Showing papers in "Physica A-statistical Mechanics and Its Applications in 1976"
TL;DR: In this paper, a renormalization group transformation is introduced with the help of which critical properties of infinite systems can be related to finite systems, and applied to the two-dimensional Ising model.
Abstract: A renormalization group transformation is introduced with the help of which critical properties of infinite systems can be related to finite systems. As a numerical example the method is applied to the two-dimensional Ising model. The critical point and critical point exponent are computed in addition to the amplitude of the logarithmic singularity in the specific heat.
370 citations
TL;DR: In this article, the theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids and their interface, and a singular energy density at the interface, which is related to the phenomenon of surface tension, is taken into account.
Abstract: The theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids and their interface. A singular energy density at the interface, which is related to the phenomenon of surface tension, is taken into account. Furthermore the momentum and the heat currents are allowed to be singular at the interface. Using the conservation laws and the Gibbs' relation for the surface, an expression for the singular entropy production density at the interface is obtained. The linear phenomenological laws between fluxes and thermodynamic forces occurring in this singular entropy production density are given. Some of these linear laws are boundary conditions for the solution of the differential equations governing the evolution of the state variables in the bulk.
238 citations
TL;DR: In this paper, the authors derived the equation of motion for each three-dimensional spin vector and showed that in the continuum limit where the spins lie dense on a line, this set of equations reduces to a nonlinear partial differential equation.
Abstract: For a one-dimensional system of classical spins with nearest neighbour Heisenberg interaction we derive the equation of motion for each three-dimensional spin vector. In the continuum limit where the spins lie dense on a line this set of equations reduces to a nonlinear partial differential equation. In addition to spin-wave solutions we obtain some other special solutions of this equation. In particular we find solitary waves having total energy localised in a finite region, with velocity of propagation inversely proportional to the width of this region. Solutions of still another type are shown to have a diffusive character. The stability of such solutions and the possibility of interaction of two or more solitary waves have not yet been studied.
219 citations
TL;DR: In this paper, the Wigner function is shown to be non-negative in all quantum states when smoothed with a gaussian whose variances are greater than or equal to those of the minimum uncertainty wave packet.
Abstract: The Wigner function, which is commonly used as a joint distribution for non-commuting observables, is shown to be non-negative in all quantum states when smoothed with a gaussian whose variances are greater than or equal to those of the minimum uncertainty wave packet.
126 citations
TL;DR: In this article, the authors derived expressions of the Faxen type for the total force, the total torque and the symmetric force-dipole moment of a sphere moving in an incompressible fluid in nonstationary flow with mixed stick-slip boundary conditions.
Abstract: The theorems derived in a previous article are employed to calculate the force density induced on a sphere moving in an incompressible fluid in nonstationary flow with mixed stick-slip boundary conditions. As applications we derive expressions of the Faxen type for the total force, the total torque and the symmetric force-dipole moment.
94 citations
TL;DR: In this paper, the surface force density induced on a sphere placed in an arbitrary nonstationary flow field of a viscous incompressible fluid for stick boundary conditions was evaluated.
Abstract: We evaluate the surface force density induced on a sphere placed in an arbitrary nonstationary flow field of a viscous incompressible fluid for stick boundary conditions. The calculation leads to a generalization of Faxen's theorem to force multipole moments of arbitrary order.
80 citations
TL;DR: In this article, the conditions of Galilei invariance, unitarity, reality and normalization lead to the Wigner kernel function in a unique way, and the conditions to obtain the correct mixed distributions also lead to a unique result.
Abstract: The joint distribution function in phase space is related to the density matrix by an integral transformation which depends on the rule of correspondence used. All the requirements which can be restrictive for the kernel function defining the transformation are studied. It is shown that the conditions of Galilei invariance, unitarity, reality and normalization lead to the Wigner kernel function in a unique way. Galilei invariance, the requirement that the free particle behaves classically, and the conditions to obtain the correct mixed distributions also lead to the same result.
77 citations
TL;DR: In this article, the compressibility of ethylene at temperatures from 0° up to 150°C and densities up to 500 amagat, the maximum pressure being 2900 atmospheres.
Abstract: The compressibility isotherms of ethylene are presented at temperatures from 0° up to 150°C and at densities up to 500 amagat, the maximum pressure being 2900 atmospheres. From the experimental results values of thermodynamic functions have been calculated at integral values of density.
60 citations
TL;DR: In this paper, the influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically using an inverse operator technique, first thermal conductivity and viscosity are treated, then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence.
Abstract: The influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically. Using an inverse operator technique, first thermal conductivity and viscosity are treated. Then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence. A relation connecting the magnitudes of the field effects on thermal conductivity, diffusion, and thermal diffusion is derived. This relation is used to estimate the field effect on diffusion.
50 citations
TL;DR: The analysis of transport coefficients based on the modified Enskog theory (MET), discussed in a previous publication, has been extended to include the self-diffusion coefficient (D) and the bulk viscosity coefficient (ηv) as mentioned in this paper.
Abstract: The analysis of transport coefficients based on the modified Enskog theory (MET), discussed in a previous publication, has been extended to include the self-diffusion coefficient (D) and the bulk viscosity coefficient (ηv). Specifically, calculated values according to the MET are compared with experiment over the range for which data are available. Fluids considered are argon, nitrogen and methane. Agreement between theory and experiment for densities less than about twice the critical density (ρc) is generally within about 10%. However, much of the data was taken at densities well in excess of 2ρc in which case agreement is still not unsatisfactory. Deviations exceeding 10% between theoretical and experimental self-diffusion coefficients were observed for densities in the approximate range 0.9 ≲ ρ/ρc ≲ 2.0. It is possible that these deviations are due to long range correlated molecular motions which are not present in the MET. The sound absorption is also briefly considered. Finally, the behavior of ηv and D at low densities is discussed.
44 citations
TL;DR: In this paper, the authors analyzed the coherence length beyond which fluctuations can amplify and induce instabilities at a macroscopic scale and established the existence of diverging form factors and long range correlations.
Abstract: Recent analyses of fluctuations in non-equilibrium systems by Prigogine, Malek-Mansour and Nicolis have indicated the existence of a minimal coherence length beyond which fluctuations can amplify and induce instabilities at a macroscopic scale. Conversely, this observation suggests the emergence of long range spatial correlations in systems undergoing non-equilibrium unstable transitions. In the present paper, this problem is analyzed for reaction-diffusion systems and illustrated on a specific model. The existence of diverging form factors and of long range correlations is established. The connection between the multi-variate master equation and the local equation developed recently by Prigogine, Malek-Mansour and Nicolis is discussed.
TL;DR: In this paper, the one-electron momentum distribution for an electron gas is investigated by a diagrammatic analysis of perturbation theory, and the exact asymptotic form for large k (k ⪢ pF; pF, the Fermi momentum) is given.
Abstract: The one-electron momentum distribution function 〈a kσ † a kσ 〉 for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that 〈a kσ † a kσ 〉 has the following exact asymptotic form for large k (k ⪢ pF; pF, the Fermi momentum): 〈a kσ † a kσ 〉 = 4 9 ( αr s π ) 2 ×( p F 8 k 8 ) g⇅(0) + ⋯ , where g⇅(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.
TL;DR: In this paper, the concept of time-local gaussian processes is introduced, which are processes for which the state variable at time t + τ is gaussian distributed around its most probable value at that time, for a specified realization a small time interval τ earlier.
Abstract: In this paper we discuss the concept of time-local gaussian processes. These are processes for which the state variable at time t + τ is gaussian distributed around its most probable value at that time, for a specified realization a small time interval τ earlier. On one hand it will be shown that these processes are related to a very simple path sum. On the other hand the associated stochastic differential equation is derived by means of the Kramers-Moyal method, and will be seen to be the most general nonlinear Fokker-Planck equation. The significance of the present formulation for nonequilibrium processes and the comprehension of critical phenomena will be evaluated.
TL;DR: In this article, the effect of hydrostatic pressure on the high-resolution proton magnetic resonance spectra of methane, ethylene, methanol and ethanol was investigated at pressures up to 2500 bar.
Abstract: This article is the first in a series of four papers, which deal with the effect of hydrostatic pressure on the high resolution proton magnetic resonance spectra of methane, ethylene, methanol and ethanol. The present paper describes the spectrometer in which high resolution spectra can be recorded at pressures up to 2500 bar. The most essential part of the spectrometer is a beryllium copper high pressure vessel in which the sample can be rotated under pressure. The positions of the spectral lines are referred to an external reference of benzene, contained in a sealed glass capillary. Frequency modulation of the transmitter is used in the measurement of the line positions. The paper describes how the apparatus can also be used for the measurement of the density dependence of the diamagnetic volume susceptibility.
TL;DR: In this paper, a non-linear transport equation for concentration fluctuations δ c ( r, t ) of the particles is derived, which is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations.
Abstract: Starting from a N -particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δ c ( r , t ) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D (ω) k 2 , where ω is the transferred frequency. It is shown that D (0) = D e , the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that D e = D 0 (1 + φ ), where D 0 is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.
TL;DR: The present work describes methods of calculation and gives the improved value B5 = 0.3335561 B42, the last digit being uncertain.
Abstract: The most accurate value of the fitth virial coefficient B 5 for a system of hard disks has been (0.3338±0.0005) B 4 2 until now, where B 2 is the second virial coefficient. The present work describes methods of calculation and gives the improved value B 5 = 0.3335561 B 4 2 , the last digit being uncertain.
TL;DR: The notion of a critical exponent was first used by Van der Waals in 1893 for describing the critical behavior of the surface tension as discussed by the authors, and it was used by Verschaffelt in 1900 to establish precise nonclassical values for the exponents beta and delta.
Abstract: The notion of a critical exponent was first used by Van der Waals in 1893 for describing the critical behavior of the surface tension. He also noticed in the early 1890's that experimental data on capillarity indicated a nonclassical value for the surface tension exponent. Verschaffelt found that this was due to the fact that the coexistence curve exponent beta was nonclassical. In 1900, he established precise nonclassical values for the exponents beta and delta. Even though from this time onwards the “cubic law” for fluid coexistence curves was accepted, the true implication of Verschaffelt's results, namely the failure of classical theory, was not appreciated. Some reasons for this lack of impact will be given.
TL;DR: In this article, the treatment of a previous paper on systems with many-particle interactions is generalized to hamiltonians containing an analytic function of a number of short-range interaction operators V, which are normalized.
Abstract: The treatment of a previous paper on systems with many-particle interactions is generalized to hamiltonians containing an analytic function of a number of short-range interaction operators V , which are normalized. An exact expression for the free energy per particle in the thermodynamic limit can be obtained from a trial hamiltonian which is linear in the operators V .
TL;DR: In this paper, Kasteleyn's treatment of the hamiltonian walk problem on lattice graphs is briefly reviewed, and the asymptotic behavior of the number of Hamiltonian walks on the kth covering of a closed oriented lattice graph is expressed in terms of the expected number of oriented trees on the graph.
Abstract: Kasteleyn's treatment of the hamiltonian walk problem on lattice graphs is briefly reviewed. The asymptotic behaviour of the number of hamiltonian walks on the kth covering of a closed oriented lattice graph is expressed in terms of the asymptotic behaviour of the number of oriented trees on the lattice graph. Asymptotic results on the enumeration of hamiltonian walks are presented for the covering and underlying lattices of the Manhattan oriented square lattice, and the covering lattices of certain orientations of the diamond and cubic lattices. The effect of boundary conditions is examined. Relations are established between hamiltonian walks and close-packed polymer configurations. An analysis of the assumptions in lattice models of the melting and glass transitions in polymers shows that the Flory-Huggins approximation underestimates the total number of polymer configurations, but that corrections can be made without altering the principal features of the models thus permitting better agreement with the experimental data.
TL;DR: In this paper, a systematic expansion method was developed to account for the effect of fluctuations on the motion of a damped Duffing oscillator, where the expansion parameter α is the magnitude of the fluctuations.
Abstract: A systematic expansion method is developed to account for the effect of fluctuations on the motion of a damped Duffing oscillator. The expansion parameter α is the magnitude of the fluctuations. To first order in α we calculate all the correlation functions and the corresponding spectral densities. The relation of this expansion to an approximation method proposed by Nordholm and Zwanzig is also discussed.
TL;DR: In this article, a simple sum over paths formulation for nonlinear diffusion process described by complex coordinates is proposed, and the general nonlinear Fokker-Planck equation is derived.
Abstract: A simple sum over paths will be considered for the general nonlinear diffusion process described by complex coordinates. In order to derive the corresponding stochastic differential equation the Feynman method used in quantum mechanics will be generalised for the present case of a coordinate dependent variance or diffusion function by means of a nonlinear coordinate transformation. The resulting equation will be seen to be the general nonlinear Fokker-Planck equation. The relevance of the present formulation for nonequilibrium phenomena, such as for example those occuring in nonlinear quantum optics, will be discussed.
TL;DR: In this article, the second order correction to the energy eigenvalues is calculated by finding zeros of the wronskian and comparing with the value obtained from second order perturbation theory.
Abstract: The Green's function and energy eigenvalues of an electron under the influence of a uniform electric field in a box with infinitely high sides is investigated. The second order correction to the energy eigenvalues is calculated by finding zeros of the wronskian and comparing with the value obtained from second order perturbation theory. Comparison is made with the limiting conditions in which the size of the box tends to infinity and the electric field tends towards zero. The results of the investigation suggest a possible criterion for localisation. The value obtained for the ground state energy is used to extend a model of Edwards to study the tail of the density of states of a disordered system in the presence of an electric field.
TL;DR: In this article, explicit expressions for the Green functions of arbitrary relativistic quadratic quantum systems are obtained by the integrals-of-motion method and by the coherent states method.
Abstract: Explicit expressions for the Green functions of arbitrary relativistic quadratic quantum systems are obtained by the integrals-of-motion method and by the coherent states method. The normal forms of the relativistic quadratic hamiltonians are briefly discussed. The important special cases, such as the motion of Dirac and Klein-Gordon charged particles in the fields of a plane wave and in the uniform electric and magnetic fields are investigated in detail.
TL;DR: In this paper, the effect of intermolecular attractive forces on the viscosity coefficient at low densities was found to be similar to that previously found for low molecular weight hydrocarbons.
Abstract: Viscosity coefficient data for the diatomic fluids fluorine and oxygen are very satisfactorily interpreted on the basis of a modified smooth hard-sphere model. The effect of intermolecular attractive forces on the viscosity coefficient at low densities is found to be similar to that previously found for low molecular weight hydrocarbons.
TL;DR: In this paper, the average local velocity field acting at a selected particle in a fluid suspension is analyzed in terms of force multipoles, and closed expressions are derived in a continuum approximation for the average velocity, vorticity and strain in terms with the macroscopic average velocity field and force multipole densities.
Abstract: A systematic study is made of the average local velocity field acting at a selected particle in a fluid suspension. The flow disturbance due to a single particle is analyzed in terms of force multipoles. The theory is developed in close analogy to that for the corresponding problem of the local electric field at a molecule in a polarizable medium. Closed expressions are derived in continuum approximation for the average local velocity, vorticity and strain in terms of the macroscopic average velocity field and force multipole densities. The effect of correlations is discussed briefly.
TL;DR: In this article, the transport coefficients of a multicomponent gas mixture are approximated by means of a variational technique and it is shown that the procedure is equivalent to a more heuristic method developed earlier.
Abstract: The transport coefficients of a multicomponent gas mixture are approximated by means of a variational technique. It is shown that the procedure is equivalent to a more heuristic method developed earlier.
TL;DR: In this paper, a generalized functional Wiener measure is defined for a generalized driftless diffusion process and the relation between the well-defined functional sum and its corresponding functional integral is studied in detail.
Abstract: The attention will be focussed on a generalized Wiener diffusion process for which the macroscopic evolution y = c1(y) equals zero, of course, and where the variance of the process obeys gs2 = c2(y). The diffusion function c2(y) may be state dependent in an arbitrary way. We invoke our treatment of the general time-local Gaussian process as presented in a previous paper. This process will be seen to define a generalized functional Wiener measure. This measure has already been used implicitly in earlier work being concerned with nonlinear, nonequilibrium Markov processes. The sum of the generalized measure over the entire function space will be shown to be exactly related to the general Fokker-Planck equation for the driftless diffusion process. The relation between the well-defined functional sum and its corresponding functional integral will be studied in detail. The analysis demonstrates in clear fashion the origin of the deviations from other approaches, and provides an extension of our previous results on nonequilibrium, nonlinear phenomena to include generalized diffusion processes.
TL;DR: In this paper, the concentration dependences of the binary diffusion coefficients of the systems He-Ar and He-O 2 were reported at 300 K and 1 atm pressure, respectively.
Abstract: The concentration dependences of the binary diffusion coefficients of the systems He-Ar and He-O 2 are reported at 300 K and 1 atm pressure. Two independent sets of data, obtained with a two-bulb cell and a shearing-cell of Loschmidt design, agree within the error of measurement. The data for the two-bulb cell were obtained at pressures where Knudsen effects are important. It was found necessary to improve the extrapolation procedure of van Heijningen et al . by using the results of the dusty-gas model as described by Mason et al.
TL;DR: In this article, it is shown that in each order the multiple-scattering intensity near the critical point is in essence a contraction of consecutive uncorrelated single scattering intensities.
Abstract: The systematic theory of multiple scattering which we gave in a previous paper is further elaborated for critical scattering. It is shown that in each order the multiple-scattering intensity near the critical point is in essence a contraction of consecutive uncorrelated single-scattering intensities. The anomaly of the critical depolarization factor is calculated and is found to be in quantitative agreement with recent experimental results. Double scattering corrections to the Ornstein-Zernike plot are discussed.
TL;DR: In this article, a free electron gas in the presence of a uniform magnetic field and confined by a cylindrically symmetric harmonic potential in the directions normal to the field is considered.
Abstract: We consider a free electron gas in the presence of a uniform magnetic field and confined by a cylindrically symmetric harmonic potential in the directions normal to the field. The density matrix in Boltzmann statistics is evaluated exactly and it is shown that the electron gas rotates uniformly under the influence of the field. The corresponding Wigner distribution function is also studied.