Dissipative Effects on Quantum Sticking

Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral and charged particles are examined. For the case of an Ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain a nonperturbative expression for the sticking rate. We find that for weak dissipative coupling $\alpha$, the low-energy threshold laws for quantum sticking are modified by an infrared singularity in the bath. The sticking probability for a neutral particle with incident energy $E\to 0$ behaves asymptotically as $s\sim E^{(1+\alpha )/2(1-\alpha )}$; for a charged particle, we obtain $s\sim E^{\alpha /2(1-\alpha )}$. Thus, “quantum mirrors”—surfaces that become perfectly reflective to particles with incident energies asymptotically approaching zero—can also exist for charged particles. We provide a numerical example of the effects for electrons sticking to porous silicon via the emission of a Rayleigh phonon.

Figure 1

The sticking probability of an electron of energy $E$ to the surface of porous silicon by the emission of a Rayleigh phonon. The perturbative result using Fermi’s golden rule is given by (red) circles, while the variational mean-field result is given by (blue) stars. The variational mean-field method gives a new threshold law for quantum sticking. We take a porosity $P=92.9\%$, giving a dielectric constant $\kappa =1.2$. The shear modulus of $G=230\mathrm{MPa}$ and Poisson’s ratio $\sigma =0.03$ are calculated using Ref. 20.