Related papers: Convergence Behavior of Variational Perturbation E…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy…
We investigate coherent oscillations in large scale transmission power grids, where large groups of generators respond in unison to a distant disturbance. Such long wavelength coherent phenomena are known as inter-area oscillations. Their…
In order to study the chaotic behavior of a system with non-local interactions, we will consider weakly coupled non-commutative field theories. We compute the Lyapunov exponent of this exponential growth in the large Moyal-scale limit to…
We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses,…
We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems when they experience transient growth or respond to harmonic forcing. This approach reconciles the…
Lattice growth models where uncorrelated random deposition competes with some aggregation dynamics that generates correlations are studied with rates of the correlated component decreasing as a power law. These models have anomalous…
While the novel applications of weak values have recently attracted wide attention, weak measurement, the usual way to extract weak values, suffers from risky approximations and severe quantum noises. In this paper, we show that the…
I review the theoretical motivation for varying fundamental couplings and discuss how these measurements can be used to constrain a number of fundamental physics scenarios that would otherwise be inacessible to experiment. As a case study I…
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
We study how weak disorder affects the growth of the Fibonacci series. We introduce a family of stochastic sequences that grow by the normal Fibonacci recursion with probability 1-epsilon, but follow a different recursion rule with a small…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
The fluctuation-dissipation relation, a central result in non-equilibrium statistical physics, relates equilibrium fluctuations in a system to its linear response to external forces. Here we provide a direct experimental verification of…
The physical processes involved in the advective-acoustic instability are investigated with 2D numerical simulations. Simple toy models, developped in a companion paper, are used to describe the coupling between acoustic and…
Coupled oscillators are among the simplest composite quantum systems in which the interplay of entanglement and interaction may be explored. We examine the effects of coupling on fluctuations of the coordinates and momenta of the…
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which…
Extreme deformation of soft matter is central to our understanding of the effects of shock, fracture, and phase change in a variety of systems. Yet, despite, the increasing interest in this area, far-from-equilibrium behaviours of soft…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…