Title: ac properties of short Josephson weak links,
Abstract: The admittance of two types of Josephson weak links is calculated, i.e., of a
one-dimensional superconducting wire with a local suppression of the order
parameter, and the second is a short S-c-S structure, where S denotes a
superconductor and c---a constriction. The systems of the first type are
analyzed on the basis of time-dependent Ginzburg-Landau equations. We show that
the impedance $Z(\Omega)$ has a maximum as a function of the frequency
$\Omega$, and the electric field $E_{\Omega}$ is determined by two
gauge-invariant quantities---the condensate momentum $Q_{\Omega}$ and the
potential $\mu$ related to charge imbalance. The structures of the second type
are studied on the basis of microscopic equations for quasiclassical Green's
functions in the Keldysh technique. For short S-c-S contacts (the Thouless
energy ${E_{\text{Th}} = D/L^{2} \gg \Delta}$) we present a formula for
admittance $Y$ valid at frequencies $\Omega$ and temperatures $T$ less than the
Thouless energy but arbitrary with respect to the energy gap $\Delta$. It is
shown that, at low temperatures, the absorption is absent [${\mathrm{Re}(Y) =
0}$] if the frequency does not exceed the energy gap in the center of the
constriction (${\Omega < \Delta \cos \varphi_{0}}$, where $2 \varphi_{0}$ is
the phase difference between the S reservoirs). The absorption gradually
increases with increasing the difference ${(\Omega - \Delta \cos \varphi_{0})}$
if $2 \varphi_{0}$ is less than the phase difference $2 \varphi_{\text{c}}$
corresponding to the critical Josephson current. In the interval ${2
\varphi_{\text{c}} < 2 \varphi_{0} < \pi}$, the absorption has a maximum. This
interval of the phase difference is achievable in phase-biased Josephson
junctions. Close to $T_{\text{c}}$ the admittance has a maximum at low $\Omega$
which is described by an analytical formula.