Theoretical and analytical radial distribution function for dense fluids

The ‘identical particles in quasi-mean potential energy field’ assumption was used to derive the approximate theoretical and analytical radial distribution function (RDF) for dense fluids through solving the two-body Schrödinger equation and using the first-order perturbation method. The theoretical and analytical expressions of RDF can save much computation time in calculating the thermodynamics properties of fluids and may make the statistical mechanics theories comparable with the equation of state method that is currently widely used in physics, chemistry and technology. The calculated properties for argon by this RDF fit well with the experimental data of reference over a very wide range of conditions, including dense fluids (liquid phase and dense gas), critical point, and dilute gas, in which the pair potential and the Axilrod-Teller three body interaction were considered. The extensive practical application of this model for science and technology needs further investigation.     

Unconditional secure two-way quantum dense key distribution

In this paper, we present a two-way quantum dense key distribution protocol. With double check modes, our scheme is secure regardless of the presence of noises. And with a quantum teleportation process, secret message can be encoded deterministically even if the quantum channel is highly lossy. Therefore, our scheme can be used in a realistic quantum channel regardless of the presence of noises and channel losses.     

Dynamical pair correlations of classical and quantum fluids perturbed with weak long-range forces

We study time dependent correlation functions of ideal classical and quantum gases using methods of equilibrium statistical mechanics. The basis for this is the path integral formalism of quantum mechanical systems. By this approach the statistical mechanics of a quantum mechanical system becomes the equivalent of a classical polymer problem in four dimensions where imaginary time is the fourth dimension. Several non-trivial results for quantum systems have been obtained earlier by this analogy. Here we will focus upon particle dynamics. First ideal gases are considered. Then interactions, that are assumed weak and of long range, are added, and methods of classical statistical mechanics are applied to obtain the leading contribution. Comparison is performed with known results of kinetic theory. These results demonstrate how methods developed for systems in thermal equilibrium also is applicable outside equilibrium. Thus, more generally, we have reason to expect that these methods will be accurate and useful for other situations of interacting many-body systems consisting of quantized particles too. To indicate so we sketch the computation of the induced Casimir force between parallel plates filled with ions for the situation where the ions are quantized, but the interaction remains electrostatic. Further in this respect we establish expressions for a leading correction to ab initio calculations for the energies of the quantized electrons of molecules. To our knowledge these two latter applications go beyond earlier results.     

The structure of quantum fluids

We outline the principal features of Bose and Fermi fluids that are revealed in particle scattering experiments at high momentum transfer. In this regime, the dynamic structure function is determined by the dominant influence of correlations which are embodied in the static one- and two-body density matrices characterizing a strongly correlated system. We analyze the general structure of these fundamental quantities and of the associated momentum distributions that enter as input quantities for determining the dynamical response. We discuss their physical interpretation and their interrelationships. We further describe the main features of advanced many-body methods, which begin on a nonperturbative basis. They permit a formal and numerical evaluation of various quantities that characterize the structure of the density matrices and therewith of quantum fluids and solids.Dedicated to Peter Mittelstaedt on the occasion of his sixtieth birthday.     

Short-range behavior of the pair correlation function in the dense electron gas

An effective Coulomb interaction taking into account the diffraction effects is used to sum the series of bubbles diagrams building up the short-range part of the pair correlation function.     

Kinetic theory of dense fluids

A kinetic theory of dense fluids is presented in this series of papers. The theory is based on a kinetic equation for subsystems which represents a subset of equations structurally invariant to the sizes of the subsystem that includes the Boltzmann equation as an element at the low density limit. There exists a H-function for the kinetic equation and the equilibrium solution is uniquely given by the canonical distribution functions for the subsystems comprising the entire system. The cluster expansion is discussed for the N-body collision operator appearing in the kinetic equation. The kinetic parts of transport coefficients are obtained by means of a moment method and their density expansions are formally obtained. The Chapman-Enskog method is discussed in the subsequent paper.     

Obtaining non-negative quantum mechanical distribution function

The distribution function obtained by smoothing the original Wigner function with a weighting function, is shown to be positive everywhere, if the weighting function itself is a Wigner transform of any normalised function. The marginal distribution is recovered with a special choice of this function.     

Anisometric molecules in dense fluids

The Kerr constant of anisometric non-polar molecules in solvents of spherical molecules is calculated using the model of an ellipsoidal cavity in an isotropic dielectric continuum. It is shown that the Kerr constants has the same form as for dilute gases:

provided that effective polarizability elements α _xx ^l * (optical) and α _xx ^s * (static) replace the vacuum values α _xx ^l and α _xx ^s in Γ*, which then reads Γ* = 1/2[(α _xx ^l * - α _yy ^l *)(α _xx ^s *) - α _yy ^s *) + circular permutation].

Each effective polarizability element α _xx * (either optical or static) is composed of two contributions, one pertaining to the anisometric solute itself and another arising from the anisotropic distortion of the polarization in the neighbouring continuum. These two contributions are of opposite signs, so that large variations of the magnitude of the Kerr effect are predicted, depending essentially upon the mean refractivity and permittivity of the solute compared with those of the solvent.     

Kinetic equations for dense fluids

It is demonstrated that the kinetic equation of Davis's effective potential theory follows directly from the application of well-defined approximations to the three-body correlations involved in the second equation of the BBGKY hierarchy. The same, simple mathematical techniques involved in this demonstration are used to derive two other kinetic equations, one of which is a generalization to high densities of the Boltzmann equation. In order to facilitate its application to the calculation of the van Hove and other correlation functions, the kinetic equation of the effective potential theory is Fourier-Laplace transformed: explicit formulae are given for the matrix elements of all operators that occur in this equation.     

Contribution of non-hard core triplet correlations to the bridge function of dense fluids

A possible extension of Rosenfeld's bridge functional to non-hard core interactions is considered. The hard-sphere bridge functional is supplemented with a contribution related to the non-hard core part of the triplet direct correlation function. The latter is estimated from a generalization of the factorization ansatz of Barrat, Hansen and Pastore. For the Lennard-Jones potential, this additional term is found to give a significant contribution to the tail of the bridge function. The relevance of this method to the case of highly asymmetric mixtures is underlined.     

Distributed quantum dense coding

We introduce the notion of distributed quantum dense coding, i.e., the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a nontrivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for any dimensions), bound entanglement is not useful for this task.     

A kinetic theory of dense fluids

A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.     

Light-scattering cross section as a function of pair distribution density

This paper presents a simple method of approximation for calculating the scattering cross section for a random orientated convex particle illuminated by a non polarized electromagnetic wave. This method is proved efficient for sphere and spheroids as the scattering efficiency is smaller than one and as the material is optically either soft or hard.     

Hydrogen-like atom with nonnegative quantum distribution function

Among numerous approaches to probabilistic interpretation of conventional quantum mechanics (CQM), the closest to N. Bohr’s idea of the correspondence principle is the Blokhintzev-Terletsky approach of the quantum distribution function (QDF) on the coordinate-momentum (q, p) phase space. The detailed investigation of this approach has led to the correspondence rule of V.V. Kuryshkin parametrically dependent on a set of auxiliary functions. According to investigations of numerous authors, the existence and the explicit form of QDF depends on the correspondence rule between classical functions A(q, p) and quantum operator A. At the same time, the QDF corresponding to all known quantization rules turns out to be alternating in sign or overly complex valued. Finally nonexistence of nonnegative QDF in CQM was proved. On the other hand, from this follows the possibility to construct quantum mechanics where a nonnegative QDF exists. We consider a certain set of auxiliary functions to construct explicit expressions for operators O(H) for the hydrogen atom. Naturally, these operators differ from the related operator Ĥ in CQM, so that spherical coordinates are no longer separable for a hydrogen-like atom in quantum mechanics with nonnegative QDF. The text was submitted by the authors in English.     

Calculation of transport coefficients for a moderately dense gas

Russian Physics Journal -     

Improving the efficiency of quantum hash function by dense coding of coin operators in discrete-time quantum walk

Li et al. first proposed a quantum hash function(QHF) in a quantum-walk architecture. In their scheme, two two-particle interactions, i.e., I interaction and π-phase interaction are introduced and the choice of I or π-phase interactions at each iteration depends on a message bit. In this paper, we propose an efficient QHF by dense coding of coin operators in discrete-time quantum walk. Compared with existing QHFs, our protocol has the following advantages: the efficiency of the QHF can be doubled and even more; only one particle is enough and two-particle interactions are unnecessary so that quantum resources are saved. It is a clue to apply the dense coding technique to quantum cryptographic protocols, especially to the applications with restricted quantum resources.     

The viscosity of simple dense fluids ; a memory-function approach

A gaussian memory function is used to compute the viscosity of dense fluid argon over a large region of states from the Lennard-Jones potential and the radial distribution function. The superposition approximation is used to evaluate the triplet correlation function and estimates of the errors introduced by this approximation are investigated. The agreement with experimental viscosities is quite satisfactory in the liquid region, but less so at lower densities and higher temperatures. The computed stress autocorrelation function exhibits those characteristics which are known from molecular dynamics studies. The stress autocorrelation remains monotonic even close to the triple point, where the same memory function leads to the well-known backscattering behaviour in the velocity autocorrelation function. This, too, is in agreement with the results of molecular dynamics.     

Structural relaxation in dense hard-sphere fluids

The long-time decay of the shear-stress autocorrelation function is shown to be quantitatively related to the decay of correlations between the orientation of bonds connecting colliding pairs of particles. Within computational uncertainties, we find that orientational correlations in high-density fluids decay as a stretched exponential in time, with an exponent that is independent of density. However, at low densities the decay is exponential. In two-dimensional systems the decay is exponential, even at high density.