Related papers: Resonances for a diffusion with small noise
Fast radio bursts (FRBs) provide a sensitive probe of ionized baryons through their dispersion measure (DM). In addition to slowly evolving cosmological terms, at least two repeaters now show clear secular DM-decrease episodes:…
We consider certain Fibonacci-like sequences $(X_n)_{n\geq 0}$ perturbed with a random noise. Our main result is that $\frac{1}{X_n}\sum_{k=0}^{n-1}X_k$ converges in distribution, as $n$ goes to infinity, to a random variable $W$ with…
A pulse of light, injected into a weakly disordered dielectric medium, typically, will leave its initial location in a short time, by diffusion. However, due to some rare configurations of disorder, there is a possibility of formation of…
The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy,…
We study resonance for the Helmholz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small…
We determine the small signal gain and noise response of an amplifier based on the nonlinear response of a quantum nanomechanical resonator. The resonator is biased in the nonlinear regime by a strong harmonic bias force and we determine…
Two simple model operators are considered which have pre-existing resonances. A potential corresponding to a small electric field, $f$, is then introduced and the resonances of the resulting operator are considered as $f\to0$. It is shown…
We study the growth of small fluctuations of magnetic field in supersonic turbulence, the small-scale dynamo. The growth is due to the fastest turbulent eddies above the resistive scale. We observe that for supersonic turbulence these…
Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized…
Diffusion-based generative models have demonstrated a capacity for perceptually impressive synthesis, but can they also be great likelihood-based models? We answer this in the affirmative, and introduce a family of diffusion-based…
Gravitational waves constitute a powerful probe of the underlying theory of gravity. In extensions of general relativity, additional degrees of freedom, such as scalar fields in the gravitational sector, can modify their propagation through…
One examines the interaction and possible resonances between supernova neutrinos and electron plasma waves. The neutrino phase space distribution and its boundary regions are analyzed in detail. It is shown that the boundary regions are too…
We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting of small amplitude. It is well known that such a perturbation does not create eigenvalues…
We characterize a novel Josephson parametric amplifier based on a flux-tunable quarter-wavelength resonator. The fundamental resonance frequency is ~1GHz, but we use higher modes of the resonator for our measurements. An on-chip tuning line…
We consider models given by Hamiltonians of the form $$H(I,\phi,p,q,t;\epsilon) = h(I) + \sum_{j = 1}^n \pm(\frac{1}{2} p_j^2 + V_j(q_j)) + \epsilon Q(I,\phi,p,q,t;\epsilon)$$ where $I,\phi$ are d-dimensional actions and angles, $p,q$ are…
We consider frequency fluctuations in self-sustained oscillators based on nonlinear underdamped resonators. An important type of such resonators are nano- and micro-electro-mechanical systems. Various noise sources are considered, with the…
The problem of finding the optimal current distribution supported by small radiators yielding the minimum quality (Q) factor is a fundamental problem in electromagnetism. Q factor bounds constrain the maximum operational bandwidth of…
Diffusion models for image generation function by progressively adding noise to an image set and training a model to separate out the signal from the noise. The noise profile used by these models is white noise -- that is, noise based on…
Let U be a given function defined on R^d and \pi(x) be a density function proportional to \exp -U(x). The following diffusion X(t) is often used to sample from \pi(x), dX(t)=-\nabla U(X(t)) dt+\sqrt2 dW(t),\qquad X(0)=x_0. To accelerate the…
Many of the powerful radio galaxies observed at high redshift are very small, presumably because they are very young. A simple model, which treats the radio source as a bubble expanding into a radially stratified medium, is capable of…