Abstract
Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise, analogous to that proposed by V.N. Nikolaevskii [1]-[5]to describe longitudinal seismic waves, is presented. The equation has a threshold of short-wave instability and symmetry, providing long wave dynamics. New mechanism of quantum chaos generating in nonlinear dynamical systems with infinite number of degrees of freedom is proposed. The hypothesis is said, that physical turbulence could be identified with quantum chaos of considered type. It is shown that the additive thermal noise destabilizes dramatically the ground state of the Nikolaevskii system thus causing it to make a direct transition from a spatially uniform to a turbulent state.
Highlights
In the present work a non-perturbative analytical approach to the studying of problem of quantum chaos in dynamical systems with infinite number of degrees of freedom is proposed
Impotent physical results follows from Theorem 2, is illustrated by example of 3D stochastic model system: How to cite this paper: Foukzon, J. (2015) New Scenario for Transition to Slow 3-D Turbulence
By this wrong assumptions the results of the numerical integration procedure of the 1D Nikolaevskii model (1.6)-(1.7) were mistakenly considered and interpreted as a very exact modeling the slow turbulence within purely non stochastic Nikolaevskii model (1.6)-(1.7)
Summary
In the present work a non-perturbative analytical approach to the studying of problem of quantum chaos in dynamical systems with infinite number of degrees of freedom is proposed. There is an erroneous the point of view, that a white noise with enough small intensity does not bring any significant contributions in turbulent modes, see for example [3] By this wrong assumptions the results of the numerical integration procedure of the 1D Nikolaevskii model (1.6)-(1.7) were mistakenly considered and interpreted as a very exact modeling the slow turbulence within purely non stochastic Nikolaevskii model (1.6)-(1.7). The results of non-perturbative modeling of super-chaotic modes, obtained in the present paper allow us to put out a quite probable hypothesis: developed turbulence in the real physical systems with infinite number of degrees of freedom is a quantum super-chaos, at that the quantitative characteristics of this super-chaos, is completely determined by non-perturbative contribution of additive (thermal) fluctuations in the corresponding classical system dynamics [18]-[20]
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