We study the spin-boson model with a sub-Ohmic bath using a variational method. The transition from coherent dynamics to incoherent tunneling is found to be abrupt as a function of the coupling strength α and to exist for any power 0 < s < 1, where the bath coupling is described by J(ω) ∼ αω s . We find non-monotonic temperature dependence of the two-level gapK and a re-entrance regime close to the transition due to non-adiabatic low-frequency bath modes. Differences between thermodynamic and dynamic conditions for the transition as well as the limitations of the simplified bath description are discussed.

A theoretical model of c-axis transport properties in cuprates is proposed. Inter-plane and in-plane charge fluctuations make hopping between planes incoherent and diffusive (the in-plane momentum is not conserved after tunneling). The non-Drude optical conductivity σc(ω) and the power-law temperature dependence of the dc conductivity are generically explained by the strong fluctuations excited in the process of tunneling. Several microscopic models of the charge fluctuation spectrum are considered.Despite the strongly two-dimensional layered structure of the high-temperature cuprate superconductors, features associated with the third dimension, perpendicular to the CuO 2 planes, may be an important ingredient in their superconductivity. In fact, it is well accepted that a certain degree of Josephson-type coupling between different planes is necessary to suppress the two-dimensional fluctuations, which will otherwise destroy the superconducting long-range order. However, the systematic dependence of the critical temperature T c on the number of layers in the unit cell (together with the absence of evidence for strong fluctuations effects above T c at optimal doping, which suggests that these fluctuations are not the major reason for this systematic dependence) points almost unambiguously to the conclusion that theories formulated for a single plane cannot be the whole story. Either hopping between planes [1], or Coulomb interaction between them [2], or both, is an important factor in raising the critical temperature (and, perhaps, in some cases also for lowering it, see Ref.[2]). In the light of this, the study of the c-axis optical and transport properties is more than just a minor diversion from the main issue.These c-axis optical and transport properties are very puzzling and anomalous [3]. Most remarkable is the fact that the temperature dependence of the dc c-axis resistivity ρ c (T ), in sharp contrast to the well-known linear T -dependence of the in-plane resistivity ρ ab (T ), is non-universal, being described in most cases by a power law ρ c (T ) ∼ T γ , where however the exponent γ can be anything in between approximately +1 and −1. The optical conductivity σ c (ω) is roughly frequency independent from low frequencies up to midinfrared frequencies (except in the case of some overdoped cuprates (Y Ba 2 Cu 3 O 7 and La 2−x Sr x CuO 4 )); the numerical value is below the Mott-Ioffe-Regel minimum metallic conductivity. This behavior, which is dramatically different from the behavior of the in-plane resistivity, has been christened "confinement" [1]. Thus, despite the dramatic differences in the raw data between the different cuprate families, one can isolate at least two elements which may be legitimately called "universal": a non-Drude optical conductivity of a magnitude below the Mott limit, and a power-law temperature dependence of the dc resistivity ρ c (T ) (albeit with a material-specific exponent). In this paper we develop a framework for the explanation of these universalities, which will hopefully ...

We study the Ambegaokar-Eckern-Sch\"{o}n (AES) model for a regular array of metallic grains coupled by tunnel junctions of conductance $g$ and calculate both paramagnetic and diamagnetic terms in the Kubo formula for the conductivity. We find analytically, and confirm by numerical path integral Monte Carlo methods, that for $0

A general elastohydrodynamic theory is developed based on the phenomenological assumption of a sharp decrease of shear relaxation time at large wave vectors k>k(xi), where k(xi) is of order of inverse of several interatomic distances a. This theory describes the low-energy excitations of glassy and amorphous solids, which contribute to anomalous linear-in-temperature specific heat and limit phonon thermal conductivity. The ratio of the wavelength of the phonon, lambda, to its mean free path, l, which is the universal property of sound absorption in glasses, is derived in this theory to be lambda/l=(2/3)(c(t)/c(l))(2)(k(xi)a)(3), where c(t) and c(l) are transverse and longitudinal sound velocities correspondingly.

The third moment frequency sum rule for the density-density correlation function is rederived in the presence of Umklapp processes. Upper and lower bounds on the electron-electron Coulomb energy are derived in two-dimensional and three-dimensional media, and the Umklapp processes are shown to be crucial in determining the spectrum of the density fluctuations (especially for the two-dimensional systems). This and other standard sum rules can be used in conjunction with experimental spectroscopies (electron-energy loss spectroscopy, optical ellipsometry, etc.) to analyse changes of the electron-electron Coulomb energy at the superconducting transition in cuprates.