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Diakonov D.,RAS Petersburg Nuclear Physics Institute | Tumanov A.G.,St Petersburg Academic University | Vladimirov A.A.,Ruhr University Bochum
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2011

We attempt to build systematically the low-energy effective Lagrangian for the Einstein-Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order, the fermion action with torsion possesses additional U(1) L×U(1) R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a pointlike 4-fermion action of a general form containing vector-vector, axial-vector, and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the "spin fluid" approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences. © 2011 American Physical Society.

Zhang X.,Beijing University of Posts and Telecommunications | Dubrovskii V.G.,RAS Ioffe Physical - Technical Institute | Sibirev N.V.,St Petersburg Academic University | Ren X.,Beijing University of Posts and Telecommunications
Crystal Growth and Design | Year: 2011

In view of a continuously growing interest in monolithic integration of dissimilar semiconductor materials in a nanostructure form, we present an analytical study of elastic strain energy in nanostructures of different isotropic geometries grown on lattice mismatched substrates. An analytical solution for the elastic stress field is derived, which is not restricted by the small aspect ratio or particular geometry. It is shown that, at a large enough aspect ratio, the relaxation of displacement fields with the vertical coordinate is exponential. This allows us to find an analytical expression for the strain energy density. The cases of rigid and elastic substrates are considered simultaneously. By minimizing the total energy, we obtain the elastic energy density as a function of aspect ratio for given nanostructure geometry. Our data indicate that the elastic energy is highly dependent on the island shape, with the relaxation becoming faster as the contact angle increases. We also present a simple expression for the elastic relaxation where the fitting coefficient depends on the geometry. A dislocation model is then considered to analyze the competition between the elastic and dislocation energies. We calculate the critical radius below which the plastic deformation is energetically suppressed. Our results demonstrate a good quantitative correlation with the available experimental data on III-V semiconductor nanowires grown on silicon substrates. © 2011 American Chemical Society.

Laussy F.P.,University of Southampton | Kavokin A.V.,University of Southampton | Kavokin A.V.,University of Rome Tor Vergata | Shelykh I.A.,University of Iceland | Shelykh I.A.,St Petersburg Academic University
Physical Review Letters | Year: 2010

We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of an exciton-polariton Bose-Einstein condensate. We consider a model microcavity where a quantum well with a two-dimensional electron gas is sandwiched between two undoped quantum wells, where a polariton condensate is formed. We show that the critical temperature for superconductivity dramatically increases with the condensate population, opening a new route towards high-temperature superconductivity. © 2010 The American Physical Society.

Beznogov M.V.,St Petersburg Academic University | Yakovlev D.G.,RAS Ioffe Physical - Technical Institute
Physical Review Letters | Year: 2013

We analyze diffusion equations in strongly coupled Coulomb mixtures of ions in dense stellar matter. Strong coupling of ions in the presence of gravitational forces and electric fields (induced by plasma polarization in the presence of gravity) produces a specific diffusion current which can separate ions with the same A/Z (mass to charge number) ratios but different Z. This Coulomb separation of ions can be important for the evolution of white dwarfs and neutron stars. © 2013 American Physical Society.

Oparin V.,St Petersburg Academic University
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2016

The usual DPLL algorithm uses splittings (branchings) on single Boolean variables. We consider an extension to allow splitting on linear combinations mod 2, which yields a search tree called a linear splitting tree. We prove that the pigeonhole principle has linear splitting trees of size 2O(n). This is near-optimal since Itsykson and Sokolov [1] proved a 2Ω(n) lower bound. It improves on the size 2Θ(n log n) for splitting on single variables; thus the pigeonhole principle has a gap between linear splitting and the usual splitting on single variables. This is of particular interest since the pigeonhole principle is not based on linear constraints. We further prove that the perfect matching principle has splitting trees of size 2O(n). © Springer International Publishing Switzerland 2016.

Dubrovskii V.G.,St Petersburg Academic University | Dubrovskii V.G.,RAS Ioffe Physical - Technical Institute
Semiconductors and Semimetals | Year: 2015

In this work, we give a detailed overview of theoretical methods used for modeling the vapor-liquid-solid (VLS) growth of III-V semiconductor nanowires. We emphasis the importance of considering kinetics of both group III and V species for understanding and control over the properties of III-V nanowires in terms of their morphology and crystal structure. The chapter reviews the well-known results but also presents some newly developed concepts. In particular, we describe very recent results for nucleation rates in III-V nanowires under different conditions, the radius self-equilibration in Ga-catalyzed GaAs nanowires, and understanding the polytypism of Au-catalyzed III-V nanowires versus the group V flux. © 2015 Elsevier Inc.

Dubrovskii V.G.,RAS Ioffe Physical - Technical Institute | Nazarenko M.V.,St Petersburg Academic University
Journal of Chemical Physics | Year: 2010

This work addresses theory of nucleation and condensation based on the continuous Fokker-Plank type kinetic equation for the distribution of supercritical embryos over sizes beyond the deterministic limit, i.e., keeping the second derivative with respect to size. The first part of the work treats the nucleation stage. It is shown that the size spectrum should be generally obtained by the convolution of the initial distribution with the Gaussian-like Green function with spreading dispersion. It is then demonstrated that the fluctuation-induced effects can be safely neglected at the nucleation stage, where the spectrum broadening due to the nonlinear boundary condition is much larger than the fluctuational one. The crossover between the known triangular and double exponential distributions under different conditions of material influx into the system is demonstrated. Some examples of size distributions at the nucleation stage in different regimes of material influx are also presented. © 2010 American Institute of Physics.

Aganezov Jr. S.,St Petersburg Academic University
BMC bioinformatics | Year: 2012

In comparative genomics, the rearrangement distance between two genomes (equal the minimal number of genome rearrangements required to transform them into a single genome) is often used for measuring their evolutionary remoteness. Generalization of this measure to three genomes is known as the median score (while a resulting genome is called median genome). In contrast to the rearrangement distance between two genomes which can be computed in linear time, computing the median score for three genomes is NP-hard. This inspires a quest for simpler and faster approximations for the median score, the most natural of which appears to be the halved sum of pairwise distances which in fact represents a lower bound for the median score.In this work, we study relationship and interplay of pairwise distances between three genomes and their median score under the model of Double-Cut-and-Join (DCJ) rearrangements. Most remarkably we show that while a rearrangement may change the sum of pairwise distances by at most 2 (and thus change the lower bound by at most 1), even the most "powerful" rearrangements in this respect that increase the lower bound by 1 (by moving one genome farther away from each of the other two genomes), which we call strong, do not necessarily affect the median score. This observation implies that the two measures are not as well-correlated as one's intuition may suggest.We further prove that the median score attains the lower bound exactly on the triples of genomes that can be obtained from a single genome with strong rearrangements. While the sum of pairwise distances with the factor 2/3 represents an upper bound for the median score, its tightness remains unclear. Nonetheless, we show that the difference of the median score and its lower bound is not bounded by a constant.

Dubrovskii V.G.,Saint Petersburg State University of Information Technologies, Mechanics and Optics | Grecenkov J.,St Petersburg Academic University
Crystal Growth and Design | Year: 2014

We present a self-consistent model for the Zeldovich nucleation rate that determines the nucleation probabilities, growth rates, and even the preferred crystal structure of Au-catalyzed III-V nanowires fabricated by the vapor-liquid-solid growth method. The obtained expression accounts for the nucleation kinetics in ternary Au-III-V alloys and shows that the nucleation rate in vapor-liquid-solid nanowires is proportional to the As concentration, As diffusion coefficient in the droplet, and activity of solid GaAs. The leading exponential term of the nucleation rate is modified due to the self-consistency renormalization. As a result, the behavior of the effective nucleation barrier versus Ga concentration is changed significantly with respect to the commonly used expression. This strongly affects the values of Ga concentrations during growth which are obtained within the self-consistent approach with the known nanowire elongation rates. In turn, the renormalized nucleation rates change the predictions regarding the zincblende-wurtzite phase transitions in III-V nanowires. In particular, our calculations show why the Au-catalyzed GaAs nanowires grown by molecular beam epitaxy at 550 °C are predominantly wurtzite, while the high temperature hydride vapor phase epitaxy at 715 °C yields pure zincblende crystal structure. We also obtain useful estimates for the As diffusion coefficients in ternary Au-Ga-As liquids at different conditions. © 2014 American Chemical Society.

Dubrovskii V.G.,RAS Ioffe Physical - Technical Institute | Cirlin G.E.,RAS Ioffe Physical - Technical Institute | Sibirev N.V.,St Petersburg Academic University | Jabeen F.,CNRS Laboratory for Photonics and Nanostructures | And 2 more authors.
Nano Letters | Year: 2011

We report on the new mode of the vapor-liquid-solid nanowire growth with a droplet wetting the sidewalls and surrounding the nanowire rather than resting on its top. It is shown theoretically that such an unusual configuration happens when the growth is catalyzed by a lower surface energy metal. A model of a nonspherical elongated droplet shape in the wetting case is developed. Theoretical predictions are compared to the experimental data on the Ga-catalyzed growth of GaAs nanowires by molecular beam epitaxy. In particular, it is demonstrated that the experimentally observed droplet shape is indeed nonspherical. The new VLS mode has a major impact on the crystal structure of GaAs nanowires, helping to avoid the uncontrolled zinc blende-wurtzite polytylism under optimized growth conditions. Since the triple phase line nucleation is suppressed on surface energetic grounds, all nanowires acquire pure zinc blende phase along the entire length, as demonstrated by the structural studies of our GaAs nanowires. © 2011 American Chemical Society.

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