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.Comment: 8 pages, 2 figures, Submitted to the Proceedings of the Seventh Workshop QFEXT'05 (Barcelona, September 5-9, 2005), Refs updated, version to appear in JPhys

Chiral phase structure of QCD with many flavors

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(Nc) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an Nf window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is Nf^{cr}=10.0\pm 0.29(fermion)[+1.55;-0.63](gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively.Comment: 7 pages, 3 figures, updated discussion of the uncertainties in the gauge secto

Optical probes of the quantum vacuum: The photon polarization tensor in external fields

The photon polarization tensor is the central building block of an effective theory description of photon propagation in the quantum vacuum. It accounts for the vacuum fluctuations of the underlying theory, and in the presence of external electromagnetic fields, gives rise to such striking phenomena as vacuum birefringence and dichroism. Standard approximations of the polarization tensor are often restricted to on-the-light-cone dynamics in homogeneous electromagnetic fields, and are limited to certain momentum regimes only. We devise two different strategies to go beyond these limitations: First, we aim at obtaining novel analytical insights into the photon polarization tensor for homogeneous fields, while retaining its full momentum dependence. Second, we employ wordline numerical methods to surpass the constant-field limit.Comment: 13 pages, 4 figures; typo in Eq. (5) corrected (matches journal version

RG flow of the Polyakov-loop potential: First status report

We study SU(2) Yang-Mills theory at finite temperature in the framework of the functional renormalization group. We concentrate on the effective potential for the Polyakov loop which serves as an order parameter for confinement. In this first status report, we focus on the behaviour of the effective Polyakov-loop potential at high temperatures. In addition to the standard perturbative result, our findings provide information about the ``RG improved'' backreactions of Polyakov-loop fluctuations on the potential. We demonstrate that these fluctuations establish the convexity of the effective potential.Comment: 10 pages, 2 figure

Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model

Magnetic catalysis describes the enhancement of symmetry breaking quantum fluctuations in chirally symmetric quantum field theories by the coupling of fermionic degrees of freedom to a magnetic background configuration. We use the functional renormalization group to investigate this phenomenon for interacting Dirac fermions propagating in (2+1)-dimensional spacetime, described by the Gross-Neveu model. We identify pointlike operators up to quartic fermionic terms that can be generated in the renormalization group flow by the presence of an external magnetic field. We employ the beta function for the fermionic coupling to quantitatively analyze the field dependence of the induced spectral gap. Within our pointlike truncation, the renormalization group flow provides a simple picture for magnetic catalysis.Comment: 14 pages, 6 figures, typos correcte

Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory

We propose a new Monte-Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.Comment: 12 pages, 6 figures, accepted in Int. J. Mod. Phys.

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.Comment: 23 pages, 9 figure

Analytical results for the confinement mechanism in QCD_3

We present analytical methods for investigating the interaction of two heavy quarks in QCD_3 using the effective action approach. Our findings result in explicit expressions for the static potentials in QCD_3 for long and short distances. With regard to confinement, our conclusion reflects many features found in the more realistic world of QCD_4.Comment: 24 pages, uses REVTe

Pressure-induced isostructural phase transition of metal-doped silicon clathrates

We propose an atomistic model for the pressure-induced isostructural phase transition of metal-doped silicon clathrates, Ba8Si46 and K8Si46, that has been observed at 14 GPa and 23 GPa, respectively. The model explains successfully the equation of state, transition pressure, change of Raman spectra and dependence on the doped cations as well as the effects of substituting Si(6c) atoms with noble metals.Comment: 5 pages, two coumn, 5 figures. See http://www.iitaka.org/down.html for more informatio