On the critical slowing down in superconductors

Paul Brookes, Giovanna Tancredi, Themis Mavrogordatos +6 more

B. U. Felderhof

The dynamics of systems described in Hartree-Fock approximation is studied near a stationary point of the free energy. It is shown that the second-order free-energy functional is a constant for the linearized self-consistent equation of motion. This leads to the stability criterion derived by Mermin. A simple collision model is constructed and is shown to satisfy the H theorem. It exhibits the effect of critical slowing down. The formalism is shown to be applicable to superconductors.

Kyozi Kawasaki, T. Tsuzuki

S. M. Alamoudi, D. Boyanovsky, Shang-Yung Wang

We present a field-theoretical method to obtain consistently the equations of motion for small amplitude fluctuations of the order parameter directly in real time for a homogeneous, neutral BCS superconductor. This method allows to study the nonequilibrium relaxation of the order parameter as an initial value problem. We obtain the Ward identities and the effective actions for small phase the amplitude fluctuations to one-loop order. Focusing on the long wavelength, low-frequency limit near the critical point, we obtain the time-dependent Ginzburg-Landau effective action to one-loop order, which is nonlocal as a consequence of Landau damping. The nonequilibrium relaxation of the phase and amplitude fluctuations is studied directly in real time. The long-wavelength phase fluctuation (Bogoliubov-Anderson-Goldstone mode) is overdamped by Landau damping and the relaxation time scale diverges at the critical point, revealing critical slowing down.

Masuo Suzuki

Phenomenological arguments on the critical slowing down is presented and “similarity law” is proposed on the indices of the critical slowing down. The similarity law is confirmed in linear spin chains near the critical field and in the kinetic Ising model near the critical temperature. It is exactly shown in the linear spin chains that the critical index of slowing down is different from that of the static susceptibility and that the dynamical susceptibility has a logarithmic singularity with respect to the frequency at the critical field and at zero temperature.

Myron B. Salamon, W. Lee, K M Ghiron +3 more