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Grebenkov D.S.,CNRS Condensed Matter Physics Laboratory | Grebenkov D.S.,St Petersburg National Research University Of Information Technologies
Journal of Physics A: Mathematical and Theoretical

We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by a one- or multidimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a propagator using Langevin and Fokker-Planck equations. The mean exit time, the moment-generating function and the survival probability are then expressed through confluent hypergeometric functions and thoroughly analyzed. We also present a rapidly converging series representation of confluent hypergeometric functions that is particularly well suited for numerical computation of eigenvalues and eigenfunctions of the governing Fokker-Planck operator. We discuss several applications of first exit times, such as the detection of time intervals during which motor proteins exert a constant force onto a tracer in optical tweezers single-particle tracking experiments; adhesion bond dissociation under mechanical stress; characterization of active periods of trend-following and mean-reverting strategies in algorithmic trading on stock markets; relation to the distribution of first crossing times of a moving boundary by Brownian motion. Some extensions are described, including diffusion under quadratic double-well potential and anomalous diffusion. © 2015 IOP Publishing Ltd. Source

Amosova L.P.,St Petersburg National Research University Of Information Technologies
Journal of Optical Technology (A Translation of Opticheskii Zhurnal)

This review discusses how the main parameters of the deposition regimes of the oxides of semiconductors and metals affect the structure and relief of a precipitated film and analyzes the orientation mechanisms of liquid crystals (LCs) by means of such films. The dependence between the deposition angles, the tilt of the crystallites, and the tilt of the LC director is reported. It is shown that, when the deposition angle of the orienting film is increased relative to the substrate plane, it can be energetically favorable to make a transition either to the planar or the homeotropic orientation of the LC, depending on the film-deposition rate. © 2013 Optical Society of America. Source

Nemilov S.V.,St Petersburg National Research University Of Information Technologies
Glass Physics and Chemistry

The main relaxation theories of glass transition (Leontovich-Mandelstam and Volkenstein- Ptitsyn) variously formulate the kinetic criteria of glass transition. Both of the approaches are shown to be equivalent in physical sense and provide a single expression that connects the rate of change of a melt temperature and the structure relaxtion time. The theory characterizes the width of a temperature band δTg in which the glass transition occurs. The values of δTg can either be obtained from the experiment or be accepted to conform to the value of a temperature step under the change of viscosity by an order of magnitude (direct method for finding by the Volkenstein-Ptitsyn theory). Using the Maxwell equation, a new equation for the calculation of the viscosity for viscoelastic relaxation was suggested, which is based on a shear modulus of glass and the cooling rate. The theory was verified basing on the published data for oxide glass. The average difference between the calculated and measured values of lgη upon glass transition comprises 0 ± 0.30. These results correspond to the cooling rate of 3 K/min and log(η, Pa s) = 12.76 ± 0.26 (for all glass considered). It is shown that the most probable cooling rate which provides the viscosity upon glass transition of ∼1012 Pa s is close to 20 K/min (oxide melts). The theory predetermines the dependence of viscosity upon glass transition on the nature of a glass-forming liquid. The disadvantages of other approaches to the problem under consideration are demonstrated. Original Russian Text © S.V. Nemilov, 2013. Source

Potapov A.S.,St Petersburg National Research University Of Information Technologies
Journal of Optical Technology (A Translation of Opticheskii Zhurnal)

This paper analyzes the necessity of using many information representations simultaneously in image-processing and -analysis systems. The difference between Kolmogorov-complexity and algorithmic-probability criteria when solving induction problems and making decisions is investigated. It is shown that making the optimum decisions (for example, in recognition or prediction problems) requires the use of many representations of information, in terms of which alternative descriptions of the images are constructed. A representational algorithmic-probability criterion is derived for determining the optimum set of representations from a given selection of images. © 2012 Optical Society of America. Source

Brody D.C.,Brunel University | Brody D.C.,St Petersburg National Research University Of Information Technologies
Journal of Physics A: Mathematical and Theoretical

In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric - the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss. © 2016 IOP Publishing Ltd. Source

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