Topological field theory of dynamical systems

Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos". Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.Comment: 18 pages, 4 figures, published versio

Research, development and application of the innovational technology of high quality pump-compressor pipes production from sections

The innovational technology of high-strength, cold- and corrosion-resistant pump-compressor pipes from sections was developed. It includes the reduction process inside three-high stand of screw rolling before piercing in the «80» pipe-rolling mill line in OAO SinTZ. The special attention is paid to the questions of fine-grained steel production and final tubes quality. It is shown that new technology is efficient from the point of tube production of high level mechanical properties

Exact singlet bond ground states for electronic models

We have proposed several 1D and 2D electronic models with the exact ground state. The ground state wave function of these models is represented in terms of "singlet bond" functions consisting of homopolar and ionic configurations. The Hamiltonians of the models include the correlated hopping of electrons, pair hopping terms and the spin interactions. One of the 1D models demonstrates spontaneous breaking of the translational symmetry. We studied also the model describing the transition point between the phases with and without an off-diagonal long-range order.Comment: 4 pages, 2 figures, Revte