5 citations · 16 across the 13 of their papers we have counts for
14 papers
A sharp gradient-corrected Lieb--Thirring inequality in one dimension with applications to density functional theory
Thiago Carvalho Corso, Louis Garrigue
We first prove a sharp Lieb-Thirring inequality with semi-classical constant and gradient correction in one dimension. In the periodic setting, the corresponding inequality also in…
A maximal Hohenberg-Kohn theorem for non-interacting systems via potential theory
Thiago Carvalho Corso
We show that for Schrödinger operators in a connected domain, the Hohenberg-Kohn theorem holds within the class of Laplace form-bounded external potentials if and only if the singl…
Strictly correlated electrons in a quantum ring: from Kohn-Sham to Kantorovich potentials
Thiago Carvalho Corso
Our goal in this paper is twofold. First, we characterize the class of pairwise interactions for which the Seidl conjecture on the structure of optimal plans for the symmetric mult…
A quantitative Hohenberg-Kohn theorem and the unexpected regularity of density functional theory in one spatial dimension
Thiago Carvalho Corso, Andre Laestadius
In this paper we investigate the (Kohn-Sham) density-to-potential map in the case of spinless fermions in one spatial dimension, whose existence has been rigorously established by…
Simulation of the magnetic Ginzburg-Landau equation via vortex tracking
Thiago Carvalho Corso, Gaspard Kemlin, Christof Melcher +1
This paper deals with the numerical simulation of the 2D magnetic time-dependent Ginzburg-Landau (TDGL) equations in the regime of small but finite (inverse) Ginzburg-Landau parame…
A rigorous formulation of Density Functional Theory for spinless fermions in one dimension
Thiago Carvalho Corso
In this paper, we present a completely rigorous formulation of Kohn-Sham density functional theory for spinless fermions living in one dimensional space. More precisely, we conside…
v-representability and Hohenberg-Kohn theorem for non-interacting Schrödinger operators with distributional potentials in the one-dimensional torus
Thiago Carvalho Corso
In this paper, we show that the ground-state density of any non-interacting Schrödinger operator on the one-dimensional torus with potentials in a certain class of distributions is…
Numerical simulation of the Gross-Pitaevskii equation via vortex tracking
Thiago Carvalho Corso, Gaspard Kemlin, Christof Melcher +1
This paper deals with the numerical simulation of the Gross-Pitaevskii (GP) equation, for which a well-known feature is the appearance of quantized vortices with core size of the o…
On a variational problem related to the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities
Thiago Carvalho Corso, Tobias Ried
We explicitly solve a variational problem related to upper bounds on the optimal constants in the Cwikel--Lieb--Rozenblum (CLR) and Lieb--Thirring (LT) inequalities, which has rece…
Trace estimates for harmonic functions along circular arcs with applications to domain decomposition on overlapping disks
Thiago Carvalho Corso, Muhammad Hassan, Abhinav Jha +1
In this paper we derive several (and in many cases sharp) estimates for the -trace norm of harmonic functions along circular arcs. More precisely, we obtain geometry-…
A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory
Thiago Carvalho Corso
In this article, we analyze the Dyson equation for the density-density response function (DDRF) that plays a central role in linear response time-dependent density functional theor…
Two-term asymptotics of the exchange energy of the electron gas on symmetric polytopes in the high-density limit
Thiago Carvalho Corso
We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynam…
Next-order correction to the Dirac exchange energy of the free electron gas in the thermodynamic limit and generalized gradient approximations
Thiago Carvalho Corso, Gero Friesecke
We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of t…
The density-density response function in time-dependent density functional theory: mathematical foundations and pole shifting
Thiago Carvalho Corso, Mi-Song Dupuy, Gero Friesecke
We establish existence and uniqueness of the solution to the Dyson equation for the density-density response function in time-dependent density functional theory (TDDFT) in the ran…