Equations of state for simple liquids from the Gaussian equivalent representation method

Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and distribution functions for simple liquids with arbitrary form of the central two-body potential of inter-molecular interaction. The proposed approach might become of great use for computing thermodynamic and structural quantities of simple particle and polymer systems. We believe that this technique can also provide an interesting possibility to reduce the sign problem of other methods of computer simulation based on a functional integral approach.Comment: 11 page

Conductance enhancement due to atomic potential fluctuations in graphene

We solve the Dirac equation, which describes charge massless chiral relativistic carriers in a two-dimensional graphene. We have identified and analysed a novel pseudospin-dependent scattering effect. We compute the tunneling conductance and generalize the analytical result in the presence of the tunable atomic potential of a graphene strip. The absence of back scattering in graphene is shown to be due to Berry's phase which corresponds to a sign change of the wave function under a spin rotation of a particle. We use the transfer matrix approach and find that the electric conductance of doped graphene increases due to atomic potential fluctuations.Comment: 4 pages, 2 figure

Josephson effect in Graphene SNS Junction with a Single Localized Defect

Imperfections change essentially the electronic transport properties of graphene. Motivated by a recent experiment reporting on the possible application of graphene as junctions, we study transport properties in graphene-based junctions with single localized defect. We solve the Dirac-Bogoliubov-de-Gennes equation with a single localized defect superconductor-normal(graphene)-superconductor (SNS) junction. We consider the properties of tunneling conductance and Josephson current through an undoped strip of graphene with heavily doped s-wave superconducting electrodes in the dirty limit. We find that spectrum of Andreev bound states are modified in the presence of single localized defect in the bulk and the minimum tunneling conductance remains the same. The Josephson junction exhibits sign oscillations.Comment: 5 pages, 4 figure

Local structure of supercritical matter

The supercritical state is currently viewed as uniform on the pressure-temperature phase diagram. Supercritical fluids have the dynamic motions of a gas but are able to dissolve materials like a liquid. They have started to be deployed in many important industrial applications stimulating fundamental theoretical work and development of experimental techniques. Here, we have studied local structure of supercritical matter by calculating static structure factor, mean force potential, self-diffusion, first coordination shell number and pair distribution function within very wide temperature ranges. Our results show a monotonic disappearance of medium-range order correlations at elevated temperatures providing direct evidence for structural crossover in the reciprocal and real spaces. Importantly, the discovered structural crossover in the reciprocal space is fundamentally inter-related to structural crossover in the real space, granting new unexpected interlinks between operating system properties in the supercritical state. Finally, we discuss an evolution analysis of the local structure and important implications for an experimental detection of structural monotonic transitions in the supercritical matter.Comment: 4 pages, 3 figure

Symmetry breaking gives rise to energy spectra of three states of matter

A fundamental task of statistical physics is to start with a microscopic Hamiltonian, predict the system's statistical properties and compare them with observable data. A notable current fundamental challenge is to tell whether and how an interacting Hamiltonian predicts different energy spectra, including solid, liquid and gas phases. Here, we propose a new idea that enables a unified description of all three states of matter. We introduce a generic form of an interacting phonon Hamiltonian with ground state configurations minimising the potential. Symmetry breaking, from the group of rotations in reciprocal space to its subgroup, leads to emergence of energy gaps of shear excitations as a consequence of the Goldstone theorem, and readily results in the emergence of energy spectra of solid, liquid and gas phases.Comment: 7 pages, 2 figures, 1 tabl

Theory of dipolaron solutions

A fundamental task of statistical physics is to predict the system's statistical properties and compare them with observable data. We formulate the theory of dipolaron solutions and analyze the screening effects for permanent and field-induced dipolarons. The mathematical treatment of the collective behaviour and microscopical morphology of dipolaron solutions are discussed. The presented computations show that the electric field shielding of dipolarons in dielectric nanosolutions is quite different from that of counterionic nano-complexes of Debye-H\"uckel theory of electrolytes. The limiting case of screening length $\lambda=0$ in dipolaron solutions corresponds to Coulomb's law for the potential and field of uniformly charged sphere.Comment: 5 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1109.436

Persistent local order heterogeneity in the supercritical carbon dioxide

The supercritical state is currently viewed as uniform and homogeneous on the pressure-temperature phase diagram in terms of physical properties. Here, we study structural properties of the supercritical carbon dioxide, and discover the existence of persistent medium-range order correlations which make supercritical carbon dioxide non-uniform and heterogeneous on an intermediate length scale, a result not hitherto anticipated. We report on the carbon dioxide heterogeneity shell structure where, in the first shell, both carbon and oxygen atoms experience gas-like type inter- actions with short range order correlations, while within the second shell oxygen atoms essentially exhibit liquid-like type of interactions with medium range order correlations due to localisation of transverse-like phonon packets. We show that the local order heterogeneity remains in the three phase-like equilibrium within very wide temperature range. Importantly, we highlight a catalytic role of atoms inside the nearest neighbor heterogeneity shell in providing a mechanism for diffusion in the supercritical carbon dioxide on an intermediate length scale. Finally, we discuss important implications for answering the intriguing question whether Venus may have had carbon dioxide oceans and urge for an experimental detection of this persistent local order heterogeneity.Comment: 5 pages, 6 figure

Unified phonon-based approach to the thermodynamics of solid, liquid and gas states

We introduce a unified approach to states of matter (solid, liquid and gas) and describe the thermodynamics of the pressure-temperature phase diagram in terms of phonon excitations. We derive the effective Hamiltonian with low-energy cutoff in two transverse phonon polarizations (phononic band gaps) by breaking the symmetry in phonon interactions. Further, we construct the statistical mechanics of states of aggregation employing the Debye approximation. The introduced formalism covers the Debye theory of solids, the phonon theory of liquids, and thermodynamic limits such as the Dulong-Petit thermodynamic limit, the ideal gas limit and the new thermodynamic limit, dubbed here the Frenkel line thermodynamic limit. We discuss the phonon propagation and localization effects in liquids above and below the Frenkel line, and explain the "fast sound" phenomenon. As a test for our theory we calculate velocity-velocity autocorrelation and pair distribution functions within the Green-Kubo formalism. We show the consistency between dynamics of phonons and pair correlations in the framework of the unified approach. New directions towards advancements in phononic band gaps engineering, hypersound manipulation technologies and exploration of exotic behaviour of fluids relevant to geo- and planetary sciences are discussed. The presented results are equally important both for practical implications and for fundamental research.Comment: 21 pages, 7 figures, 3 table

The Frenkel Line: a direct experimental evidence for the new thermodynamic boundary

Supercritical fluids play a significant role in elucidating fundamental aspects of liquid matter under extreme conditions. They have been extensively studied at pressures and temperatures relevant to various industrial applications. However, much less is known about the structural behaviour of supercritical fluids and no structural crossovers have been observed in static compression experiments in any temperature and pressure ranges beyond the critical point. The structure of supercritical state is currently perceived to be uniform everywhere on the pressure-temperature phase diagram, and to change only in a monotonic way even moving around the critical point, not only along isotherms or isobars. Conversely, we observe structural crossovers for the first time in a deeply supercritical sample through diffraction measurements in a diamond anvil cell and discover a new thermodynamic boundary on the pressure-temperature diagram. We explain the existence of these crossovers in the framework of the phonon theory of liquids using molecular dynamics simulations. The obtained results are of prime importance since it implies a global reconsideration of the mere essence of the supercritical phase. Furthermore, this discovery may pave the way to new unexpected applications and to the exploration of exotic behaviour of confined fluids relevant to geo- and planetary sciences.Comment: 11 pages, 5 figure

Thermally triggered phononic gaps in liquids at THz scale

In this paper we present inelastic X-ray scattering experiments in a diamond anvil cell and molecular dynamic simulations to investigate the behavior of phononic excitations in liquid Ar. The spectra calculated using molecular dynamics were found to be in a good agreement with the experimental data. Furthermore, we observe that, upon temperature increases, a low-frequency transverse phononic gap emerges while high-frequency propagating modes become evanescent at the THz scale. The effect of strong localization of a longitudinal phononic mode in the supercritical phase is observed for the first time. The evidence for the high-frequency transverse phononic gap due to the transition from an oscillatory to a ballistic dynamic regimes of motion is presented and supported by molecular dynamics simulations. This transition takes place across the Frenkel line thermodynamic limit which demarcates compressed liquid and non-compressed fluid domains on the phase diagram and is supported by calculations within the Green-Kubo phenomenological formalism. These results are crucial to advance the development of novel terahertz thermal devices, phononic lenses, mirrors, and other THz metamaterials.Comment: 8 pages, 5 figures. arXiv admin note: text overlap with arXiv:1512.0720