Quantum mode-coupling theory for binary mixtures

We extend the quantum mode-coupling theory of neat liquids to the case of binary mixtures, in order to study supercooled liquids where quantum fluctuations may compete with thermal fluctuations. We apply the theory to a generic model of a binary mixture of Lennard-Jones particles. Our treatment may be used to study quantum aging and exotic glass melting scenarios in structural supercooled quantum liquids.     

On the mode-coupling theory of vibrational line broadening in near-critical fluids

Molecular-dynamics simulations of a neat atomic fluid, coupled with a simple model for vibrational frequency perturbations, are used to investigate vibrational line broadening near the liquid-gas critical point. All features of our simulations are in qualitative agreement with recent Raman experiments on nitrogen. We also use our simulation results to assess the validity of the mode-coupling theories that have been used to analyze experiment. We find that the theoretical results are not in good agreement with simulation, both for the temperature dependence of the linewidth, and for the frequency time-correlation functions. However, the mode-coupling prediction that critical line broadening is due to the diverging correlation time of the frequency fluctuations is shown to be correct.     

Slow dynamics of the high density Gaussian core model

We numerically study crystal nucleation and glassy slow dynamics of the one-component Gaussian core model (GCM) at high densities. The nucleation rate at a fixed supercooling is found to decrease as the density increases. At very high densities, the nucleation is not observed at all in the time window accessed by long molecular dynamics (MD) simulation. Concomitantly, the system exhibits typical slow dynamics of the supercooled fluids near the glass transition point. We compare the simulation results of the supercooled GCM with the predictions of mode-coupling theory (MCT) and find that the agreement between them is better than any other model glassformers studied numerically in the past. Furthermore, we find that a violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than canonical glassformers. Analysis of the probability distribution of the particle displacement clearly reveals that the hopping effect is strongly suppressed in the high density GCM. We conclude from these observations that the GCM is more amenable to the mean-field picture of the glass transition than other models. This is attributed to the long-ranged nature of the interaction potential of the GCM in the high density regime. Finally, the intermediate scattering function at small wavevectors is found to decay much faster than its self part, indicating that dynamics of the large-scale density fluctuations decouples with the shorter-ranged caging motion.     

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory (cited: 2)

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa-tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site modelwith Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode-coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.     

Transport properties of normal liquid helium: comparison of various methodologies

We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.     

Dynamics of interacting Brownian particles: a diagrammatic formulation

We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion, we introduce a basis that consists of orthogonalized many-particle density fluctuations. We obtain an exact hierarchy of equations of motion for time-dependent correlations of orthogonalized density fluctuations. To simplify this hierarchy we neglect contributions to the vertices from higher-order cluster expansion terms. An iterative solution of the resulting equations can be represented by diagrams with three- and four-leg vertices. We analyze the structure of the diagrammatic series for the time-dependent density correlation function and obtain a diagrammatic interpretation of reducible and irreducible memory functions. The one-loop self-consistent approximation for the latter function coincides with mode-coupling approximation for Brownian systems that was derived previously using a projection operator approach.     

A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium

Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids.     

Nuclear magnetic resonance proton dipolar order relaxation in thermotropic liquid crystals: a quantum theoretical approach

By means of the Jeener-Broekaert nuclear magnetic resonance pulse sequence, the proton spin system of a liquid crystal can be prepared in quasiequilibrium states of high dipolar order, which relax to thermal equilibrium with the molecular environment with a characteristic time (T1D). Previous studies of the Larmor frequency and temperature dependence of T1D in thermotropic liquid crystals, that included field cycling and conventional high-field experiments, showed that the slow hydrodynamic modes dominate the behavior of T1D, even at high Larmor frequencies. This noticeable predominance of the cooperative fluctuations (known as order fluctuations of the director, OFD) could not be explained by standard models based on the spin-lattice relaxation theory in the limit of high temperature (weak order). This fact points out the necessity of investigating the role of the quantum terms neglected in the usual high temperature theory of dipolar order relaxation. In this work, we present a generalization of the proton dipolar order relaxation theory for highly correlated systems, which considers all the spins belonging to correlated domains as an open quantum system interacting with quantum bath. As starting point, we deduce a formulation of the Markovian master equation of relaxation for the statistical spin operator, valid for all temperatures, which is suitable for introducing a dipolar spin temperature in the quantum regime, without further assumptions about the form of the spin-lattice Hamiltonian. In order to reflect the slow dynamics occurring in correlated systems, we lift the usual short-correlation-time assumption by including the average over the motion of the dipolar Hamiltonian together with the Zeeman Hamiltonian into the time evolution operator. In this way, we calculate the time dependence of the spin operators in the interaction picture in a closed form, valid for high magnetic fields, bringing into play the spin-spin interactions within the microscopic time scale. Then, by adopting the spin-temperature density operator to represent the collective state of the spin system, and removing the traditional hypothesis of high temperature, we deduce an expression for the first order quantum contribution to T1D (-1), in terms of spectral densities, with coefficients in form of spin traces. The properties that distinguish our result from the high-temperature T1D (-1) are as follows. (a) It is exclusively associated to cooperative fluctuations. (b) Because of its quantum character, it relies on both considering the lattice degrees of freedom quantum mechanically and including the spin-spin interactions in the microscopic time scale. With regard to the average dipolar Hamiltonian, only the nonsecular part plays a relevant role. (c) Associated with the structure of the spin operator involved in the quantum contribution, a term arises which is proportional to the number of spins in the correlated molecular domains, showing that the quantum contribution may be of macroscopic size in highly correlated systems. When applied to nematic liquid crystals, the new term exhibits the typical nu(-1/2) Larmor frequency dependence through the spectral density of the OFD, in consistence with the experimental results.     

Polar solvation dynamics in supercritical fluids: a mode-coupling treatment

A mode-coupling treatment of polar solvation dynamics in supercritical fluids is presented. The equilibrium solvation time correlation function for the solute fluctuating transition frequency is obtained from the mode-coupling theory method and from molecular-dynamics simulations. The theory is shown to be in good agreement with the simulation. The solvation time correlation function exhibits three distinct time scales, with rapid initial decay, followed by a recurrence at intermediate times, and a slowly decaying long-time tail. Our theoretical analysis shows that the short-time decay arises from the coupling of the solute energy gap to the solvent polarization modes, the recurrence at intermediate times is due to the energy modes, while the slow long-time decay reflects the coupling to the number density modes.     

Electrostatic relaxation and hydrodynamic interactions for self-diffusion of ions in electrolyte solutions

The concentration dependence of self-diffusion of ions in solutions at large concentrations has remained an interesting yet unsolved problem. Here we develop a self-consistent microscopic approach based on the ideas of mode-coupling theory. It allows us to calculate both contributions which influence the friction of a moving ion: the ion atmosphere relaxation and hydrodynamic interactions. The resulting theory provides an excellent agreement with known experimental results over a wide concentration range. Interestingly, the mode-coupling self-consistent calculation of friction reveal a nonlinear coupling between the hydrodynamic interactions and the ion atmosphere relaxation which enhances ion diffusion by reducing friction, particularly at intermediate ion concentrations. This rather striking result has its origin in the similar time scales of the relaxation of the ion atmosphere relaxation and the hydrodynamic term, which are essentially given by the Debye relaxation time. The results are also in agreement with computer simulations, with and without hydrodynamic interactions.     

A mode-coupling theory treatment of the transport coefficients of the Lennard-Jones fluid

We apply mode-coupling theory to study shear viscosity and self-diffusion coefficient of the Lennard-Jones fluid throughout the entire fluid region of the phase diagram. Theoretical results are compared with the extensive simulation data and good agreement is found. In addition, theory is compared to the experimental data on the transport coefficients of inert gas fluids.     

Multiple short time power laws in the orientational relaxation of nematic liquid crystals

Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Quantum diffusive dynamics of macromolecular transitions

We study the role of quantum fluctuations of atomic nuclei in the real-time dynamics of non-equilibrium macro-molecular transitions. To this goal we introduce an extension of the dominant reaction pathways formalism, in which the quantum corrections to the classical overdamped Langevin dynamics are rigorously taken into account to order ?(2). We first illustrate our approach in simple cases, and compare with the results of the instanton theory. Then we apply our method to study the C7(eq) → C7(ax) transition of alanine dipeptide. We find that the inclusion of quantum fluctuations can significantly modify the reaction mechanism for peptides. For example, the energy difference which is overcome along the most probable pathway is reduced by as much as 50%.     

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular, mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wave vector dependence of multipoint correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multipoint correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular, explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multipoint correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.     

Scattering function and the dynamics of phase separation in polymer mixtures under shear flow

The phenomenological mean-field theory describing concentration fluctuations and spinodal decomposition of binary mixtures of long flexible macromolecules is generalized to mixtures under steady shear flow. This shear flow leads to a partial orientation and stretching of the coils, as well as to an anisotropic deformation of concentration fluctuations. Generalizing the approach of Onuki and Kawasaki, we obtain the collective scattering function describing these concentration fluctuations in the mixture under shear flow. Both the steady-state situation in the one-phase region and the initial stages of spinodal decomposition for concentrations inside of the spinodal curve are considered.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Berlin, March 30–April 3, 1987.