Resonant Enhancement and Dissipation in Nonequilibrium van der Waals Forces

Dispersion forces between molecules that are in relative motion, coupled to baths at different temperatures, or in excited states, are calculated using a Green function Liouville space expansion that extends the celebrated McLachlan response theory to the nonlinear regime. Our dynamical theory is applicable to systems that may be in any initial nonequilibrium state and that are subject to an arbitrary time-dependent coupling. In contrast to equilibrium forces which are attractive, nonequilibrium forces may be attractive or repulsive, exhibit chemically specific resonances, are far stronger, and may be nonconservative (with either positive or negative dissipation).

Figure 1

Interaction energy of two harmonic oscillators as a function of their resonant frequencies, ${\omega }_b/{\omega }_a$ and their temperatures, ${\beta }_b/{\beta }_a$. The nonequilibrium force (${\beta }_a\ne {\beta }_b$) has a resonance that is absent from the equilibrium force. In the shaded regions the steady-state force is repulsive. The dimensionless parameters are ${\beta }_a\hslash {\omega }_a=1$ and ${\beta }_a\hslash \gamma =0.03$

Figure 2

Reversible [$f_r\propto {\chi }^{\prime }(\omega )$] and irreversible [$f_i\propto {\chi }^{\prime \prime }(\omega )$] components of the intermolecular force for harmonically modulated coupling $\tilde{J}(\omega )$. Resonances in the force occur at $\omega =\pm {\omega }_a\pm {\omega }_b$. The shaded region indicates a domain of negative dissipation. The dimensionless parameters are ${\beta }_a\hslash {\omega }_a=1$, ${\beta }_a\hslash {\omega }_b=1.5$, and ${\beta }_a\hslash \gamma =0.08$