We study the behaviour of charge oscillations in superconducting Cooper pair boxes weakly interacting with an environment. We found that, due to the noise and dissipation induced by the environment, the stability properties of these nanodevices differ according to whether the charge oscillations are interpreted as an effect of macroscopic quantum coherence, or semiclassically in terms of the Gross–Pitaevskii equation. More specifically, occupation number states, used in the quantum interpretation of the oscillations, are found to be much more unstable than coherent ones, typical of the semiclassical explanation.
Euclidean Q-balls of fluctuating SDW/CDW in the 'nested' Hubbard model of high-T
c superconductors as the origin of pseudogap and superconducting behavior
Euclidean Q-ball type solutions carrying Cooper/local-pair condensates inside finite volume with classically oscillating in Matsubara time spin-/charge densities (SDW/CDW) are found in the 'nested' repulsive Hubbard model of high-T
c superconductors. An exchange between fermions with coherently oscillating SDW/CDW inside the Q-balls provides `pairing glue', that couples fermions into Cooper/local-pairs. Euclidean Q-ball solutions arise below some temperature
T∗ due to global invariance of the effective theory under the phase rotation of the SDW/CDW fluctuations amplitudes, that conserves a 'Noether charge' Q along the Matsubara time axis. At
T∗ the classical SDW/CDW fluctuations arise via 1
st order phase transition, while superconducting condensate density inside Q-balls is zero at
T∗ and possesses a steep maximum at
T<T∗, causing a similar maximum in specific heat of the Q-balls 'gas'. Below
T∗ the volume of the Q-balls is inversely proportional to the square of SDW/CDW fluctuation amplitude. The fermionic spectral gap inside Euclidean Q-balls arises in the vicinity of the 'nested' regions of the bare Fermi surface and scales with the square root of the superconducting density. All the described solutions are found analytically from the Eliashberg like equations for the two cases of 'nesting' wave vectors: a CDW wave vector
QCDW, connecting regions near the Fermi surface with equal signs of the superconducting order parameter, or for a SDW wave vector
QSDW, connecting regions with the opposite signs of the
d-wave superconducting order parameter. Possible relation of the presented theory with thermodynamic time-crystals and different properties of superconductors is discussed.
We investigate the nonequilibrium pair density wave order parameter in a simple microscopic model with the ground state
d− wave spatially uniform superconductivity. After pushing the system out of equilibrium by a short-time induced order parameter, the system can exhibit robust free nondecaying oscillations of nonuniform superconducting order. In the weak nonequilibrium regime, the frequency of these oscillations is about
2Δ/ℏ and the amplitude can be explained qualitatively by features of equilibrium free energy. In case when the system was taken far from equilibrium, it transits to a non-linear regime where even metastable coexistence of
d− wave superconducting and pair density wave gaps are possible.