27 citations · 211 across the 28 of their papers we have counts for
34 papers
Geometry of wave damping on the torus
Kiril Datchev, Perry Kleinhenz, Antoine Prouff
Energy decay rates of damped waves on the torus depend on the behavior of the damping near the undamped region and on the geometry of the damped set. In this paper we refine these…
Approximate normalizations for approximate density functionals
Adam Clay, Kiril Datchev, Wenlan Miao +3
It seems self-evident that a density functional calculation should be normalized to the number of electrons in the system. We present multiple examples where the accuracy of the ap…
Exponential time-decay for a one dimensional wave equation with coefficients of bounded variation
Kiril Datchev, Jacob Shapiro
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Und…
Low energy scattering asymptotics for planar obstacles
T. J. Christiansen, K. Datchev
We compute low energy asymptotics for the resolvent of a planar obstacle, and deduce asymptotics for the corresponding scattering matrix, scattering phase, and exterior Dirichlet-t…
Newton polygons and resonances of multiple delta-potentials
Kiril Datchev, Jeremy L. Marzuola, Jared Wunsch
We prove explicit asymptotics for the location of semiclassical scattering resonances in the setting of -dependent delta-function potentials on . In the cases of two…
Propagation of singularities for the wave equation
Dean Baskin, Kiril Datchev
This expository note gives a digest version of Hormander's propagation of singularities theorem for the wave equation.
Seven Useful Questions in Density Functional Theory
Steven Crisostomo, Ryan Pederson, John Kozlowski +6
We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and w…
Semiclassical resolvent bounds for compactly supported radial potentials
Kiril Datchev, Jeffrey Galkowski, Jacob Shapiro
We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator in dimension , where ,…
Semiclassical resonance asymptotics for the delta potential on the half line
Kiril Datchev, Nkhalo Malawo
We compute resonance width asymptotics for the delta potential on the half-line, by deriving a formula for resonances in terms of the Lambert W function and applying a series expan…
On the interaction of metric trapping and a boundary
Kiril Datchev, Jason Metcalfe, Jacob Shapiro +1
By considering a two ended warped product manifold, we demonstrate a bifurcation that can occur when metric trapping interacts with a boundary. In this highly symmetric example, as…
Resolvent estimates, wave decay, and resonance-free regions for star-shaped waveguides
T. J. Christiansen, K. Datchev
Using coordinates , we introduce the notion that an unbounded domain in is star shaped with respect to . For s…
Sharp polynomial decay rates for the damped wave equation with Hölder-like damping
Kiril Datchev, Perry Kleinhenz
We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples…
Semiclassical Estimates for Scattering on the Real Line
Kiril Datchev, Jacob Shapiro
We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has…
Wave asymptotics for waveguides and manifolds with infinite cylindrical ends
T. J. Christiansen, K. Datchev
We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off reso…
Exponential lower resolvent bounds far away from trapped sets
Kiril Datchev, Long Jin
We give examples of semiclassical Schrödinger operators with exponentially large cutoff resolvent norms, even when the supports of the cutoff and potential are very far apart. The…
Iterative reconstruction of the wavespeed for the wave equation with bounded frequency boundary data
Kiril Datchev, Maarten V. de Hoop
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded…
Resonances and lower resolvent bounds
Kiril Datchev, Semyon Dyatlov, Maciej Zworski
We show how the presence of resonances close to the real axis implies exponential lower bounds on the norm of the cut-off resolvent on the real axis.
Quantitative limiting absorption principle in the semiclassical limit
Kiril Datchev
We give an elementary proof of Burq's resolvent bounds for long range semiclassical Schroedinger operators. Globally, the resolvent norm grows exponentially in the inverse semiclas…
Nontrapping surfaces of revolution with long living resonances
Kiril R. Datchev, Daniel D. Kang, Andre P. Kessler
We study resonances of surfaces of revolution obtained by removing a disk from a cone and attaching a hyperbolic cusp in its place. These surfaces include ones with nontrapping geo…
Approximation and equidistribution of phase shifts: spherical symmetry
Kiril Datchev, Jesse Gell-Redman, Andrew Hassell +1
Consider a semiclassical Hamiltonian \begin{equation*} H_{V, h} := h^{2} Δ+ V - E \end{equation*} where is a semiclassical parameter, is the positive Laplacian on $\mat…
Resonance free regions for nontrapping manifolds with cusps
Kiril Datchev
We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrodinger equation,…
Sharp polynomial bounds on the number of Pollicott-Ruelle resonances
Kiril Datchev, Semyon Dyatlov, Maciej Zworski
We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlat…
Semiclassical resolvent estimates at trapped sets
Kiril Datchev, András Vasy
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-tra…
Fractal Weyl laws for asymptotically hyperbolic manifolds
Kiril Datchev, Semyon Dyatlov
For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined b…