Theory of the Blochwave oscillations in small Josephson junctions
Abstract
A quantumstatistical theory of the lowtemperature behavior of Josephson junctions with very small capacitance C and quasiparticle conductivity G, driven by a small current I(t), is developed. In such junctions the “secondary” quantum macroscopic effects (tunneling and interference) are significant for all values of the Josephson phase difference ϕ, so that new features in the junction dynamics arise, including quantum “Blochwave” oscillations. Here the junction dynamics is analyzed in detail starting from a simple macroscopic Hamiltonian. The simplest way to analyze the Blochwave oscillations turns out to be a Langevintype equation for the operator of the junction “quasicharge” q. In particular, this equation shows that the frequency f _{B} of these oscillations is related by the fundamental equationf_B = (bar I  Gbar V)/2e to the dc currentbar I and voltagebar V. The main effects suppressing or masking the Blochwave oscillations can be analyzed using the equation for the density matrix of the system traced over the states of the quasiparticles. This analysis has made it possible to establish the main conditions for the experimental observation of the predicted effects and to present a general picture of the low temperature dynamics of Josephson junctions.
 Publication:

Journal of Low Temperature Physics
 Pub Date:
 May 1985
 DOI:
 10.1007/BF00683782
 Bibcode:
 1985JLTP...59..347L