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Unconventional superconductivity as a synchronization problem in nuclear oscillator networks

We formulate the problem of unconventional $d-$wave superconductivity, with phase fluctuations, pseudogap phenomenon, and local Cooper pairs, in terms of a synchronization problem in random, quantum dissipative, elasto-nuclear oscillator networks. The nodes of the network correspond to {\it localized, collective quadrupolar vibrations} of nuclei-like, elastic inhomogeneities embedded in a dissipative medium. Electrons interacting with such vibrations form local Cooper pairs, with a superfluid $d-$wave pseudogap $Δ_{PG}$, due to an effective, short range attractive interaction of $d_{x^2-y^2}$ character. Phase coherent, bulk superconductivity, with a $d-$wave gap $Δ$, is stabilized when the oscillator network is asymptotically entangled in a nearly decoherence-free environment. Phase coherence will in turn be destroyed, at $T_c$, when the thermal noise becomes comparable to the coupling between oscillators, the superfluid density $K$. The $2Δ/k_B T_c$ ratio is a function of Kuramoto's order parameter, $r=\sqrt{1-K_c/K}$, for the loss of synchronization at $K_c$, and is much larger than the nonuniversal $2Δ_{PG}/k_B T^*$ ratio, where $T^*$ is the temperature at which $Δ_{PG}$ is completely destroyed by thermal fluctuations. We discuss our findings in connection to the available data for various unconventionally high-temperature superconductors.