arXiv subjects

Nicolas Weiss

Publications and source records attributed to Nicolas Weiss.

5 recordsLinked to original sources

arXiv2026

Cosmological Weight-Shifting Matrices

We construct matrices that shift the scaling dimension of scalar fields for arbitrary de Sitter Feynman diagrams. Acting on a set of master integrals, these weight-shifting matrices shift the scaling dimensions of individual edges of a given diagram by an integer. They can thus be applied to a broader range of problems and are simpler to implement than earlier derivative-based approaches. By introducing a Kronecker product representation of our matrix formulation, we generalise weight-shifting operators beyond four-point functions to arbitrary tree-level diagrams. As an application, we obtain explicit expressions for several massless wavefunction coefficients in four-dimensional de Sitter space, starting from conformally coupled seed functions. Our construction provides a systematic and graph-local approach to generating cosmologically relevant correlators from simpler master integrals.

hep-th↗

arXiv2026

Exact Volumes of Semi-Algebraic Convex Bodies

We compute the volumes of convex bodies that are given by inequalities of concave polynomials. These volumes are found to arbitrary precision thanks to the representation of periods by linear differential equations. Our approach rests on work of Lairez, Mezzarobba, and Safey El Din. We present a novel method to identify the relevant critical values. Convexity allows us to reduce the required number of creative telescoping steps by an exponential factor. We provide an implementation based on the ore_algebra package in SageMath. We present examples computed with our implementation in 2, 3 and 4 dimensions.

math.AG↗

arXiv2025

Connection Matrices in Macaulay2

In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of finite holonomic rank, we implement the computation of the encoded system of linear PDEs in connection form with respect to an elimination term order that depends on a chosen positive weight vector. We also implement the gauge transformation for carrying out a change of basis over the field of rational functions. We demonstrate all implemented algorithms with examples.

math.AG↗

arXiv2024

Complexity of equal 0-surgeries

We say that two knots are friends if they share the same 0-surgery. Two friends with different sliceness status would provide a counterexample to the 4-dimensional smooth Poincar\'e conjecture. Here we create a census of all friends with small crossing numbers c and tetrahedral complexities t, and compute their smooth 4-genera. In particular, we compute the minimum of c(K)+c(K') and of t(K)+t(K') among all friends K and K'. Along the way, we classify all 0-surgeries of prime knots of at most 15 crossings. Moreover, we determine for many friends in our census if their traces are equivalent or not. For that, we develop a new obstruction for two traces being homeomorphic coming from symmetry-exceptional slopes of hyperbolic knots. This is enough to also determine the minimum value of c(K)+c(K') among all friends K and K' whose traces are not homeomorphic.

math.GT↗

arXiv2018

Upgrade of a low-temperature scanning tunneling microscope for electron-spin resonance

Electron spin resonance with a scanning tunneling microscope (ESR-STM) combines the high energy resolution of spin resonance spectroscopy with the atomic scale control and spatial resolution of STM. Here we describe the upgrade of a helium-3 STM with a 2D vector-field magnet ($B_z$ = 8.0 T, $B_x$ = 0.8 T) to an ESR-STM. The system is capable of delivering RF power to the tunnel junction at frequencies up to 30 GHz. We demonstrate magnetic field sweep ESR for the model system TiH/MgO/Ag(100) and find a magnetic moment of $(1.004 \pm 0.001)$ $\mu_B$. Our upgrade enables to toggle between a DC mode, where the STM is operated with the regular control electronics, and an ultrafast-pulsed mode that uses an arbitrary waveform generator for pump-probe spectroscopy or reading of spin-states. Both modes allow for simultaneous radiofrequency excitation, which we add via a resistive pick-off tee to the bias voltage path. The RF cabling from room temperature to the 350 mK stage has an average attenuation of 18 dB between 5 and 25 GHz. The cable segment between the 350 mK stage and the STM tip presently attenuates an additional $34_{-3}^{+5}$ dB from 10 to 26 GHz and $38_{-2}^{+3}$ dB between 20 and 30 GHz. We discuss our transmission losses and indicate ways to reduce this attenuation. We finally demonstrate how to synchronize the arrival times of RF and DC pulses coming from different paths to the STM junction, a prerequisite for future pulsed ESR experiments.

physics.ins-det↗