Dyson Maps and Unitary Evolution for Maxwell Equations in Tensor Dielectric Media

Abstract

A reformulation of Maxwell equations for an inhomogeneous, anisotropic, passive and non-dispersive medium results in a quantum-like Dirac equation that admits unitary time evolution. In contrast to other approaches, there is no a-priori introduction of the Riemann-Silberstein-Weber (RSW) vector but the Maxwell equations are considered in their standard fields, with given constitutive relations. From the electromagnetic conservation quantities a pseudo-Hermitian dynamics is found together with a Dyson map that recovers the full Hermicity of the dynamics in an extended Hilbert space that describes the physical notion of unitary evolution. As an example, a uniaxial tensor dielectric medium is considered, with the explicit Dyson map yielding an optimal representation in a set of generalized RSW vectors. In this newly discovered form, a Quantum Computing (QC) implementation for simulation of electromagnetic wave propagation in complex media can be made, with further extension into plasmas.

12 pages, 5 figures

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• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics
• Some Comments on Unitary Qubit Lattice Algorithms for Classical Problems
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