ON THE CORRESPONDENCE BETWEEN NEWTONIAN AND FUNCTIONAL MECHANICS
2011; World Scientific; Linguagem: Inglês
10.1142/9789814343763_0028
ISSN1793-5121
AutoresEvgeny Piskovskiy, И. В. Волович,
Tópico(s)Rheology and Fluid Dynamics Studies
ResumoQP-PQ: Quantum Probability and White Noise AnalysisQuantum Bio-Informatics IV, pp. 363-372 (2011) No AccessON THE CORRESPONDENCE BETWEEN NEWTONIAN AND FUNCTIONAL MECHANICSE.V. PISKOVSKIY and I.V. VOLOVICHE.V. PISKOVSKIYMoscow Institute of Physics and Technology Institustkiy lane 9, 141700 Dolgoprudny, Moscow Region, Russia and I.V. VOLOVICHSteklov Mathematical Institute Gubkin St.8, 119991 Moscow, Russiahttps://doi.org/10.1142/9789814343763_0028Cited by:12 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The world view underlying traditional science is based on reductionism and determinism when there is an empty space (vacuum) and material points which move along the Newtonian trajectories. This approach may be called "mechanistic" or "Newtonian". Quantum mechanics, in its Copenhagen interpretation, also adopts this world view. However this world view is not satisfactory by at least two reasons. First, there is uncertainty in the derivation of the position and velocity of the material point and second, it can not solve the time irreversibility problem. Moreover, the Newtonian approach is not well suited for applications of mathematics and physics to life science. Recently a new approach to classical mechanics was proposed in which the basic notion is not the trajectory but a probability distribution. In this functional mechanics approach one deals with the mean trajectories and one has corrections to the Newtonian equation of motion. In this note we consider correspondence between the Newtonian trajectories for an anharmonic oscillator and the averaged trajectories in the functional mechanics and compute the dependence of the characteristic time from the dispersion. FiguresReferencesRelatedDetailsCited By 12Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equationsG. M. Timofeev and A. S. Trushechkin8 September 2022 | International Journal of Modern Physics A, Vol. 37, No. 20n21Microscopic solutions of kinetic equations and the irreversibility problemA. S. Trushechkin25 July 2014 | Proceedings of the Steklov Institute of Mathematics, Vol. 285, No. 1Microscopic and soliton-like solutions of the Boltzmann--Enskog and generalized Enskog equations for elastic and inelastic hard spheresAnton Trushechkin1 Jan 2014 | Kinetic & Related Models, Vol. 7, No. 4Инфинитное движение в классической функциональной механикеАндрей Игоревич Михайлов and Andrey Igorevich Mikhailov1 Jan 2013 | Вестник Самарского государственного технического университета. Серия «Физико-математические науки», Vol. 1(30)О строгом определении микроскопических решений уравнения Больцмана - ЭнскогаАнтон Сергеевич Трушечкин and Anton Sergeevich Trushechkin1 Jan 2013 | Вестник Самарского государственного технического университета. Серия «Физико-математические науки», Vol. 1(30)Rolling in the Higgs model and elliptic functionsI. Ya. Arefeva, I. V. Volovich and E. V. Piskovskiy5 August 2012 | Theoretical and Mathematical Physics, Vol. 172, No. 1Asymptotic expansion of solutions in a rolling problemI. Ya. Aref'eva and I. V. Volovich28 July 2012 | Proceedings of the Steklov Institute of Mathematics, Vol. 277, No. 1Asymptotic properties of quantum dynamics in bounded domains at various time scalesIgor V Volovich and Anton S Trushechkin24 February 2012 | Izvestiya: Mathematics, Vol. 76, No. 1Derivation of the particle dynamics from kinetic equationsA. S. Trushechkin6 May 2012 | P-Adic Numbers, Ultrametric Analysis, and Applications, Vol. 4, No. 2Асимптотические свойства квантовой динамики в ограниченных областях на различных масштабах времениИгорь Васильевич Волович, Igor Vasil'evich Volovich, Антон Сергеевич Трушечкин and Anton Sergeevich Trushechkin1 Jan 2012 | Известия Российской академии наук. Серия математическая, Vol. 76, No. 1Скатывание в модели Хиггса и эллиптические функцииИрина Ярославна Арефьева, Irina Yaroslavna Aref'eva, Игорь Васильевич Волович, Igor Vasil'evich Volovich and Евгений Викторович Писковский et al.1 Jan 2012 | Теоретическая и математическая физика, Vol. 172, No. 1On functional approach to classical mechanicsEvgeny V. Piskovskiy4 August 2011 | P-Adic Numbers, Ultrametric Analysis, and Applications, Vol. 3, No. 3 Quantum Bio-Informatics IVMetrics History PDF download
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