Conductance distribution in 1D systems: dependence on the Fermi level and the ideal leads

The correct definition of the conductance of finite systems implies a connection to the system of the massive ideal leads. Influence of the latter on the properties of the system appears to be rather essential and is studied below on the simplest example of the 1D case. In the log-normal regime this influence is reduced to the change of the absolute scale of conductance, but generally changes the whole distribution function. Under the change of the system length L, its resistance may undergo the periodic or aperiodic oscillations. Variation of the Fermi level induces qualitative changes in the conductance distribution, resembling the smoothed Anderson transition.Comment: Latex, 22 pages, 11 include

Comment on "Can disorder really enhance superconductivity?"

The paper by Mayoh and Garcia-Garcia [arXiv:1412.0029v1] is entitled "Can disorder really enhance superconductivity?". In our opinion, the answer given by the authors is not satisfactory, and we present the alternative picture. Our reply to the comment [arXiv:1502.06282] is added in the end, in order to reveal a series of untrue statements contained in it.Comment: Latex, 5 pages, reply to [arXiv:1502.06282] is added in the en

Computer Model of a "Sense of Humour". I. General Algorithm

A computer model of a "sense of humour" is proposed. The humorous effect is interpreted as a specific malfunction in the course of information processing due to the need for the rapid deletion of the false version transmitted into consciousness. The biological function of a sense of humour consists in speeding up the bringing of information into consciousness and in fuller use of the resources of the brain.Comment: 10 pages, 3 figures included; continuation of this series to appea

Triviality, Renormalizability and Confinement

According to recent results, the Gell-Mann - Low function \beta(g) of four-dimensional \phi^4 theory is non-alternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means possibility to construct the continuous theory with finite interaction at large distances. This conclusion is in visible contradiction with the lattice results indicating triviality of \phi^4 theory. This contradiction is resolved by a special character of renormalizability in \phi^4 theory: to obtain the continuous renormalized theory, there is no need to eliminate a lattice from the bare theory. In fact, such kind of renormalizability is not accidental and can be understood in the framework of Wilson's many-parameter renormalization group. Application of these ideas to QCD shows that Wilson's theory of confinement is not purely illustrative, but has a direct relation to a real situation. As a result, the problem of analytical proof of confinement and a mass gap can be considered as solved, at least on the physical level of rigor.Comment: Latex, 15 page

Density of States near the Anderson Transition in a Space of Dimensionality d=4-epsilon

Asymptotically exact results are obtained for the average Green function and the density of states in a Gaussian random potential for the space dimensionality d=4-epsilon over the entire energy range, including the vicinity of the mobility edge. For N\sim 1 (N is an order of the perturbation theory) only the parquet terms corresponding to the highest powers of 1/epsilon are retained. For large N all powers of 1/epsilon are taken into account with their coefficients calculated in the leading asymptotics in N. This calculation is performed by combining the condition of renormalizability of the theory with the Lipatov asymptotics.Comment: 11 pages, PD

Anderson Transition and Generalized Lyapunov Exponents (comment on comment by P.Markos, L.Schweitzer and M.Weyrauch, cond-mat/0402068)

The generalized Lyapunov exponents describe the growth of the second moments for a particular solution of the quasi-1D Schroedinger equation with initial conditions on the left end. Their possible application in the Anderson transition theory became recently a subject for controversy in the literature. The approach to the problem of the second moments advanced by Markos et al (cond-mat/0402068) is shown to be trivially incorrect. The difference of approaches by Kuzovkov et al (cond-mat/0212036, cond-mat/0501446) and the present author (cond-mat/0504557, cond-mat/0512708) is discussed.Comment: Latex, 5 page

T_c of disordered superconductors near the Anderson transition

According to the Anderson theorem, the critical temperature T_c of a disordered superconductor is determined by the average density of states and does not change at the localization threshold. This statement is valid under assumption of a self-averaging order parameter, which can be violated in the strong localization region. Stimulating by statements on the essential increase of T_c near the Anderson transition, we carried out the systematic investigation of possible violations of self-averaging. Strong deviations from the Anderson theorem are possible due to resonances at the quasi-discrete levels, resulting in localization of the order parameter at the atomic scale. This effect is determined by the properties of individual impurities and has no direct relation to the Anderson transition. In particular, we see no reasons to say on "fractal superconductivity" near the localization threshold.Comment: Latex, 19 pages, 9 figures include

How to observe the localization law \sigma(\omega) (-i\omega) for conductivity?

The Berezinskii localization law \sigma(\omega) (-i\omega) for frequency-dependent conductivity was never questioned from the theoretical side, but never observed experimentally. In fact, this result is valid for closed systems, while most of actual systems are open. We discuss several possibilities for observation of this law and experimental difficulties arising at this way.Comment: Latex, 4 pages, 4 figures include

On 't Hooft's representation of the \beta-function

It is demonstrated, that 't Hooft's renormalization scheme (in which \beta-function has exactly the two-loop form) is generally in conflict with the natural physical requirements and specifies the type of the field theory in an arbitrary manner. It violates analytic properties in the coupling constant plane and provokes misleading conclusion on accumulation of singularities near the origin. It artificially creates renormalon singularities, even if they are absent in the physical scheme. The 't Hooft scheme can be used in the framework of perturbation theory but no global conclusions should be drawn from it.Comment: LaTex, 9 pages, 2 figures include

Upper critical dimension in the scaling theory of localization

It is argued that the Thouless number g(L) is not the only parameter relevant in scale transformations, and that the second parameter connected with off-diagonal disorder should be introduced. A two-parameter scaling theory is suggested that explains a phenomenon of the upper critical dimension from the viewpoint of scaling ideas.Comment: Latex, 8 pages, 2 figure