arXiv subjects

Klaus Klingmuller

Publications and source records attributed to Klaus Klingmuller.

8 recordsLinked to original sources

arXiv2009

Worldline Monte Carlo for fermion models at large N_f

Strongly-coupled fermionic systems can support a variety of low-energy phenomena, giving rise to collective condensation, symmetry breaking and a rich phase structure. We explore the potential of worldline Monte Carlo methods for analyzing the effective action of fermionic systems at large flavor number N_f, using the Gross-Neveu model as an example. Since the worldline Monte Carlo approach does not require a discretized spacetime, fermion doubling problems are absent, and chiral symmetry can manifestly be maintained. As a particular advantage, fluctuations in general inhomogeneous condensates can conveniently be dealt with analytically or numerically, while the renormalization can always be uniquely performed analytically. We also critically examine the limitations of a straightforward implementation of the algorithms, identifying potential convergence problems in the presence of fermionic zero modes as well as in the high-density region.

hep-th↗

arXiv2008

Geothermal Casimir Phenomena

We present first worldline analytical and numerical results for the nontrivial interplay between geometry and temperature dependencies of the Casimir effect. We show that the temperature dependence of the Casimir force can be significantly larger for open geometries (e.g., perpendicular plates) than for closed geometries (e.g., parallel plates). For surface separations in the experimentally relevant range, the thermal correction for the perpendicular-plates configuration exhibits a stronger parameter dependence and exceeds that for parallel plates by an order of magnitude at room temperature. This effect can be attributed to the fact that the fluctuation spectrum for closed geometries is gapped, inhibiting the thermal excitation of modes at low temperatures. By contrast, open geometries support a thermal excitation of the low-lying modes in the gapless spectrum already at low temperatures.

quant-ph↗

arXiv2007

Worldline Approach to Chiral Fermions

We propose to apply ``worldline numerics'' to a numerical calculation of quark determinants. The Gross-Neveu model with a U(1) chiral symmetry is considered as a first test. The worldline approach allows for an analytic renormalisation, and only finite parts of the determinant require a numerical calculation. It is shown that the discretisation of the worldlines, which is central to the numerical treatment, preserves chiral symmetry exactly. Numerical results for a kink configuration as a scalar background field are shown and compared with analytical results. The case of finite fermion chemical potential is also briefly discussed.

hep-lat↗

arXiv2006

Casimir edge effects

We compute Casimir forces in open geometries with edges, involving parallel as well as perpendicular semi-infinite plates. We focus on Casimir configurations which are governed by a unique dimensional scaling law with a universal coefficient. With the aid of worldline numerics, we determine this coefficient for various geometries for the case of scalar-field fluctuations with Dirichlet boundary conditions. Our results facilitate an estimate of the systematic error induced by the edges of finite plates, for instance, in a standard parallel-plate experiment. The Casimir edge effects for this case can be reformulated as an increase of the effective area of the configuration.

quant-ph↗

arXiv2006

Worldline algorithms for Casimir configurations

We present improved worldline numerical algorithms for high-precision calculations of Casimir interaction energies induced by scalar-field fluctuations with Dirichlet boundary conditions for various Casimir geometries. Significant reduction of numerical cost is gained by exploiting the symmetries of the worldline ensemble in combination with those of the configurations. This facilitates high-precision calculations on standard PCs or small clusters. We illustrate our strategies using the experimentally most relevant sphere-plate and cylinder-plate configuration. We compute Casimir curvature effects for a wide parameter range, revealing the tight validity bounds of the commonly used proximity force approximation (PFA). We conclude that data analysis of future experiments aiming at a precision of 0.1% must no longer be based on the PFA. Revisiting the parallel-plate configuration, we find a mapping between the D-dimensional Casimir energy and properties of a random-chain polymer ensemble.

quant-ph↗

arXiv2006

Quantum energies with worldline numerics

We present new results for Casimir forces between rigid bodies which impose Dirichlet boundary conditions on a fluctuating scalar field. As a universal computational tool, we employ worldline numerics which builds on a combination of the string-inspired worldline approach with Monte-Carlo techniques. Worldline numerics is not only particularly powerful for inhomogeneous background configurations such as involved Casimir geometries, it also provides for an intuitive picture of quantum-fluctuation-induced phenomena. Results for the Casimir geometries of a sphere above a plate and a new perpendicular-plates configuration are presented.

hep-th↗

arXiv2006

Casimir effect for curved geometries: PFA validity limits

We compute Casimir interaction energies for the sphere-plate and cylinder-plate configuration induced by scalar-field fluctuations with Dirichlet boundary conditions. Based on a high-precision calculation using worldline numerics, we quantitatively determine the validity bounds of the proximity force approximation (PFA) on which the comparison between all corresponding experiments and theory are based. We observe the quantitative failure of the PFA on the 1% level for a curvature parameter a/R > 0.00755. Even qualitatively, the PFA fails to predict reliably the correct sign of genuine Casimir curvature effects. We conclude that data analysis of future experiments aiming at a precision of 0.1% must no longer be based on the PFA.

quant-ph↗

arXiv2005

Pair production in inhomogeneous fields

We employ the recently developed worldline numerics, which combines string-inspired field theory methods with Monte-Carlo techniques, to develop an algorithm for the computation of pair-production rates in scalar QED for inhomogeneous background fields. We test the algorithm with the classic Sauter potential, for which we compute the local production rate for the first time. Furthermore, we study the production rate for a superposition of a constant E field and a spatially oscillating field for various oscillation frequencies. Our results reveal that the approximation by a local derivative expansion fails already for frequencies small compared to the electron mass scale, whereas for strongly oscillating fields a derivative expansion for the averaged field represents an acceptable approximation. The worldline picture makes the nonlocal nature of pair production transparent and facilitates a profound understanding of this important quantum phenomenon.

hep-ph↗