From surface to random criticality in layered planar Ising models

A general case of a spatially nonuniform planar layered Ising model, or an equivalent quantum Ising chain, is analysed with an exact functional real space renormalization group. Various surface, finite size, quasiperiodic and random layer (McCoy-Wu) universality classes are obtained and discussed within a single theoretical framework leading to new insights into the nature of random criticality.Comment: 11 pages; REVTeX 3.

Statistics of branched flow in a weak correlated random potential

Recent images of electron flow through a two-dimensional electron gas (2DEG) device show branching behavior that is reproduced in numerical simulations of motion in a correlated random potential [cond-mat/0010348]. We show how such branching naturally arises from caustics in the classical flow and find a simple scaling behavior of the branching under variation of the random potential strength. Analytic results describing the statistical properties of the branching are confirmed by classical and quantum numerical tests.Comment: 4 pages, 4 figure

Defending Time-Symmetrized Quantum Theory

Recently, several authors have criticized time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was the proof, which appeared in various forms, showing that counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with the standard quantum theory. I argue here that the apparent contradiction appears due to inappropriate usage of traditional time asymmetric approach to counterfactuals, and that the contradiction disappears when the problem is analyzed in terms of time-symmetric counterfactuals. I analyze various aspects of time-symmetry of quantum theory and defend the time-symmetrized formalism.Comment: 19 pages, LaTe

About Algorithm for Transformation of Logic Functions (ATLF)

In this article the algorithm for transformation of logic functions which are given by truth tables is considered. The suggested algorithm allows the transformation of many-valued logic functions with the required number of variables and can be looked in this sense as universal.Comment: 25 pages, in English, German and Russia

A New Approach to Understanding Ontogenesis and The Theory of Aging

This paper proposes an original theory of aging of multicellular organisms. The cells of multicellular organisms, in contrast to unicellular organisms, are burdened with a two- part genome: housekeeping and specialized (multicellular), responsible for ontogenesis and terminal differentiation. The two parts of the genome compete for limited adaptive resources thereby interfering with the ability of the house-keeping part of the genome to adequately perform reparative and adaptive functions in post mitotic cells. The necessity to complete the ontgenesis program, leads to increased activity of the multicellular components of the genome. As a result, the allocation of cellular resources to specialized genome con-tinuously increases with time. This leads to a deficit of reparative and adaptive capacity in post mitotic cells. Suggestions for future research focus on identifying groups of genes responsible for regulation of growth rate of specialized genome and suppressing ability of the cell division. A better understanding of the relationship between the two parts of the genome will not only help us to manipulate ontogenesis and aging, but will also improve our understanding of cancer development and ontogenesis.Comment: 16 pages, 1 figure, 82 ref; Keywords: Aging, Ontogenesis, Genom

Probability and the Many-Worlds Interpretation of Quantum Theory

Two works related to the concept of probability in the framework of the many-worlds interpretation are presented. The first deals with recent controversy in classical probability theory. Elga and D. Lewis argues that Sleeping Beauty should have different credences for the result of a fair coin toss in a particular situation. It is argued that when the coin is replaced by a quantum coin, the credence is unambiguous and since one should not expect a difference between classical and quantum coins, this provides a particular resolution of the controversy. Second work is an analysis of a recent criticism by Byrne and Hall of Everett-type approach presented by Chalmers. It is shown that the criticism has no universal validity and that the Byrne and Hall rejection of any Everett-type interpretation of quantum mechanics is unfounded.Comment: 15 pages. Contribution to the conference: Reconsideration of Foundations of Quantum Mechanics, Sweeden 2001. Section 3 has overlap with quant-ph/000105

Tachyonic Preheating

I review the theory of preheating after inflation, focusing on the recently found tachyonic preheating in the theories with spontaneous symmetry breaking. This occurs due to the tachyonic instability of the scalar field near the top of its effective potential. Contrary to the common expectation, tachyonic instability converts most of the energy into that of colliding classical waves very rapidly, within a single oscillation. Efficient tachyonic preheating is typical for the hybrid inflationary scenario, including SUSY motivated and brane inflation models.Comment: 18 pages, contribution to the Proceedings of PASCOS 200

Almost commuting matrices with respect to normalized Hilbert-Schmidt norm

Almost-commuting matrices with respect to the normalized Hilbert-Schmidt norm are considered. Normal almost commuting matrices are proved to be near commuting.Comment: 11 page

Elementary Particles in a Quantum Theory Over a Galois Field

We consider elementary particles in a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily describes a particle and its antiparticle simultaneously. {\it In other words, the very existence of antiparticles is a strong indication that nature is described rather by a finite field (or at least a field with a nonzero characteristic) than by complex numbers.} As a consequence, the spin-statistics theorem is simply a requirement that standard quantum theory should be based on complex numbers and elementary particles cannot be neutral. The Dirac vacuum energy problem has a natural solution and the vacuum energy (which in the standard theory is infinite and negative) equals zero as it should be.Comment: Latex, 37 pages, no figures. Minor changes in motivation. In particular, it is noted that the very existence of antiparticles is a strong indication that nature is described rather by a finite field (or at least a field with a nonzero characteristic) than by complex number

Characterization of sofic groups and equations over groups

We give the following characterization of sofic (weakly sofic) groups: a group $G$ is sofic (weakly sofic) if and only if any system of equations solvable in any alternating group (any finite group) is solvable over $G$.Comment: This paper has been withdrawn by the author due to all its results are in 1506.06940. The paper 1506.06940 contains more general and clearly written result