Theory of collective excitations in simple liquids

We present a parameter-free theory of the collective excitations in simple liquids such as liquid metals or rare gases. The theory is based on the mode-coupling theory (MCT), which has been previously applied successfully for explaining the liquid-to glass transition. The only input is the liquid structure factor. We achieve good agreement both for the liquid dispersion (maximum of the longitudinal current spectrum) and width (damping) with experimental findings. The time-dependent memory function predicted by MCT has a two-step exponential decay as previously found in computer simulations. Furthermore MCT predicts a scaling of the liquid dispersion with the effective hard-sphere diameter of the materials. This scaling is obeyed by the available experimental data.     

Evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wavelength and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wavelength with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by x-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.     

Selective-pivot sampling of radial distribution functions in asymmetric liquid mixtures

We present a new method for selectively sampling radial distribution functions and effective interaction potentials in asymmetric liquid mixtures using a Monte Carlo simulation. We demonstrate its efficiency for hard-sphere mixtures, and for model systems with more general interactions, and compare our simulations with several analytical approximations. For interaction potentials containing a hard-sphere contribution, the algorithm yields the contact value of the radial distribution function.     

Second-order Percus-Yevick theory for a confined hard-sphere fluid

A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions depend upon the positions of four particles (two hard spheres and two walls treated as giant hard spheres), this is the most demanding application of the second-order theory that has been attempted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations showed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a singlet approximation (in the sense that correlation functions that depend on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard spheres, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.     

Static and dynamic behaviours of multivortex states in a superconducting sample with mesoscopic pinning sites

This preliminary work has focused on the static transitions between the multivortex states interacting with square arrays of the mesoscopic pinning sites in superconducting samples. Our results were obtained from an extensive series of numerical simulations as functions of the magnetic field, pinning radius, and sample size. We have presented a wide range of multivortex configurations from commensurate dimer states to more concentric vortex shells at the matching fields. The stability of these states was also studied by means of the current-voltage V(I) curves which illustrate dynamic phase transitions as a function of applied driving force. These transitions manifested themselves as either a sudden jump in velocity or a nonlinear increase with velocity fluctuations in V(I) curves. We have investigated whether that the phase transitions between the pinned regime and the elastic flow regime are indicative of the stability of the initial vortex states. The variety of intermediate flow phases is attributed to large pinning size (reentrant behavior), strong commensurability and caging effects. In particular, three-shell vortex structures were obtained in the presence of larger pinning sites at adequate matching magnetic fields.     

Dynamic critical behavior near the superfluid transition in 3He-4He mixtures in two loop order

We calculated in two loop order the field theoretic renormalization group functions taking into account the decomposition of the dynamical vertex functions into the static vertex functions and genuine dynamical parts. The observation of this nonperturbative structure simplifies the theoretical expressions obtained by perturbation theory considerably and makes tractable a complete two loop calculation of the critical dynamics near the superfluid transition of 3He-4He mixtures (model F'). As a result, we obtain various transport coefficients, which govern the nonasymptotic and nonuniversal temperature dependence. We also correct long-standing results for the critical dynamics of the superfluid transition in pure 4He (model F) and for the dynamics of structural or magnetic phase transitions (model C).     

Overview of phases and phase transitions

We provide an overview of some modern developments in the theory of phases and phase transitions in classical and quantum systems. We show the link between non-ergodicity and fidelity in quantum systems and discuss topological phase transitions. We show that the quantum phase transitions are associated with qualitative changes in some properties of the quantum wavefunctions across the phase transition. We discuss the topological phase transition associated with p-wave superconductor since it is a topic of wide interest because of the possible observation of Majorana fermions.     

Dynamics in dense suspensions of charge-stabilized colloidal particles

The dynamic behavior of charge-stabilized colloidal particles in suspension was studied by photon correlation spectroscopy with coherent X-rays (XPCS). The short-time diffusion coefficient, D(Q) , was measured for volume concentrations φ ⩽ 0.18 and compared to the free particle diffusion constant D₀ and the static structure factor S(Q) . The data show that indirect, hydrodynamic interactions are relevant for the system and hydrodynamic functions were derived. The results are in striking contrast to the predictions of the PA (pairwise-additive approximation) model, but show features typical for a hard-sphere system. The observed mobility is however considerably smaller than the one of a respective hard-sphere system. The hydrodynamic functions can be modelled quantitatively if one allows for an increased effective viscosity relative to the hard-sphere case.     

Raman spectroscopy of atomic fluorine

We have measured the Raman scattering cross section of atomic fluorine for transitions between the ground fine-structure electronic states. The fluorine was contained a in heated, static chamber. Gas temperature, determined from the rotational Raman spectrum of molecular fluorine, was used as an input to calculate the degree of fluorine dissociation (assuming thermodynamic and chemical equilibrium). The Raman frequency shift and depolarization ratio were also determined. Our results indicate that Raman scattering can be used as a probe for atomic fluorine.     

Weighted-density approaches for polymer structure at solid–polymer interfaces

Weighted-density approximations (WDAs), which are based on the weighting function for the second-order direct correlation functions (DCFs) of the uniform polymeric fluids, have been developed to investigate the structural and thermodynamic properties of polymer melts at interfaces. The advantage is the simplicity of calculation of the weighting functions and their accuracies in the applications. They were applied to study the local density distributions and adsorption isotherms of the freely jointed tangent hard-sphere chain, Yukawa chain, and hard-sphere chain mixture in slit pores. The polymer reference interaction model (PRISM) integral equation with the Percus–Yevick (PY) closure has been used to calculate the second-order DCF of the polymeric fluids required as inputs. The mean-field approximation (MFA) has been used to calculate the weighting function for the attractive contribution of a freely jointed tangent Yukawa chain fluid, having attraction among the beads. The calculated results show that (i) for the freely jointed tangent hard-sphere chain, the present theory is in excellent agreement with the computer simulations over a wide range of chain lengths and bulk densities, (ii) the WDA approach for the attraction provides an accurate method for the local density distributions of a freely jointed tangent Yukawa chain fluid, and that (iii) the present theory also yields a reasonably good result for the structural properties of the freely jointed hard-sphere chain mixtures composed of the chain and monomer.     

The ground-state phase diagram of the spinless 1D falicov-kimball model: Numerical studies

Extrapolation of small-cluster exact-diagonalization calculations is used to study the ground state phase diagram of the spinless one-dimensional Falicov-Kimball model at half filling. Our results show that the phase diagram has an extremely simple structure for the Coulomb interactionsU≥2. Here the ground states are the most homogeneous configurations (mhc) with the smallest periods. Valence transitions are discontinuous and only of the type insulator-insulator. In this region the finite size effects are negligible and thus the picture of valence transitions is definitive. ForU<2 the phase diagram exhibits a more complicated structure. Here we have specified a domain where the ground states are the mhc and a metallic domain where the ground states are mixtures of configurations with the empty configuration. The boundary between these two domains is the boundary of discontinuous insulator-metal transitions. Unlike the caseU≥2 the valence transitions are gradual in the weak coupling limit. This work was supported by the Slovak scientific grant agency VEGA, contract No. 4177/97.     

Universal cubic equation of state and contact values of the radial distribution functions for multi-component additive hard-sphere mixtures

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.     

Inhomogeneous Tsallis distributions in the HMF model

We study the maximization of the Tsallis functional at fixed mass and energy in the Hamiltonian Mean Field (HMF) model. We give a thermodynamical and a dynamical interpretation of this variational principle. This leads to q-distributions known as stellar polytropes in astrophysics. We study phase transitions between spatially homogeneous and spatially inhomogeneous equilibrium states. We show that there exists a particular index q _c = 3 playing the role of a canonical tricritical point separating first and second order phase transitions in the canonical ensemble and marking the occurence of a negative specific heat region in the microcanonical ensemble. We apply our results to the situation considered by Antoni and Ruffo [Phys. Rev. E 52, 2361 (1995)] and show that the anomaly displayed on their caloric curve can be explained naturally by assuming that, in this region, the QSSs are polytropes with critical index q _c = 3. We qualitatively justify the occurrence of polytropic (Tsallis) distributions with compact support in terms of incomplete relaxation and inefficient mixing (non-ergodicity). Our paper provides an exhaustive study of polytropic distributions in the HMF model and the first plausible explanation of the surprising result observed numerically by Antoni and Ruffo (1995). In the course of our analysis, we also report an interesting situation where the caloric curve presents both microcanonical first and second order phase transitions.     

Raman spectroscopy of hot compressed hydrogen and nitrogen: implications for the intramolecular potential

Raman measurements of molecular hydrogen ( and ) and nitrogen () have been made under simultaneous conditions of high temperature and high static pressure. Measurements have been made on H2 and D2 to 50 GPa and 1600 K, and on to 50 GPa and 2000 K. In all three materials the familiar molecular stretching mode (vibron) is accompanied in the high-temperature Raman spectra by one or more lower-frequency peaks due to transitions from excited vibrational states. We find that the frequency differences between these bands decreases with pressure, implying that the anharmonicity of the corresponding part of the intramolecular potential also decreases. This is accompanied by an increase in the measured linewidths of the bands that is consistent with a decrease of the depth of the potential and an approaching molecular dissociation.     

Rydberg spectroscopy in an optical lattice: blackbody thermometry for atomic clocks

We show that optical spectroscopy of Rydberg states can provide accurate in situ thermometry at room temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25-30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the strontium clock transition. We demonstrate that magic-wavelength lattices exist for both strontium and ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with 10(-16) accuracy provide 10 mK resolution and yield a blackbody uncertainty for the clock transition of 10(-18).     

Dynamics of chain molecules in disordered materials

The dynamic behavior of hard chains in disordered materials composed of fixed hard spheres is studied using discontinuous molecular dynamics simulations. The matrix induces entanglements in the chain fluid, i.e., for high matrix densities the diffusion coefficient D scales with the chain length N as D is approximately N(-2). At high matrix densities the rotational relaxation time becomes very large but the translational diffusion is not affected significantly; i.e., the chains display a dynamic heterogeneity reminiscent of probe diffusion in supercooled liquids and glasses. We show that this is because some chains are trapped, and move via a hopping mechanism. There are no signatures of this dynamic heterogeneity in the matrix static structure, however, which is identical to that of a hard-sphere liquid.     

Inhomogeneous mode-coupling theory and growing dynamic length in supercooled liquids

We extend mode-coupling theory (MCT) to inhomogeneous situations, relevant for supercooled liquid in an external field. We compute the response of the dynamical structure factor to a static inhomogeneous external potential and provide the first direct evidence that the standard formulation of MCT is associated with a diverging length scale. We find that the so-called cages are, in fact, extended objects. Although close to the transition the dynamic length grows as |T-T(c)|(-1/4) in both the beta and alpha regimes, our results suggest that the fractal dimension of correlated clusters is larger in the alpha regime. We derive inhomogeneous MCT equations valid to second order in gradients.     

Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state (EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory (PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid. The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact (RDFC) of mixtures. The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.