Eur. Phys. J. D 44, 351-358 (2007)
https://doi.org/10.1140/epjd/e2007-00195-4

Friction of the surface plasmon by high-energy particle-hole pairs

Are memory effects important?

¹ Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, 28049 Madrid, Spain
² Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 (ULP-CNRS), BP 43, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
³ Institut für Physik, Universität Augsburg, Universitätsstraße 1, 86135 Augsburg, Germany
⁴ Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

Corresponding author: ^a weick@physik.fu-berlin.de

Received: 28 March 2007
Published online: 20 June 2007

Abstract

We show that the dynamics of the surface plasmon in metallic nanoparticles damped by its interaction with particle-hole excitations can be modelled by a single degree of freedom coupled to an environment. In this approach, the fast decrease of the dipole matrix elements that couple the plasmon to particle-hole pairs with the energy of the excitation allows a separation of the Hilbert space into low- and high-energy subspaces at a characteristic energy that we estimate. A picture of the spectrum consisting of a collective excitation built from low-energy excitations which interacts with high-energy particle-hole states can be formalised. The high-energy excitations yield an approximate description of a dissipative environment (or “bath") within a finite confined system. Estimates for the relevant timescales establish the Markovian character of the bath dynamics with respect to the surface plasmon evolution for nanoparticles with a radius larger than about 1 nm.