Related papers: Fundamental limits to nanoparticle extinction
We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical…
Using molecular dynamics simulations, we show that free diffusion of a nanoscale particle (molecule) with asymmetric structure critically depends on the orientation in a finite timescale of picoseconds to nanoseconds. In a timescale of ~100…
We establish upper and lower universal bounds for potentials of weighted designs on the sphere $\mathbb{S}^{n-1}$ that depend only on quadrature nodes and weights derived from the design structure. Our bounds hold for a large class of…
We consider the symmetric simple exclusion system on $\mathbb{Z}^d$, $d \ge 2$, starting from a class of ``step'' initial conditions in which particles are constrained within a half-space. One may count the number $N_t$ of particles that…
We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…
In scattering theory, the unitary limit is defined by an infinite scattering-length and a zero effective range, corresponding to a phase-shift \pi/2, independent of energy. This condition is satisfied by a rank-1 separable potential…
We prove the optimal upper bound sum || f ||_4^4 << q^{eps} where f runs over an orthonormal basis of Maass cusp forms of prime level q and bounded spectral parameter.
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases we…
We calculate cosmological and astrophysical bounds on the couplings between standard model fields and tensor unparticles. The present day density of tensor unparticles from neutrino-neutrino and photon-photon annihilation is calculated.…
We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the…
We consider the asymmetric simple exclusion process (ASEP) on the one-dimensional finite lattice $\{1,2,\ldots,N\}$. The particles can be created/annihilated at the boundaries with given rates. These rates are $L^\infty$ functions of time…
The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and…
We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any…
We give effective upper bounds for the number of purely inseparable points on non isotrivial curves over function fields of positive characteristic and of transcendence degree one. These bounds depend on the genus of the curve, the genus of…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
We present shape-independent upper limits to the power--bandwidth product for a single resonance in an optical scatterer, with the bound depending only on the material susceptibility. We show that quasistatic metallic scatterers can nearly…
We study the length of cycles in the model of spatial random permutations in Euclidean space. In this model, for given length $L$, density $\rho$, dimension $d$ and jump density $\varphi$, one samples $\rho L^d$ particles in a…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
A universal property of resonant subwavelength scatterers is that their optical cross-sections are proportional to a square wavelength, $\lambda^2$, regardless of whether they are plasmonic nanoparticles, two-level quantum systems, or RF…