Exchange interaction and correlations radically change behaviour of a quantum particle in a classically forbidden region

TL;DR

This paper reveals how exchange interactions and correlations fundamentally alter the behavior of quantum particles in classically forbidden regions, affecting decay rates, tunneling, and spin interactions.

Contribution

It demonstrates that exchange interactions cause power-law decay and extra nodes in wavefunctions, challenging traditional exponential decay models and showing their impact on tunneling and spin interactions.

Findings

Exchange interaction causes power-law decay of electron orbitals.

Decay behavior varies with system dimensionality and Fermi momentum.

Tunneling coefficients become temperature-dependent due to exchange effects.

Abstract

Exchange interaction strongly influences the long-range behaviour of localised electron orbitals and quantum tunneling amplitudes. It violates the oscillation theorem (creates extra nodes) and produces a power-law decay instead of the usual exponential decrease at large distances. For inner orbitals inside molecules decay is $r^{-2}$, for macroscopic systems $\cos{(k_f r)} r^{-\nu}$, where $k_f$ is the Fermi momentum and $\nu=3$ for 1D, $\nu=$3.5 for 2D and $\nu=$4 for 3D crystal. Correlation corrections do not change these conclusions. Slow decay increases the exchange interaction between localized spins and the under-barrier tunneling amplitude. The under-barrier transmission coefficients in solids (e.g. for point contacts) become temperature-dependent.