Violation of correspondence principle may occur for very macroscopic byt isolated quantum systems on rather short timescales as illustrated by the case of Hyperion, the chaotically tumbling moon of Saturn, for which quantum and classical predictions are expected to diverge on a timescale of approximately 20 years. Motivated by Hyperion, we review salient features of “quantum chaos” and show tha...

A method is presented for calculating the stress relaxation due to scission in elastomeric components that operate at a fixed deformation while at an elevated temperature. A relationship is established between stresses at different temperatures that is called the correspondence principle for scission/healing materials. Two examples involving cylinders illustrate its use. The first example invol...

The case l = 1 is the mean ergodic theorem, and the result can be viewed as a generalization of that theorem. The l = 2 case was proven by Conze and Lesigne [Conze and Lesigne, 1984], and various special cases for higher l have been shown by Zhang [Zhang, 1996], Frantzikinakis and Kra [Frantzikinakis and Kra, 2005], Lesigne [Lesigne, 1993], and Host and Kra [Host and Kra, 2005]. Tao’s argument ...

The Heisenberg uncertainty principle is known to be connected the entropic principle. This correspondence obtained employing a Gaussian probability distribution for wave functions associated Shannon entropy. Independently, due quantum gravity effects has been extended Generalized Uncertainty Principle (GUP). In this work, we show that GUP derived from considering non-extensive entropies, propos...

The inverse conjecture for the Gowers norms U(V ) for finite-dimensional vector spaces V over a finite field F asserts, roughly speaking, that a bounded function f has large Gowers norm ‖f‖Ud(V ) if and only if it correlates with a phase polynomial φ = eF(P ) of degree at most d− 1, thus P : V → F is a polynomial of degree at most d− 1. In this paper, we develop a variant of the Furstenberg cor...

A new formulation for wave propagation in an anelastic medium is developed. The phenomenological theory of linear viscoelasticity provides the basis for describing the attenuation and dispersion of seismic waves. The concept of a spectrum of relaxation mechanisms represents a convenient description of the constitutive relation of linear viscoelastic solids; however, Boltzmann's superposition pr...

New principles are introduced for the formulation of dynamic problems in viscoelasticity for the most general case of anisotropy. One is a variational principle derived from irreversible thermodynamics. The other a correspondence principle between viscoelasticity and elasticity. Applications to the mmics of viscoelastic plates and rods are developed as examples. The variational principles are a...