A finite-temperature liquid-quasicrystal transition in a lattice model

We consider a tiling model of the two-dimensional square-lattice, where each site is tiled with one of the sixteen Wang tiles. The ground states of this model are all quasi-periodic. The systems undergoes a disorder to quasi-periodicity phase transition at finite temperature. Introducing a proper order-parameter, we study the system at criticality, and extract the critical exponents characterizing the transition. The exponents obtained are consistent with hyper-scaling

Polarization of interacting bosons with spin

We demonstrate rigorously that in the absence of explicit spin-dependent forces one of the ground states of interacting bosons with spin is always fully polarized -- however complicated the many-body interaction potential might be. Depending on the particle spin, the polarized ground state will generally be degenerate with other states, but one can specify the exact degeneracy. For T>0 the magnetization and susceptibility necessarily exceed that of a pure paramagnet. These results are relevant to recent experiments exploring the relation between triplet superconductivity and ferromagnetism, and the Bose-Einstein condensation of atoms with spin. They eliminate the possibility, raised in some theoretical speculations, that the ground state or positive temperature state might be antiferromagnetic.Comment: v4: as published in PR

Can HERA See an eu−−>ece u --> e c Signal of a Virtual Leptoquark?

Virtual leptoquarks could be detected at HERA through some nonstandard effects. Here we explore the possibility that virtual leptoquarks could be discovered via $e u --> e c$ scattering, assuming integrated luminosity of 200 pb$^{-1}$ and charm identification efficiency of 1%. We study the implications of low energy data for the leptoquarks couplings and find that the most relevant bound for the HERA cross sections comes from inclusive $c --> e^+e^-~+~any$. This bound implies that the $e u --> e c$ cross sections for virtual leptoquarks are just too small for observation of the signal. With an improvement by a factor of ~2 on the luminosity or on charm identification it could be possible to see virtual leptoquarks with {\it maximum couplings} up to ~1.5 - 2 TeV. However, the prospects for discovering the virtual particles if their couplings are somewhat below present bounds are very dim. We point out that this cross section could be very large for leptoquarks lighter than HERA's kinematical limit, and if such a leptoquark is discovered we recommend searching for a possible $e u --> e c$ signal. Our results may also serve as an update on the maximum cross sections for leptoquark mediated $e u --> \mu c$ scattering.Comment: 15 Pages (LaTeX), including 4 postscript figures at the end of the file. Feynman diagrams available by reques

A simple physical model for scaling in protein-protein interaction networks

It has recently been demonstrated that many biological networks exhibit a scale-free topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has been reproduced by evolutionary models. Here we consider the network of protein-protein interactions and demonstrate that two published independent measurements of these interactions produce graphs that are only weakly correlated with one another despite their strikingly similar topology. We then propose a physical model based on the fundamental principle that (de)solvation is a major physical factor in protein-protein interactions. This model reproduces not only the scale-free nature of such graphs but also a number of higher-order correlations in these networks. A key support of the model is provided by the discovery of a significant correlation between number of interactions made by a protein and the fraction of hydrophobic residues on its surface. The model presented in this paper represents the first physical model for experimentally determined protein-protein interactions that comprehensively reproduces the topological features of interaction networks. These results have profound implications for understanding not only protein-protein interactions but also other types of scale-free networks.Comment: 50 pages, 17 figure

The breakdown of the Nagaoka phase in the 2D t-J model

In the limit of weak exchange, J, at low hole concentration, the ground state of the 2D t-J model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, Nagaoka's state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on the hole concentration and scales as a power of the system size, N

Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum

In single Hilbert space, Pauli's well-known theorem implies that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian signifies that the time operator and the Hamiltonian possess completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate to a semibounded or discrete Hamiltonian despite some well-known illustrative counterexamples. In this paper we evaluate Pauli's theorem against the single Hilbert space formulation of quantum mechanics, and consequently show the consistency of assuming a bounded, self-adjoint time operator canonically conjugate to a Hamiltonian with an unbounded, or semibounded, or finite point spectrum. We point out Pauli's implicit assumptions and show that they are not consistent in a single Hilbert space. We demonstrate our analysis by giving two explicit examples. Moreover, we clarify issues sorrounding the different solutions to the canonical commutation relations, and, consequently, expand the class of acceptable canonical pairs beyond the solutions required by Pauli's theorem.Comment: contains corrections to minor typographical errors of the published versio

Phase diagram for a Cubic Consistent-Q Interacting Boson Model Hamiltonian: signs of triaxiality

An extension of the Consistent-Q formalism for the Interacting Boson Model that includes the cubic QxQxQ term is proposed. The potential energy surface for the cubic quadrupole interaction is explicitly calculated within the coherent state formalism using the complete chi-dependent expression for the quadrupole operator. The Q-cubic term is found to depend on the asymmetry deformation parameter gamma as a linear combination of cos(3gamma) and cos^2(3\gamma) terms, thereby allowing for triaxiality. The phase diagram of the model in the large N limit is explored, it is described the order of the phase transition surfaces that define the phase diagram, and moreover, the possible nuclear equilibrium shapes are established. It is found that, contrary to expectations, there is only a very tiny region of triaxiality in the model, and that the transition from prolate to oblate shapes is so fast that, in most cases, the onset of triaxiality might go unnoticed.Comment: 18 pages, 19 figure

Glass Transition in a 2D Lattice Model

The dynamics of compaction of hard cross-shaped pentamers on the 2D square lattice is investigated. The addition of new particles is controlled by diffusive relaxation. It is shown that the filling process terminates at a glassy phase with a limiting coverage density \rho_{rcp}=0.171626(3), lower than the density of closest packing \rho_{cp}=0.2, and the long time filling rate vanishes like (\rho_{rcp}-\rho(t))^2. For the entire density regime the particles form an amorphous phase, devoid of any crystalline order. Therefore, the model supports a stable random packing state, as opposed to the hard disks system. Our results may be relevant to recent experiments studying the clustering of proteins on bilayer lipid membranes