Faculty at School of Natural Sciences

Santosh Kumar

Santosh Kumar

Associate Professor


Contact Information

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

 

  • 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

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)

  • 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/