Symmetries, integrating factors and Nambu mechanics

1996 ◽  
Vol 223 (5) ◽  
pp. 355-358 ◽  
Author(s):  
G Ünal
1994 ◽  
Vol 09 (29) ◽  
pp. 2727-2732 ◽  
Author(s):  
DEBENDRANATH SAHOO ◽  
M. C. VALSAKUMAR

We investigate the problem of quantization of Nambu mechanics — a problem posed by Nambu [Phys. Rev.D7, 2405 (1973)] — along the line of Wigner–Weyl–Moyal (WWM) phase-space quantization of classical mechanics and show that the quantum analog of Nambu mechanics does not exist.


Author(s):  
W. T. van Horssen

Abstract In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.


2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Gülden Gün ◽  
Teoman Özer

We analyze Noether and -symmetries of the path equation describing the minimum drag work. First, the partial Lagrangian for the governing equation is constructed, and then the determining equations are obtained based on the partial Lagrangian approach. For specific altitude functions, Noether symmetry classification is carried out and the first integrals, conservation laws and group invariant solutions are obtained and classified. Then, secondly, by using the mathematical relationship with Lie point symmetries we investigate -symmetry properties and the corresponding reduction forms, integrating factors, and first integrals for specific altitude functions of the governing equation. Furthermore, we apply the Jacobi last multiplier method as a different approach to determine the new forms of -symmetries. Finally, we compare the results obtained from different classifications.


2004 ◽  
Vol 19 (3-4) ◽  
pp. 199-203 ◽  
Author(s):  
Cosmas K. Zachos ◽  
Thomas L. Curtright

2015 ◽  
Vol 59 (2) ◽  
pp. 63-83
Author(s):  
Dariusz Wojakowski

The article contains an analysis of the academic and popular political discourses concerning the Ukrainian nation. Its aim is to point out atypical phenomena which could constitute little-known factors destabilizing or integrating national self-representation in Ukraine. The inconsistency of these concepts occurs above all at the level of macro-social discourses. What is involved is the presence in politics of content associated with the radical right and its primordial understanding of the nation, accompanied by low support for any sort of national or civil idea among the inhabitants of Ukraine. In the academic discourse the dominant western European theories of nation clash with a specific understanding of the terminology used in Russian scholarship. On the other hand, in local discourses at the meso-social level, there are phenomena that could be integrating factors for the image of the Ukrainian nation. There, language, popular culture, and various ideas about the past intermingle. In southern Ukraine, concepts can be found in which the nation is a political category quite aside from ethnic differences or the language of communication. Soviet times introduced the state factor, which is independent of ethnicity and which was later given content (rather worse than better) by the Ukrainian state. In these cases, Ukrainianness appears as a superior principle in regards to ethnic differentiation. The political situation of Ukraine since 2014, however, does not favor the development of this model of the Ukrainian nation.


2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Atsushi Horikoshi

Abstract Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is hidden in Hamiltonian dynamics, that is, the classical time evolution of variables including redundant degrees of freedom can be formulated as Nambu mechanics. In the present paper we show that the Nambu mechanical structure is also hidden in some quantum or semiclassical dynamics, that is, in some cases the quantum or semiclassical time evolution of expectation values of quantum mechanical operators, including composite operators, can be formulated as Nambu mechanics. We present a procedure to find hidden Nambu structures in quantum/semiclassical systems of one degree of freedom, and give two examples: the exact quantum dynamics of a harmonic oscillator, and semiclassical wave packet dynamics. Our formalism can be extended to many-degrees-of-freedom systems; however, there is a serious difficulty in this case due to interactions between degrees of freedom. To illustrate our formalism we present two sets of numerical results on semiclassical dynamics: from a one-dimensional metastable potential model and a simplified Henon–Heiles model of two interacting oscillators.


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