arXiv subjects

Igor V. Ovchinnikov

Publications and source records attributed to Igor V. Ovchinnikov.

26 records · Page 2Linked to original sources

arXiv2015

Transfer operators and topological field theory

The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed supersymetric theory of stochastic differential equations (SDE). It turns out that the stochastically generalized TO (GTO) of the DS theory is the finite-time Fokker-Planck evolution operator. As a result comes the supersymmetric trivialization of the so-called sharp trace and sharp determinant of the GTO, with the former being the Witten index, which is also the stochastic generalization of the Lefschetz index so that it equals the Euler characteristic of the (closed) phase space for any flow vector field, noise metric, and temperature. The enabled possibility to apply the spectral theorems of the DS theory to the Fokker-Planck operators allows to extend the previous picture of the spontaneous topological supersymmetry (Q-symmetry) breaking onto the situations with negative ground state's attenuation rate. The later signifies the exponential growth of the number of periodic solutions/orbits in the large time limit, which is the unique feature of chaotic behavior proving that the spontaneous breakdown of Q-symmetry is indeed the field-theoretic definition and stochastic generalization of the concept of deterministic chaos. In addition, the previously proposed low-temperature classification of SDEs, i.e., thermodynamic equilibrium / noise-induced chaos ((anti)instanton condensation, intermittent) / ordinary chaos (non-integrability of the flow vector field), is complemented by the discussion of the high-temperature regime where the sharp boundary between the noise-induced and ordinary chaotic phases must smear out into a crossover, and at even higher temperatures the Q-symmetry is restored. The Weyl quantization is discussed in the context of the Ito-Stratonovich dilemma.

math-ph↗

arXiv2013

Topological field theory of dynamical systems. II

This paper is a continuation of the study [Chaos.22.033134] of the relation between the stochastic dynamical systems (DS) and the Witten-type topological field theories (TFT). Here, it is discussed that stochastic expectation values of a DS must be complemented on the TFT side by $(-1)^{\hat F}$, where $\hat F$ is the ghost number operator. The role of this inclusion is to unfold the natural path-integral representation of the TFT, \emph{i.e.}, the Witten index that equals up to a topological factor to the partition function of the stochastic noise, into the physical partition function of TFT/DS. It is also shown that on the DS side, the TFT's wavefunctions are the conditional probability densities.

math-ph↗

arXiv2012

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.

math-ph↗

arXiv2011

Self-Organized Criticality as Witten-type Topological Field Theory with Spontaneously Broken Becchi-Rouet-Stora-Tyutin Symmetry

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of the conditions for the SOC is the slow driving noise, which unambiguously suggests Stratonovich interpretation of the corresponding stochastic differential equation (SDE). This, in turn, necessitates the use of Parisi-Sourlas-Wu stochastic quantization procedure, which straightforwardly leads to a model with BRST-exact action, i.e., to a W-TFT. In the parameter space of the SDE, there must exist full-dimensional regions where the BRST-symmetry is spontaneously broken by instantons, which in the context of SOC are essentially avalanches. In these regions, the avalanche-type SOC dynamics is liberated from overwise a rightful dynamics-less W-TFT, and a Goldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent modulii of instantons (avalanches) and being gapless are responsible for the critical avalanche distribution in the low-energy, long-wavelength limit. The above arguments are robust against moderate variations of the SDE's parameters and the criticality is "self-tuned". The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC. It also suggests that there may in principle exist a connection between some of SOC's and the concept of topological quantum computing.

nlin.AO↗

arXiv2008

Voltage-Controlled Surface Magnetization of Itinerant Ferromagnet Ni_(1-x)Cu_x

We argue that surface magnetization of a metallic ferromagnet can be turned on and off isothermally by an applied voltage. For this, the material's electron subsystem must be close enough to the boundary between para- and ferromagnetic regions on the electron density scale. For the 3d series, the boundary is between Ni and Cu, which makes their alloy a primary candidate. Using Ginzburg-Landau functional, which we build from Ni_(1-x)Cu_x empirical properties, ab-initio parameters of Ni and Cu, and orbital-free LSDA, we show that the proposed effect is experimentally observable.

cond-mat.mtrl-sci↗

arXiv2007

Hydrodynamic Tensor-DFT with correct susceptibility

In a previous work we developed a family of orbital-free tensor equations for DFT [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equations hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work we assumed that the cumulants vanish above a certain order (N). Here we show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a non-perturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained while the Thomas Fermi and von-Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate our previous assertion that as the order of the theory is increased, new additional transverse sound modes appear mimicking the RPA transverse dispersion region.

cond-mat.mtrl-sci↗

arXiv2005

Bogoliubov-like mode in the Tonks-Girardeau Gas

We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wave-length asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: $ω(q)=q \sqrt{\barρU(q)/m}$, where $\barρ$ is the bosons density and $U(q)$ is a Fourier component of the two-body potential.

cond-mat.str-el↗

arXiv2004

A Liouville equation for systems which exchange particles with reservoirs: transport through a nano-device

A Redfield-like Liouville equation for an open system that couples to one or more leads and exchanges particles with them is derived. The equation is presented for a general case. A case study of time-dependent transport through a single quantum level for varying electrostatic and chemical potentials in the leads is presented. For the case of varying electrostatic potentials the proposed equation yields, for the model study, the results of an exact solution.

physics.chem-ph↗