arXiv subjects

A. E. Thomsen

Publications and source records attributed to A. E. Thomsen.

3 recordsLinked to original sources

arXiv2019

Weyl Consistency Conditions and $γ_{5}$

The treatment of $γ_{5}$ in Dimensional Regularization leads to ambiguities in field-theoretic calculations, of which one example is the coefficient of a particular term in the four-loop gauge $β$-functions of the Standard Model. Using Weyl Consistency Conditions, we present a scheme-independent relation between the coefficient of this term and a corresponding term in the three-loop Yukawa $β$-functions, where a semi-naïve treatment of $γ_{5}$ is sufficient, thereby fixing this ambiguity. We briefly outline an argument by which the same method fixes similar ambiguities at higher orders.

hep-th↗

arXiv2016

CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension

We consider a one-dimensional system of particles with strong zero-range interactions. This system can be mapped onto a spin chain of the Heisenberg type with exchange coefficients that depend on the external trap. In this paper, we present an algorithm that can be used to compute these exchange coefficients. We introduce an open source code CONAN (Coefficients of One-dimensional N-Atom Networks) which is based on this algorithm. CONAN works with arbitrary external potentials and we have tested its reliability for system sizes up to around 35 particles. As illustrative examples, we consider a harmonic trap and a box trap with a superimposed asymmetric tilted potential. For these examples, the computation time typically scales with the number of particles as $O(N^{3.5 \pm 0.4})$. Computation times are around 10 seconds for $N=10$ particles and less than 10 minutes for $N=20$ particles.

cond-mat.quant-gas↗

arXiv2016

Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity

We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles for general interaction strengths and up to 30 particles in the strongly interacting case. We also calculate the contact coefficient in the strongly interacting regime. The different theoretical predictions are compared to recent experimental results with few-atom systems. Firstly, we find that the local density approximation suffers from great ambiguity in the few-atom regime, yet it works surprisingly well for some models. Secondly, we find that the strong interaction theories quickly break down when the number of particles increase or the interaction strength decreases.

cond-mat.quant-gas↗