Related papers: Dichotomy theorem separating complete integrabilit…
We formulate and prove Cutkosky's Theorem regarding the discontinuity of Feynman integrals in the massive one-loop case up to the involved intersection index. This is done by applying the techniques to treat singular integrals developed in…
This is the third installment in a series of papers concerning the Bounded Real Lemma for infinite-dimensional discrete-time linear input/state/output systems. In this setting, under appropriate conditions, the lemma characterizes when the…
It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin-$\frac{1}{2}$ XXZ Heisenberg chain. These charges have been proven to be essential for…
In this paper we study the general concept of integrability in the broad sense within the frame of differential Galois theory. We concentrate on the gradient systems which are not integrable. In spite of it, if we consider them as the real…
Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
Yang--Mills theories in four space-time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang--Mills…
In recent papers by the authors (S.~Motonaga and K.~Yagasaki, Obstructions to integrability of nearly integrable dynamical systems near regular level sets, submitted for publication, and K.~Yagasaki, Nonintegrability of nearly integrable…
We prove the local existence theorem and establish an extension principle for the spherically symmetric Einstein Yang--Mills system (SSEYM) with $H^1$ data. This in addition implies Cauchy stability for the system. In contrast to a massless…
We study the rectification of spin current in $XXZ$ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product states algorithm we find that a large rectification (of the…
Recent renormalization group studies of impurities in spin-1/2 chains appear to be inconsistent with Bethe ansatz results for a special integrable model. We study this system in more detail around the integrable point in parameter space and…
We construct, to the first two non-trivial orders, the next conserved charge in the su(2|3) sector of N=4 Super Yang-Mills theory. This represents a test of integrability in a sector where the interactions change the number of sites of the…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…
We investigate how symmetries and conserved quantities relate to the occurrence of the boundary time crystal (BTC) phase in a generalized spin model with Lindblad dissipation. BTCs are a non-equilibrium phase of matter in which the system,…
We consider the integrable one-dimensional spin-$1$ chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-$1/2$ model, by a continuous anisotropy parameter and at the isotropic…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
Mazur's inequality renders statements about persistent correlations possible. We generalize it in a convenient form applicable to any set of linearly independent constants of motion. This approach is used to show rigorously that a fraction…
In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…