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Heinz von Foerster 100
Organizing Institutions:
Heinz von Foerster Gesellschaft / Wien
ASC – American Society for Cybernetics
WISDOM – Wiener Institut für
  sozialwissenschaftliche Dokumentation und Methodik

Institut für Zeitgeschichte | Universität Wien
AINS – Austrian Institute for Nonlinear Studies
Dieter Schuch

Nonlinear Quantum Mechanics, Complex Classical Mechanics and Conservation Laws for Closed and Open Systems

Institut für Theoretische Physik
Goethe-Universität Frankfurt am Main
Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany

The paradox of wave-particle duality was solved by quantum mechanics, e.g., in the form of Schrödinger’s wave equation. Already in the same year when Schrödinger published his equation, Madelung postulated a hydrodynamic formulation in terms of a modified Hamilton-Jacobi equation, essentially for the phase of the complex wave function, corresponding to the trajectory picture of classical dynamics and a continuity equation in position space for the probability distribution corresponding to the amplitude of the wave function. The interesting aspect is that, for the time-independent Schrödinger equation for example, these two equations are not independent of each other but coupled via a kind of conservation law. A similar conservation law can also be found in time-dependent quantum mechanics in cases where exact solutions in the form of Gaussian wave packets exist. In all these cases, the relevant differential equations can be written in terms of complex nonlinear Riccati equations that can be linearised in the time-independent case to the usual Schrödinger equation and, in the time-dependent case, to a complex Newtonian equation. So, what do we gain from the nonlinear formulation? The answer becomes obvious if we consider open systems with irreversible non-unitary dynamics and dissipation of energy. The whole formalism can be extended to also take into account these aspects in an effective way, leading to further nonlinear evolution equations and dynamical invariants and conservation laws beyond the Lagrange-Hamilton formalism. An interesting result of the nonlinear formulation is now the appearance of new qualitative effects like Hopf bifurcations that are usually well-known in classical nonlinear dynamics but alien to quantum mechanics. The interrelations between these aspects for time-dependent and time-independent quantum mechanics will be discussed.


Dieter Schuch - CV

1973 - 1982 • Johann Wolfgang Goethe-University, Frankfurt am Main, Germany

June 1978 • Diplom, Chemie (M.Sc. Chemistry) (Supervisor: H. Hartmann)
November 1982 • Dr. phil. nat., Institute of Physical and Theoretical Chemistry
Goethe University, Frankfurt am Main (Supervisor: H. Hartmann)
July 1992 • Dr. habil., Institute of Theoretical Physics
Goethe-University, Frankfurt am Main
August 2002 • Apl-Professor, Institute of Theoretical Physics
Goethe-University, Frankfurt am Main

Jan. 1980 - Mar. 1985 Research Assistant with Prof. Hermann Hartmann, Institute of Physical & Theoretical Chemistry, Goethe-University, Frankfurt am Main, Germany and member of the Editorial Office, May 1984 - March 1985 Editor, “Theoretica Chimica Acta”, Springer Verlag, Germany
Jul. 1985 - Apr. 1986 & Research Award – Deutsche Forschungsgemeinschaft (DFG)
Oct. 1986 - Jan. 1988
Apr. 1986 - Sep. 1986 Guest Lecturer/Research Fellow with Dr. Enrico Clementi, IBM Corporation, Kingston, New York, USA
Apr. 1988 - Mar. 1992 Special Lecturer and Research Fellow, Institute of Physical and Theoretical Chemistry, Goethe-University, Frankfurt am Main, Germany
May 1989 - June 1990 Habilitation Award – Deutsche Forschungsgemeinschaft (DFG)
Feb. 1992 - Aug. 2002 Privatdozent, Institute of Theoretical Physics, Goethe-University, Frankfurt am Main, Germany
Jul. 1992 - present Lecturer and Member, Institute of Theoretical Physics, Goethe-University, Frankfurt am Main, Germany
Jan. 1996 - Mar. 1996 Guest Professor, Research Project with Prof. Peter Schwerdtfeger, Department of Chemistry, University of Auckland, New Zealand
Nov. 2000, Jan. 2002, Guest Professor, Joint Research Project with Prof. Marcos Moshinsky,
Jan. 2006, Feb. 2007 Instítuto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico
Aug. 2002 - present Apl-Professor, Institute of Theoretical Physics, Goethe-University, Frankfurt am Main, Germany
Feb. 2008 - Sep. 2008 Joint Research Project with PD Dr. Robert Berger, Frankfurt Institute for Advanced Studies (FIAS), Frankfurt am Main, Germany
Jul. 2009 and Aug. 2011 Organizer of the International Conference “Symmetries in Science XIV and XV”, Bregenz, Austria
Jul. 2010 - Aug. 2010 Invited Lecturer, Latin American School of Physics (ELAF) XL, Mexico City, Mexico

• Gesellschaft Deutscher Chemiker
• Bunsengesellschaft für Physikalische Chemie
• American Chemical Society
• Deutsche Physikalische Gesellschaft
• Gesellschaft Deutscher Naturforscher & Ärzte
• New York Academy of Sciences

• Irreversibility and dissipation in classical and quantum mechanics
• Nonlinearities in quantum mechanics
• Wave packet dynamics
• Nonlinear dynamics
• Exactly solvable problems in classical and quantum mechanics
• Macroscopic quantum effects

Some 150 contributions have been made at conferences, invited lectures and seminars, the majority being presented internationally.

Some 60 publications in renowned international journals.