Searcharxiv⌕ Search

arXiv subjects

S. Thurner

Publications and source records attributed to S. Thurner.

18 recordsLinked to original sources
arXiv2021

Energy distribution of inelastic gas in a box is dominated by a power law -- a derivation in the framework of sample space reducing processes

We use the framework of sample space reducing processes (SSR) as an alternative to Boltzmann equation based approaches, to derive the energy and velocity distribution functions of an inelastic gas in a box as an example for a dissipative, driven system. SSR processes do not assume molecular chaos and are characterized by a specific type of eigenvalue equation whose solutions represent stationary distribution functions. The equations incorporate the geometry of inelastic collisions and a driving mechanism in a transparent way. Energy is injected by boosting particles that hit the walls of the container to high energies. The numerical solution of the resulting equations yields power laws over the entire energy region. The exponents decrease with the driving rate from about $2$ to below $1.5$ and depend on the coefficient of restitution. Results are confirmed with a molecular dynamics simulation in 3D with the same driving mechanism. We believe that these distribution functions are observable in experimental situations; the abundance of power laws in driven dissipative systems might be a sign of the generality of the result.

cond-mat.stat-mech↗
arXiv2000

Scaling-violation phenomena and fractality in the human posture control systems

By analyzing the movements of quiet standing persons by means of wavelet statistics, we observe multiple scaling regions in the underlying body dynamics. The use of the wavelet-variance function opens the possibility to relate scaling violations to different modes of posture control. We show that scaling behavior becomes close to perfect, when correctional movements are dominated by the vestibular system.

physics.bio-ph↗
arXiv1999

Distribution of fermionic and topological observables on the lattice

We analyze the topological and fermionic vacuum structure of four-dimensional QCD on the lattice by means of correlators of fermionic observables and topological densities. We show the existence of strong local correlations between the topological charge and monopole density on the one side and the quark condensate, charge and chiral density on the other side. Visualization of individual gauge configurations demonstrates that instantons (antiinstantons) carry positive (negative) chirality, whereas the quark charge density fluctuates in sign within instantons.

hep-lat↗
arXiv1999

Field Strength Correlators and Gluon Condensates at Finite Temperature from Renormalization Group Smoothing

We summarize recent attempts to extract characteristics of non-perturbative vacuum structure from lattice measurements of the gauge invariant field strength correlator. As an alternative to cooling, we propose to apply the renormalization group (RG) smoothing method in lattice studies. For pure SU(2) gauge theory we present magnetic and electric correlation lengths and condensates related to various correlators over a temperature range of 0.7 T_{dec} < T < 1.9 T_{dec}

hep-lat↗
arXiv1999

Monopole characteristics in various Abelian gauges

Renormalization group (RG) smoothing is employed on the lattice to investigate and to compare the monopole structure of the SU(2) vacuum as seen in different gauges (maximally Abelian (MAG), Polyakov loop (PG) and Laplacian gauge (LG)). Physically relevant types of monopoles (LG and MAG) are distinguished by their behavior near the deconfining phase transition. For the LG, Abelian projection reproduces well the gauge independent monopole structure encoded in an auxiliary Higgs field. Density and localization properties of monopoles, their non-Abelian action and topological charge are studied. Results are presented confirming the Abelian dominance with respect to the non-perturbative static potential for all gauges considered.

hep-lat↗
arXiv1998

Correlated Instanton Orientations in the SU(2) Yang-Mills Vacuum and Pair Formation in the Deconfined Phase

Using the renormalization group motivated smoothing technique we study the semiclassical structure of the pure Yang-Mills vacuum. We carefully check that identified clusters of topological charge behave like instantons around their centers. Looking at distance distributions of clusters we find instanton-antiinstanton pair formation in the deconfined phase. We use suitably normalized gauge invariant field strength correlators to obtain first quantitative information on the relative color orientation of instantons. We give further evidence for a modified instanton profile in the confined phase and present a simple alternative model for it.

hep-lat↗
arXiv1998

Gauge invariant properties of Abelian monopoles

Using a renormalization group motivated smoothing technique, we investigate the large scale structure of lattice configurations at finite temperature, concentrating on Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Monopoles are mostly found in regions of large action and topological charge, rather independent of the gauge chosen to detect them. Gauge invariant properties around Abelian monopoles, the local non-Abelian action and topological density, are studied. We show that the local averages of these densities along the monopole trajectories are clearly above the background, which supports the existence of monopoles as physical objects. Characteristic changes of the vacuum structure at the deconfinement transition can be attributed to the corresponding Abelian monopoles, to an extent that depends on the gauge chosen for Abelian projection. All three Abelian projections reproduce the full SU(2) string tension within 10 percent which is preserved by smoothing.

hep-lat↗
arXiv1998

Abelian monopoles in finite temperature lattice gauge fields: Classically perfect action, smoothing and various Abelian gauges

Using the renormalization group motivated smoothing technique, the large scale structure of lattice configurations at finite temperature is characterized in terms of Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Abundance and anisotropy of monopoles at deconfinement and gauge invariant properties like local non-Abelian action and topological density are studied. Monopoles are predominantly found in regions of large action and topological charge, rather independent of the chosen gauge.

hep-lat↗
arXiv1998

Action and topological density carried by Abelian monopoles in finite temperature pure SU(2) gauge theory: an analysis using RG smoothing

We test a new parametrization of a suitably truncated classically perfect action for SU(2) pure gauge theory with respect to self-consistency and locate the deconfinement transition on a 12^3X4 lattice. Using the technique of smoothing (blocking followed by inverse blocking) we demonstrate clustering of action and topological charge density. Concentrating on the Abelian monopoles found in smoothed configurations after Abelian projection from the maximally Abelian gauge, we present evidence for their role as carriers of non-Abelian action and topological charge.

hep-lat↗
arXiv1998

Towards a Topological Mechanism of Quark Confinement

We report on new analyses of the topological and chiral vacuum structure of four-dimensional QCD on the lattice. Correlation functions as well as visualization of monopole currents in the maximally Abelian gauge emphasize their topological origin and gauge invariant characterization. The (anti)selfdual character of strong vacuum fluctuations is reveiled by smoothing. In full QCD, (anti)instanton positions are also centers of the local chiral condensate and quark charge density. Most results turn out generically independent of the action and the cooling/smoothing method.

hep-lat↗
arXiv1997

Topology at the Deconfinement Transition Uncovered by Inverse Blocking in SU(2) Pure Gauge Theory with Fixed Point Action

Renormalization group transformations as discussed recently in deriving fixed point actions are used to analyse the vacuum structure near to the deconfinement temperature. Monte Carlo configurations are generated using the fixed point action. We compare equilibrium configurations with configurations obtained by inverse blocking from a coarser lattice. The absence of short range vacuum fluctuations in the latter does not influence the string tension. For the inversely blocked configurations we find the following: (i) the topological susceptibility chi_top is consistent with the phenomenological value in the confinement phase, (ii) chi_top drops across the deconfinement transition, (iii) density and size of instantons are estimated, (iv) the topological density is found to be correlated to Abelian monopole currents and (v) the density of spacelike monopole currents becomes a confinement order parameter.

hep-lat↗
arXiv1997

Topology without cooling: instantons and monopoles near to deconfinement

In an attempt to describe the change of topological structure of pure SU(2) gauge theory near deconfinement a renormalization group inspired method is tested. Instead of cooling, blocking and subsequent inverse blocking is applied to Monte Carlo configurations to capture topological features at a well-defined scale. We check that this procedure largely conserves long range physics like string tension. UV fluctuations and lattice artefacts are removed which otherwise spoil topological charge density and Abelian monopole currents. We report the behaviour of topological susceptibility and monopole current densities across the deconfinement transition and relate the two faces of topology to each other. First results of a cluster analysis are described.

hep-lat↗
arXiv1997

Coexistence of monopoles and instantons for different topological charge definitions and lattice actions

We compute instanton sizes and study correlation functions between instantons and monopoles in maximum abelian projection within SU(2) lattice QCD at finite temperature. We compare several definitions of the topological charge, different lattice actions and methods of reducing quantum fluctuations. The average instanton size turns out to be $σ\approx 0.2$ fm. The correlation length between monopoles and instantons is $ζ\approx 0.25$ fm and hardly affected by lattice artifacts as dislocations. We visualize several specific gauge field configurations and show directly that there is an enhanced probability for finding monopole loops in the vicinity of instantons. This feature is independent of the topological charge definition used.

hep-lat↗
arXiv1997

Instantons and monopoles in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons in both pure and full QCD. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This feature is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover we investigate how monopole loops and instantons are correlated with the chiral condensate. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.

hep-lat↗
arXiv1996

Relations Between Monopoles, Instantons and Chiral Condensate

We analyze the interplay of topological objects in four dimensional QCD. The distributions of color magnetic monopoles obtained in the maximum abelian gauge are computed around instantons in both pure and full QCD. We find an enhanced probability of encountering monopoles inside the core of an instanton on gauge field average. For specific gauge field configurations we visualize the situation graphically. Moreover we investigate how monopole loops and instantons are locally correlated with the chiral condensate.

hep-lat↗
arXiv1995

Correlation functions between monopoles and instantons

We analyze the relation between instantons and abelian projected monopoles in both phases of pure QCD by calculating local correlation functions between topological charge densities and monopole densities. On an $8^{3} \times 4$ lattice, it turns out that topological quantities are correlated approximately two lattice spacings. The monopole-instanton correlations are rather insensitive under cooling of gauge fields.

hep-lat↗
arXiv1994

Monopole density around static color sources

We analyze the vacuum structure with respect to magnetic monopoles of quenched QCD in the presence of static color sources. Distributions of the monopole density around static quarks and mesons are computed in both phases of QCD. We observe a suppression of the monopole density in the vicinity of external sources. In the confinement phase the density of color magnetic monopoles is reduced along the flux tube between a static quark-antiquark pair.

hep-lat↗