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NATO ASI series. Series B : Physics

Beyond the Hall Effect: Practical Engineering from Relativistic Quantum Field Theory

Y. Srivastava

Published Jan 1, 1986• 0 citations
Publisher
DOI
10.1007/978-1-4684-5221-1_34

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It is theoretically shown that the coherent hopping dynamics of a non-relativistic particle in engineered tight-binding lattices subjected to combined ac and dc driving forces can mimic in Fock space relativistic quantum field theories (QFTs) of strongly interacting fields, enabling access to extreme dynamical regimes beyond weak coupling and perturbative predictions. In particular, the simulation of a QFT model describing a Dirac field strongly coupled to a scalar bosonic field via a Yukawa coupling is proposed, suggesting the possibility of implementing this model using engineered lattices of evanescently coupled optical waveguides with a bent optical axis.
Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantum computation. Moreover, it is possible to see new connections between principal models of computation, namely, computation over the continuum and computation over the integers (Turing computation). Thus we identify a basic problem in QFT, namely Wightman's computation problem for domains of holomorphy, which we call WHOLO. Inspired by the same analytic functions which are central to the famous CPT theorem of QFT, it is possible to obtain a computational complexity structure for QFT and shed new light on certain complexity classes for this problem WHOLO.