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.

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...

The atomic ground state density at the nucleus is bounded from above by a certain explicitly given positive constant times the third power of the nuclear charge.

The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley–Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its minimal degree solution described. As a result, the sum of the properly normalized components of the ground state in size L is computed and shown to be equal to the number of Horizontally and Verti...