arXiv subjects

Richard M. Stratt

Publications and source records attributed to Richard M. Stratt.

6 recordsLinked to original sources

arXiv2024

Exceptionally Large Fluctuations in Orientational Order: The Lessons of Large-Deviation Theory for Liquid Crystalline Systems

How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on isotropic-phase samples display increasingly large orientational fluctuations ("pseudo-nematic domains") as the samples approach their nematic phase. The growing length scale of those locally ordered domains is readily seen in simulation as an ever-slower convergence of the distribution of orientational order parameters with $N$. But the rare-event character and exceptionally slow time scales of the largest fluctuations make them difficult to sample accurately. We show in this paper how taking a large-deviation-theory perspective enables us to leverage simulation-derived information more effectively. A key insight of the theory is that finding quantities such as orientational order parameters (extensive variables), is completely equivalent to deducing the conjugate (intensive) thermodynamic field required to equilibrate that amount of order - and that knowing the relationship between the two (the "equation of state") can easily be turned into knowing the relative free energy of that degree of order. A variety of well-known thermodynamic integration strategies are already founded on this idea, but instead of applying an artificially imposed external field, we use a priori statistical mechanical insights into the small and large-field limits to construct a simulation-guided, interpolated, equation of state. The free energies that result mostly need information from the most probable configurations, making the simulation process far more efficient than waiting for (or artificially generating) large fluctuations.

cond-mat.soft↗

arXiv2014

The potential energy landscape and inherent dynamics of a hard-sphere fluid

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly non-analytic character of their potentials makes it a challenge to think of that behavior in potential-energy-landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential-energy landscape) correctly predict the occurrence of dynamic heterogeneity and non-zero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.

cond-mat.soft↗

arXiv2007

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move - an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that removes the concept of potential barriers from the problem, and (2) a way of finding optimum pathways within this new ensemble. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable. We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers, it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen model of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper.

cond-mat.soft↗

arXiv2007

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape

How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential energy landscape ensemble, it is possible to make direct connections between the geometry of the landscape and the long-time dynamical behaviors of systems such as supercooled liquids. We show, in particular, that the onset of slow dynamics in such systems is governed directly by the lengths of their geodesics - the shortest paths through their landscapes within the special ensemble. The more convoluted and labyrinthine these geodesics are, the slower that dynamics is. Geodesics in the landscape ensemble have sufficiently well-defined characteristics that is straightforward to search for them numerically, a point we illustrate by computing the geodesic lengths for an ordinary atomic liquid and a binary glass-forming atomic mixture. We find that the temperature dependence of the diffusion constants of these systems, including the precipitous drop as the glass-forming system approaches its mode-coupling transition, is predicted quantitatively by the growth of the geodesic path lengths.

cond-mat.soft↗

arXiv2007

A microscopically-based, global landscape perspective on slow dynamics in condensed matter

A complete understanding of the precipitous onset of slow dynamics in systems such as supercooled liquids requires making direct connections between dynamics and the underlying potential energy landscape. With the aid of a switch in ensembles, we show that it is possible to formulate a landscape-based mechanism for the onset of slow dynamics based on the rapid lengthening of the geodesic paths that traverse the landscape. We confirm the usefulness of this purely geometric analysis by showing that it successfully predicts the diffusion constants of a standard model supercooled liquid.

cond-mat.soft↗

arXiv1998

Instantaneous Pair Theory for High-Frequency Vibrational Energy Relaxation in Fluids

Notwithstanding the long and distinguished history of studies of vibrational energy relaxation, exactly how it is that high frequency vibrations manage to relax in a liquid remains somewhat of a mystery. Both experimental and theoretical approaches seem to say that there is a natural frequency range associated with intermolecular motions in liquids, typically spanning no more than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent can absorb any vibrational energy within this "band", but how is it that molecules can rid themselves of superfluous vibrational energies significantly in excess of these values? We develop a theory for such processes based on the idea that the crucial liquid motions are those that most rapidly modulate the force on the vibrating coordinate -- and that by far the most important of these motions are those involving what we have called the mutual nearest neighbors of the vibrating solute. Specifically, we suggest that whenever there is a single solvent molecule sufficiently close to the solute that the solvent and solute are each other's nearest neighbors, then the instantaneous scattering dynamics of the solute-solvent pair alone suffices to explain the high frequency relaxation. The many-body features of the liquid only appear in the guise of a purely equilibrium problem, that of finding the likelihood of particularly effective solvent arrangements around the solute. These results are tested numerically on model diatomic solutes dissolved in atomic fluids (including the experimentally and theoretically interesting case of I_2 in Xe). The instantaneous pair theory leads to results in quantitative agreement with those obtained from far more laborious exact molecular dynamics simulations.

physics.chem-ph↗