Abstract
Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise analogous to that proposed by Nikolaevskii V.N. 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 says 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 causing it to make a direct transition from a spatially uniform to a turbulent state.
Highlights
In the presented 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
We note that concrete structure of the Nikolaevskii chaos is determined by the solution ߣሺݔǡ ݐǡ ߝሻ variety by transcendental master equation (2.7)
Assume that for almost all points ሺݔǡ ݐሻ אԹ ൈ Թା, there exist a function ݑሺݔǡ ݐሻ such that ఎ՜۳ ቀݑఎሺݔǡ ݐǡ ߝǡ ߱ሻ െ ݑሺݔǡ ݐሻቁଶ൨ ൌ ͲǤThen we will say that a function ݑሺݔǡ ݐሻ is a quasidetermined solution (QD-solution of the equation (2.1)
Summary
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