Search

Within the coexistence region between liquid and vapor the equilibrium pressure of a simulated fluid exhibits characteristic jumps and plateaus when plotted as a function of density at constant temperature. These features exclusively pertain to a finite-size sample in a periodic box, as they are washed out in the bulk limit. Below the critical density, at each pressure jump the shape of the liquid drop undergoes a morphological transition, changing from spherical to cylindrical to slab-like as the density is increased. We formulate a simple theory of these shape transitions, which is adapted from a calculation originally developed by Binder and coworkers [{\em J. Chem. Phys.} {\bf 120}, 5293 (2004)]. Our focus is on the pressure equation of state (rather than on the chemical potential, as in the original work) and includes an extension to elongated boxes. Predictions based on this theory well agree with extensive Monte Carlo data for the cut-and-shifted Lennard-Jones fluid. We further discuss on the thermodynamic stability of liquid drops with shapes other than the three mentioned above, like those found deep inside the liquid-vapor region in simulations starting from scratch. Our theory classifies these more elaborate shapes as metastable., Comment: 14 pages, 8 figures

Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10\% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid., Comment: 17 pages, 12 figures

We look for minimal chiral sets of fermions beyond the standard model that are anomaly free and, simultaneously, vectorlike particles with respect to colour SU(3) and electromagnetic U(1). We then study whether the addition of such particles to the standard model particle content allows for the unification of gauge couplings at a high energy scale, above $5.0 \times 10^{15}$ GeV so as to be safely consistent with proton decay bounds. The possibility to have unification at the string scale is also considered. Inspired in grand unified theories, we also search for minimal chiral fermion sets that belong to SU(5) multiplets. Restricting to representations up to dimension 50, we show that some of these sets can lead to gauge unification at the GUT and/or string scales., Comment: 13 pages, 5 figures, 8 tables; Comments and references added, final version to appear in Phys. Rev. D

We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the energy regimes is made. The linear stability of fixed points is studied, yielding exact analytical expressions for parameter values at which a period-doubling bifurcation occurs. The dynamics is apparently ergodic at certain energies in all three models, in contrast to the regularity of the circular and elliptic billiard dynamics in the field-free case. This finding is confirmed using a sensitive test involving Lyapunov weighted dynamics. In the last part of the paper a time dependence is introduced in the billiard boundary, where it is shown that for the circular billiard the average velocity saturates for zero gravitational force but in the presence of gravitational it increases with a very slow growth rate, which may be explained using Arnold diffusion. For the oval billiard, where chaos is present in the static case, the particle has an unlimited velocity growth with an exponent of approximately 1/6.

An extension of the adjoint SU(5) model with a flavour symmetry based on the Z_4 group is investigated. The Z_4 symmetry is introduced with the aim of leading the up- and down-quark mass matrices to the Nearest-Neighbour-Interaction form. As a consequence of the discrete symmetry embedded in the SU(5) gauge group, the charged lepton mass matrix also gets the same form. Within this model, light neutrinos get their masses through type-I, type-III and one-loop radiative seesaw mechanisms, implemented, respectively, via a singlet, a triplet and an octet from the adjoint fermionic 24 fields. It is demonstrated that the neutrino phenomenology forces the introduction of at least three 24 fermionic multiplets. The symmetry SU(5)xZ_4 allows only two viable zero textures for the effective neutrino mass matrix. It is showed that one texture is only compatible with normal hierarchy and the other with inverted hierarchy in the light neutrino mass spectrum. Finally, it is also demonstrated that Z_4 freezes out the possibility of proton decay through exchange of colour Higgs triplets at tree-level., Comment: 25 pages, 4 figures, 3 tables

The scattering of a Gaussian wavepacket in armchair and zigzag graphene edges is theoretically investigated by numerically solving the time dependent Schr\"odinger equation for the tight-binding model Hamiltonian. Our theory allows to investigate scattering in reciprocal space, and depending on the type of graphene edge we observe scattering within the same valley, or between different valleys. In the presence of an external magnetic field, the well know skipping orbits are observed. However, our results demonstrate that in the case of a pseudo-magnetic field, induced by non-uniform strain, the scattering by an armchair edge results in a non-propagating edge state., Comment: 8 pages, 7 figures

A flavour symmetry based on Z_4 is analysed in the context of SU(5) Grand Unification with the standard fermionic content plus three right-handed neutrinos. The role of Z_4 is to forbid some Yukawa couplings of up- and down-quarks to Higgs scalars such that the quark mass matrices M_u, M_d have Nearest-Neighbour-Interaction (NNI) structure, once they are generated through the electroweak symmetry breaking. It turns out in this framework that Z_4 is indeed the minimal discrete symmetry and its implementation requires the introduction of at least two Higgs quintets, which leads to a two Higgs doublet model at low energy scale. Due to the SU(5) unification, it is shown that the charged lepton mass matrix develops also NNI form. However, the effective neutrino mass matrix exhibits a non parallel pattern, in the framework of the type-I seesaw mechanism. Analysing all possible zero textures allowed by gauge-horizontal symmetry SU(5) x Z_4, it is seen that only two patterns are in agreement with the leptonic experimental data and they could be further distinguished by the light neutrino mass spectrum hierarchy. It is also demonstrated that Z_4 freezes out the possibility of proton decay through exchange of colour Higgs triplets at tree-level., Comment: 14 pages, 5 figures, 4 tables, two columns; revised version

We show that Nearest-Neighbour Interaction (NNI) textures for the quark mass matrices can be obtained through the introduction of an Abelian flavour symmetry. The minimal realisation requires a Z_4 symmetry in the context of a two Higgs doublet model. It is further shown that the NNI textures can be in agreement with all present experimental data on quark masses and mixings, provided one allows for deviations of Hermiticity in the quark mass matrices at the 20% level., Comment: 11 pages, 1 figure; references and minor corrections added

All quark mass matrices with texture zeroes obtained through weak basis transformations are confronted with the experimental data. The reconstruction of the quark mass matrices M_u and M_d at the electroweak scale is performed in a weak basis where the matrices are Hermitian and have a maximum of three vanishing elements. The same procedure is also accomplished for the Yukawa coupling matrices at the grand unification scale in the context of the Standard Model and its minimal supersymmetric extension as well as of the two Higgs doublet model. The analysis of all viable power structures on the quark Yukawa coupling matrices that could naturally appear from a Froggatt-Nielsen mechanism is also presented., Comment: RevTeX4, 3 tables, 21 pages; misprints corrected and one reference added

The implementation of seesaw mechanisms to give mass to neutrinos in the presence of an anomaly-free U(1)_X gauge symmetry is discussed in the context of minimal extensions of the standard model. It is shown that type-I and type-III seesaw mechanisms cannot be simultaneously implemented with an anomaly-free local U(1)_X, unless the symmetry is a replica of the well-known hypercharge. For combined type-I/II or type-III/II seesaw models it is always possible to find nontrivial anomaly-free charge assignments, which are however tightly constrained, if the new neutral gauge boson is kinematically accessible at LHC. The discovery of the latter and the measurement of its decays into third-generation quarks, as well as its mixing with the standard Z boson, would allow one to discriminate among different seesaw realizations., Comment: 5 pages, 3 figures; final version to appear in Phys. Rev. D

Thermodynamic and structural properties of the tangent diatomic fluid are studied in the framework provided by the Reference Interaction Site Model (RISM) theory, coupled with a Modified Hypernetted Chain closure. The enforcement of the internal thermodynamic consistency of the theory is described in detail. The results we obtain almost quantitatively agree with available or newly generated simulation data. We envisage the possibility to extend the consistent RISM formalism to generic, more realistic molecular fluids., Comment: Typeset with LaTeX, 6 pages, 3 figures (5 subfigures), 28 references, submitted to Chem. Phys. Lett