Cambridge University Press eBooks

What about quantum dynamics? More advanced principles

Jerome R. Busemeyer, Peter Bruza

Published Jul 26, 2012• 0 citations

Abstract

What about a process theory? How does quantum theory explain changes in confidence across time or how does quantum theory predict the time that it takes to make a decision? So far we have only made use of the structural part of quantum theory introduced in Chapter 2. This chapter introduces some of the basic principles for quantum dynamics. It is useful to compare quantum dynamics with Markov dynamics (Howard, 1971). Markov theory is a general mathematical framework for describing probabilistic-dynamic systems, which is commonly used in all areas of cognitive and decision sciences. For example, it is the mathematical basis that underlies random walk/diffusion models of decision making (Busemeyer & Diederich, 2009), or stochastic models of information processing (Townsend & Ashby, 1983), or multinomial processing tree models of memory retrieval (Batchelder & Reiffer, 1999), or the even more general field of stochastic processes (Bhattacharya & Waymire, 1990). Quantum theory provides an alternative general mathematical framework for describing probabilistic-dynamic systems (Gudder, 1979). However, quantum theory is similar in many ways to Markov theory, and so if you already know Markov theory, then it will be easy to learn about quantum dynamics too. This chapter introduces the Kolmogorov forward equation used to describe time evolution in Markov models, as well as the quantum analogue – the Schrödinger equation – which describes time evolution in quantum models. This chapter examines the similarities and differences between these two types of evolution, and why they are both useful for cognitive and decision modelling.

DOI: 10.1017/cbo9780511997716.009

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