Renormalized energy of ground and first excited state of Fr\"{o}hlich polaron in the range of weak coupling

Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fr\"{o}hlich Hamiltonian is performed using the Feynman-Pines diagram technique. Renormalized spectral parameters of ground and first excited (phonon repeat) polaron state are accurately calculated for a weak electron-phonon coupling at $T=0$ K. It is shown that the stronger electron-phonon interaction shifts the energy of both states into low-energy region of the spectra. The ground state stays stationary and the excited one decays at a bigger coupling constant.Comment: 12 pages, 5 figure

Effect of ionic ordering in conductivity experiments of DNA aqueous solutions

The effects of ionic ordering in DNA water solutions are studied by conductivity experiments. The conductivity measurements are performed for the solutions of DNA with KCl salt in the temperature range from 28 to 70 C. Salt concentration vary from 0 to 2 M. The conductivity of solutions without DNA but with the same concentration of KCl salt are also performed. The results show that in case of salt free solution of DNA the melting process of the double helix is observed, while in case of DNA solution with added salt the macromolecule denaturation is not featured. For salt concentrations lower than some critical one (0.4 M) the conductivity of DNA solution is higher than the conductivity of KCl water solution without DNA. Starting from the critical concentration the conductivity of KCl solution is higher than the conductivity of DNA solution with added salt. For description of the experimental data phenomenological model is elaborated basing on electrolyte theory. In framework of the developed model a mechanism of counterion ordering is introduced. According to this mechanism under the low salt concentrations electrical conductivity of the system is caused by counterions of DNA ion-hydrate shell. Increasing the amount of salt to the critical concentration counterions condense on DNA polyanion. Further increase of salt concentration leads to the formation of DNA-salt complexes that decreases the conductivity of the system.Comment: 12 pages, 6figures. Ukr. J. Phys. (2014

Energy spectrum of localized quasiparticles renormalized by multi-phonon processes at finite temperature

The theory of renormalized energy spectrum of localized quasi-particle interacting with polarization phonons at finite temperature is developed within the Feynman-Pines diagram technique. The created computer program effectively takes into account multi-phonon processes, exactly defining all diagrams of mass operator together with their analytical expressions in arbitrary order over the coupling constant. Now it is possible to separate the pole and non-pole mass operator terms and perform a partial summing of their main terms. The renormalized spectrum of the system is obtained within the solution of dispersion equation in the vicinity of the main state where the high- and low-energy complexes of bound states are observed. The properties of the spectrum are analyzed depending on the coupling constant and the temperature.Comment: 16 pages, 3 figures, 3 table

Single-scale diagrams and multiple binomial sums

The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.Comment: 10 pp LaTeX, misprints in app. A and minor misprints in the text correcte