Related papers: Quantized rational chip-firing
Let K be a field of characteristic zero, alpha algebraic of degree n over K. Given a proper parametrization psi of a rational curve C, we present a new algorithm to compute the hypercircle associated to the parametrization psi. As a…
We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows.…
Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field…
The parallel chip-firing game is a periodic automaton on graphs in which vertices "fire" chips to their neighbors. In 1989, Bitar conjectured that the period of a parallel chip-firing game with n vertices is at most n. Though this…
Quasiperiodic systems serve as fertile ground for studying localisation, due to their propensity already in one dimension to exhibit rich phase diagrams with mobility edges. The deterministic and strongly-correlated nature of the…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
Let $W$ be a complex reflection group of the form $G(l,1,n)$. Following [BK12, BPW12, Gor06, GS05, GS06, KR08, MN11], the theory of deform quantising conical symplectic resolutions allows one to study the category of modules for the…
The kinetics of ordering and concurrent ordering and clustering is analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. A simplified energy eigenstructure, or…
Let $G$ be a finite group. The co-prime order graph of $G$ is the graph whose vertex set is $G$, and two distinct vertices $x,y$ are adjacent if gcd$(o(x),o(y))$ is either $1$ or a prime, where $o(x)$ and $o(y)$ are the orders of $x$ and…
We construct fermionic conformal field theories (CFTs) whose spectra are characterized by quantum stabilizer codes. We exploit our construction to search for fermionic CFTs with supersymmetry by focusing on quantum stabilizer codes of the…
We propose to use the steered quantum coherence (SQC) as a signature of quantum phase transitions (QPTs). By considering various spin chain models, including the transverse-field Ising model, \textit{XY} model, and \textit{XX} model with…
Given a quotient of a regular noetherian separated algebraic space $X$ over a field by an affine algebraic group $G$ having finite stabilizers (with some mild technical conditions), G. Vezzosi and A. Vistoli defined the geometric part of…
In a graph $G = (V,E)$, a k-ruling set $S$ is one in which all vertices $V$ \ $S$ are at most $k$ distance from $S$. Finding a minimum k-ruling set is intrinsically linked to the minimum dominating set problem and maximal independent set…
Starting from the motional property of functional field based on the action principle of path integral formulation while proposing maximum coherence motion principle and maximum locally entangled-qubits motion principle as guiding…
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…
This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…
In this paper, we develop an algebraic K-stability theory (e.g. special test configuration theory and optimal destabilization theory) for log Fano $\mathbb R$-pairs, and construct a proper K-moduli space to parametrize K-polystable log Fano…
A \emph{$k$-track} layout of a graph consists of a vertex $k$ colouring, and a total order of each vertex colour class, such that between each pair of colour classes no two edges cross. A \emph{$k$-queue} layout of a graph consists of a…
In a graph whose vertices are assigned integer ranks, a path is well-ranked if the endpoints have distinct ranks or some interior point has a higher rank than the endpoints. A ranking is an assignment of ranks such that all nontrivial paths…
Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which…