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Technical University of Munich

Simulations for Precision Measurements

Overview

The Simulations for Precision Measurements group develops and applies advanced numerical models to support and interpret high-precision spin precession experiments.
Accurate simulations are essential to understand systematic effects, optimize experimental geometries, and quantify subtle interactions in complex electromagnetic environments.
Our simulation efforts bridge the gap between finite-element field modeling, particle tracking, and Monte Carlo–based inference, providing a unified digital framework for precision measurement design and data interpretation.

Scientific Motivation

Spin precession experiments—such as those used in EDM searches and spin clock studies—require precise knowledge of magnetic, electric, and gravitational field configurations and their effects on particle dynamics.
Minute gradients or field imperfections can mimic the sought-after physical signals.
Detailed numerical simulations enable:

  • quantification of systematic shifts in precession frequency,
  • study of diffusion, depolarization, and geometric-phase effects,
  • optimization of cell design, electrode geometry, and shielding,
  • and validation of data analysis and inference pipelines under realistic conditions.

Finite Element Simulations (COMSOL Multiphysics)

For modeling static and quasi-static fields, we employ COMSOL Multiphysics and in-house numerical solvers to compute:

  • 3D magnetic and electric field distributions,
  • interactions with materials of different permeabilities and conductivities,
  • temporal drifts and eddy current effects during switching sequences,
  • and shielding performance of multi-layer magnetic enclosures.

These simulations are crucial for:

  • Spin clock and HeXeEDM experiment design,
  • characterization of field uniformity inside magnetic shields,
  • and development of optimized coil geometries for precision field control.

COMSOL models are regularly benchmarked against analytical calculations and field-mapping data from the experimental setups.

Geant4 Simulations for Ultracold Neutrons (UCN)

For dynamic particle transport and detection processes, we use Geant4-based Monte Carlo simulations tailored to ultracold neutrons and low-energy charged particles.
In collaboration with the University of Heidelberg, we build upon the open-source project Building Geant4 Apptainer with LEPP patches,
which provides a reproducible, containerized environment for large-scale particle simulations on distributed computing clusters.

This framework allows:

  • realistic modeling of UCN trajectories, wall collisions, and depolarization processes,
  • simulation of magnetic and electric field maps from FEM calculations within Geant4,
  • inclusion of material-dependent reflection and absorption probabilities,
  • and integration with data analysis tools for likelihood-based EDM inference.

The approach ensures reproducibility and facilitates collaborative development between experimental and computational teams.

Monte Carlo Spin Precession Simulations (SRK Framework)

A central component of our simulation toolkit is the Spin Runge–Kutta (SRK) framework — a Monte Carlo–based code for tracking the spin dynamics of individual particles in three-dimensional, time-dependent field configurations. This framework integrates both particle trajectories and spin vectors according to the classical equation of motion using a high-order Runge–Kutta solver. Each simulated particle experiences realistic magnetic field gradients, wall reflections, and motional fields arising from v×E.

Ensemble simulations reveal that under such realistic conditions, the spin-phase distributions deviate from Gaussian statistics and instead follow q-Gaussian (power-law) distributions. These non-Gaussian phase tails play a crucial role in understanding frequency extraction biases, spin dephasing, and systematic uncertainties in EDM and spin-clock measurements.

The SRK approach allows for direct simulation of Ramsey-type precession sequences, magnetic-gradient-induced shifts, and motional false EDMs, providing a microscopic link between field imperfections and experimentally observed spin-precession frequencies.

Contact / Links

For collaboration, thesis opportunities, or further inquiries, please contact:

Foto von Peter Fierlinger

Prof. Dr.sc.nat. Peter Fierlinger

Publications and finished Theses

  • Degenkolb, Skyler, et al. "Towards Precise Simulations and Inference for the Neutron EDM." arXiv preprint arXiv:2509.02791 (2025).
  • Bales, Matthew J., Peter Fierlinger, and Robert Golub. "Non-extensive statistics in spin precession." Europhysics Letters 116.4 (2017): 43002.

Involved Persons and Former Members

Currently Involved persons: 

Former Members: 

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