We review the calculation of the the effective potential with particular emphasis on cases when the tree potential or the renormalisation-group-improved, radiatively corrected potential exhibits non-convex behaviour. We illustrate this in a simple Yukawa model which exhibits a novel kind of dimensional transmutation. We also review briefly earlier work on the Standard Model. We conclude that, d...

This work presents a new methodology for computing ground states of Bose–Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a preprocessing step, a low-dimensional (coarse) generalized finite element space is constructed. It is based on a local orthogonal decomposition of the solution space and exhibits high approximation properties....

We consider the crossing and non-crossing O(1) dense loop models on a semi-infinite strip, with inhomogeneities (spectral parameters) that preserve the integrability. We compute the components of the ground state vector and obtain a closed expression for their sum, in the form of Pfaffian and determinantal formulas.

We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small, we prove the existence of a ground state.

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of gro...

We consider theoretically a Josephson junction with a superconducting critical current density which has a random sign along the junction's surface. We show that the ground state of the junction corresponds to the phase difference equal to π 2. Such a situation can take place in superconductor-ferromagnet-superconductor junctions.

In this article, we use Palais–Smale approaches to describe the achieved and nonachieved domains. We characterizes the achieved domain by the existence of a ground state solution for the energy functional J in Ω.

In this work, we construct the non-relativistic Lee model on some class of three dimensional Riemannian manifolds by following a novel approach introduced by S. G. Rajeev [1]. This approach together with the help of heat kernel allows us to perform the renormalization non-perturbatively and explicitly. For completeness, we show that the ground state energy is bounded from below for different cl...