petrosky@physics.utexas.edu

Curriculum Vitae

Center for Complex Quantum Systems

(Formerly The Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems)

Irreversibility and Foundation of Physics

Nonlinear and Nonintegrable Dynamical Systems

Complex Spectral Representations of Unstable Hamiltonian Systems

Kinetic Equations in Non-Equilibrium Physics

Matter-Field Interacting Systems

Quantum Coherence and Decoherence

Anomalous Decay Process of Electrons in Quantum Nano-wire

Complex Spectral Representation of the Hamiltonian and the Liouvillian in Nanocience Workshop

May 18-19, 2012, The University of Texas at Austin

Workshop Announcement

Workshop Program

The 11th international workshop on “Resonance and Non-Hermitian Quantum Mechanics 2016,” August 3–5, 2016, Osaka University, Osaka, JAPAN

**Short Biography**

Tomio Petrosky is currently a Senior Research Scientist at the Center for Complex Quantum Systems at the University of Texas at Austin. He received his Undergraduate, Masters and Ph.D. degrees from the Department of Physics, Science University of Tokyo. Dr. Petrosky is the author of nearly 170 articles. He was awarded the “Le Prix Georges Vanderlinden” from Académie Royale, des Sciences, des Lettres & des Beaux-Arts de Belgique on December 14, 1991. He was presented the “Métropole Award,” a special award of 100 years anniversary of the International Solvay Conference at the XXth International Sovlay Conference on Chemistry in Brussels, Belgium on November 30, 1995. He was the recipient of the “Peter the Great” Gold Medal presented by the Russian Academy of the Natural Sciences in 2000. He was a guest editor for the special issue of the Interdisciplinary Journal of Nonlinear Science “Chaos” for Celebrating the 100th Anniversary of Ilya Prigogine’s Birth (Focus Issue: Dissipative Structures and Irreversibility in Nature) that has been published at October 2017.

**Tomio Y. Petrosky – Selected Publications **

“Anomalous Diffusion with an Apparently Negative Diffusion Coefficient in One-Dimensional Quantum Molecular Chain Model” Sho Nakade, Kazuki Kanki, Satoshi Tanaka, and Tomio Petrosky, *Symmetry*, 13(3), 506 (2021).

“Anomalous diffusion of a quantum Brownian particle in a one-dimensional molecular chain” Sho Nakade, Kazuki Kanki, Satoshi Tanaka, and Tomio Petrosky, *Phys. Rev. E* 102, 032137 (2020).

“Classical Radiation Damping and Emission of Optical Vertex as Microscopic Irreversible Process” Tomio Petrosky, *J. Adv. Simulat. Sci. Eng.,* Vol. 6, No. 1, 56-66 (2019).

“Theoretical Issue of Cyclotron Radiation and Optical Vortex“ Tomio Petrosky, *J. Plasma Fusion Res*. Vol.94, No.3, 131-135 (2018).

“Microscopic Description of Irreversibility in Quantum Lorentz Gas by Complex Spectral Analysis of the Liouvillian outside the Hilbert space” T. Petrosky, K. Hashimoto, K. Kanki, and S. Tanaka, *Chaos.* Oct;2( 10):104616 (2017).

“Dissipative structures and irreversibility in nature: Celebrating 100th birth anniversary of Ilya Prigogine (1917–2003)” Dilip Kondepudi, Tomio Petrosky, and John A. Pojman,* Chaos* 27, 104501 (2017). https://doi.org/10.1063/1.5008858

“Analytical investigation of an isomerization system using the resonance overlap criterion” H. Fukuda, T. Petrosky and T. Konishi,, *Prog. Theor. Exp. Phys.* ** **093A01 (2016).

“Higher-order time-symmetry-breaking phase transition due to meeting of an exceptional point and a Fano resonance” Satoshi Tanaka, Savannah Garmon, Kazuki Kanki, and Tomio Petrosky, *Phys. Rev. A ***94**, 022105 (2016).

“Spontaneous breaking of a PT-symmetry in the Liouvillian dynamics at a non-Hermitian degeneracy point” K. Kanki, K. Hashimoto, S. Tanaka, and T. Petrosky, in *Non-Hermitian Hamiltonians in Quantum Physics*, edited by Fabio Bagarello, Roberto Passante and Camillo Trapani (Springer International Publishing, Switzerland, pp. 289-304 (2016).

“Physical aspect of exceptional point in the Liouvillian dynamics for a quantum Lorentz gas” K. Hashimoto, K. Kanki, S. Tanaka, and T. Petrosky, in *Non-Hermitian Hamiltonians in Quantum Physics*, edited by Fabio Bagarello, Roberto Passante and Camillo Trapani (Springer International Publishing, Switzerland, pp. 263-279 (2016).

“Microscopic description of quantum Lorentz gas and extension of the Boltzmann equation to entire space-time scale” K. Hashimoto, K. Kanki, S. Tanaka, and T. Petrosky, *Phys. Rev. E* **93**, 02213 (2016).

“Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas” Kazunari Hashimoto, Kazuki Kanki, Hisao Hayakawa, and Tomio Petrosky, *Prog. Theor. Exp. Phys.* 023A02 (2015).

“Optically tunable bound states in continuum” Yingyue Boretz, Gonzalo Ordonez, Satoshi Tanaka, and Tomio Petrosky,* Phys. Rev. A* **90**, 023853 (2014).

“Enhanced resonant force between two entangled identical atoms in photonic crystal” R. Incardone, T. Fukuta, S. Tanaka, T. Petrosky, L. Rizzuto and R. Passante, *Phys. Rev. A*** 89**, 062117 (2014).

“Quasi bound states in continuum induced by an external oscillating field” K. Noba, Y. Uesaka, N. Yamada, S. Tanaka, and T. Petrosky, *J. of Physics A* **85**, 38530 (2014).

“Nonperturbative approach for the electronic Casimir-Polder effect in a one-dimensional semiconductor” Satoshi Tanaka, Roberto Passante, Taku Fukuta, and Tomio Petrosky, *Phys. Rev. A*** 88**, 022518 (2013).

“Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy” Roberto Passante, Lucia Rizzuto, Salvatore Spagnolo, Satoshi Tanaka, and Tomio Petrosky, *Phys. Rev. A*** 85**, 062109 (2012).

“Dynamical suppression and enhancement of instability for an unstable state by a periodic external field” Nobuhisa Yamada, Ken-ichi Noba, Satoshi Tanaka, and Tomio Petrosky, *Phys. Rev. B* **86**, 014302 (2012).

“Nontrivial Eigenvalues of the Liouvillian of an Open Quantum System” Ruri Nakano, N. Hatano, and T. Petrosky, Int. *J. Theor. Phys.* No. 50, 1134-1142, (2011).

“Kinetic equations for classical and quantum Brownian particles and eigenfunction expansions as generalized functions,” Kazuki Kanki, Satoshi Tanaka, and Tomio Petrosky, *J. Math. Phys*., **52**, 063301 (2011).

“Nonequilibrium transport of quantum molecular chain in terms of the complex Liouvillian spectrum” Satoshi Tanaka, Kazuki Kanki, and Tomio Petrosky,* Phys. Rev. E* **83**, 051118 (2011).

“Level repulsion and threefold degeneracy of eigenstates of the Liouvillan in the Kirkwood gaps of Asteroid belt” Tomio Y. Petrosky, *Prog. Theor. Phys.* Vol. 125, 411-434, (2011).

“Band Structure and Accumulation Point in the Spectrum of Quantum Collision Operator in a One-Dimensional Molecular Chain” B. A. Tay, K. Kanki, S. Tanaka and T. Petrosky, *J. Math. Phys*. **52**, 023302 (2011).

“Dual Spaces Structure of Quantum Kinetic Equations— Quantum Systems vs Classical Systems” Buang Ann Tay and Tomio Petrosky *Prog. Theor. Phys. Supplement* **184 **533, 2010.

“Accumulation point in the spectrum of the collision operator for a one-dimensional polaron system” K. Kanki, S. Tanaka, B. A. Tay, and T. Petrosky *Prog. Theor. Phys. Supplement* **184 **523, 2010.

“Hofstadter’s butterfly type of singular spectrum of a collision operator for a model of molecular chains” T. Petrosky, N. Hatano, K. Kanki, and S. Tanaka *Prog. Theor. Phys. Supplement* **184 **457, 2010.

“Emergence of quantum hydrodynamic sound mode of a quantum Brownian particle in a one-dimensional molecular chain” S. Tanaka, K. Kanki and T. Petrosky *Phys. Rev. B ***80 **094304, 2009.

“Two-channel quantum wire with an adatom impurity: Role of the van Hove singularity in the quasibound state in continuum, decay rate amplification and the Fano effect” S. Garmon , H. Nakamura, N. Hatano and T. Petrosky *Phys. Rev. B ***80 **115318, 2009.

“Biorthonormal eigenbasis of a Markovian master equation for the quantum Brownian motion” B. A. Tay and T. Petrosky *J. Math. Phys. ***49**113301, 2008.

“Some Properties of the Resonant State in Quantum Mechanics and Its Computation” Naomichi Hatano, Keita Sasada, Hiroaki Nakamura and Tomio Petrosky *Progess of Theoretical Physics* **119**187, 2008.

“Quasi-bound states in continuum in a two channel quantum wire with an adatom” Hiroaki Nakamura, Naomichi Hatano, Sterling. Garmon and Tomio Petrosky *Virtual Journal of Nanoscale Science & Technology ***16**, 2007.

“Electron Trapping in a 1D Semiconductor Superlattice with Multiple Impurities ” S. Tanaka, S. Garmon, G. Ordonez, and T. Petrosky *Virtual Journal of Nanoscale Science & Technology ***16**, 2007.

“Thermal Symmetry of Markovian Master Equation” Ban Ann Tay and Tomio Petrosky *Phys. Rev. A* **76**042102, 2007.

“Quasibound States in Continuum in a Two Channel Quantum Wire with an Adatom” Hiroaki Nakamura, Naomichi Hatano, Sterling Garmon and Tomio Petrosky *Phys. Rev. Letters* **99**210404, 2007.

“Electron Trapping in a 1D Semiconductor Superlattice with Multiple Impurities” S. Tanaka, S. Garmon, G. Ordonez, and T. Petrosky *Phys. Rev. B ***76**153308, 2007.

“On von Neumann’s Hypothesis of Collapse of the Wave Function and Quantum Zeno Paradox in Continuous Measurement ” Tomio Petrosky and Dongil Kim *Journal of Physics by Institute of Physics*, 2007.

“Quantum and classical dynamics of dissipative systems” Ilya Prigogine, Tomio Petrosky and Gonzalo Ordonez Special Volume in Memory of Ilya Prigogine, Advances in Chemical Physics Vol. 135, 2007. (John Wiley & Sons, Hoboken, New Jersey)

“Complex Systems and the The Arrow of Time” Tomio Yamakoshi Petrosky Series of Complex Systems Vol. 7 (in Japanese), 2006. (Kyoritu Shuppan, Tokyo)

“Nonanalytic enhancement of the charge transfer from adatom to one-dimensional semiconductor superlattice and optical absorption spectrum” Satoshi Tanaka, Sterling Garmon and Tomio Petrosky *Phys. Rev. B ***73**, 115340, 2006.

“Strong Coupled Matter-Field and Non-Analytic Decay Rate of Dipole Molecules in a Waveguide” T. Petrosky, Chu-Ong Ting, and Sterling Garmon *Phys. Rev. Letters* **94**, 043601, 2005.

“Resonance overlap, secular effects, and nonintegrability: An approach from ensemble theory” Chun-Biu Li, Dean J. Driebe, and T. Petrosky *Phys. Rev. E ***69**, 066120, 2004.

“Stochastic Maxwell-Lorentz Equation in Radiation Damping” T. Petrosky *International Journal of Quantum Chemistry*** 98**, 103-111, 2004.

“Classical radiation damping. Role of nonintegrability” T. Petrosky, G. Ordonez and I. Prigogine *Phys. Rev. A ***68**, 022107, 2003.

“Chaotic scattering and the magneto-Coulomb map” B. Hu, W. Horton and T. Petrosky *Phys. Rev. E*** 65**, 056212, 2002.

“Space time formulation of quantum transitions'” T. Petrosky, G. Ordonez and I. Prigogine *Phys. Rev. A* **64**, 062101, 2001.

“Quantum transitions and dressed unstable states” G. Ordonez, T. Petrosky and I. Prigogine *Phys. Rev. A ***63**, 052106, 2001.

“Quantum transitions and nonlocality” T. Petrosky, G. Ordonez and I. Prigogine *Phys. Rev. A* **62** 42106, 2000.

“Transport Theory and Collective Modes I: Case of moderately dense gases” T. Petrosky *Foundation of Physics* **29**, 1417-1456, 1999.

“Transport Theory and Collective Modes II: Long-time tail and Green-Kubo Formalism” T. Petrosky *Foundation of Physics ***29**, 1581-1605, 1999.

“Semigroup Representation of the Vlasov Evolution” I. Prigogine and T. Petrosky *J. Plasma Physics ***59**, 611-618, 1998.

“The Liouville Space Extension of Quantum Mechanics” T. Petrosky and I. Prigogine Advances in Chemical Physics Volume 99, eds. I. Prigogine and S. Rice John Wiley and Sons, 1-120, 1997.

“Liouville Extension of Quantum Mechanics: One-dimensional Gas with Delta Function Interaction” T. Petrosky and G. Ordonez *Phys. Rev. A* **56**, 3507-3528, 1997.

“Extension of scattering theory for finite times: three-body scattering” T. Petrosky, G. Ordonez and T. Miyasaka *Phys. Rev. A* **53**, 4075-4103, 1996.

“Poincaré Resonance and the Extension of Classical Dynamics” T. Petrosky and I. Prigogine *Chaos, Solitons and Fractals* **7**, No. 4, 441-498, 1996.

“Long-time behaviour of self-dressing and indirect spectroscopy” R. Passante, T. Petrosky and I. Prigogine *Physica A* **218**, 437-456, 1995.

“Complex Spectral Representation and Time-symmetry Breaking” T. Petrosky and I. Prigogine *Chaos, Solitons and Fractals ***4**, No. 1, 311-359, 1994.

“Virtual Transitions, Self-Dressing and Indirect Spectroscopy” R. Passante, T. Petrosky and I. Prigogine *Optics Communications ***99**, 55-60, 1993.

“Order and Disorder in the Approach to Equilibrium of a Classical Gas” D. Driebe and T. Petrosky *J. Stat. Phys.* **67**, 369-394, 1992.

“Quantum Theory of Non-integrable Systems” T. Petrosky, I. Prigogine and S. Tasaki *Physica A* **173**, 175-242, 1991.

“Quantum Zeno Effect” T. Petrosky, S. Tasaki and I. Prigogine *Physics Letters A* **151**, 109-113, 1990.

“Laws and Events: The Dynamical Basis of Self-Organization” T. Petrosky and I. Prigogine *Can. J. Phys. ***68**, 670-682, 1990.

“Laws and Events: The Dynamical Basis of Self-Organization” T. Petrosky and I. Prigogine *Can. J. Phys. ***68**, 670-682, 1990.

“Subdynamics and Nonintegrable Systems” T. Petrosky and H. Hasegawa *Physica A* **160**, 351-385, 1989.

“Poincaré’s Theorem and Unitary Transformations for Classical and Quantum Theory “T. Petrosky and I. Prigogine*Physica A ***147**, 439-460, 1988.

“An Alternative to Quantum Theory” I. Prigogine and T. Petrosky *Physica A* **147**, 461-486, 1988.

“Intrinsic Irreversibility and Quantum Theory” I. Prigogine and T. Petrosky *Physica A* **147**, 33-47, 1987.

“Chaos and Cometary Clouds in the Solar System” T. Petrosky *Physics Letters A ***117**, 328-332, 1986.

“Chaos and Nonunitary Evolution in Nonintegrable Hamiltonian Systems” T. Petrosky *Phys. Rev. A* **32**, 3716-3725, 1985.

“Limit of Classical Chaos in Quantum Systems” T. Petrosky and W. C. Schieve *Phys. Rev. A* **31**, 3907-3911, 1985.

“Chaos and Irreversibility in a Conservative Nonlinear Dynamical System with a Few Degrees of Freedom”

T. Petrosky *Phys. Rev. A* 29, 2078-2091, 1984.

“The Derivation of the Quantum Kinetic Equation and Two-Time Resolvent Method” T. Petrosky and W. C. Schieve *J. Stat. Phys.* **29**, 711-744, 1982.

“Theory of Irreversible Process in Non-equilibrium Quantum System I, General Formalism ” N. Mishima, T. Petrosky and R. Suzuki *J. Stat. Phys.* **21**, 347-392, 1979.

“Theory of Irreversible Process in Non-equilibrium Quantum System II, Cluster Expansion and Contraction for Homogenous System ” T. Petrosky *J. Stat. Phys* **21**, 393-413, 1979.

“Quantum Statistical Hierarchy Equation in Nonequilibrium Systems ” N. Mishima, T. Petrosky and M. Yamazaki*J. Stat. Phys* **14**, 359-380, 1976.

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