Viswanath Ramakrishna

Professor - Mathematical Sciences
vish@utdallas.edu
972-883-6873
FO2408C
UTD Webpage
Tags: Mathematical Science

Professional Preparation

Ph.D. - Systems Science and Mathematics
Washington University in St. Louis - 1991
M.S. - Systems Science and Mathematics
Washington University in St. Louis - 1988
M. Sc - Mathematics
Indian Institute of Technology, Madras, India - 1986
B. Sc(Honours) - Physics
St. Stephen's College, University of Delhi, India - 1984

Research Areas

Research Interests
My central focus in research is the mathematics of control theory, especially as applied to new applications arising in the microworld. In addition to the core research in the theory of control and estimation of nonlinear systems, and its interaction with the theory of partial differential equations and exterior differential systems (and their Lie symmetries), I have been involved for the past five years in research in chemical physics. The principal thrust here has been the development of systematic design of external laser impulses for femtosecond photochemistry. Once again, since the mathematical basis is control theory and its role in the quantum regime these techniques are applicable to similar areas of application (and have indeed been applied) such as semiconductor heterostructures, inversion of molecular potentials and dipoles.
I am currently working on developing algorithms for design of basic logic gates for quantum computation with a single atom or molecule (interacting with an external pulse) as the physical vehicle. Other related research has been in (collaboration with L. R. Hunt) the areas of nonlinear inversion and a version of the stable and unstable manifold theorems for systems interacting with an external input. Our hope is to extend this to say something meaningful about signal processing, filtering, and estimation in a nonlinear context. In addition I am interested in obtaining results on exterior differential systems of varying dimensions for applications to nonlinear partial differential equations with degeneracies.
Overview
Control, optimization, computation, applications in material and molecular sciences

Publications

On the Exponential of Some Structured Matrices, V. Ramakrishna & F. Costa, Journal of Physics A: Mathematical and General, Vol 37, 11613-11627, 2004. 2004 - Publication
T. Constantinescu and V. Ramakrishna, Parametrizing Quantum States and Channels, Quantum Information Processing, Volume 2, No 3, 221-248, 2003. 2003 - Publication
Optimal Discrimination of Multiple Quantum Systems: Controllability Analysis, G. Turinici, V. Ramakrishna, B. Li and H. Rabitz, Journal of Physics A: Mathematical and General, Vol 37, 273-282, 2004. 2003 - Publication
V. Ramakrishna, R. J. Ober, K. L. Flores and H. Rabitz, Control of a coupled two spin system without hard pulses, Physical Review A, 65, 063405 - 1 -9, 2002 (also nominated for the Virtual Journal of Ultrafast Science, July 2002). 2002 - Publication
T. Constantinescu and V. Ramakrishna, On a Parametrization of Purifications of a Qubit, Quantum Information Processing, Volume 1, No 5, 409-424, (manuscript published in 2003 - though the issue is dated in 2002). 2002 - Publication
B. Li, G. Turinici, V. Ramakrishna and H. Rabitz, Optimal dynamic discrimination of similar molecules through quantum learning control, The Journal of Physical Chemistry B, 106, 8125-8131, 2002. 2002 - Publication
Constructive control of quantum systems using factorizations of unitary operators, S. Schirmer, A. Greentree, V. Ramakrishna and H. Rabitz, Journal of Physics A: Mathematical and General, 35, 8315-8339, 2002. 2002 - Publication
Control of Molecular Systems With Very Few Phases, V. Ramakrishna, Chemical Physics, Vol 267, 25-32, June 2001. 2001 - Publication
Parameter Variations, Relative Degree and Stable Inversion, V. Ramakrishna, L. R. Hunt and G. Meyer, to appear in Automatica, Vol 37, 871-880, 2001. 2001 - Publication
Quantum Control by Decompositions of SU(2), V. Ramakrishna, K. Flores, H. Rabitz and R. Ober, Physical Review A, Vol 62, 054309 - 1 to 054309 - 11, October 2000. 2000 - Publication

Appointments

Professor
University of Texas at Dallas, [2005–Present]
Associate Professor
University of Texas at Dallas, [2001–2005]
Assistant Professor
University of Texas at Dallas, [1995–2001]
Member Research Staff
Princeton University [1992–1995]
Visiting Assistant Professor
The University of California at Davis [1991–1992]
Instructor
Washington University in St. Louis [1990–1991]
Research Fellow
Washington University in St. Louis [1986–1991]
Teaching Assistant
Washington University in St. Louis [1922–1990]

Projects

Constructive Techniques for the Control of Finite Dimensional Quantum Systems With Amplitude Bounds
2018–2018 Constructive Techniques for the Control of Finite Dimensional Quantum Systems With Amplitude Bounds, in the SIAM Conference on Control and its Applications, San Diego
Control of Quantum Mechanical Processes
2012–2012 Control of Quantum Mechanical Processes, University of Dallas
Control Applications in Chemical Physics
199–199 Control Applications in Chemical Physics, II Mexican School on Gravitation and Mathematical Physics, Tlaxcala, Mexico, 35th Anniversary of Cinvestav.
Path Planning for Systems with Drift, Motivated by and Applied to Quantum Control
2018–2018 Path Planning for Systems with Drift, Motivated by and Applied to Quantum Control, to be given on Dec 2000, CDC Conference, Sydney, Australia.
Controllability of Quantum Systems: Theoretical and Constructive
2002–200 Controllability of Quantum Systems: Theoretical and Constructive, presented in Workshop on Quantum Control: Mathematical and Numerical Challenges, organized by the Centre de Recherches Mathematique of Universite de Montreal, Montreal, Canada