Related papers: Higher K-energy functionals and higher Futaki inva…
The Dean-Kawasaki (DK) equation, which is at the basis of stochastic density functional theory (SDFT), was proposed in the mid-nineties to describe the evolution of the density of interacting Brownian particles, which can represent a large…
Wavefunctions are proposed for a class of Lagrangian branes in three complex-dimensional space. The branes are asymptotic to Legendrian surfaces of genus g. The expansion of these wavefunctions in appropriate coordinates conjecturally…
We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by…
We refine the invariant on $K_2(A[C_{p_e}]/I_m,(T-1))$ constructed in a previous paper to one which is an isomorphism for all $\lambda$-rings $A$.
To study scattering amplitudes at high-energy, the T-product of two currents can be expanded in terms of coefficient functions (impact factors) and matrix elements of ``composite color dipoles'' made of Wilson line operators with rapidity…
Since the seminal works of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting…
It is well known that tau functions of the KP hierarchy satisfy addition formulas. We consider the general addition formula in the determinant form and take a certain limit of it. It expresses certain shifts of a tau function in terms of…
The thermal partition functions of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local zeta-function approach. The relation with the surface terms previously…
A classical result in the study of Ginzburg-Landau equations is that, for Dirichlet or Neumann boundary conditions, if a sequence of functions has energy uniformly bounded on a logarithmic scale then we can find a subsequence whose…
The J-flow is a parabolic flow on Kahler manifolds. It was defined by Donaldson in the setting of moment maps and by Chen as the gradient flow of the J-functional appearing in his formula for the Mabuchi energy. It is shown here that under…
We introduce the magnetic equivariant K-theory groups as the K-theory groups associated to magnetic groups and their respective magnetic equivariant complex bundles. We restrict the magnetic group to its subgroup of elements that act…
A new three parameter formula is proposed for ground-state bands in even-even soft rotors or called transitional nuclei. The new formula blends those of very soft nuclei and well deformed nuclei. Especially, it is found in fact that the…
We consider the K-theory of the Hilbert scheme of points in the complex plane, which under McKay correspondence is isomorphic to the space of symmetric functions $\Lambda^n$. We prove a formula conjectured by Boissi\`ere for the…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
Kostka functions $K^{\pm}_{\lambda, \mu}(t)$ associated to complex reflection groups are a generalization of Kostka polynomials, which are indexed by a pair $\lambda, \mu$ of $r$-partitions and a sign $+, -$. It is expected that there…
We present an approach based on density-functional theory for the calculation of fundamental gaps of both finite and periodic two-dimensional (2D) electronic systems. The computational cost of our approach is comparable to that of total…
The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using…
Fromager and Lasorne [Electron. Struct. 6 025002 (2024)] have recently derived an in-principle exact Kohn-Sham density functional theory (KS-DFT) of electrons and nuclei, where the nuclear density and the (so-called conditional) electronic…
In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…
This paper introduces a $K$-function for assessing second-order properties of inhomogeneous random measures generated by marked point processes. The marks can be geometric objects like fibers or sets of positive volume, and the presented…