Equilibrium free energies from nonequilibrium metadynamics

In this Letter we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes, such as Wang-Landau sampling.     

A study of the linear free energy model for DNA structures using the generalized Hamiltonian formalism

We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.     

Ginzburg-Landau Free Energy of Crystalline Color Superconductors: A Matrix Formalism from Solid-State Physics

The Ginzburg-Landau (GL) free energy of crystalline color superconductors is important for understanding the nature of the phase transition to the normal quark matter and predicting the preferred crystal structure. So far the GL free energy at zero temperature has only been evaluated up to the sixth order in the condensate. To give quantitative reliable predictions we need to evaluate the higher-order terms. In this work, we present a new derivation of the GL free energy by using the discrete Bloch representation of the fermion field. This derivation introduces a simple matrix formalism without any momentum constraint, which may enable us to calculate the GL free energy to arbitrary order by using a computer.     

Core-electron binding energies in free and supported metal clusters

Core-electron binding energy shifts in free and supported clusters are discussed using the Born-Haber formalism. For grounded clusters this approach shows that the shift reflects the decrease in the average atomic cohesive energy of the cluster relative to that of the bulk metal. This shift is closely related to the surface-atom core level shift. For free clusters there is a second term reflecting the unit charge left on the cluster by the emission of the photoelectron. In small clusters this term results in the suppression of conduction electron screening. Clusters supported on amorphous carbon remain charged in the final-state, and are similar to free clusters, but have smaller shifts because the substrate reduces the energy of the final state by forming an image charge. The shift in monolayer islands on metallic substrates is determined largely by the adsorption enthalpy of the adatoms.     

Phase shift calculation for low-energy electron scattering from mercury

Summary The relativistic formalism is used to study the scattering of electrons from mercury at low energy. A method of numerical integration is applied to calculate phase shifts by including a local exchange approximation and phenomenological polarization potential. The phase shifts are found to exhibit a resonant behaviour which is in conformity with the results of some earlier calculations. In contrast to the previous methods, this approach has a general validity over the entire energy range and is free from divergences. The author of this paper has agreed to not receive proofs for correction.     

Higher order mean field expansions for lattice gauge theories

The leading contribution to the free energy of lattice gauge theories is evaluated in the mean field expansion to the two-loop level. The methods are general but we only deal with theU(1) case in this paper. The corrections improve the agreement with Monte Carlo calculations. We show that in order to obtain a satisfactory formalism it is necessary to include a new redundant parameter, γ, in the mean field expansion. For γ→0 we recover the usual mean field expansion whereas for γ→∞ we obtain the weak coupling expansion. Thus γ measures the amount of resummation that is done by the mean field formalism.     

The Discrete N-Vector Ferromagnet: Connection to a Percolation with Frustration Features

We extend the Kasteleyn–Fortuin formalism to the discrete N-vector ferromagnet. We show that the free energy and the correlation functions of this model are related, when the number of states tends to 1, to the mean number of clusters and to the pair connectedness of a polychromatic bond percolation type problem which combines frustration and connectivity features.     

NEW EXACTLY SOLVABLE SUPERSYMMETRIC PERIODIC POTENTIALS

Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of one-dimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schr?dinger equation for this potential is named the Mathieu equation mathematically. We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.     

Density-functional method for surface properties of two-component plasmas of liquid metals

A general density-functional formalism for an inhomogeneous two-component liquid metal is described. The expression for the free energy is obtained and the gradient approximation is used for its simplification. Both electronic and ionic gradients are present in the theory.     

ON A DYNAMIC THEORY OF QUENCHED RANDOM SYSTEM

A dynamical theory for quenched random system is developed in the framework of CTPGf. Tn steady states the results ob- tained coincide with Chose following from the quenched average of the free energy. The order parameter q, a matrix in general, becomes an integral part of the second order connected CTPGF.An equation to determine q is derived from the Dyson-Schwinger equation in this formalism. Some general properties of the CTPGF in a quenched random system are discussed.     

Separation of the massless spin-1 equation in Robertson-Walker space-time

The massless spin-1 free field equation is studied via the Newman-Penrose formalism and separated by the Chandrasekhar-Teukolski method. The temporal and angular equations are explicitly integrated. The radial equations are solved in the flat-universe case. The closed-universe case shows, in principle, the existence of a discrete spectrum of the energy of the massless particles.     

Schrödinger-Like Relativistic Wave Equation of Motion for the Lorentz-Scalar Potential

A Schrödinger-like relativistic wave equation of motion for the Lorentz-scalar potential is formulated based on a Lagrangian formalism of relativistic mechanics with a scaled time as the evolution parameter. Applications of this Schrödinger-like formalism for the Lorentz-scalar potential are given: For the square-step potential, the predictions of this formalism are free from the Klein paradox, and for the Coulomb potential, this formalism yields the exact bound-state eigenenergies and eigenfunctions.     

Quantum-statistical mechanics of a system of charged particles at high temperatures

If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ³?1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum. In this paper we calculated the two-particle Slater sum using an expansion according toe ² and the resolvent formalism. From the binary distribution function the correlation energy and the free energy as well were determined up to ordere ⁶. Symmetry effects were taken into account.     

Surface energy and solute strain energy effects in surface segregation

Previous models of surface segregation have generally been based on the assumption that a decrease in surface free energy constitutes the predominant driving force for the phenomenon. In contrast, grain boundary segregation models have been founded on the postulate that the major driving force for that phenomenon is the reduction in lattice strain energy which accompanies the transfer of misfitting solute atoms from the lattice to the boundary. These two concepts have been combined here into a single unified formalism of surface segregation. In addition, the temperature dependence of surface composition of both nickel-rich and gold-rich nickelgold alloys has been measured by Auger electron spectroscopy. Comparisons of the predictions of the combined formalism with the experimental results show excellent agreement between measured and calculated heats of adsorption (segregation). Furthermore, the present formalism provides estimates of the entropies of adsorption which can be used to explain apparent incompatibilities between the behavior of gold-rich and nickel-rich alloys.     

A new approach to radial and axial gauges

We develop a new path integral formulation of QCD in radial and axial gauges. This formalism yields free propagators which are free of gauge poles. We find that radial gauges are ghost free. In axial gauges ghosts cannot generally be excluded from the formalism due to the need to fix the residual gauge freedom.     

Microscopic calculations of spin polarized neutron matter at finite temperature

The properties of spin polarized neutron matter are studied both at zero and finite temperature within the framework of the Brueckner–Hartree–Fock formalism, using the Argonne v18 nucleon–nucleon interaction. The free energy, energy and entropy per particle are calculated for several values of the spin polarization, densities and temperatures together with the magnetic susceptibility of the system. The results show no indication of a ferromagnetic transition at any density and temperature.     

The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case

We study the fluctuations of free energy, energy and entropy in the high temperature regime for the Sherrington-Kirkpatrick model of spin glasses. We introduce here a new dynamical method with the help of brownian motions and continuous martingales indexed by the square root of the inverse temperature as parameter, thus formulating the thermodynamic formalism in terms of random processes. The well established technique of stochastic calculus leads us naturally to prove that these fluctuations are simple gaussian processes with independent increments, a generalization of a result proved by Aizenman, Lebowitz and Ruelle [1].     

Rigorous Treatment of the Liquid-Vapor Transition in a Polydisperse System with Kac Interaction

Within the canonical formalism, we consider a polydisperse lattice-gas model and a polydisperse continuous system interacting with the Kac potential. We obtain rigorous expressions for free energy densities. We also exhibit phase diagrams of the bidisperse lattice-gas model.