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Classical mechanics as nonlinear quantum mechanics [PDF]

, 2007
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation
Andrei Yu. Khrennikov, Guillaume Adenier, Hrvoje Nikolić, Pekka Lahti, Theo M. Nieuwenhuizen, Vladimir I. Man'ko   +5 more
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Subdynamics as a mechanism for objective description [PDF]

, 1999
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship.
Bassano Vacchini, Bell J., Berchielli A., Englert B.-G., Giulini D., Lanz O., Ludovico Lanz, Ludwig G., Olaf Melsheimer, Zubarev D. N.   +9 more
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Berry's phase in noncommutative spaces [PDF]

, 2002
We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study the Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on the parameter of
Alavi S A, Banerjee R, Berry M V, Espinosa O, Jellal A, Kochan D, Mezincescu L, Muthukumar B, S A Alavi, Seiberg N, Zunger Y   +10 more
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Thermodynamics for Trajectories of a Mass Point [PDF]

, 2014
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated geometrically as ...
Kurihara, Yoshimasa, Phan, Khiem Hong, Quach, Nhi My Uyen   +2 more
core   +2 more sources

On obtaining classical mechanics from quantum mechanics [PDF]

, 2006
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations.
Ashtekar A, Ashtekar A, Ashtekar A, Ghanashyam Date, Schilling T, Willis J   +5 more
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Nambu Quantum Mechanics: A Nonlinear Generalization of Geometric Quantum Mechanics [PDF]

, 2002
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal
Abramovitz, Adler, Amati, Amati, Amati, Anandan, Anandan, Arnold, Ashtekar, Awata, Baez, Balasubramanian, Banks, Bars, Bayen, Bayen, Blaschke, Bloch, Brody, Chang, Chang, Chia-Hsiung Tze, Cirelli, Crane, Crane, de Wit, Dito, Djordje Minic, Faddeev, Faddeev, Filipov, Gelfand, Gibbons, Gross, Gross, Gunaydin, Gursey, Heslot, Hoppe, Horava, Jacobson, Kempf, Kempf, Kempf, Kibble, Kozlov, Li, Minic, Minic, Minic, Nahm, Nambu, Okubo, Pandit, Pioline, Ratiu, Shapere, Smolin, Takhtajan, Weinberg, Witten, Witten, Yoneya, Yoneya, Yoneya, Zachos, Zakharov   +66 more
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Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space

, 2003
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator.
A J Bracken, Bayen F, Berezin F A, Berry M V, Berry M V, Dubin D A, Fröman N, Groenewold H, Gutzwiller M C, Jordan T F, Koopman B O, Maslov V P, Moyal J E, Muga J G, Osborn T A, Percival I, von Neumann J, Weyl H, Weyl H   +18 more
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Generalization of Classical Statistical Mechanics to Quantum Mechanics and Stable Property of Condensed Matter

, 2005
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new general ...
Anandan J., Anastopoulos C., Ballentine L. E., Curtright T., Eisenberg E., F. C. MA, Halliwell J. J., Harrison W. A., Holstein B. R., Isidro J. M., Jorgensen P. E. T., Liu Q. H., Marnelius R., N. ZHANG, Oh P., Prezhdo O. V., Schiff L. I., Tsiper E. V., Y. C. HUANG   +18 more
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Depicting qudit quantum mechanics and mutually unbiased qudit theories

, 2014
We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these ...
Ranchin, André
core   +2 more sources

Randomness in Classical Mechanics and Quantum Mechanics

, 2009
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is fundamental and ...
A. Yu Khrennikov, A.N. Pechen, A.S. Trushechkin, A.Yu Khrennikov, B. Dragovich, E. Gozzi, I. Prigogine, I.V. Volovich, I.V. Volovich, I.V. Volovich, Igor V. Volovich, L. Accardi, L. Boltzmann, L.D. Landau, M. Ohya, R. Feynman, V.S. Vladimirov, V.S. Vladimirov, V.V. Kozlov, Yu.I. Manin   +19 more
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