Carolyne M. Van Vliet
Adjunct Professor of Physics, University of Miami
University of Montreal
B. S. Free University of Amsterdam (1949)
M. A. Free University of Amsterdam (1953)
Ph.D. Free University of Amsterdam (1956)
Quantum transport in condensed
Electronic behavior in submicron
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
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
Click here for Curriculum Vitae
List of Publications
Carolyne M. Van Vliet, Linear momentum quantization in periodic structures II, Physica A 389, 1585-1593 (2010).
Carolyne M. Van Vliet and Andres Barrios, Quantum electron transport beyond linear response, Physica A 315,
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
C. M. Van Vliet, "Electron Distributions in Solids Containing Multiple
State Impurity Centers", Comptes Rendus 7e 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).