Dynamical Causal Modeling from a Quantum Dynamical Perspective
- Department of Psychology, University of Michigan, 1012 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043 (United States)
- Istanbul Technical University, Informatics Institute, Group for Science and Methods of Computing, Maslak, 34469, Istanbul (Turkey)
Recent research suggests that any set of first order linear vector ODEs can be converted to a set of specific vector ODEs adhering to what we have called ''Quantum Harmonical Form (QHF)''. QHF has been developed using a virtual quantum multi harmonic oscillator system where mass and force constants are considered to be time variant and the Hamiltonian is defined as a conic structure over positions and momenta to conserve the Hermiticity. As described in previous works, the conversion to QHF requires the matrix coefficient of the first set of ODEs to be a normal matrix. In this paper, this limitation is circumvented using a space extension approach expanding the potential applicability of this method. Overall, conversion to QHF allows the investigation of a set of ODEs using mathematical tools available to the investigation of the physical concepts underlying quantum harmonic oscillators. The utility of QHF in the context of dynamical systems and dynamical causal modeling in behavioral and cognitive neuroscience is briefly discussed.
- OSTI ID:
- 21428585
- Journal Information:
- AIP Conference Proceedings, Vol. 1281, Issue 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3498312; (c) 2010 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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