Ph.D. - Systems Science and Mathematics
Washington University in St. Louis - 1991
Viswanath Ramakrishna
Professor - Mathematical Sciences
Professional Preparation
M.S. - Systems Science and Mathematics
Washington University in St. Louis - 1988
Washington University in St. Louis - 1988
M. Sc - Mathematics
Indian Institute of Technology, Madras, India - 1986
Indian Institute of Technology, Madras, India - 1986
B. Sc(Honours) - Physics
St. Stephen's College, University of Delhi, India - 1984
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 sciencesPublications
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]
University of Texas at Dallas, [2005–Present]
Associate Professor
University of Texas at Dallas, [2001–2005]
University of Texas at Dallas, [2001–2005]
Assistant Professor
University of Texas at Dallas, [1995–2001]
University of Texas at Dallas, [1995–2001]
Member Research Staff
Princeton University [1992–1995]
Princeton University [1992–1995]
Visiting Assistant Professor
The University of California at Davis [1991–1992]
The University of California at Davis [1991–1992]
Instructor
Washington University in St. Louis [1990–1991]
Washington University in St. Louis [1990–1991]
Research Fellow
Washington University in St. Louis [1986–1991]
Washington University in St. Louis [1986–1991]
Teaching Assistant
Washington University in St. Louis [1922–1990]
Washington University in St. Louis [1922–1990]