Related papers: Chaos in a Nonlinear Wavefunction Model: An Altern…
In two previous papers the author described ``Islands of Instability" that may appear in wavefunction models with nonlinear evolution (of a type proposed originally in the context of the Measurement Problem). Such ``IsoI" represent a new…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
The behaviour of a chaotic system and its effect on existing quantum correlation has been holographically studied in presence of non-conformality. Keeping in mind the gauge/gravity duality framework, the non-conformality in the dual field…
We formulate the conditions under which the dynamics of a continuously measured quantum system becomes indistinguishable from that of the corresponding classical system. In particular, we demonstrate that even in a classically chaotic…
We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is…
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
We consider a quantum many-body system - the Bose-Hubbard system on three sites - which has a classical limit, and which is neither strongly chaotic nor integrable but rather shows a mixture of the two types of behavior. We compare quantum…
In a recent Letter [PRL 101, 074101 (2008)], Kapulkin and Pattanayak presented evidence that a quantum Duffing oscillator, sufficiently damped so that it is not classically chaotic, becomes chaotic in the transition region between quantum…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
A new quantum mechanical description of the dynamics of wave packet under continuous measurement is formulated via Bohmian mechanics. The solution to this equation is found through a wave packet approach which establishes a direct…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
The natural measure in a map with type-III intermittent chaos is used to define critical exponents for the average of a variable from a dynamical system near bifurcation. Numerical experiments were done with maps and verify the analytical…
Recent numerical results seem to suggest that in certain regimes of typical particle velocities the gravitational $N-$body problem (for $3\leq N\lesssim 10^3$) is intrinsically less chaotic when the post-Newtonian (PN) force terms are…
In paper [1] unpredictable points were introduced based on Poisson stability, and this gives rise to the existence of chaos in the quasi-minimal set. This time, an unpredictable function is determined as an unpredictable point in the…
Some of the so-called imponderables and counterintuitive puzzles associated with the Copenhagen interpretation of quantum mechanics appear to have alternate, parallel explanations in terms of nonlinear dynamics and chaos. These include the…
Paper I of this series introduced a nonlinear version of quantum mechanics that blocks cats, and paper II postulated a random part of the wavefunction to explain outcomes in experiments such as Stern-Gerlach or EPRB. However, an ad hoc…