Adamsgay0109

Chemisorption on the surface of metal nanocrystallites (NCs) sometimes induces their reshaping. This interesting phenomenon was observed experimentally in various systems. Related theoretical studies imply that it can be described using the Wulff rule with the surface tension dependent on the coverage of the NC facets by adsorbate. There is, however, no agreement as to how the surface tension should be calculated in this case. Relying on the laws of statistical physics, I clarify the situation in this area in general and also in the framework of the mean-field approximation in three situations (i) with adsorption-desorption equilibrium, (ii) with a fixed amount of adsorbate at a NC, and (iii) with a fixed amount of adsorbate at facets of a NC. Under these conditions, the surface tension is shown to be described by the same expressions.Random walks are fundamental models of stochastic processes with applications in various fields, including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.We introduce the notion of mixed symmetry quantum phase transition (MSQPT) as singularities in the transformation of the lowest-energy state properties of a system of identical particles inside each permutation symmetry sector μ, when some Hamiltonian control parameters λ are varied. We use a three-level Lipkin-Meshkov-Glick model, with U(3) dynamical symmetry, to exemplify our construction. After reviewing the construction of U(3) unitary irreducible representations using Young tableaux and the Gelfand basis, we first study the case of a finite number N of three-level atoms, showing that some precursors (fidelity susceptibility, level population, etc.) of MSQPTs appear in all permutation symmetry sectors. Using coherent (quasiclassical) states of U(3) as variational states, we compute the lowest-energy density for each sector μ in the thermodynamic N→∞ limit. Extending the control parameter space by μ, the phase diagram exhibits four distinct quantum phases in the λ-μ plane that coexist at a quadruple point. selleck The ground state of the whole system belongs to the fully symmetric sector μ=1 and shows a fourfold degeneracy, due to the spontaneous breakdown of the parity symmetry of the Hamiltonian. The restoration of this discrete symmetry leads to the formation of four-component Schrödinger cat states.Logopoles are a recently proposed class of solutions to Laplace's equation with intriguing links to both solid spheroidal and solid spherical harmonics. They share the same finite-line singularity as the former and provide a generalization of the latter as multipoles of negative order. In a previous paper [Majic and Le Ru, Phys. Rev. Res. 1, 033213 (2019)2643-156410.1103/PhysRevResearch.1.033213], we introduced and discussed the properties and applications of these new functions in the special case of axisymmetric problems (with azimuthal index m=0). This allowed us to focus on the physical properties without the added mathematical complications. Here we expand these concepts to the general case m≠0. The chosen definitions are motivated to conserve some of the most interesting properties of the m=0 case. This requires the inclusion of Legendre functions of the second kind with degree -m≤n less then m (in addition to the usual n≥|m|) and we show that these are also related to the exterior spheroidal harmonics. We show that logopoles can also be defined for n≤m and discuss in particular logopoles of degree n=-m, which correspond to the potential of line segments of uniform polarization density.The Hamiltonian mean-field model is investigated in the presence of a field. The self-consistent equations for the magnetization and the energy per particle are derived, and the field effect on the caloric curve is presented. The analytical geometric approach to Hamiltonian dynamics, under the hypothesis of quasi-isotropy, allows us to calculate the field effect on the energy-dependent microcanonical mean Ricci curvature and its fluctuations. Notably, the method proved suitable to identify that stable and metastable solutions of the Lyapunov exponent exhibit intriguing distinct curvature behavior very close to the critical point at extremely low field values. In addition, finite-size molecular dynamics (MD) simulations are used to observe the evolution of the magnetization and their components, including the stability properties of the solutions. Most importantly, comparison of finite-size MD calculations of the Lyapunov exponent and related properties with those via the geometric approach unveil the sensible dependence of these microcanonical quantities on energy, number of particles, and field, before a quasisaturation behavior at high fields. Finally, relaxation properties from out-of-equilibrium initial conditions are discussed in light of MD simulations.The spectral distribution of light scattered by microscopic thermal fluctuations in binary mixture gases was investigated experimentally and theoretically. Measurements of Rayleigh-Brillouin spectral profiles were performed at a wavelength of 532 nm and at room temperature, for mixtures of SF_6-He,SF_6-D_2, and SF_6-H_2. In these measurements, the pressure of the gases with heavy molecular mass (SF_6) is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of SF_6 and the very small polarizabilities of He, H_2, and D_2, under the chosen pressure conditions these low mass species act as spectators and do not contribute to the light scattering spectrum, while they influence the motion and relaxation of the heavy SF_6 molecules. A generalized hydrodynamic model was developed that should be applicable for the particular case of molecules with heavy and light disparate masses, as is the case for the heavy SF_6 molecule, and the lighter collision partners.