Faculty at School of Natural Sciences

Santosh Kumar

Santosh Kumar

Associate Professor

School of Natural Sciences


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/