Effect of geometric and electronic structures on the finite temperature behavior of Na58_{58}, Na57_{57}, and Na55_{55} clusters

An analysis of the evolutionary trends in the ground state geometries of Na$_{55}$ to Na$_{62}$ reveals Na$_{58}$, an electronic closed--shell system, shows namely an electronically driven spherical shape leading to a disordered but compact structure. This structural change induces a strong {\it connectivity} of short bonds among the surface atoms as well as between core and surface atoms with inhomogeneous strength in the ground state geometry, which affects its finite--temperature behavior. By employing {\it ab initio} density--functional molecular dynamics, we show that this leads to two distinct features in specific heat curve compared to that of Na$_{55}$: (1) The peak is shifted by about 100 K higher in temperature. (2) The transition region becomes much broader than Na$_{55}$. The inhomogeneous distribution of bond strengths results in a broad melting transition and the strongly connected network of short bonds leads to the highest melting temperature of 375 K reported among the sodium clusters. Na$_{57}$, which has one electron less than Na$_{58}$, also possesses stronger short--bond network compared with Na$_{55}$, resulting in higher melting temperature (350 K) than observed in Na$_{55}$. Thus, we conclude that when a cluster has nearly closed shell structure not only geometrically but also electronically, it show a high melting temperature. Our calculations clearly bring out the size--sensitive nature of the specific heat curve in sodium clusters.Comment: 7 pages, 11 figure

First principles investigation of finite-temperature behavior in small sodium clusters

A systematic and detailed investigation of the finite-temperature behavior of small sodium clusters, Na_n, in the size range of n= 8 to 50 are carried out. The simulations are performed using density-functional molecular-dynamics with ultrasoft pseudopotentials. A number of thermodynamic indicators such as specific heat, caloric curve, root-mean-square bond length fluctuation, deviation energy, etc. are calculated for each of the clusters. Size dependence of these indicators reveals several interesting features. The smallest clusters with n= 8 and 10, do not show any signature of melting transition. With the increase in size, broad peak in the specific heat is developed, which alternately for larger clusters evolves into a sharper one, indicating a solidlike to liquidlike transition. The melting temperatures show irregular pattern similar to experimentally observed one for larger clusters [ M. Schmidt et al., Nature (London) 393, 238 (1998) ]. The present calculations also reveal a remarkable size-sensitive effect in the size range of n= 40 to 55. While Na_40 and Na_55 show well developed peaks in the specific heat curve, Na_50 cluster exhibits a rather broad peak, indicating a poorly-defined melting transition. Such a feature has been experimentally observed for gallium and aluminum clusters [ G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); G. A.Breaux et al., Phys. Rev. Lett. 94, 173401 (2005) ].Comment: 8 pages, 11 figure

SU(2) x U(1) Yang-Mills theories in 3d with Higgs field and Gribov ambiguity

We study the structure of the gauge propagators of a 3d version of the electroweak interaction in terms of the Higgs vacuum expectation value., of the non-Abelian gauge coupling g, and of the Abelian gauge coupling g', when nonperturbative effects related to the non-Abelian gauge fixing are introduced by means of an adapted path integral measure. In the perturbative regime of small nonAbelian coupling g and sufficiently large, nu the well-known standard Z and W propagators are recovered, together with a massless photon. In general, depending on the relative magnitudes of g, g' and., we uncover a quite different propagator structure. In a later stage of research, the results here derived can be used to study the associated phase diagram in more depth

Nonperturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges : Nielsen identities and a BRST-invariant two-point correlation function

In order to construct a gauge-invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge-invariant transverse configurations A(h). Such configurations can be obtained through the minimization of the functional A(min)(2) along the gauge orbit within the BRST-invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative aspects of the theory in a BRST-invariant and gauge-parameter-independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter alpha entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST-invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST-invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use to probe the pole structure of the massive gauge boson in a gauge-invariant fashion

Geometric, electronic properties and the thermodynamics of pure and Al--doped Li clusters

The first--principles density functional molecular dynamics simulations have been carried out to investigate the geometric, the electronic, and the finite temperature properties of pure Li clusters (Li$_{10}$, Li$_{12}$) and Al--doped Li clusters (Li$_{10}$Al, Li$_{10}$Al$_2$). We find that addition of two Al impurities in Li$_{10}$ results in a substantial structural change, while the addition of one Al impurity causes a rearrangement of atoms. Introduction of Al--impurities in Li$_{10}$ establishes a polar bond between Li and nearby Al atom(s), leading to a multicentered bonding, which weakens the Li--Li metallic bonds in the system. These weakened Li--Li bonds lead to a premelting feature to occur at lower temperatures in Al--doped clusters. In Li$_{10}$Al$_2$, Al atoms also form a weak covalent bond, resulting into their dimer like behavior. This causes Al atoms not to `melt' till 800 K, in contrast to the Li atoms which show a complete diffusive behavior above 400 K. Thus, although one Al impurity in Li$_{10}$ cluster does not change its melting characteristics significantly, two impurities results in `surface melting' of Li atoms whose motions are confined around Al dimer.Comment: 9 pages, 7 figure

Triumph Over Tragedy: Living in Recovery

https://digitalcommons.pcom.edu/bridging_gaps2015/1002/thumbnail.jp

Semiclassical analysis of the phases of 4d SU(2) Higgs gauge systems with cutoff at the Gribov horizon

We present an analytical study of continuum 4d SU(2) gauge-Higgs models with a single Higgs field with fixed length in either the fundamental or adjoint representation. We aim at analytically probing the renowned predictions of Fradkin and Shenker on the phase diagram in terms of confinement versus Higgs behavior, obtained for the lattice version of the model. We work in the Landau version of the ' t Hooft R xi gauges in which case we can access potential nonperturbative physics related to the existence of the Gribov copies. In the fundamental case, we clearly show that in the perturbative regime of small gauge coupling constant g and large Higgs vacuum expectation value (vev) nu, there is a Higgs phase with Yukawa gauge boson propagators without Gribov effects. For a small value of the Higgs vev nu and/or large g, we enter a region with Gribov-type propagators that have no physical particle interpretation: the gauge bosons are as such confined. The transition between both behaviors is found to be continuous. In the adjoint case, we find evidence of a more drastic transition between the different behaviors for the propagator of the off- diagonal gauge bosons, whereas the "photon,'' i.e. the diagonal component of the gauge field, displays a propagator of the Gribov-type. In the limit of infinite Higgs condensate, we show that a massless photon is recovered. We compare our findings with those of Fradkin and Shenker as well as with more recent numerical lattice simulations of the fundamental Higgs model. We also carefully discuss in which region of the parameter space (nu, g) our approximations are trustworthy