• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Эффект туннельного захвата
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
September 18, 2026
When Pictures Hinder Understanding: Illustrations May Impede Learning of Abstract Ideas
Illustrations can help remember specific actions but do not always make abstract ideas easier to learn. Researchers from HSE University and Humboldt University compared how people learn from texts with different levels of abstractness. They found that participants remembered illustrations better and performed better on related tasks after reading a multimedia text about yoga asanas than after reading an abstract text about the Nash equilibrium. The findings could help improve the selection of illustrations for educational and informational materials. The study has been published in Learning and Instruction.
September 17, 2026
'I Wish That People Would Place Greater Trust in Science'
When Tatiana Eremicheva chose Fundamental and Computational Linguistics as her field of study, she thought it would be about learning languages. Instead, she discovered it was about helping people. In this interview for the HSE Young Scientists project, she discusses science as a way of understanding the world, billiards as a team-building activity, and why learning to read is not always as easy as it seems.
September 15, 2026
Immunity to Chaos: How Personal Resources Help Us Cope with the Challenges of a Turbulent World
International conflicts, crises and digital overload—the modern world puts our minds to the test every day. Traditional psychology often focuses on the consequences: anxiety, depression, and psychosomatic disorders. But what if we looked at the problem differently—through the lens of the resources that prevent us from breaking down? Psychological immunity is precisely this set of resources. Alena Zolotareva and her group, Psychological Immunity as a Resource for Positive Functioning, are developing an integrative model of this phenomenon, adapting diagnostic tools and preparing for large-scale empirical research. Why do psychologists need to collaborate with medical professionals, and how could their research transform preventive care in clinics and corporations?

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Эффект туннельного захвата

Наноструктуры. Математическая физика и моделирование. 2014. Т. 11. № 1. С. 27–36.
Vybornyi E., Karasev M.
We consider the one-dimensional Schrodinger operator in the semiclassical regime assuming that its double-well potential is the sum of a finite “physically given” well and a square shape probing well whose width or depth can be varied (tuned). We study the dynamics of initial state localized in the physical well. It is shown that if the probing well is not too close to the physical one and if its parameters are specially tuned, then the tunnel catch effect appears, i.e. the initial state starts tunneling oscillations between the physical and probing wells. The asymptotic formula for the probability of finding the state in the probing well is obtained. We also calculate the leading term of the tunneling splitting of energy levels in this double well potential.
Priority areas: mathematics
Language: Russian
Full text
Keywords: туннельный эффектквазиклассическое приближениеуравнение Шредингера
Similar publications
Vague stimulating ideas, images and metaphors in scientific thinking: researchers' work with horizons of unclear knowledge
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
On phase-lock area parquet in a special slow-fast limit of model of Josephson junction.
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Infinitely many graph manifolds with unique geometrical piece that admit arbitrarily many Anosov flows
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the study of geodesic flows in negative curvature surface by Anosov and Sinai. Not every closed manifold admits an Anosov flow for well-known reasons: the fundamental group of a 3-manifold M admitting an Anosov flow must have exponential growth, and M must be universally covered by R3. Nevertheless, there ...
Added: August 31, 2026
New bound on S1× S2-setting Bell locality of a nonseparable Werner state
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a  nonseparable Werner state with a ...
Added: July 21, 2026
On functional equations for Chow polylogarithms
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity. To prove this, we study ...
Added: July 16, 2026
On Goncharov’s conjecture in next to Milnor degree
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Strong Approximations for Markov Chains Weakly Converging to Diffusions
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Bifurcations and Structural Stability of Generic PC-HC Families
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
On the minimum number of maximal distance-k independent sets in trees
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
On Arithmetic Mirror Symmetry for smooth Fano fourfolds
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$,  on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
On the dimension of the space of static potentials on three-manifolds
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Using predefined vector systems to speed up neural network multimillion class classification
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Homogeneous maximizers of the Blaschke-Santalo-type functionals
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2  sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of  N>2 sets. We also discuss links to the ...
Added: February 13, 2026
Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Asymptotics of eigenfunctions of perturbed resonance oscillator near upper boundaries of spectral clusters
A. V. Pereskokov, Journal of Mathematical Sciences 2025 Vol. 291 No. 4 P. 544–553
We study the eigenvalue problem for a perturbed resonance oscillator. We find asymptotic expansions of coherent states of the algebra su(2). We show that the asymptotic eigenfunctions are localized near a circle and construct an expansion of asymptotic eigenfunctions near this circle. ...
Added: December 7, 2025
Phase-locking in dynamical systems and quantum mechanics
Glutsyuk A., Александров А. А., Горский А. С., / Series arXiv "math". 2025.
In this study, we discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrodinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the ...
Added: June 23, 2025
Туннелирование с осциллирующим эффектом основных состояний квадратичного оператора на гиперболоиде
Vybornyi E., Rumiantseva S., Математические заметки 2024 Т. 116 № 6 С. 862–880
In this paper, we consider the problem of constructing a semiclassical asymptotic estimate of the splitting between a pair of close lower-lying energy levels for a quadratic operator defined on the irreducible representation of the Lie algebra su(1,1). In Darboux coordinates on the hyperboloid the Hamiltonian defines the landscape of a symmetric double well. It ...
Added: November 12, 2024
Asymptotic expansion of solutions of the 2nd order difference equations in an unbounded domain
Sofia V. Rumyantseva, Acta Applicandae Mathematicae 2025 Vol. 195 Article 4
Difference equations play a crucial role in a wide array of mathematical and physical tasks. In this article, we focus on the analysis of a second order linear homogeneous difference equation with smooth coefficients via WKB method. It is well-known that such equations exhibit two WKB solutions in a segment devoid of turning and singular ...
Added: November 2, 2024
Phase retrieval and phaseless inverse scattering with background information
Hohage T., Novikov R., Sivkin V., Inverse Problems 2024 Vol. 40 No. 10 Article 105007
We consider the problem of finding a compactly supported potential in the multidimensional Schr & ouml;dinger equation from its differential scattering cross section (squared modulus of the scattering amplitude) at fixed energy. In the Born approximation this problem simplifies to the phase retrieval problem of reconstructing the potential from the absolute value of its Fourier ...
Added: October 22, 2024
Квазиклассические асимптотики осциллирующего туннелирования для квадратичного гамильтониана на алгебре su(1,1)
Vybornyi E., Rumiantseva S., Математические заметки 2022 Т. 112 № 5 С. 665–681
The paper considers the problem of constructing semiclassical asymptotics of tunnel splitting of the spectrum of an operator given on an irreducible representation of the Lie algebra su(1, 1). It is assumed that the operator is a quadratic function of the generators of the algebra. Coherent states and coherent unitary transformation are presented, which make ...
Added: November 7, 2022
Coherent States in a Problem with Infinitely Multiple Spectrum
Chetverikov V., Mamsurov I., , in: Proceedings of 2022 IEEE Moscow Workshop on Electronic and Networking Technologies (MWENT).: M.: IEEE, 2022. P. 1–4.
The solutions of the Schrodinger (Schrodinger – Pauli) equations and the Dirac equation in the 2+1 space for the two-dimensional motion of a charged particle in a uniform and constant magnetic field, as well as the construction of coherent states based on the solutions obtained are considered. A specific feature of this problem is the ...
Added: October 25, 2022
Квазифейнмановские формулы дают решение многомерного уравнения Шредингера с неограниченным потенциалом
Remizov I., Starodubtseva M., Математические заметки 2018 Т. 104 № 5 С. 790–795
краткое сообщение - нет аннотации ...
Added: September 29, 2018
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit