Islands, craters, and a moving surface step on a hexagonally reconstructed (100) noble metal surface

Deposition/removal of metal atoms on the hex reconstructed (100) surface of Au, Pt and Ir should present intriguing aspects, since a new island implies hex -> square deconstruction of the substrate, and a new crater the square -> hex reconstruction of the uncovered layer. To obtain a microscopic understanding of how islands/craters form in these conditions, we have conducted simulations of island and crater growth on Au(100), whose atomistic behavior, including the hex reconstruction on top of the square substrate, is well described by mean s of classical many-body forces. By increasing/decreasing the Au coverage on Au(100), we find that island/craters will not grow unless they exceed a critical size of about 8-10 atoms. This value is close to that which explains the nonlinear coverage dependence observed in molecular adsorption on the closely related surface Pt (100). This threshold size is rationalized in terms of a transverse step correlation length, measuring the spatial extent where reconstruction of a given plane is disturbed by the nearby step.Comment: 11 pages, 5 figures, accepted for publication in Surface Science (ECOSS-18

Geometry of mixed states for a q-bit and the quantum Fisher information tensor

After a review of the pure state case, we discuss from a geometrical point of view the meaning of the quantum Fisher metric in the case of mixed states for a two-level system, i.e. for a q-bit, by examining the structure of the fiber bundle of states, whose base space can be identified with a co-adjoint orbit of the unitary group. We show that the Fisher Information metric coincides with the one induced by the metric of the manifold of SU(2), i.e. the 3-dimensional sphere $S^3$, when the mixing coefficients are varied. We define the notion of Fisher Tensor and show that its anti-symmetric part is intrinsically related to the Kostant Kirillov Souriau symplectic form that is naturally defined on co-adjoint orbits, while the symmetric part is nontrivially again represented by the Fubini Study metric on the space of mixed states, weighted by the mixing coefficients.Comment: 20 pages; Abstract and Introduction modified, references added. Final published versio

Bent surface free energy differences from simulation

We present a calculation of the change of free energy of a solid surface upon bending of the solid. It is based on extracting the surface stress through a molecular dynamics simulation of a bent slab by using a generalized stress theorem formula, and subsequent integration of the stress with respect to strain as a function of bending curvature. The method is exemplified by obtaining and comparing free energy changes with curvature of various reconstructed Au(001) surfaces.Comment: 14 pages, 2 figures, accepted for publication in Surface Science (ECOSS-19

Continuum in the Excitation Spectrum of the S=1 Compound CsNiCl_3

Recent neutron scattering experiments on CsNiCl_3 reveal some features which are not well described by the nonlinear sigma model nor by numerical simulations on isolated S=1 spin chains. In particular, in real systems the intensity of the continuum of multiparticle excitations, at T=6K, is about 5 times greater than predicted. Also the gap is slightly higher and the correlation length is smaller. We propose a theoretical scenario where the interchain interaction is approximated by a staggered magnetic field, yielding to a correct prediction of the observed quantities.Comment: 4 pages, 2 figures (.eps), RevTe

From the Equations of Motion to the Canonical Commutation Relations

The problem of whether or not the equations of motion of a quantum system determine the commutation relations was posed by E.P.Wigner in 1950. A similar problem (known as "The Inverse Problem in the Calculus of Variations") was posed in a classical setting as back as in 1887 by H.Helmoltz and has received great attention also in recent times. The aim of this paper is to discuss how these two apparently unrelated problems can actually be discussed in a somewhat unified framework. After reviewing briefly the Inverse Problem and the existence of alternative structures for classical systems, we discuss the geometric structures that are intrinsically present in Quantum Mechanics, starting from finite-level systems and then moving to a more general setting by using the Weyl-Wigner approach, showing how this approach can accomodate in an almost natural way the existence of alternative structures in Quantum Mechanics as well.Comment: 199 pages; to be published in "La Rivista del Nuovo Cimento" (www.sif.it/SIF/en/portal/journals

Detecting a many-body mobility edge with quantum quenches

The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to "localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.Comment: v2: references added v3: minor revisions, added reference

Edge States in Gauge Theories: Theory, Interpretations and Predictions

Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the dimensionality of spacetime. The intimate connection of these observables to charge fractionation, vertex operators and topological field theories is described. The edge observables, however, may or may not exist as well-defined operators in a fully quantized theory depending on the boundary conditions imposed on the fields and their momenta. The latter are obtained by requiring the Hamiltonian of the theory to be self-adjoint and positive definite. We show that these boundary conditions can also have nice physical interpretations in terms of certain experimental parameters such as the penetration depth of the electromagnetic field in a surrounding superconducting medium. The dependence of the spectrum on one such parameter is explicitly exhibited for the Higgs model on a spatial disc in its London limit. It should be possible to test such dependences experimentally, the above Higgs model for example being a model for a superconductor. Boundary conditions for the 3+1 dimensional $BF$ system confined to a spatial ball are studied. Their physical meaning is clarified and their influence on the edge states of this system (known to exist under certain conditions) is discussed. It is pointed out that edge states occur for topological solitons of gauge theories such as the 't Hooft-Polyakov monopoles.Comment: 36 pages, LATEX File (revised because figures had problems

Surface molecular dynamics simulation with two orthogonal surface steps: how to beat the particle conservation problem

Due to particle conservation, Canonical Molecular Dynamics (MD) simulations fail in the description of surface phase transitions involving coverage or lateral density changes. However, a step on the surface can act effectively as a source or a sink of atoms, in the simulation as well as in real life. A single surface step can be introduced by suitably modifying planar Periodic Boundary Conditions (PBC), to accommodate the generally inequivalent stacking of two adjacent layers. We discuss here how, through the introduction of two orthogonal surface steps, particle number conservation may no longer represent a fatal constraint for the study of these surface transitions. As an example, we apply the method for estimating temperature-induced lateral density increase of the reconstructed Au (001) surface; the resulting anisotropic cell change is consistent with experimental observations. Moreover, we implement this kind of scheme in conjunction with the variable curvature MD method, recently introduced by our group.Comment: 9 pages, 5 figures, accepted for publication in Surface Science (ECOSS-19