Applications of Jarzynski's relation in lattice gauge theories

Jarzynski's equality is a well-known result in statistical mechanics, relating free-energy differences between equilibrium ensembles with fluctuations in the work performed during non-equilibrium transformations from one ensemble to the other. In this work, an extension of this relation to lattice gauge theory will be presented, along with numerical results for the $\mathbb{Z}_2$ gauge model in three dimensions and for the equation of state in $\mathrm{SU}(2)$ Yang-Mills theory in four dimensions. Then, further applications will be discussed, in particular for the Schr\"odinger functional and for the study of QCD in strong magnetic fields.Comment: 7 pages, 2 figures, presented at the 34th International Symposium on Lattice Field Theory (Lattice 2016), 24-30 July 2016, Southampton, U

Jarzynski’s theorem for lattice gauge theory

Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.Comment: 1+29 pages, 2 pdf figures1+29 pages, 2 pdf figures; v2: 1+34 pages, 2 pdf figures: presentation of the theorem proof in section 2 improved with additional details, discussion in sections 3 and 4 expanded, misprints corrected; matches the journal versio

Critical dynamics in trapped particle systems

We discuss the effects of a trapping space-dependent potential on the critical dynamics of lattice gas models. Scaling arguments provide a dynamic trap-size scaling framework to describe how critical dynamics develops in the large trap-size limit. We present numerical results for the relaxational dynamics of a two-dimensional lattice gas (Ising) model in the presence of a harmonic trap, which support the dynamic trap-size scaling scenario.Comment: 7 page

Experimental and Numerical Study of the Effect of Surface Patterning on the Frictional Properties of Polymer Surfaces

We describe benchmark experiments to evaluate the frictional properties of laser patterned low-density polyethylene as a function of sliding velocity, normal force and humidity. The pattern is a square lattice of square cavities with sub-mm spacing. We find that dynamic friction decreases compared to non-patterned surfaces, since stress concentrations lead to anticipated detachment, and that stick-slip behavior is also affected. Friction increases with humidity, and the onset of stick-slip events occurs in the high humidity regime. Experimental results are compared with numerical simulations of a simplified 2-D spring-block model. A good qualitative agreement can be obtained by introducing a deviation from the linear behavior of the Amontons-Coulomb law with the load, due to a saturation in the effective contact area with pressure. This also leads also to the improvement of the quantitative results of the spring-block model by reducing the discrepancy with the experimental results, indicating the robustness of the adopted simplified approach, which could be adopted to design patterned surfaces with controlled friction properties

Tuning friction with composite hierarchical surfaces

N.M.P. is supported by the European Research Council PoC 2015 “Silkene” No. 693670, by the European Commission H2020 under the Graphene Flagship Core 1 No. 696656 (WP14 “Polymer Nanocomposites”) and FET Proactive “Neurofibres” grant No. 732344. G.C. and F.B. are supported by H2020 FET Proactive “Neurofibres” grant No. 732344

Static and dynamic friction of hierarchical surfaces

N.M.P. was supported by the European Research Council (ERC StG Ideas BIHSNAM Grant No. 279985 and ERC PoC SILKENE Grant No. 693670) and by the European Commission under the Graphene Flagship (WP14 “Polymer nanocomposites”, Grant No. 696656). G.C. and F.B. were supported by BIHSNAM