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Register a new userDetecting and characterizing frequency fluctuations of vibrational modes
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We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the complex amplitude sensitively depend on the frequency noise statistics and its power spectrum. The analysis applies to classical and to quantum vibrations.
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We numerically study the evolution of the vibrational density of states $D(omega)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(omega) sim omega^2$) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes instead obey $D(omega) sim omega^4$, irrespective of the glass stability. However, the prefactor of this quartic law becomes smaller in more stable glasses, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glass stability and soft vibrational motion in amorphous solids.
Thermal transport through nanosystems is central to numerous processes in chemistry, material sciences, electrical and mechanical engineering, with classical molecular dynamics as the key simulation tool. Here we focus on thermal junctions with a molecule bridging two solids that are maintained at different temperatures. The classical steady state heat current in this system can be simulated in different ways, either at the interfaces with the solids, which are represented by thermostats, or between atoms within the conducting molecule. We show that while the latter, intramolecular definition feasibly converges to the correct limit, the molecule-thermostat interface definition is more challenging to converge to the correct result. The problem with the interface definition is demonstrated by simulating heat transport in harmonic and anharmonic one-dimensional chains illustrating unphysical effects such as thermal rectification in harmonic junctions.
Hydrophobic effects drive diverse aqueous assemblies, such as micelle formation or protein folding, wherein the solvent plays an important role. Consequently, characterizing the free energetics of solvent density fluctuations can lead to important insights into these processes. Although techniques such as the indirect umbrella sampling (INDUS) method (Patel et al. J. Stat. Phys. 2011, 145, 265-275) can be used to characterize solvent fluctuations in static observation volumes of various sizes and shapes, characterizing how the solvent mediates inherently dynamic processes, such as self-assembly or conformational change, remains a challenge. In this work, we generalize the INDUS method to facilitate the enhanced sampling of solvent fluctuations in dynamical observation volumes, whose positions and shapes can evolve. We illustrate the usefulness of this generalization by characterizing water density fluctuations in dynamic volumes pertaining to the hydration of flexible solutes, the assembly of small hydrophobes, and conformational transitions in a model peptide. We also use the method to probe the dynamics of hard spheres.
Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small system exchanging energy with a bath is usually understood as a limitation of conventional statistical mechanics. We interpret this ambiguity as resulting from a stochastically fluctuating temperature coupled with the phase space variables giving rise to a broad temperature distribution. With this ansatz, we develop the equilibrium statistics and dynamics of small systems. Numerical evidence using an analytically tractable model shows that the effects of temperature fluctuations can be detected in equilibrium and dynamical properties of the phase space of the small system. Our theory generalizes statistical mechanics to small systems relevant to biophysics and nanotechnology.
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $omega$ as $omega^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_text{exc}(omega)sim omega^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_text{exc}(omega)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $omega^3$.
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