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Working paper

We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of the single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the 3- and 4-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat.

Added: Jul 17, 2019

Working paper

We consider a general continuous mean-variance problem where the cost functional has an integral and a terminal-time component. We transform the problem into a superposition of a static and a dynamic optimization problem. The value function of the latter can be considered as the solution to a degenerate HJB equation either in viscosity or in Sobolev sense (after regularization) under suitable assumptions a nd with implications with regards to the optimality of strategies.

Added: Oct 15, 2015

Working paper

In recent paper of Falkovich and Levitov it was shown, that geometry of separatrixes for viscous electronic flow in graphene is sensitive to boundary conditions. Here we discover theis relation in details. Also we propose, how boundary conditions could be probed experimentally, using weak magnetic field and observed features of separatrixes.

Added: Apr 4, 2018

Working paper

Drovosekov A. B., Kreines N. M., Savitsky A. O. et al. arxiv.org. cond-mat. Cornell University, 2015

A set of thin film Mn<sub>x</sub>Si<sub>1-x</sub> alloy samples with different manganese concentration x = 0.44 - 0.63 grown by the pulsed laser deposition (PLD) method onto the Al<sub>2</sub>O<sub>3</sub> (0001) substrate was investigated in the temperature range 4 - 300 K using ferromagnetic resonance (FMR) measurements in the wide range of frequencies (f = 7 - 60 GHz) and magnetic fields (H = 0 - 30 kOe). For samples with x = 0.52 - 0.55, FMR data show clear evidence of ferromagnetism with high Curie temperatures T<sub>c</sub> ~ 300 K. These samples demonstrate complex and unusual character of magnetic anisotropy described in the frame of phenomenological model as a combination of the essential second order easy plane anisotropy contribution and the additional forth order uniaxial anisotropy contribution with easy direction normal to the film plane. We explain the obtained results by a polycrystalline (mosaic) structure of the films caused by the film-substrate lattice mismatch. The existence of extra strains at the crystallite boundaries leads to an essential inhomogeneous magnetic anisotropy in the film plane.

Added: Jun 17, 2016

Working paper

Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients insure the possibility of the odd-frequency pairing: 1) the topological surface states, 2) the induced pair potential, and 3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac cone in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

Added: Apr 14, 2017

Working paper

Polynomial convergence rate to stationarity is shown for extended Erlang -- Sevastyanov's model.

Added: Dec 16, 2014

Working paper

In the seminal work "Pomset logic: A noncommutative extension of classical linear logic" Retor\'e introduced Pomset logic, an extension of linear logic with a self-dual noncommutative connective. Pomset logic is defined by means of proof-nets, later a deep inference system BV was designed for this extension, but equivalence of system has not been proven up to now. As for a sequent calculus formulation, it has not been known for either of these logics, and there are convincing arguments that such a sequent calculus in the usual sense simply does not exist for them.
In an on-going work on semantics we discovered a system similar to Pomset logic, where a noncommutative connective is no longer self-dual. Pomset logic appears as a degeneration, when the class of models is restricted. This will be shown in a forthcoming paper.
Motivated by these semantic considerations, in the current work we define a semicommutative multiplicative linear logic, which is multiplicative linear logic extended with two nonisomorphic noncommutative connectives (not to be confused with very different Abrusci-Ruet noncommutative logic). We develop a syntax of proof-nets and show how this logic degenerates to Pomset logic.
However, a more important problem than just finding yet another noncommutative logic is finding a sequent calculus for this logic. We introduce decorated sequents, which are sequents equipped with an extra structure of a binary relation of reachability on formulas. We define a decorated sequent calculus for semicommutative logic and prove that it is cut-free, sound and complete. This is adapted to "degenerate" variations, including Pomset logic. Thus, in particular, we give a (sort of) sequent calculus formulation for Pomset logic, which is one of the key results of the paper.

Added: Jul 13, 2017

Working paper

Polynomial convergence rates in total variation are established in Erlang-Sevastyanov's type problem with an infinite number of servers and a general distribution of service under assumptions on the intensity of serving.

Added: Oct 23, 2014

Working paper

We study a model of a spatial evolutionary game, based on the Prisoner's dilemma for two regular arrangements of players, on a square lattice and on a triangular lattice. We analyze steady state distributions of players which evolve from irregular, random initial configurations. We find significant differences between the square and triangular lattice, and we characterize the geometric structures which emerge on the triangular lattice.

Added: Nov 21, 2018

Working paper

In this letter the phenomenon of macroscopic quantization is investigated using the particle on the ring interacting with the dissipative environment as an example. It is shown that the phenomenon of macroscopic quantization has the clear physical origin in that case. It follows from the angular momentum conservation combined with momentum quantization for bare particle on the ring . The existence an observable which can take only integer values in the zero temperature limit is rigorously proved. With the aid of the mapping between particle on the ring and Ambegaokar-Eckern-Schon model, which can be used to describe single-electron devices, it is demonstrated that this observable is analogous to the "effective charge" introduced by Burmistrov and Pruisken for the single-electron box problem. Different consequences of the revealed physics are discussed, as well as a generalization of the obtained results to the case of more complicated systems.

Added: Feb 9, 2015

Working paper

Bakurskiy S. V., Klenov N. V., Soloviev I. I. et al. arxiv.org. cond-mat. Cornell University, 2018. No. 1808.07090.

We study the peculiarities in current-phase relations (CPR) of the SIsFS junction in the region of 0 to p
transition. These CPR consist of two independent branches corresponding to 0− and p− states of the contact.
We have found that depending on the transparency of the SIs tunnel barrier the decrease of the s-layer thickness
leads to transformation of the CPR shape going in the two possible ways: either one of the branches exists only
in discrete intervals of the phase difference j or both branches are sinusoidal but differ in the magnitude of their
critical currents. We demonstrate that the difference can be as large as 10% under maintaining superconductivity
in the s layer. An applicability of these phenomena for memory and logic application is discussed.

Added: Oct 28, 2018

Working paper

We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose non-linear drift parts are sums of the subdifferential of a convex function and a bounded part. This generalizes a classical result by one of the authors (Veretennikov) to infinite dimensions.

Added: Oct 22, 2014

Working paper

We propose a superconducting spin-triplet valve of a new type. This spin valve consists of a bilayer
that involves a superconductor and an itinerant magnetic material, with the magnet showing an
intrinsic non-collinear magnetic order characterized by a wave vector Q that may be aligned in a
few equivalent preferred directions under control of a weak external magnetic field. Re-orienting the
direction of Q allows one to controllably modify long-range spin-triplet superconducting correlations
in the magnetic material, leading to spin-valve switching behavior. This new type of superconducting
spin valve may be used as a magnetic memory element for cryogenic nanoelectronics. It has the
following advantages in comparison with superconducting spin valves proposed earlier: (i) it contains
only one magnetic layer, which may be more easily fabricated and controlled; (ii) its ground states
are separated by a potential barrier, which solves the “half-select” problem of the addressed switch
of such memory elements.

Added: Sep 30, 2017

Working paper

Weyl semimetal is a three-dimensional material with a conical spectrum near an even number of point nodes, where two bands touch each other. Here we study spectral properties of surface electron states in such a system. We show that the density of surface states possesses a logarithmic singularity for the energy to 0. It decreases linearly at the intermediate energy of surface electron states and approaches zero. This universal behavior is a hallmark of the topological order that offers a new wide range of applications.

Added: Mar 8, 2016

Working paper

Thin superconducting ﬁlms are usually regarded as type-II superconductors even when they are made of a type-I materials. The reason is a strong inﬂuence of the stray magnetic ﬁelds outside the superconductive sample. While very thin ﬁlms indeed reach this limit, there is a sufﬁciently large interval of ﬁlm thicknesses in which the magnetic properties cannot be classiﬁed as either of the two conventional superconductivity types. We demonstrate that in this interval superconducting condensate and magnetic ﬁeld reveal exotic spatial proﬁles that are very sensitive to system parameters, in particular, the temperature and applied ﬁeld. Magnetic properties of such systems can be attributed to a special regime of intertype superconductivity. Its physical origin lies in the removal of inﬁnite degeneracy of the superconducting state at the critical Bogomolnyi point. Here we demonstrate that qualitative characteristics of obtained condensate-ﬁeld structures and the way they change with the temperature and applied ﬁeld are independent of the choice of the in-plane boundary conditions for the order parameter and magnetic ﬁeld.

Added: Dec 24, 2018