Abstract
Free electron systems are ubiquitous in nature and have demonstrated intriguing effects in their collective interactions with weak electric and magnetic fields, especially in aqueous environments. Starting from the Dirac Hamiltonian, a fully relativistic expression is derived for the electron energy shift in the presence of a spatiotemporally constant, weak electromagnetic field. The expectation value of this energy shift is then computed explicitly using the Fourier transforms of the fermionic fields. To first order in the electromagnetic fields, the average relativistic energy shift is found to be completely independent of the electron spin-polarization coefficients. This effect is also considerably larger than that predicted in quantum mechanics by the analogous Zeeman shift. Finally, in the non-relativistic limit, it is shown how to discriminate between achiral and completely polarized states, which leads to a concluding discussion of possible mesoscopic and macroscopic manifestations of electron spin states across many orders of magnitude in the physical world, with stark implications for biological and other complex systems.
Highlights
Static Electromagnetic Effects on FreeDeviations from linear response theory in liquids have been examined from several experimental and theoretical perspectives that have highlighted the role of nonequilibrium effects
It has been demonstrated in this article, starting from the Dirac Hamiltonian for a free electron, that a quantum field theory (QFT) treatment predicts energy shifts induced by magnetic fields acting on the electron spin state that are several orders of magnitude larger than the quantum
For the fully relativistic treatment, where all four Dirac spinor components are retained, it is observed that the average energy splitting to first order in the potentials is completely independent of the spin-state polarization coefficients
Summary
Deviations from linear response theory in liquids have been examined from several experimental and theoretical perspectives that have highlighted the role of nonequilibrium effects Such nonlinear responses—and their role in light-driven, mechanical–structural phase transitions—originate from the strong coupling of electronic and vibrational degrees of freedom. This effect has been described for Fröhlich polarons, where the impulsive movement of an electron in the highly nonlinear regime induces persistent coherent phonons (quantized vibrations). Such nonlinearities pose significant challenges for molecular dynamics (MD) simulations of dissipative systems that are hallmarks of biology, and which reflect the flow of energy under nonequilibrium conditions. Fluorescence upconversion experiments in the ultraviolet, combined with nonequilibrium MD simulations, have observed deviations from the linear response approximation for the relaxation dynamics of photoexcited tryptophan in water
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