1,257 research outputs found
Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory
In Elementary Cycles theory elementary quantum particles are consistently
described as the manifestation of ultra-fast relativistic spacetime cyclic
dynamics, classical in the essence. The peculiar relativistic geometrodynamics
of Elementary Cycles theory yields de facto a unification of ordinary
relativistic and quantum physics. In particular its classical-relativistic
cyclic dynamics reproduce exactly from classical physics first principles all
the fundamental aspects of Quantum Mechanics, such as all its axioms, the
Feynman path integral, the Dirac quantisation prescription (second
quantisation), quantum dynamics of statistical systems, non-relativistic
quantum mechanics, atomic physics, superconductivity, graphene physics and so
on. Furthermore the theory allows for the explicit derivation of gauge
interactions, without postulating gauge invariance, directly from relativistic
geometrodynamical transformations, in close analogy with the description of
gravitational interaction in general relativity. In this paper we summarise
some of the major achievements, rigorously proven also in several recent
peer-reviewed papers, of this innovative formulation of quantum particle
physics.Comment: 35 page
Spatial patterns of tree yield explained by endogenous forces through a correspondence between the Ising model and ecology.
Spatial patterning of periodic dynamics is a dramatic and ubiquitous ecological phenomenon arising in systems ranging from diseases to plants to mammals. The degree to which spatial correlations in cyclic dynamics are the result of endogenous factors related to local dynamics vs. exogenous forcing has been one of the central questions in ecology for nearly a century. With the goal of obtaining a robust explanation for correlations over space and time in dynamics that would apply to many systems, we base our analysis on the Ising model of statistical physics, which provides a fundamental mechanism of spatial patterning. We show, using 5 y of data on over 6,500 trees in a pistachio orchard, that annual nut production, in different years, exhibits both large-scale synchrony and self-similar, power-law decaying correlations consistent with the Ising model near criticality. Our approach demonstrates the possibility that short-range interactions can lead to long-range correlations over space and time of cyclic dynamics even in the presence of large environmental variability. We propose that root grafting could be the common mechanism leading to positive short-range interactions that explains the ubiquity of masting, correlated seed production over space through time, by trees
Global integration of the Schr\"odinger equation within the wave operator formalism: The role of the effective Hamiltonian in multidimensional active spaces
A global solution of the Schr\"odinger equation, obtained recently within the
wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A:
Math. Theor. 48, 225205 (2015)], is generalized to take into account the case
of multidimensional active spaces. An iterative algorithm is derived to obtain
the Fourier series of the evolution operator issuing from a given
multidimensional active subspace and then the effective Hamiltonian
corresponding to the model space is computed and analysed as a measure of the
cyclic character of the dynamics. Studies of the laser controlled dynamics of
diatomic models clearly show that a multidimensional active space is required
if the wavefunction escapes too far from the initial subspace. A suitable
choice of the multidimensional active space, including the initial and target
states, increases the cyclic character and avoids divergences occuring when
one-dimensional active spaces are used. The method is also proven to be
efficient in describing dissipative processes such as photodissociation.Comment: 33 pages, 11 figure
Entropy production of cyclic population dynamics
Entropy serves as a central observable in equilibrium thermodynamics.
However, many biological and ecological systems operate far from thermal
equilibrium. Here we show that entropy production can characterize the behavior
of such nonequilibrium systems. To this end we calculate the entropy production
for a population model that displays nonequilibrium behavior resulting from
cyclic competition. At a critical point the dynamics exhibits a transition from
large, limit-cycle like oscillations to small, erratic oscillations. We show
that the entropy production peaks very close to the critical point and tends to
zero upon deviating from it. We further provide analytical methods for
computing the entropy production which agree excellently with numerical
simulations.Comment: 4 pages, 3 figures and Supplementary Material. To appear in Phys.
Rev. Lett.
Classical geometry to quantum behavior correspondence in a Virtual Extra Dimension
In the Lorentz invariant formalism of compact space-time dimensions the
assumption of periodic boundary conditions represents a consistent
semi-classical quantization condition for relativistic fields. In
[arXiv:0903.3680] we have shown, for instance, that the ordinary Feynman path
integral is obtained from the interference between the classical paths with
different winding numbers associated with the cyclic dynamics of the field
solutions. By means of the boundary conditions, the kinematics information of
interactions can be encoded on the relativistic geometrodynamics of the
boundary [arXiv:1110.0315]. Furthermore, such a purely four-dimensional theory
is manifestly dual to an extra-dimensional field theory. The resulting
correspondence between extra-dimensional geometrodynamics and ordinary quantum
behavior can be interpreted in terms of AdS/CFT correspondence. By applying
this approach to a simple Quark-Gluon-Plasma freeze-out model we obtain
fundamental analogies with basic aspects of AdS/QCD phenomenology.Comment: 60 pages. Version published in Annals of Physics (2012). Minor
correction
Three-fold way to extinction in populations of cyclically competing species
Species extinction occurs regularly and unavoidably in ecological systems.
The time scales for extinction can broadly vary and inform on the ecosystem's
stability. We study the spatio-temporal extinction dynamics of a paradigmatic
population model where three species exhibit cyclic competition. The cyclic
dynamics reflects the non-equilibrium nature of the species interactions. While
previous work focusses on the coarsening process as a mechanism that drives the
system to extinction, we found that unexpectedly the dynamics to extinction is
much richer. We observed three different types of dynamics. In addition to
coarsening, in the evolutionary relevant limit of large times, oscillating
traveling waves and heteroclinic orbits play a dominant role. The weight of the
different processes depends on the degree of mixing and the system size. By
analytical arguments and extensive numerical simulations we provide the full
characteristics of scenarios leading to extinction in one of the most
surprising models of ecology
- …