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Of all publications in the section: 42
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Working paper
Russkov A., Roman Chulkevich, Shchur L. math. arxive. Cornell University, 2020. No. 2006.00561.
The parallel annealing method is one of the promising approaches for large scale simulations as potentially scalable on any parallel architecture. We present an implementation of the algorithm on the hybrid program architecture combining CUDA and MPI. The problem is to keep all general-purpose graphics processing unit devices as busy as possible redistributing replicas and to do that efficiently. We provide details of the testing on Intel Skylake/Nvidia V100 based hardware running in parallel more than two million replicas of the Ising model sample. The results are quite optimistic because the acceleration grows toward the perfect line with the growing complexity of the simulated system.
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
Kagan M., Mazur E. Working papers by Cornell University. Cornell University, 2020. No. arXiv:2006.13303.
The properties of a two-dimensional low density (n<<1) electron system with strong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V are considered. Electronic hoppings only at neighboring sites on the square lattice are taken into account, thus W = 8t. The calculations were carried out for a lattice of 24x24 sites with periodic boundary conditions. In the framework of the Bogoliubov - de Gennes approach we observed an appearance of inhomogeneous states of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the matrix of the unpaired normal states.
Working paper
Alfimov M., Feigin B. L., Hoare B. et al. hep-th. arXiv. Cornell University, 2020. No. 2003.xxxxx.
We propose a system of fermionic screening fields depending on a continuous parameter b, which defines eta-deformed OSp(n|2m) sigma-model in the limit b to infinity and a super-renormalizable QFT in b to 0. In the sigma-model regime  we show that leading UV asymptotic of the one-loop RG group flow equations coincides with perturbation around Gaussian theory. In perturbative regime b to 0 we show that the tree level two-particle scattering matrix matches the expansion of the trigonometric OSp(n|2m) R-matrix.
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
Alfimov M., Gromov N., Kazakov V. hep-th. arXiv. Cornell University, 2020. No. 2003.03536.
We review the applications of the Quantum Spectral Curve (QSC) method to the Regge (BFKL) limit in N=4 supersymmetric Yang-Mills theory.  QSC, based on quantum integrability of the AdS_5/CFT_4 duality, was initially developed as a tool for the study of the spectrum of anomalous dimensions of local operators in the N=4 SYM in the planar, N_c to infinity limit.  We explain how to apply the QSC for the BFKL limit, which requires non-trivial analytic continuation in spin S and extends the initial construction to non-local light-ray operators. We give a brief review of high precision non-perturbative numerical solutions and analytic perturbative data resulting from this approach. We also describe as a simple example of the QSC construction at the leading order in the BFKL limit. We show that the QSC substantially simplifies in this limit and reduces to the Faddeev-Korchemsky Baxter equation for Q-functions.   Finally, we review recent results for the  Fishnet CFT, which carries a number of similarities with the Lipatov's integrable spin chain for interacting reggeized gluons.
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.