Santosh Kumar | Department of Physics

Profile

Santosh Kumar
Santosh
Kumar
Associate Professor
Department of Physics
School of Natural Sciences (SoNS)
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 
07/19Present
Associate Professor,
Shiv Nadar University,
Gautam Buddha Nagar, Uttar Pradesh
I currently work here
07/13
06/19
Assistant Professor,
Shiv Nadar University,
Gautam Buddha Nagar, Uttar Pradesh
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.

Conferences (Select): 
  • 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)

Synergistic Effect of Singly Charged Oxygen Vacancies and Ligand-Field for Regulating Transport Properties of Resistive Switching Memories, Dip Das, Arabinda Barman, Santosh Kumar, Anil Sinha, Mukul Gupta, Rahul Singhal, Priya Johari, and Aloke Kanjilal, The Journal of Physical Chemistry C (Accepted, October 2019).
DOI Link: https://doi.org/10.1021/acs.jpcc.9b08078

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).
[Chosen as an IOPselect article.]
DOI Link: https://doi.org/10.1088/1751-8121/ab433c

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

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

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

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

Asymptotic Eigenvalue Density for the Quotient Ensemble of Wishart MatricesS. 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

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

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:

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

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

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

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

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:

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:

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:

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:

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

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, 4899 (2017).
DOI Link:

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:

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

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:

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:

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

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

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:

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:

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

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:

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

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

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

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:

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

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, L. Wei, IEEE International Symposium on Information Theory and Its Applications (ISITA), (2016).
Web Link:

Projects

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 2018-19
Title: Classical and Quantum-mechanical explorations of a particle in a random potential
Student: 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.