Electron-electron scattering and nonequilibrium noise in Sharvin contacts

We consider wide ballistic microcontacts with electron-electron scattering in the leads and calculate electric noise and nonlinear conductance in them. Due to a restricted geometry the collisions of electrons result in a shot noise even though they conserve the total momentum of electrons. We obtain the noise and the conductivity for arbitrary relations between voltage $V$ and temperature $T$. The positive inelastic correction to the Sharvin conductance is proportional to $T$ at low voltages $eV \ll T$, and to $|V|$ at high voltages. At low voltages the noise is defined by the Nyquist relation and at high voltages the noise is related with the inelastic correction to the current by the Shottky formula $S_{\mathrm{in}} = 2e\,I_{\mathrm{in}}$.