Related papers: Direct methods to Lieb-Thirring kinetic inequaliti…
In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator…
The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three…
We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality principle and the smooth perturbation theory…
In this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb-Thirring constant when the eigenvalues of a Schr\"odinger operator $-\Delta+V(x)$…
In this paper, we establish some Stein-Weiss type inequalities with general kernels on the upper half space and study the existence of extremal functions for this inequality with the optimal constant. Furthermore, we also investigate the…
In this paper we prove sharp Lieb-Thirring (LT) inequalities for the family of shifted Coulomb Hamiltonians. More precisely, we prove the classical LT inequalities with the semi-classical constant for this family of operators in any…
Calculations using the (exact) fermionic functional renormalization group are usually truncated at the second order of the corresponding hierarchy of coupled ordinary differential equations. We present a method for the systematic…
We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born--Oppenheimer approximations.
Using measure-capacity inequalities we study new functional inequalities, namely L^q-Poincar\'{e} inequalities and L^q-logarithmic Sobolev inequalities. As a consequence, we establish the asymptotic behavior of the solutions to the…
We state and prove four types of Lieb-Robinson bounds valid for many-body open quantum systems with power law decaying interactions undergoing out of equilibrium dynamics. We also provide an introductory and self-contained discussion of the…
In this paper we give both an historical and technical overview of the theory of Harnack inequalities for nonlinear parabolic equations in divergence form. We start reviewing the elliptic case with some of its variants and geometrical…
The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened…
We review various theoretical methods that have been used in recent years to calculate dynamical correlation functions of many-body systems. Time-dependent correlation functions and their associated frequency spectral densities are the…
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
In this paper we obtain the estimates on some dynamic integral inequalities in three variables which can be used to study certain dynamic equations. We give some applications to convey the importance of our result.