J. Güémez

Probability distribution for a lattice gas model

A simple method, based on the use of conditional probabilities, for calculating the probability distribution for the particles of a gas enclosed in a vessel is developed. The method is applied to a lattice gas with binary interactions. For this gas model, numerical analysis shows the appearance, for sufficiently low temperatures, of two humps in the corresponding probability distribution. This result suggests the onset of a liquid-vapor phase transition. Various characteristics of the phenomenon, such as the onset temperature, are studied in terms of the density and the size of the system. The connection with catastrophe theory is discussed.

Probability distribution for a lattice gas model: II. Thermodynamic limit

Abstract The behavior of the probability distribution for a lattice gas obtained in a preciding paper is analyzed in the so-called thermodynamic limit. Two situations, corresponding to cases in which the ratio between the subvolume under consideration and the total volume remains finite or tends to zero, are discussed. The latter case allows us to write the probability distribution in terms of the intensive parameters. The numerical analysis of the probability distribution in this case and the implication of the results in order to explain the features of a liquid-vapor phase transition are reported.

Single-particle energy and velocity distributions for finite simple systems in the microcanonical ensemble

The probability distribution for the energy (velocity) of a particle in the microcanonical ensemble is obtained for some simple systems. Although in the thermodynamic limit the distribution has the well-known Boltzmann (Maxwell-Boltzmann) form (characteristic of the canonical ensemble), for finite systems this is not the case. This fact is important in the analysis of the results obtained from pedagogical computer simulations with a very small number of particles and constant total energy (i.e. simulations that generate the microcanonical ensemble).

A probabilistic approach to the site-percolation problem

A simple method, based on the use of conditional probabilities, for deriving the particle cluster distribution is presented for the site-percolation problem. The method is applied to a Bethe lattice (or Cayley tree). Two approximations to the behaviour of the obtained probability distribution in the thermodynamic limit are considered. The first one corresponds to the case of finite clusters, and leads to a binomial-like distribution. The second one allows us to treat the case of the existence of clusters spanning the lattice, and thus to investigate the onset of the percolating cluster. The extrema (maxima) of the corresponding distributions are analytically and numerically analyzed. Well-known results for the Bethe lattice, such as the critical probability, pc, and the percolation probability, P∞(p), are obtained.

A probabilistic analysis of the Walker-Vause model for liquid binary mixtures

A simple method to calculate the probability distribution for a binary fluid mixture is presented. The method is applid to the Walker-Vause binary liquid model and different temperature vs composition phase diagrams are obtained. These diagrams are obtained using catastrophe theory methods. Comparison with some experimental data are also discussed and a simplified model leading to closed-loop phase diagrams is considered.

Non-markovian far-infrared spectra of HF in liquid SF6

Non-markovian far-infrared spectra calculations for dilute solutions of HF in liquid SF6 at two different temperatures are presented in the range 0 to 250 cm-1. The fine rotational structure appearing in these spectra is discussed as function of the parameters involved in the theoretical absorption coefficient. A comparison with the spectra of other diatomic polar molecules (HCl, DCl) is also reported.

Numerical study of T 1 and T 2 rotational relaxation times of HCl in liquid Ar

Energy relaxation (T 1) and dephasing (T 2) processes are analysed for the rotational relaxation of diatomic polar molecules in rare-gas liquids under markovian assumption. Bath autocorrelation functions defining the markovian relaxation superoperator, which contains all information about T 1 and T 2 processes, are derived for an intermolecular potential approximated by a truncated series of Legendre polynomials P J . Hence, analytical expressions for T 1 and T 2 are obtained in terms of a reduced set of parameters regarding both the diatomic and the liquid as their mutual interaction. Numerical contribution to T 1 and T 2 processes, from P 1 and P 2 terms, is given for a HCl-Ar solution by using a dynamical quasiharmonic model to describe the solvent liquid structure.

Rotational relaxation and dephasing of diatomic polar molecules in rare-gas liquids

Abstract The rotational relaxation of a diatomic polar molecule in a rare-gas liquid host is studied by a consideration of a quantum rigid rotor weakly interacting with a thermal bath. Dephasing (T 2 ) and population decay (T 1 ) are evaluated through second order in the Markovian limit. The rates are expressed in terms of temperature and frequency dependent bath correlation functions of the interaction. Explicit expressions are presented using a stochastic Hamiltonian to describe diatomic-solvent molecular interactions. Numerical applications for HCl in liquid Ar, Kr and Xe are reported.

A quasiharmonic model calculation for non-markovian far-infrared spectra of HCl in Kr and Xe liquids

The far-infrared spectra (0–200 cm−1) of dilute solutions of HCl in liquid Kr and Xe have been calculated by applying of a non-markovian spectral theory called PTOC (partial time ordering cumulants) and by using a quasiharmonic model for the liquid structure recently reported by us (A. Calvo Hernandez et al., 1987, J. chem. Phys., 86, 4597) and successfully applied to HCl−Ar solution (Ibid., 86, 4607). The bath correlation functions which appear in the spectral theory involve a reduced set of parameters regarding both the HCl−Kr and HCl−Xe interactions and the liquid structure. From comparison between theoretical and experimental spectra it is possible to deduce quantitative values for the above parameters. The pronounced rotational fine structure of the experimental spectra for HCl in Kr and Xe liquids is quite well explained by the actual model.

Teaching spontaneous magnetization by using a probability distribution

The equilibrium magnetization distribution for an Ising-spin model in the mean-field approximation is used to present a simple study of the ferromagnetic phase transition in the absence of external magnetic field (spontaneous magnetization). For temperatures below a critical one (the Curie Temperature) this distribution exhibits two peaks, showing that two states of magnetization are possible. At the Curie temperature the distribution presents a plateau, showing large fluctuations in the magnetization. A scaling-like analysis of the distribution shows that the Curie point can be characterized as an unstable fixed point of a recursion relation.