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Contribution to symplectic structure in quantization rule due to noncommutativity of adiabatic parameters
Russian Journal of Mathematical Physics. 2016. Vol. 23. No. 2. P. 207-218.
A geometric construction of the ` ala Planck action integral (quantization rule)
determining adiabatic terms for fast-slow systems is considered. We demonstrate that in
the first (after zero) adiabatic approximation order, this geometric rule is represented by a
deformed fast symplectic 2-form. The deformation is controlled by the noncommutativity
of the slow adiabatic parameters. In the case of one fast degree of freedom, the deformed
symplectic form incorporates the contraction of the slow Poisson tensor with the adiabatic
curvature.
The same deformed fast symplectic structure is used to represent the improved adiabatic
invariant in a geometric form.
Matveenko A., Matveenko Vladimir, Montenegrin Journal of Economics 2014 Vol. 10 No. 2 P. 7-20
Relation between curvature and the elasticity of substitution is the old question important for economic theory. Opinions of economists concerning presence or absence of a link between these two concepts radically diverge. Also now there is a steady trend of the use of the Arrow-Pratt coefficient of relative risk aversion and the coefficient of relative ...
Added: January 17, 2015
M.V. Karasev, Russian Journal of Mathematical Physics 2014 Vol. 21 No. 2 P. 197-218
For quantum, as well classical slow-fast systems, we develop a general method which allows one to compute the adiabatic invariant (approximate integral of motion), its symmetries, the adiabatic guiding center coordinates and the effective scalar Hamiltonian in all orders of a small parameter. The scheme does not exploit eigenvectors or diagonalization but is based on ...
Added: April 9, 2014
Grushin V. V., Dobrokhotov S. Y., Сергеев С. А., Труды Математического института им. В.А. Стеклова РАН 2013 Т. 281 С. 170-187
We construct asymptotic solutions to the wave equation with velocity rapidly oscillating a smoothly varying background and with localized initial perturbations. First, using adiabatic approximation in the operator form, we perform homogenization that leads to a linearized Boussinesq-type equation with smooth coefficients and weak “anomalous” dispersion. Then, asymptotic solutions to this and, as a consequence, ...
Added: October 11, 2013
M.V. Karasev, Russian Journal of Mathematical Physics 2015 Vol. 22 No. 1 P. 20-25
For slow–fast Hamiltonian systems with one fast degree of freedom, we describe the construction of the complete adiabatic invariant and the complete adiabatic term at once in all asymptotic orders by using the small parameter “dynamics” and parallel translations in the phase space. ...
Added: April 9, 2014
Grushin V. V., Dobrokhotov S. Y., Математические заметки 2014 Т. 95 № 3 С. 359-375
The system of equations of gravity surface waves is considered in the case where the basin's bottom is given by a rapidly oscillating function against a background of slow variations of the bottom. Under the assumption that the lengths of the waves under study are greater than the characteristic length of the basin bottom's oscillations ...
Added: May 21, 2014
Bruning J., Grushin V. V., Dobrokhotov S. Y. et al., Теоретическая и математическая физика 2011 Т. 167 № 2 С. 171-192
We show that the Foldy-Wouthuysen transformation and its generalizations are simplified if the methods of pseudodifferential operators are used, which also allow estimating the exactness of the transition from the Dirac equation to the reduced equations for electrons and positrons. The methods and techniques used can be useful not only in studying asymptotic solutions of ...
Added: March 3, 2013
Bruning J., Grushin V. V., Dobrokhotov S. Y., Математические заметки 2012 Т. 92 № 2 С. 163-180
An example of Schrodinger and Klein-Gordon equations with fast oscillating coefficients is used to show that they can be averaged by an adiabatic approximation based on V.P. Maslov's operator method. ...
Added: December 24, 2012
M.V. Karasev, / Cornell University. Series math "arxiv.org". 2014. No. 1404.1790v2.
For slow–fast quantum systems, we compute first corrections to the quantum action and to the effective slow Hamiltonian. ...
Added: April 9, 2014
Karasev M., Russian Journal of Mathematical Physics 2010 Vol. 17 No. 2 P. 207-217
For a generic quantum integrable system, we describe the asymptotics of the eigenstate density and of the trace of the evolution operator in all orders of the quantization parameter. This is done by using quantum symplectic geometry, which makes the given quantum system to be equivalent to a deformed classical system with arbitrary accuracy with ...
Added: April 12, 2012
Aseeva N., Gromov E., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2012 № 1 (94) С. 42-53
Цель работы: Предложен новый механизм стабилизации коротких солитонов огибающей в рамках нелинейного эволюционного уравнения Шредингера третьего порядка с учетом индуцированного рассеяния Рамана, кубичной нелинейности, нелинейной дисперсии, линейной дисперсии третьего порядка, пространственно неоднородной линейной дисперсии второго порядка и потерь. Научный подход: Исследование проведено с использованием адиабатического приближения, при котором волновой пакет распространяется с сохранением своей формы. ...
Added: June 9, 2012
Pereskokov A., Липская А. В., Вестник Московского энергетического института 2010 № 6 С. 99-109
Рассмотрены радиально-симметричные решения уравнения типа Хартри, содержащего как кулоновский потенциал, так и интегральную нелинейность с потенциалом взаимодействия Юкавы. В квазиклассическом приближении выведены и исследованы уравнения для самосогласованного потенциала. Выписано правило квантования типа Бора-Зоммерфельда. Найдены асимптотические собственные значения и собственные функции. ...
Added: December 16, 2012
A. V. Pereskokov, Journal of Mathematical Sciences 2017 Vol. 226 No. 4 P. 462-516
We study the nonlinear eigenvalue problem for two-dimensional Hartree type equations with selfaction potentials possessing logarithmic singularity and depending on the distance between points. To find a series of asymptotic eigenvalues, we derive a counterpart of the Bohr–Sommerfeld quantization rule. The corresponding asymptotic eigenfunctions are localized near a plane segment. ...
Added: December 20, 2017
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016