Quantum Variables in Finance and Neuroscience II

Background:A path-integral algorithm, PATHINT used previously for several systems, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems into qPATHINT. Previous publications applied qPATHINT to two systems developed by the author, in neocortical interactions and financial options. Also, previous publications using classical PATHINT have developed a statistical mechanics of neocortical interactions (SMNI) that has been fitted to EEG data under attentional experimental paradigms. Classical PATHINT also has been published demonstrating development of Eurodollar options in industrial applications.Objective:A study is required to see if the qPATHINT algorithm can scale sufficiently to further develop real-world calculations in these two systems, requiring interactions between classical and quantum scales. A new algorithm is needed to develop interactions between classical and quantum scales.Method:Both systems are developed using mathematical-physics methods of path integrals in quantum spaces. Supercomputer pilot studies using XSEDE.org resources tested various dimensions for their scaling limits. For the financial options study, all traded Greeks are calculated for Eurodollar options in quantum-money spaces. For the neuroscience study, tripartite neuron-astrocyte-neuron Ca-ion waves are propagated for 100's of msec. For the neuroscience system, the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time, in the absence of shocks, that is used to calculate classical-physics interactions among scales.Results:The mathematical-physics and computer parts of the study are successful for both systems. A 3-dimensional path-integral propagation of qPATHINT for both systems is within normal computational bounds on supercomputers. The neuroscience quantum path-integral also has a closed solution at arbitrary time that tests the multiple-scale model including the quantum scale.Conclusion:Each of the two systems considered contribute insight into applications of qPATHINT to the other system, leading to new algorithms presenting time-dependent propagation of interacting quantum and classical scales. This can be achieved by propagating qPATHINT and PATHINT in synchronous time for the interacting systems, which is a future set of studies