**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Green's function

Summary

In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.
This means that if \operatorname{L} is the linear differential operator, then

- the Green's function G is the solution of the equation \operatorname{L} G = \delta, where \delta is Dirac's delta function;
- the solution of the initial-value problem \operatorname{L} y = f is the convolution (G \ast f).

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people (1)

Related concepts

No results

Related publications (21)

Loading

Loading

Loading

Related units (1)

Related courses (13)

PHYS-324: Classical electrodynamics

The goal of this course is the study of the physical and conceptual consequences of Maxwell equations.

PHYS-426: Quantum physics IV

Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented, including non-perturbative effects, such as tunneling and instantons.

PHYS-425: Quantum physics III

To introduce several advanced topics in quantum physics, including
semiclassical approximation, path integral, scattering theory, and
relativistic quantum mechanics

The kinetic theory of rarefied gases and numerical schemes based on the Boltzmann equation, have evolved to the cornerstone of non-equilibrium gas dynamics. However, their counterparts in the dense regime remain rather exotic for practical non-continuum scenarios. This problem is partly due to the fact that long-range interactions arising from the attractive tail of molecular potentials, lead to a computationally demanding Vlasov integral. This study focuses on numerical remedies for efficient stochastic particle simulations based on the Enskog–Vlasov kinetic equation. In particular, we devise a Poisson type elliptic equation which governs the underlying long-range interactions. The idea comes through fitting a Green function to the molecular potential, and hence deriving an elliptic equation for the associated fundamental solution. Through this transformation of the Vlasov integral, efficient Poisson type solvers can be readily employed in order to compute the mean field forces. Besides the technical aspects of different numerical schemes for treatment of the Vlasov integral, simulation results for evaporation of a liquid slab into the vacuum are presented. It is shown that the proposed formulation leads to accurate predictions with a reasonable computational cost.

2018Quantum Field Theory(QFT) as one of the most promising frameworks to study high energy and condensed matter physics, has been mostly developed by perturbative methods. However, perturbative methods can only capture a small island of the space of QFTs.QFT in hyperbolic space can be used to link the conformal bootstrap and massive QFT. Conformal boundary correlators also can be studied by their general properties such as unitarity, crossing symmetry and analicity. On the other hand, by sending the curvature radius to infinity we reach to the flat-space limit in hyperbolic space. This allows us to use conformal bootstrap methods to study massive QFT in one higher dimension and calculate observables like scattering amplitudes or finding bounds on the couplings of theory. The main goal of my research during my Ph.D. would be to study QFTs in hyperbolic space to better understand strongly coupled QFTs.Hamiltonian truncation is a numerical method to study strongly coupled QFTs by imposing a UV cutoff. We use this method to study strongly coupled QFT in hyperbolic space background. For simplicity, we start with scalar field theory in 2-dimensional AdS. We expect to extract the spectrum of our theory as a function of AdS curvature and find the boundary correlation functions.

Related lectures (29)