Island formation without attractive interactions

We show that adsorbates on surfaces can form islands even if there are no attractive interactions. Instead strong repulsion between adsorbates at short distances can lead to islands, because such islands increase the entropy of the adsorbates that are not part of the islands. We suggest that this mechanism cause the observed island formation in O/Pt(111), but it may be important for many other systems as well.Comment: 11 pages, 4 figure

Cross-Composition: A New Technique for Kernelization Lower Bounds

We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the logical OR of a sequence of instances of L. Building on work by Bodlaender et al. (ICALP 2008) and using a result by Fortnow and Santhanam (STOC 2008) we show that if an NP-complete problem cross-composes into a parameterized problem Q then Q does not admit a polynomial kernel unless the polynomial hierarchy collapses. Our technique generalizes and strengthens the recent techniques of using OR-composition algorithms and of transferring the lower bounds via polynomial parameter transformations. We show its applicability by proving kernelization lower bounds for a number of important graphs problems with structural (non-standard) parameterizations, e.g., Chromatic Number, Clique, and Weighted Feedback Vertex Set do not admit polynomial kernels with respect to the vertex cover number of the input graphs unless the polynomial hierarchy collapses, contrasting the fact that these problems are trivially fixed-parameter tractable for this parameter. We have similar lower bounds for Feedback Vertex Set.Comment: Updated information based on final version submitted to STACS 201

Kernelization Lower Bounds By Cross-Composition

We introduce the cross-composition framework for proving kernelization lower bounds. A classical problem L AND/OR-cross-composes into a parameterized problem Q if it is possible to efficiently construct an instance of Q with polynomially bounded parameter value that expresses the logical AND or OR of a sequence of instances of L. Building on work by Bodlaender et al. (ICALP 2008) and using a result by Fortnow and Santhanam (STOC 2008) with a refinement by Dell and van Melkebeek (STOC 2010), we show that if an NP-hard problem OR-cross-composes into a parameterized problem Q then Q does not admit a polynomial kernel unless NP \subseteq coNP/poly and the polynomial hierarchy collapses. Similarly, an AND-cross-composition for Q rules out polynomial kernels for Q under Bodlaender et al.'s AND-distillation conjecture. Our technique generalizes and strengthens the recent techniques of using composition algorithms and of transferring the lower bounds via polynomial parameter transformations. We show its applicability by proving kernelization lower bounds for a number of important graphs problems with structural (non-standard) parameterizations, e.g., Clique, Chromatic Number, Weighted Feedback Vertex Set, and Weighted Odd Cycle Transversal do not admit polynomial kernels with respect to the vertex cover number of the input graphs unless the polynomial hierarchy collapses, contrasting the fact that these problems are trivially fixed-parameter tractable for this parameter. After learning of our results, several teams of authors have successfully applied the cross-composition framework to different parameterized problems. For completeness, our presentation of the framework includes several extensions based on this follow-up work. For example, we show how a relaxed version of OR-cross-compositions may be used to give lower bounds on the degree of the polynomial in the kernel size.Comment: A preliminary version appeared in the proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) under the title "Cross-Composition: A New Technique for Kernelization Lower Bounds". Several results have been strengthened compared to the preliminary version (http://arxiv.org/abs/1011.4224). 29 pages, 2 figure

Finite-Size Scaling of Vector and Axial Current Correlators

Using quenched chiral perturbation theory, we compute the long-distance behaviour of two-point functions of flavour non-singlet axial and vector currents in a finite volume, for small quark masses, and at a fixed gauge-field topology. We also present the corresponding predictions for the unquenched theory at fixed topology. These results can in principle be used to measure the low-energy constants of the chiral Lagrangian, from lattice simulations in volumes much smaller than one pion Compton wavelength. We show that quenching has a dramatic effect on the vector correlator, which is argued to vanish to all orders, while the axial correlator appears to be a robust observable only moderately sensitive to quenching.Comment: version to appear in NP

Large rescaling of the Higgs condensate: theoretical motivations and lattice results

In the Standard Model the Fermi constant is associated with the vacuum expectation value of the Higgs field, `the condensate', usually believed to be a cutoff-independent quantity. General arguments related to the `triviality' of $\Phi^4$ theory in 4 space-time dimensions suggest, however, a dramatic renormalization effect in the continuum limit that is clearly visible on the relatively large lattices available today. The result can be crucial for the Higgs phenomenology and in any context where spontaneous symmetry breaking is induced through scalar fields.Comment: LATTICE99(Higgs) 3 pages, 3 figure

Indications on the Higgs boson mass from lattice simulations

The `triviality' of $\Phi^4_4$ has been traditionally interpreted within perturbation theory where the prediction for the Higgs boson mass depends on the magnitude of the ultraviolet cutoff $\Lambda$. This approach crucially assumes that the vacuum field and its quantum fluctuations rescale in the same way. The results of the present lattice simulation, confirming previous numerical indications, show that this assumption is not true. As a consequence, large values of the Higgs mass $m_H$ can coexist with the limit $\Lambda\to \infty$. As an example, by extrapolating to the Standard Model our results obtained in the Ising limit of the one-component theory, one can obtain a value as large as $m_H=760 \pm 21$ GeV, independently of $\Lambda$.Comment: 3 pages, 2 figures, Lattice2003(higgs

Non-equilibrium thermodynamics and liquid helium II

The thermodynamics of irreversible processes, based on the O n s a g e r reciprocal relations, is applied to a system consisting of a mixture of two substances, of which one can go over into the other. The mixture is enclosed in two communicating reservoirs at different temperatures T and T + ΔT. The situations, in which systems arrive, when one, two or more differences between the values of state parameters in the two reservoirs are kept fixed, are called “stationary states of first, second etc. order”. For the stationary state of the first order with fixed ?T the corresponding pressure difference ?P is calculated. This gives the thermomolecular pressure effect ΔP/ΔT = —Q*/v T = (h — U*)/v T, where h and v. are the mean specific enthalpy and volume. This equation shows the connection with the mechano-caloric effect Q*, since application of the O n s a g e r relations shows that Q* is the “heat of transfer” i.e. the heat supplied per unit of time from the surroundings to the reservoir at temperature T, when one unit of mass is transferred from one reservoir to the other in the stationary state of the second order with fixed ΔP and ΔT = 0 (uniform temperature). Similarly U* is the “energy of transfer”. The influence of ΔT on the relative separation (thermal effusion) and the “chemical affinity” of the two components is also calculated. The heat conduction can be split into an “abnormal” part due to the coupling of diffusion and chemical reaction between the components and a “normal” part also present when no reaction takes place. The results can be applied to liquid helium II, considered in the two-fluid theory as a mixture of “normal” (1) and “superfluid” (2) atoms, capable of the “chemical reaction” 1 ⇔ 2. When it is supposed that chemical equilibrium is immediately established and that only superfluid atoms can pass through a sufficiently narrow capillary, the above mentioned equation leads . to G o r t e r's formula v ΔP/ΔT = χ1 ∂s/∂χ1, where χ1 is the fraction of normal atoms and s the mean specific entropy of the mixture. Under the same circumstances only the “normal” part of the heat conduction subsists