Alexander Rothkopf

Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, nonholonomic systems-subject to nonintegrable velocity constraints or position inequality constraints-have long resisted a general extremized action treatment. In this work, we construct an explicit and general action for nonholonomic motion, motivated by the classical limit of the quantum Schwinger-Keldysh action formalism, rediscovered by Galley. Our formulation recovers the correct dynamics of the Lagrange-d'Alembert equations via extremization of a scalar action. We validate the approach on canonical examples using direct numerical optimization of the novel action, bypassing equations of motion. Our framework extends the reach of variational mechanics and offers new analytical and computational tools for constrained systems.

Real time evolution of a scalar field theory is investigated. The severe sign problem is circumvented using the Complex Langevin equation. The naive application of the method breaks down for extended real times due to the appearance of boundary terms. We use the kernel freedom of the complex Langevin equation to push the breakdown to larger real-times. We search for the optimal kernel using machine learning methods. Thus, we extend the available range for 1+1d scalar simulations beyond the state of the art simulations.

Real time evolution of a scalar field theory is investigated. The severe sign problem is circumvented using the Complex Langevin equation. The naive application of the method breaks down for extended real times due to the appearance of boundary terms. We use the kernel freedom of the complex Langevin equation to push the breakdown to larger real-times. We search for the optimal kernel using machine learning methods. Thus, we extend the available range for 1+1d scalar simulations beyond the state of the art simulations.

The breaking of space-time symmetries and the non-conservation of the associated Noether charges constitutes a central artifact in lattice field theory. In prior studies we have shown how to overcome this limitation for classical actions describing point particle motion, using the world-line formalism of general relativity. The key is to treat coordinate maps (from an abstract parameter space into space-time) as dynamical and dependent degrees of freedom, which remain continuous after discretization of the underlying parameter space. Here we present latest results where we construct a reparameterization invariant classical action for scalar fields, which features dynamical coordinate maps. We highlight the following achievements of our approach: 1) global space-time symmetries remain intact after discretization and the associated Noether charges remain exactly preserved 2) coordinate maps adapt to the dynamics of the scalar field leading to adaptive grid resolution guided by the symmetries.

We reinvestigate the interactions between static color sources in a finite temperature gluonic medium using both high resolution isotropic and anisotropic quenched lattice QCD ensembles. The underlying ill-posed inverse problem, related to the extraction of spectral functions, is attacked with a range of different methods, including Bayesian inference, Padé interpolation and model fits. Among the latter we include a tail amended Gaussian ansatz and a HTL-inspired fit ansatz. We reconfirm the presence of a dominant low lying spectral feature that supports the existence of a potential picture for the in-medium evolution of the static charges at late real times. Using the raw unmodified lattice data, all applicable methods show clear signs of screening of the real part of the potential. After applying a subtraction procedure featured in a previous study, we find however that screening disappears from the extracted potential. Paths toward the resolution of this puzzle are discussed. Published by the American Physical Society 2024