Eur. Phys. J. B (2016) 89: 72
https://doi.org/10.1140/epjb/e2016-50749-0

Regular Article

Quantum interferences revealed by neutron diffraction accord with a macroscopic-scale quantum-theory of ferroelectrics KH_2(1−ρ)D_2ρPO₄^*

¹ Sorbonne Universités, UPMC Univ. Paris 06, UMR 8233, MONARIS, 75005 Paris, France
² Laboratoire Léon Brillouin (CEA-CNRS), C.E. Saclay, 91191 Gif-sur-Yvette Cedex, France

^a e-mail: francois.fillaux@upmc.fr

Received: 26 October 2014
Received in final form: 19 January 2016
Published online: 21 March 2016

Abstract

Neutron diffraction by single-crystals KH_2(1−ρ)D_2ρPO₄ at 293 K reveal quantum interferences consistent with a static lattice of entangled proton-deuteron scatterers. These crystals are represented by a macroscopic-scale condensate of phonons with continuous space-time-translation symmetry and zero-entropy. This state is energetically favored and decoherence-free over a wide temperature-range. Projection of the crystal state onto a basis of four electrically- and isotopically-distinct state-vectors accounts for isotope and pressure effects on the temperature of the ferroelectric-dielectric transition, as well as for the latent heat. At the microscopic level, an incoming wave realizes a transitory state either in the space of static positional parameters (elastic scattering) or in that of the symmetry species (energy transfer). Neutron diffraction, vibrational spectroscopy, relaxometry and neutron Compton scattering support the conclusion that proton and deuteron scatterers are separable exclusively through resonant energy-transfer.