Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

**non**-

**trivial**center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem. Expand abstract.

**non**-

**trivial**center regions, that is, regions whose boundary evaluates to a

**non**-

**trivial**center element, a resolution of this issue seems possible. We use such

**non**-

**trivial**center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

5/10 relevant

Preprints.org

Type-B Anomaly Matching and the 6D (2,0) Theory

**non**-

**trivial**functions of exactly-marginal couplings that can be determined from the $S^4$ partition function. In this paper, we examine the fate of these anomalies in vacua of the Higgs-branch moduli space, where conformal symmetry is spontaneously broken. We argue

**non**-perturbatively that these anomalies are covariantly constant on conformal manifolds. In some cases, this can be used to show that they match in the broken and unbroken phases. Thus, we uncover a new class of data on the Higgs branch of 4D $\mathcal N=2$ conformal field theories that are exactly computable. An interesting application of this matching occurs in $\mathcal N=2$ circular quivers that deconstruct the 6D (2,0) theory on a torus. In that context, we argue that 4D supersymmetric localisation can be used to calculate

**non**-

**trivial**data involving $\frac{1}{2}$-BPS operators of the 6D theory as exact functions of the complex structure of the torus.

4/10 relevant

arXiv

Asymptotic formulas for harmonic series in terms of a **non**-**trivial** zero
on the critical line

**non**-

**trivial**zeros of the Riemann zeta function on the critical line. The series is obtained by evaluating the complex magnitude of an alternating and

**non**-alternating series representation of the Riemann zeta function. Consequently, if the asymptotic limit of the harmonic series is known, then we obtain the Euler-Mascheroni constant with $\log(k)$. We further numerically compute these series for different

**non**-

**trivial**zeros. We also investigate a recursive formula for

**non**-

**trivial**zeros.

10/10 relevant

arXiv

Some properties of ergodicity coefficients with applications in spectral graph theory

**non**-

**trivial**eigenvalue in absolute value can be bounded by using Tp. Expand abstract.

**non**-

**trivial**eigenvalue in absolute value of real constant row-sum matrices by the use of vector norm based ergodicity coefficients Tp. If the constant row-sum matrix is nonsingular, then it is also shown how its smallest

**non**-

**trivial**eigenvalue in absolute value can be bounded by using Tp. In the last section, these two results are applied to bound the spectral radius of the Laplacian matrix as well as the algebraic connectivity of its associated graph. Many other results are obtained. In particular, Theorem 2.15 is a convergence theorem for Tp and Theorem 4.7 compares some ergodicity coefficients to each other.

4/10 relevant

arXiv

Magnetic field-induced type-II Weylsemimetallic state in geometrically frustrated Shastry-Sutherland lattice GdB4

**non**-

**trivial**Berry phase, detected in de Haas-van Alphen experiments and chiral-anomaly-induced negative magnetoresistance. Expand abstract.

**non**-

**trivial**phase of matter with pairs of Weyl nodes in the k-space, which act as monopole and anti-monopole pairs of Berry curvature. Two hallmarks of the Weyl metallic state are the topological surface state called the Fermi arc and the chiral anomaly. It is known that the chiral anomaly yields anomalous magneto-transport phenomena. In this study, we report the emergence of the type-II Weyl semimetallic state in the geometrically frustrated

**non**-collinear antiferromagnetic Shastry-Sutherland lattice (SSL) GdB4 crystal. When we apply magnetic fields perpendicular to the noncollinear moments in SSL plane, Weyl nodes are created above and below the Fermi energy along the M-A line (tau-band) because the spin tilting breaks the time-reversal symmetry and lifts band degeneracy while preserving C4z or C2z symmetry. The unique electronic structure of GdB4 under magnetic fields applied perpendicular to the SSL gives rise to a

**non**-

**trivial**Berry phase, detected in de Haas-van Alphen experiments and chiral-anomaly-induced negative magnetoresistance. The emergence of the magnetic field-induced Weyl state in SSL presents a new guiding principle to develop novel types of Weyl semimetals in frustrated spin systems.

4/10 relevant

arXiv

Non-**trivial** $d$-wise Intersecting families

**non**-

**trivial**$d$-wise intersecting family of $k$-element subsets of $[n]$ is one of the following two families: \begin{align*} &\mathcal{H}(k,d) = \{A \in \binom{[n]}{k} : [d-1] \subset A, A \cap [d,k+1] \neq \emptyset\} \cup \{[k+1] \setminus \{i \} : i \in [d - 1]\} \\ &\mathcal{A}(k,d) = \{ A \in \binom{[n]}{k} : |A \cap [d+1]| \geq d \}. \end{align*} The celebrated Hilton-Milner Theorem states that $\mathcal{H}(k,2)$ is the unique extremal

**non**-

**trivial**intersecting family for $k>3$. We prove the conjecture and prove a stability theorem, stating that any large enough

**non**-

**trivial**$d$-wise intersecting family of $k$-element subsets of $[n]$ is a subfamily of $\mathcal{A}(k,d)$ or $\mathcal{H}(k,d)$.

10/10 relevant

arXiv

Topological Quantum Computing Using Nanowire Devices

**non**-

**trivial**parameter regions. Expand abstract.

**non**-

**trivial**exchange statistics can be used for topological quantum computing. In branched nanowire networks one can exchange Majorana states by time-dependently tuning topologically

**non**-

**trivial**parameter regions. In this work, we simulate the exchange of four Majorana modes in T-shaped junctions made out of p-wave superconducting Rashba wires. We derive concrete experimental predictions for (quasi-)adiabatic braiding times and determine geometric conditions for successful Majorana exchange processes. Contrary to the widespread opinion, we show for the first time that in the adiabatic limit the gating time needs to be smaller than the inverse of the squared superconducting order parameter and scales linearly with the gating potential. Further, we show how to circumvent the formation of additional Majorana modes in branched nanowire systems, arising at wire intersection points of narrow junctions. Finally, we propose a multi qubit setup, which allows for universal and in particular topologically protected quantum computing.

4/10 relevant

arXiv

Analysis of the Riemann zeta function

**non**-

**trivial**zeros of the Riemann Zeta function; 6) determine why the Riemann Zeta function has

**non**-

**trivial**zeros on the critical line; 7) understand why the Riemann Zeta function cannot have

**non**-

**trivial**zeros in the critical strip other than the critical line.

5/10 relevant

arXiv

Divisor Functions and the Number of Sum Systems

**non**-negative integers $j, r$ count the number of ways of representing $n$ as an ordered product of $j+r$ factors, of which the first $j$ must be

**non**-trivial, and their natural extension to negative integers $r.$ We give recurrence properties and explicit formulae for these novel arithmetic functions. Specifically, the functions $c_j^{(-j)}(n)$ count, up to a sign, the number of ordered factorisations of $n$ into $j$ square-free

**non**-

**trivial**factors. These functions are related to a modified version of the M\"obius function and turn out to play a central role in counting the number of sum systems of given dimensions. \par Sum systems are finite collections of finite sets of

**non**-negative integers, of prescribed cardinalities, such that their set sum generates consecutive integers without repetitions. Using a recently established bijection between sum systems and joint ordered factorisations of their component set cardinalities, we prove a formula expressing the number of different sum systems in terms of associated divisor functions.

4/10 relevant

arXiv

On the (non) existence of superregular boson clouds around extremal Kerr black holes and its connection with number theory

**non**-

**trivial**boson clouds having such superregularity conditions cannot exist in the background of an exact extremal Kerr BH. The only exception to this conclusion is in the limit $n\rightarrow \infty$ and $m\ll n$. In such a large $n$ limit consistency in the separation constants leads to a quadratic Diophantine equation of Pell's type for the integer numbers $(l,m)$. Such Pell's equation can be readily solved using standard techniques. In that instance well behaved spheroidal harmonics are obtained, and thus, well behaved

**non**-

**trivial**superregular clouds can be computed. Of course, this situation, does not preclude the existence of other kind of smooth cloud solutions for any other $n$, not necessarily large (e.g. clouds with a

**non**-integer $\kappa$) when using a better behaved coordinate system at the horizon (e.g. Wheeler's tortoise coordinate or proper radial distance).

4/10 relevant

arXiv