Dr. Carolyne M. Van Vliet

Carolyne M. Van Vliet

Adjunct Professor of Physics, University of Miami

Professor Emerita,
University of Montreal

B. S. Free University of Amsterdam (1949)
M. A. Free University of Amsterdam (1953)
Ph.D. Free University of Amsterdam (1956)

Research Areas:

Non-equilibrium Statistical Mechanics

Fluctuations and Stochastic processes

Quantum transport in condensed matter

Electronic behavior in submicron quantum devices

In the late seventies and early eighties, Dr. Van Vliet developed with her coworkers in Montreal a many-body Master Equation (ME), using the interaction-picture and projection operators in the Liouville space, thus extending earlier work by Van Hove, Zwanzig, Kubo, and others. The so-obtained Pauli-Van Hove-Van Vliet ME has diagonal as well as non-diagonal terms, with irreversibility vested in the diagonal part. Using the formalism of second quantization for an electron gas in interaction with impurities or phonons, a fully quantum mechanical Boltzmann transport equation (QBE), applicable to both extended and localized electronic states, was obtained. This QBE has proven to be a major tool for transport and conductivity calculations in modern submicron devices with extreme quantum confinement, leading to reduced dimensional current flow, such as occurring in quantum wells (2D), quantum wires (1D) and quantum dots (OD). With several coworkers (Vasilopoulos, Charbonneau, et alii) she has successfully formulated quantitative theories for the quantum Hall effect, magneto-phonon resonances, cyclotron resonance, the Aharonov- Bohm effect, among other phenomena. Presently, she has succeeded to go beyond linear response, obtaining general expressions for the current density in arbitrary electric and magnetic fields, using quantum-field theory and the Wigner-function formalism. Applications to hot electron conduction involving Landau states, localized 'tail'-states, and quantum wells, are underway.

The study of noise in materials, in electronic devices and photonic devices, provides detailed information on the processes underlying the operation of these devices, as well as of the sensitivity for detection and processing of small signals. Dr. Van Vliet has developed many physical theories and mathematical procedures for a great many devices, such as junction devices, photo avalanche diodes, stair case diodes, etc. She is the originator of the theory of Generation-Recombination noise (1956;1965) and the Green's function description of Transport noise (1965;1981;1994). The connection with Brownian motion (Smoluchowski, Ornstein and Uhlenbeck; Chandrasekhar; others) has been stressed in early as well as very recent publications. She has also developed a quantum electrodynamical theory of bremsstrahlung and infrared divergence of cross sections in condensed matter using the field quantization of the vector potential A and the electrical field E_(perp.) . The connection with soft photon emission and 1/f noise is still a matter of debate.

Dr. Van Vliet has also published papers of a 'pure' mathematical nature, involving Mellin transforms, Fredholm integral equations and other topics.

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Selected Publications:

Carolyne M. Van Vliet, "Random Walk and 1/f Noise", Physica A 303, 421-426 (2002).

Carolyne M. Van Vliet, "Quantum Transport in Solids", Advances in the Mathematical Sciences - CRM's 25 Years, (L.Vinet, Ed.) Vol.11, 421-449, The American Math. Soc., Providence, RI (1997).

Carolyne M. Van Vliet, "On Van Kampen's Objections Against Linear Response Theory", J. of Statistical Physics 53, 49-60 (1988).

Carolyne M. Van Vliet and P. Vasilopoulos, "The Quantum Boltzmann Equation and Some Applications to Transport Phenomena", J. Phys. Chem. of Solids, 49, 639-649 (1988).

C. M. Van Vliet, M. Charbonneau, and P. Vasilopoulos, "Linear Response Theory Revisited": IV." Applications", J. Math. Phys. 25, 1391-1403 and 3358 (1984); III. "One-Body Response Formulas", J. Math. Phys. 23, 308-336 (1982); II. "The Master-Equation Approach", J. Math. Phys. 20, 2573-2595 (1979); I. "The Many-Body Van Hove Limit", J. Math. Phys. 19, 1345-1370 (1978).

C.M. Van Vliet, A. Friedmann, and L.M. Rucker, "Theory of Carrier Multiplication and Noise in Photo-Avalanche Devices": II."Two-Carrier Processes", IEEE Trans. Electr. Dev. 26, 752-764 (1979); I. "One-Carrier Processes", IEEE Trans. Electr. Dev. 26, 746-751 (1979).

Carolyne M. Van Vliet and James J. Brophy, "Noise in Beta"-alumina solid electrolytes: Theory and experiment", Physical Review B 47, 11149-11158 (1993).

C. M. Van Vliet, "Electron Distributions in Solids Containing Multiple State Impurity Centers", Comptes Rendus 7^e Congres Int. sur la Physique des Semiconducteurs, Dunod, Paris, 831-837 (1964).

Carolyne M. Van Vliet, "Irreversible Thermodynamics and Carrier Density Fluctuations in Semiconductors", Physical Review 110, 50-62 (1958).

List of Publications
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