Viswanath Ramakrishna

Viswanath Ramakrishna

Professor - Mathematical Sciences
Assistant Department Head
 
972-883-6873
FO 2.408C
Tags: control optimization computation and applications in material and molecular sciences

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

Overview
Control, optimization, computation, applications in material and molecular sciences
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.

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
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
T. Constantinescu and V. Ramakrishna, Parametrizing Quantum States and Channels, Quantum Information Processing, Volume 2, No 3, 221-248, 2003. 2003 - 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
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
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
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

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

Non-Unitary Models in Quantum Control
2018–2018 Non-Unitary Models in Quantum Control, presented by Dr. R. Kosut on my behalf the IEEE Conference on Decision and Control, Las Vegas, NV.
Path Planning for Systems With Drift on Compact Lie Groups
2018–2018 Path Planning for Systems With Drift on Compact Lie Groups, UTD Mathematical Sciences Colloquium Talk
Parametrizing Orthogonal and Other Structured Matrices in Dimension Four
2004–2005 Parametrizing Orthogonal and Other Structured Matrices in Dimension Four, in the Reflection Coefficients: Theory & Applications Workshop, Mathematical Sciences Dept, UTD.
Novel Parametrizations of Quantum States & Channels
2018–2018 Novel Parametrizations of Quantum States & Channels, in the Conference on Modern Problems of Theoretical & Mathematical Physics, organized by UNESCO Regional Bureau for Science in Europe, Georgian Academy of Sciences & Tbilisi State University, Georgia (Note: I was unable to attend due to the elaborate visa requirements of the Georgian consulate).
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.