO Antenna Systems, Wireless Personal Communications 92, 381 (2017).- T. Wirtz, D. Waltner, M. Kieburg,
**S. Kumar**, The Correlated Jacobi and the Correlated Cauchy-Lorentz Ensembles, Journal of Statistical Physics 162, 495 (2016). **S. Kumar**, Exact evaluations of some Meijer G-functions and probability of all eigenvalues real for product of two Gaussian matrices, Journal of Physics A: Mathematical and Theoretical 48, 445206 (2015).**S. Kumar**, Random matrix ensembles involving Gaussian Wigner and Wishart matrices, and Biorthogonal structure, Physical Review E 92, 032903 (2015).**S. Kumar**, Eigenvalue statistics for the sum of two complex Wishart matrices, Europhysics Letters 107, 60002 (2014).- A. Nock,
**S. Kumar**, H.-J. Sommers, and T. Guhr, Distributions of Off-Diagonal Scattering Matrix Elements: Exact Results Annals of Physics 342, 103 (2014). **S. Kumar**, A. Nock, H.-J. Sommers, T. Guhr, B. Dietz, M. Miski-Oglu, A. Richter, and F. Schäfer, Distribution of scattering matrix elements in quantum chaotic scattering, Physical Review Letters 111, 030403 (2013).**S. Kumar**, Random matrix ensembles: Wang-Landau algorithm for spectral densities, Europhysics Letters 101, 20002 (2013).**S. Kumar**and A Pandey, Entanglement in random pure states: spectral density and average von Neumann entropy Journal of Physics A: Mathematical and Theoretical 44, 445301 (2011).**S. Kumar**and A. Pandey, Crossover ensembles of random matrices and skew-orthogonal polynomials, Annals of Physics 326, 1877 (2011).**S. Kumar**and A. Pandey, Conductance distributions in chaotic mesoscopic cavities Journal of Physics A: Mathematical and Theoretical 43, 285101 (2010).**S. Kumar**and A. Pandey, Jacobi crossover ensembles of random matrices and statistics of transmission eigenvalues Journal of Physics A: Mathematical and Theoretical 43, 085001 (2010).**S. Kumar**and A. Pandey, Random Matrix Model for Nakagami–Hoyt Fading, IEEE Transactions on Information Theory 56, 2360 (2010).**S. Kumar**and A. Pandey, Universal spectral correlations in orthogonal-unitary and symplectic-unitary crossover ensembles of random matrices, Physical Review E 79, 026211 (2009).

- 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)

- Investigation of Electronic Transport Properties in Mesoscopic Systems Using Random Matrix Theory, PI: Santosh Kumar, SERB Core Research Grant (CRG) Funding, Amoung sanctioned: ₹ 23,24,148, 3 years (2023-2026)

- Investigation of Electronic Transport Properties in Mesoscopic Systems Using Random Matrix Theory, PI: Santosh Kumar, SERB Extra Mural Research Funding (EMR), Amoung sanctioned: ₹ 15,54,371, 3 years (2017-2020)

- Y. Gurbani, S. M. Kamil, and
**S. Kumar**,*Associative Memory on Small World Networks*, AIP Conference Proceedings**2377**, 040005 (2021)

DOI Link: https://doi.org/10.1063/5.0063386 - D. Carrillo,
**S. Kumar**, G. Fraidenraich, P. H. J. Nardelli, and D. B. da Costa,*Achievable Sum Rate and Outage Capacity of GFDM Systems with MMSE Receivers,*ICC 2020 - 2020 IEEE International Conference on Communications (ICC), pp. 1-6 (2020)

DOI Link: https://doi.org/10.1109/ICC40277.2020.9149450 - G. Srikanth, V. K. Chakka, and
**S. Kumar**,*Convergence of MassiveMIMO Frequency Selective Channels,*TENCON 2019 - 2019 IEEE Region 10 Conference (TENCON), pp. 1499-1503 (2019)

Web Link: https://ieeexplore.ieee.org/document/8929694 **S. Kumar**,*Laguerre unitary ensemble to Gaussian unitary ensemble crossover: Eigenvalue statistics,*Indian Academy of Sciences Conference Series**2**(1), 131 (2019)

Web Link: https://www.ias.ac.in/describe/article/conf/002/0019**S. Kumar**,*Volume of metric balls in real Grassmann manifold with an application to frames,*R.-A. Pitaval, and L. Wei, IEEE International Symposium on Information Theory and Its Applications (ISITA) (2016).

Web Link: http://ieeexplore.ieee.org/document/7840528/