Related papers: Quantum extended crystal PDE's
We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired in the Lie (super)algebra structure, is explicitly applied to the particular case of…
It is shown, that extended particle-like objects should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytic results concerning the general properties and asymptotic rates of…
In this paper, we consider a confined physical scenario to prove global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media (IPM) equation. The result is proved using the…
We prove a scale-invariant, semi-global existence result and a trapped surface formation result in the context of coupled Einstein-Yang-Mills theory, without symmetry assumptions. More precisely, we prove a scale-invariant semi-global…
We explore equilibrium solutions of non-topological solitons in a general class of scalar field theories which include global U(1) symmetry. We find new types of solutions, tube-shaped and crust-shaped objects, and investigate their…
Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is considered. The connection with the ordinary and supersymmetric…
In physics literature about supersymmetry, many authors refer to "super Minkowski spaces". These spaces are affine supermanifolds with certain distinguished spin structures. In these notes, we make the notion of such spin structures precise…
For the quite extensively developed PDE backstepping methodology for coupled linear hyperbolic PDEs, we provide a generalization from finite collections of such PDEs, whose states at each location in space are vector-valued, to previously…
The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds is well known. We bring this solution into a TQFT-like form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is…
Amorphous solids exhibit quasi-universal low-temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create {\it in silico} glasses spanning from hyperquenched to…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
We extend finding geometrically-significant preserved quantities by solving specific PDEs to the affine transformations and subgroups. This can be viewed not only as a purely geometrical problem but also as a subcase of finding physical…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We re-examine the question of the stability of quantum supermembranes. In the past, the instability of supermembranes was established by using a regulator, i.e. approximating the membrane by SU(N) super Yang-Mills theory and letting $N…
In this letter, we find the first dynamically stable non-singular solution spherically symmetric SU(2) Einstein-Yang-Mills equation. This solutions is regular at r=0 and asymptotically flat. Since the Yang-Mills field strength decay…
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
An extension of the algebraic-geometric method for nonlinear integrable PDE's is shown to lead to new piecewise smooth weak solutions of a class of $N$-component systems of nonlinear evolution equations. This class includes, among others,…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
The Einstein-Yang-Mills equations are the source of many interesting solutions within general relativity, including families of particle-like and black hole solutions, and critical phenomena of more than one type. These solutions,…