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It is shown that the famous Allen -- Dynes asymtotic limit for superconducting transition temperature in very strong coupling region $T_{c}>frac{1}{2pi}sqrt{lambda}Omega_0$ (where $lambdagg 1$ - is Eliashberg - McMillan electron - phonon coupling constant and $Omega_0$ - the characteristic frequency of phonons) in antiadiabatic limit of Eliashberg equations $Omega_0/Dgg 1$ ($Dsim E_F$ is conduction band half-width and $E_F$ is Fermi energy) is replaced by $T_c>(2pi^4)^{-1/3}(lambda DOmega_0^2)^{1/3}$, with the upper limit for $T_c$ given by $T_c<frac{2}{pi^2}lambda D$.
The discovery of record - breaking values of superconducting transition temperature $T_c$ in quite a number of hydrides under high pressure was an impressive demonstration of capabilities of electron - phonon mechanism of Cooper pairing. This lead to
The standard Eliashberg - McMillan theory of superconductivity is essentially based on the adiabatic approximation. Here we present some simple estimates of electron - phonon interaction within Eliashberg - McMillan approach in non - adiabatic and ev
The weak-coupling limits of the gap and critical temperature computed within Eliashberg theory surprisingly deviate from the BCS theory predictions by a factor of $1/sqrt{e}$. Interestingly, however, the ratio of these two quantities agrees for both
The influence of antiadiabatic phonons on the temperature of superconducting transition is considered within Eliashberg - McMillan approach in the model of discrete set of (optical) phonon frequencies. A general expression for superconducting transit
The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional electron-phonon superconductors, including the retardation of the interaction and the effect of the Coulomb pseudopotential, to predict the critical tempe