Fizika Nizkikh Temperatur: Volume 44, Number 7 (July 2018), p. 857-865    ( to contents , go back )

Phase dynamics of discrete breathers periodically tunneling in weakly coupled nonlinear chains

Yuriy A. Kosevich

Institute of Chemical Physics, Russian Academy of Sciences, 4 Kosygina ul., Moscow 119991, Russia
Plekhanov Russian University of Economics, 36 Stremyanny per., Moscow 117997, Russia
E-mail: yukosevich@gmail.com

Received February 1, 2018

Abstract

We present a brief discussion of the phase-coherent dynamics of discrete breathers (intrinsic localized modes) in a system of two weakly coupled nonlinear chains and its comparison with periodic tunneling of quantum particles in a double-well potential and with macroscopic quantum tunneling of two weakly linked Bose–Einstein condensates. We consider the dynamics of relative phase of classically-tunneling discrete breathers in two weakly coupled nonlinear chains and show that the dynamics of the relative phase in the π/2 tunneling mode coincides with the experimentally observed dynamics of the relative phase of quantum particles, periodically tunneling in a double-well potential, both for noninteracting and strongly repulsively interacting particles. The observed coincidence demonstrates the correspondence between the dynamics of classical localized excitations in two weakly coupled nonlinear chains and tunneling dynamics of quantum object in the double-well potential. We show that in both π/2 and winding tunneling modes the relative phase experiences periodic jumps by π in the instants of complete depopulation of one of the weakly coupled chains or potential wells. The connection of the observed phase dynamics with the non-quantum uncertainty principle is discussed.

PACS: 05.45.Yv Solitons; 63.22.–m Phonons or vibrational states in low-dimensional structures and nanoscale materials;
PACS: 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations;
PACS: 74.50.+r Tunneling phenomena; Josephson effects.

Key words: discrete breathers, weakly coupled anharmonic chains, dynamics of relative phase, π/2 tunneling mode, winding tunneling mode, periodic tunneling, classical and quantum objects, non-quantum uncertainty principle.

Published online: May 28, 2018

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