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Of all publications in the section: 37
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Working paper
Elena R. Loubenets. quant-ph. arXiv. Cornell University, 2012. No. 1210.3270.
Working paper
Ducomet B., Zlotnik A., Romanova A. V. arxiv.org. math. Cornell University, 2013. No. 1309.7280 .
An initial-boundary value problem for the $n$-dimensional ($n\geq 2$) time-dependent Schrödinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we first construct higher order scheme with splitting space averages having much better spectral properties for $n\geq 3$. Next we apply the Strang-type splitting with respect to the potential and, third, construct discrete transparent boundary conditions (TBC). For the resulting method, the uniqueness of solution and the unconditional uniform in time $L^2$-stability (in particular, $L^2$-conservativeness) are proved. Owing to the splitting, an effective direct algorithm using FFT (in the coordinate directions perpendicular to the leading axis of the parallelepiped) is applicable for general potential. Numerical results on the 2D tunnel effect for a P\"{o}schl-Teller-like potential-barrier and a rectangular potential-well are also included.
Working paper
Семенякин Н. С. arxiv.org. cond-mat. Cornell University, 2016
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.
Working paper
Elena R. Loubenets. quant-ph. arXiv. Cornell University, 2014. No. 1402.4023v1.
Working paper
Ioselevich P., Ostrovsky P., Fominov Y. et al. Working papers by Cornell University. Cornell University, 2016
We study Josephson junctions with weak links consisting of two parallel disordered arms with magnetic properties -- ferromagnetic, half-metallic or normal with magnetic impurities. In the case of long links, the Josephson effect is dominated by mesoscopic fluctuations. In this regime, the system realises a $\varphi_0$ junction with sample-dependent $\varphi_0$ and critical current. Cooper pair splitting between the two arms plays a major role and leads to $2\Phi_0$ periodicity of the current as a function of flux between the arms. We calculate the current and its flux and polarization dependence for the three types of magnetic links.
Working paper
Zatelepin A., Shchur L. Working papers by Cornell University. Cornell University, 2010. No. 1008.3573.
We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin clusters are presented. Fractal dimensions are measured and compared to exact theoretical predictions.
Working paper
V. A. Avetisov, Ivanov V. A., Meshkov D. A. et al. Statistical mechanics. arXie. arXive, 2013. No. 1303.
The relaxation of an elastic network, constructed by a contact map of a fractal (crumpled) polymer globule is investigated. We found that: i) the slowest mode of the network is separated from the rest of the spectrum by a wide gap, and ii) the network quickly relaxes to a low–dimensional (one-dimensional, in our demonstration) manifold spanned by slowest degrees of freedom with a large basin of attraction, and then slowly approaches the equilibrium not escaping this manifold. By these dynamic properties, the fractal globule elastic network is similar to real biological molecular machines, like myosin. We have demonstrated that unfolding of a fractal globule can be described as a cascade of equilibrium phase transitions in a hierarchical system. Unfolding manifests itself in a sequential loss of stability of hierarchical levels with the temperature change.
Working paper
Kostinskiy A., Matveev A., Silakov V. Preprint IOFAN. PL. Gen. Phys. Insth, 1990. No. 87.
Kinetical processes in the non- equilibrium nitrogen-oxygen plasma
Working paper
Marshakov A., Fock V. arxiv.org. math. Cornell University, 2014
We describe a class of integrable systems on Poisson submanifolds of the affine Poisson-Lie groups PGLˆ(N), which can be enumerated by cyclically irreducible elements the co-extended affine Weyl groups (Wˆ×Wˆ)♯. Their phase spaces admit cluster coordinates, whereas the integrals of motion are cluster functions. We show, that this class of integrable systems coincides with the constructed by Goncharov and Kenyon out of dimer models on a two-dimensional torus and classified by the Newton polygons. We construct the correspondence between the Weyl group elements and polygons, demonstrating that each particular integrable model admits infinitely many realisations on the Poisson-Lie groups. We also discuss the particular examples, including the relativistic Toda chains and the Schwartz-Ovsienko-Tabachnikov pentagram map.
Working paper
S. M. Khoroshkin, M. G. Matushko. arxiv.org. math. Cornell University, 2019. No. 1910.08966.
We present a construction of an integrable model as a projective type limit of spin Calogero-Sutherland model with N fermionic particles, where N tends to infinity. It is implemented in the multicomponent fermionic Fock space. Explicit formulas for limits of Dunkl operators and the Yangian generators are presented by means of fermionic fields.
Working paper
Avetisov V, Krapivsky P. L., Nechaev S. K. Condenced Matter, Disordered Systems and Neural Networks. arXiv:1506.05037v1. Cornell Unigversity, 2015
We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. Analyzing in detail the spectral density of ensembles of linear subgraphs, we discuss its ultrametric nature and show that near the spectrum boundary, the tails of the spectral density exhibit a Lifshitz singularity typical for Anderson localization. We pay attention to an intriguing connection of the spectral density to the Dedekind $\eta$-function. We conjecture that ultrametricity emerges in rare-event statistics and is inherit to generic complex sparse systems.
Working paper
Eminov P. A. High Energy Physics - Phenomenology (hep-ph). Cornell University Library, 2015. No. 1.
The neutrino dispersion in the magnetized medium was analyzed as a function of the neutrino spin and mass. It was shown that in a super-strong magnetic field plasma contribution to the neutrino energy greatly exceeds the analogous correction in the field-free case.
Working paper
A. S. Vasenko, Golubov A. A., Silkin V. M. et al. arxiv.org. cond-mat. Cornell University, 2017. No. 1606.00905.
Working paper
Shchur L. math. arxive. Cornell University, 2018. No. 1808.09251.
We review recent advances in the analysis of the Wang--Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the Wang-Landau probability. Properties of the TMES can explain some features of the Wang-Landau algorithm, for example, the flatness of the histogram. We show that the Wang--Landau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of the Wang-Landau algorithm consists of two simulation stages: the original Wang-Landau procedure for the first stage and a 1/t modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels.
Working paper
Burovski E., Малютин А. А., Shchur L. arxiv.org. cond-mat. Cornell University, 2018. No. arXiv:1811.08784.
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.
Working paper
Andrew G. Semenov. arxiv.org. cond-mat. Cornell University, 2013
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.
Working paper
Zlotnik Alexander, Zlotnik Ilya. arxiv.org. math. Cornell University, 2014. No.  arXiv:1405.3147.
We consider the Cauchy problem for the 1D generalized Schrödinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transpa\-rent boundary conditions (TBCs) has recently been constructed. Now we engage the Richardson extrapolation to improve significantly the accuracy in time step. To study its properties, we give results of numerical experiments and enlarged practical error analysis for three typical examples. The resulting method is able to provide high precision results in the uniform norm for reasonable computational costs that is unreachable by more common 2nd order methods in either space or time step. Comparing our results to the previous ones, we obtain much more accurate results using much less amount of both elements and time steps.
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.