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.

Recently Dr. Van Vliet published a graduate textbook "Equilibrium and Non-Equilibrium Statistical Mechanics", World Scientific Publishing Company, Singapore and New Jersey, 2008

Facsimile Book Cover (pdf)

Errata and Addenda (pdf)

Table Of Contents

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List of Publications

Selected Publications:

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