Statistical Mechanics
Self-Assembly of Geometric Space from Random Graphs (1901.09870v1)
Christy Kelly, Carlo A Trugenberger, Fabio Biancalana
2019-01-28
We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein-Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein-Hilbert action. Working in a configuration space where the geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging geometric space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of geometric space. The model is intended as a setting for subsequent studies of emergent time mechanisms.
Thermal forces from a microscopic perspective (1901.09840v1)
Pietro Anzini, Gaia Maria Colombo, Zeno Filiberti, Alberto Parola
2019-01-28
Thermal gradients lead to macroscopic fluid motion if a confining surface is present along the gradient. This fundamental nonequilibrium effect, known as thermo-osmosis, is held responsible for particle thermophoresis in colloidal suspensions. A unified approach for thermo-osmosis in liquids and in gases is still lacking. Linear Response Theory is generalised to inhomogeneous systems,leading to an exact microscopic theory for the thermo-osmotic flow showing that the effect originates from two independent physical mechanisms, playing different roles in the gas and liquid phases, reducing to known expressions in the appropriate limits.
Reaction kinetics in the few-encounter limit (1901.09815v1)
David Hartich, Aljaz Godec
2019-01-28
The classical theory of chemical reactions can be understood in terms of diffusive barrier crossing, where the rate of a reaction is determined by the inverse of the mean first passage time (FPT) to cross a free energy barrier. Whenever a few reaction events suffice to trigger a response or the energy barriers are not high, the mean first passage time alone does not suffice to characterize the kinetics, i.e., the kinetics do not occur on a single time-scale. Instead, the full statistics of the FPT are required. We present a spectral representation of the FPT statistics that allows us to understand and accurately determine FPT distributions over several orders of magnitudes in time. A canonical narrowing of the first passage density is shown to emerge whenever several molecules are searching for the same target, which was termed the 'few-encounter limit'. The few-encounter limit is essential in all situations, in which already the first encounter triggers a response, such as misfolding-triggered aggregation of proteins or protein transcription regulation.
Relation between heterogeneous frozen regions in supercooled liquids and non-Debye spectrum in the corresponding glasses (1901.09796v1)
Matteo Paoluzzi, Luca Angelani, Giorgio Parisi, Giancarlo Ruocco
2019-01-28
Recent molecular dynamics simulation of glasses brought compelling evidenced of the existence -- besides the phonons that are Goldstone (G) vibrational modes-- of non-Goldstone (nG) modes. Different strategies have been exploited to modify the relative weight of G to nG modes in the vibrational density of states
, as for example by freezing the dynamics of a fraction p of particles. Here we first show that the nG to G ratio ---as measured by the behavior of
with
--- is enhanced when vibrations are associated with an inherent structure deep in the energy landscape, obtained by a fast quench of a supercooled liquid equilibrated at
. Secondly, by comparing
with the same quantity obtained by pinning
particles,
, we suggest that
. Finally, we provide an estimate of
a function of
, at the dynamical crossover temperature
, with
in the range
.
Disorderless quasi-localization of polar gases in one-dimensional lattices (1901.09762v1)
W. Li, A. Dhar, X. Deng, K. Kasamatsu, L. Barbiero, L. Santos
2019-01-28
One-dimensional polar gases in deep optical lattices present a severely constrained dynamics due to the interplay between dipolar interactions, energy conservation, and finite bandwidth. The appearance of dynamically-bound nearest-neighbor dimers enhances the role of the
dipolar tail, resulting, in the absence of external disorder, in quasi-localization via dimer clustering for very low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets with a finite doping of mobile, but confined, holons. Our results, which can be extrapolated to other power-law interactions, are directly relevant for current and future lattice experiments with magnetic atoms and polar molecules.
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