On the Continuity of Granulometry

Stimulation of the Fluctuation Superconductivity byPTSymmetry

“…We successfully validate our theory by carrying out measurements of far from equilibrium transport in mesoscale-patterned superconducting wires.An Hermitian character of the Hamiltonian expressed by the condition H † = H is a cornerstone of quantum mechanics as it ensures that the energies of its stationary states are real. Yet it was discovered not long ago [1] that the weaker requirement H ‡ = H, where ‡ represents combined parity reflection and time reversal (PT ), introduces new classes of complex Hamiltonians [2] whose spectra are still real and positive [1,[3][4][5]. This generalization of Hermiticity opened a new field of research in quantum mechanics and beyond that had been enjoying ever since a rapid growth.We focus here on the superconducting fluctuations above the superconductor -normal metal transition in quasi 1D superconducting wire of the finite length L driven far from equilibrium by an electric field E, see Fig.…”

“…An Hermitian character of the Hamiltonian expressed by the condition H † = H is a cornerstone of quantum mechanics as it ensures that the energies of its stationary states are real. Yet it was discovered not long ago [1] that the weaker requirement H ‡ = H, where ‡ represents combined parity reflection and time reversal (PT ), introduces new classes of complex Hamiltonians [2] whose spectra are still real and positive [1,[3][4][5]. This generalization of Hermiticity opened a new field of research in quantum mechanics and beyond that had been enjoying ever since a rapid growth.…”

“…We show below using the technique developed in Refs. [1,5,6] that PT -symmetry ofL R holds at low drives. At large E exceeding the certain critical value, E c , the PT -invariance breaks down and the two lowest energy states ε 0 and ε 1 of H eff merge.…”