Sudarshan: Seven Science Quests
Quantum Mechanics of Open Systems
A metastable quantum state decaying is an example of an open system. More generally, a system which is not closed but interacting with its surroundings has a non-Hamiltonian evolution. Boltzmannís collision formula is a well known example; as is the classical Newton's Law of Cooling. Measurement in quantum mechanics always involves an open system.

For a bipartite system governed by a Hamiltonian, one can calculate the evolution of one part. This could be described by a linear non-Hamiltonian process. The general formalism of this is the method of stochastic maps. Sudarshan had formulated this in the early sixties under the title "Stochastic Processes in Quantum Mechanics". A decade later, along with Gorini and Kossakowski he developed the theory of stochastic semigroups.

The generally accepted view was that such maps had to be "completely positive". Such maps can be obtained by the contraction of the unitary evolution of an extended simply separable (i.e., a bipartite unentangled) system; Jordan, Shaji, and Sudarshan showed that this is not valid for entangled bipartite systems by explicit calculations.

The separability of a bipartite system state is of interest in Quantum Computing. For the past decade, Sudarshan has been studying various aspects of this; and his students have studied the detailed evolution of bipartite systems and the methods of controlling decoherence.

With the von Neumann postulates a quantum measurement gives one or other possible values with a probability dictated by the state. The first such model was constructed by Sudarshan in which he coupled a classical system with a quantum system by an explicit Hamiltonian. The basic Stern-Gerlach experiment was studied in detail within this framework.

See more detailed REVIEW and REFERENCES below.
Schedule of symposium talks for Quantum Mechanics of Open Systems.
Next topic overview: I. V-A Universal Theory of Weak Interactions

REFERENCES

An Improved Method for the Determination of the Mass of Particles from Scattering Versus Range and its Application to the Mass of K Mesons; with S. Biswas and B. Peters, Proc. Ind. Acad. Sci. 38, 418 (1953).

The Range Energy Relation in Nuclear Emusion; with R. R. Daniel and B. Peters, Proc. Ind. Acad. Sci.41, 40 (1955).

Stochastic Dynamics of Quantum-Mechanical Systems; with P. M. Mathews and J. Rau, Phys. Rev. 121, 920-924 (1961).

Dynamical Mappings of Density Operators in Quantum-Mechanics II. Time Dependent Mappings; with T. F. Jordan and M. A. Pinsky, J. Math. Phys. 3, 848-852 (1962).

Study of Spurious Scattering in Nuclear Emulsions and the Effect of Higher Order Differences in Scattering Measurements; with P. J. Lavakare, Nuovo. Cim. Suppl. 20, 251 (1962).

Irreversibility and Dynamical Maps of Statistical Operators; with V. Gorini, Lecture Notes in Phys. 29, 260, Springer Verlag, Berlin (1974).

Interaction between Classical and Quantum Systems, a New Approach to Quantum Measurements I; with T. N. Sherry, Phys. Rev. D18, 4580 (1978).

Interaction between Classical and Quantum Systems and the Measurement of Quantum Observables, Pramana 6, 117 (1976).

Interaction between Classical and Quantum Systems, a New Approach to Quantum Measurements II: Theoretical Considerations; with T. N. Sherry, Phys. Rev. D20, 857 (1979).

Interaction between Classical and Quantum Systems, a New Approach to Quantum Measurements III: Illustration; with S. R. Gautum and T. N. Sherry, Phys. Rev. D20, 3081 (1979).

Quantum Dynamical Semigroups and Complete Positivity. An Application to Isotropic Spin Relaxation. Presented at the IX Int. Colloquium on Group Theoretical Methods in Physics, Cocoyoc, Mexico (June 1980). In Proc. Lecture Notes in Physics,135, Springer Verlag, Berlin; with Gorini and Verri.

Quantum Measurement and Dynamical Maps. From SU(3) to Gravity (Festschrift in honor of Yuval Ne'eman), E. Gotsman and G. Tauber (eds.), Cambridge University Press (1986), p. 433.

Quantum Dynamics, Metastable States and Contractive Semigroups, Phys. Rev. A 46, 37 (1992).

Unstable Systems in Generalized Quantum Theory; with Charles B. Chiu and G. Bhamathi
Advances in Chemical Physics XCIX, John Wiley & Sons, Inc. (1997), pp. 121-210.

Mapping the Schrodinger Picture of Open Quantum Dynamics; with T. Jordan and Anil Shaji, http://arxiv.org/pdf/quant-ph/0505123 (2004).

Dynamics of Initially Entangled Open Systems; with A. Shaji and T. Jordan, Phys. Rev. A70, 052110 (2004).

Relations between Quantum Maps and Quantum States; with M. Asorey, A. Kossakowski and G. Marmo, (2005) in press.

On the Meaning and Interpretation of Tomography in Abstract Hilbert Spaces; with V. I. Man’ko, G. Marmo and F. Zaccaria, Repts on Math. Phys. 55, 405 (2005).
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Next topic overview: I. V-A Universal Theory of Weak Interactions

 

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Sudarshan Symposium, Nov. 5-7, 2006
Curriculum Vitae
Seven Science Quests
V-A: Universal Theory
of Weak Interaction
Symmetry
Spin Statistics
Quantum Optical Coherence:
Sudarshan Representation
Quantum Zeno Effect
Theory of Tachyons
Quantum Mechanics
of Open Systems
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