Junior Research Fellow in Mathematics, Trinity College
+44 1865 615306
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science issue 2193 volume 472 page 20150733-20150733 (14 September 2016)
Effective Approximation for the Semiclassical Schrödinger Equation
Foundations of Computational Mathematics issue 4 volume 14 page 689-720 (19 August 2014)
I am interested in investigating numerical methods for quantum systems described by a range of equations such as the linear, nonlinear and stochastic versions of the Schrödinger equation in the semiclassical as well as the atomic regime. I am also interested in related equations of Quantum Mechanics such as the Pauli, Dirac and Klein–Gordon equations.
My interest is equally spread between the design and convergence analysis of numerical methods applicable to such equations. I am currently working with Lie algebraic techniques such as the Magnus expansion and Zassenhaus splittings, whose combination is very effective for the simulation of equations with time-varying fields and holds great promise for control of quantum systems.
I am also interested in applications of these numerical methods in Theoretical Chemistry, Material Sciences and Physics including study of laser-matter interactions, ionization, femtochemisty etc., and am also very open to collaboration in these fields.
Prizes, Awards, and Scholarships:
2016–2019 Junior Research Fellowship in Mathematics, Trinity College, Oxford, UK.
2012–2015 King's College Studentship, King's College, Cambridge, UK.
2009 E. M. Burnett Prize for Distinction in Part III Maths, Hughes Hall, Cambridge, UK.
Major / Recent Publications:
2018 Iserles, A., Kropielnicka, K. and Singh, P., “Compact schemes for laser-matter interaction in Schrödinger equation”. Submitted.
2018 Singh, P. “Algebraic theory for higher-order methods in computational quantum mechanics", Submitted. arXiv:1510.06896 [math.NA].
2018 Iserles, A., Kropielnicka, K. and Singh, P., “Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials”. Submitted. arXiv:1801.06912 [math.NA].
2018 Iserles, A., Kropielnicka, K. and Singh, P., “Magnus–Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential”. Accepted, SIAM Journal on Numerical Analysis. arXiv:1801.06913 [math.NA].
2016 Bader, P., Iserles, A., Kropielnicka, K. and Singh, P. “Efficient methods for time-dependence in semiclassical Schrödinger equations". Proceedings of the Royal Society A, 472.
2014 Bader, P., Iserles, A., Kropielnicka, K. and Singh, P. “Effective approximation for the semiclassical Schrödinger equation". Foundations of Computational Mathematics, 14, 4, 689–720.