Open Statistical Physics 2019

The 2019 Open Statistical Physics meeting took place on Wednesday, 27 March 2019. This year, we had a single session of talks in the morning and early afternoon, finishing with a brief parallel session.

Schedule

Time Session A Session B
10:00Coffee
10:25Welcome address
10:30Hague
11:00Dettman
11:30Prellberg
12:00Lunch break
13:00James
13:30Flicker
14:00Mestel
14:30Tea break
15:00MühlbacherRose
15:30MoodieCoghi
16:00VasiloiuRodrigues
16:30Close and Departure

Participants

Ibai Aedo (Open)
Francesco Coghi (Queen Mary)
Carl Dettmann (Bristol)
Michael Ewatola (Open)
Felix Flicker (Oxford)
Uwe Grimm (Open)
Jim Hague (Open)
Matthew Haynes (Open)
Andrew James (Open)
Gerhard Kling (Open)
Ben Mestel (Open)
Jordan Moodie (Birmingham)
Peter Mühlbacher (Warwick)
Marc Pradas (Open)
Thomas Prellberg (Queen Mary)
Nathann Teixeira Rodrigues (Queen Mary)
Dominic Rose (Nottingham)
Paul Upton (Open)
Loredana Vasiloiu (Nottingham)
Michael Wilkinson (Open)

Talks and Abstracts

Francesco Coghi (Queen Mary)

Large deviation perspective on the "efficiency" of reset processes

Reset processes are stochastic processes which randomly reset at some time to their initial condition. They have have attracted much interest in the nonequilibrium statistical physics community in the last few years, and many results concerning the appearance of nonequilibrium steady states have been found. We focus on studying large deviations of a particular observable associated to a discrete reset process: the ratio between current and number of reset steps, which can be regarded as a form of efficiency. We discuss its large deviation shape, and present some open questions related to the appearance of a change of scaling in the underlying process.

Carl Dettmann (Bristol)

Spectral statistics in spatial networks

Diffusion processes on networks can be described using the spectrum of the graph Laplacian. This spectrum and that of the related adjacency matrix have been studied for the most popular model of spatial networks, the random geometric graph. Degeneracies are related to graph symmetries, which can be quantified as a function of parameters in one, two or three dimensions. The spectral statistics can also be compared with relevant models from random matrix theory.
(work with Orestis Georgiou and Georgie Knight)

Felix Flicker (Oxford)

The classical dimer model on Penrose tilings

We study the classical dimer model on Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (dimer coverings free of unmatched vertices, `monomer' defects). Matchings with the maximum number of dimers have a monomer density of 81-50*(the golden ratio), approximately 0.098, in the thermodynamic limit. These matchings divide the tiling into a fractal of nested closed regions bounded by loops that cannot be crossed by monomers. These loops connect second-nearest neighbour even-valence vertices, each of which lies on such a loop. Assigning a charge to each monomer with a sign fixed by its bipartite sublattice, we find that each bounded region has an excess of one charge, and a corresponding set of monomers, with adjacent regions having opposite net charge. The infinite tiling is charge neutral. We devise a simple algorithm for generating maximum matchings, which form a connected manifold under local monomer-dimer rearrangements.

Jim Hague (Open)

A minimal model for nematic cell ordering in tissue

Recent advances mean that samples of artificial tissue can now be grown. Hence there is a need for theoretical understanding of these tissues commensurate with the size of experimental systems. We present a minimal model for predicting cell orientations and modification of tissue shape resulting from the active forces in cells. The extracellular matrix (ECM), a biopolymer network found between cells, is represented by an elastic network. Cells in the model induce tension in this network according to their symmetries. This in turn influences nearby cells leading to nematic order and change of tissue shape. Simulated annealing solutions of the model show close agreement with experimental results for artificial neural tissue. Thus, the subtle interplay between forces generated by cells and the ECM that leads to the ordering of tissues is reproduced. Applications of the model are discussed.

Andrew James (Open)

Non-thermal behaviour due to confinement in 1D and 2D

It is generally expected that an out-of-equilibrium quantum system will `thermalise' after some length of time, unless it is integrable (i.e. possesses infinitely many conserved charges). However, rare states that defy this tendency can occur in a model's spectrum, yielding non-thermal behaviour and anomalous dynamics. I will describe how confinement in a paradigmatic quantum model (in 1D and 2D) can lead to rare states extending deep into its spectrum, and what the implications are for thermalisation and dynamics.

Ben Mestel (Open)

Fitting multiple power-law probability distributions to data with an application to Icelandic volcanism

Building on the work of Clauset, Shalizi and Newman for a single-power law, maximum-likelihood estimates are obtained for the exponents of a multiple power-law model for a one-dimensional probability distribution valid for x >= x_1 > 0 with change points 0 < x_1 < x_2 < ... < x_l < infty between the power-laws comprising the distribution. An algorithm is presented to find the optimal set of change points for the Kolmogorov-Smirnov distance and to apply a bootstrap method to obtain a p-value to test the statistical validity of the fit. The method is then applied to study the eruption volume-frequency relationships for Icelandic volcanism during the Holocene, focussing on the various volcanic zones within the Icelandic system.
This is joint work with Eleanor Mestel (University of Birmingham), Oliver Shorttle (University of Cambridge) and Sæmundur Halldórsson (University of Iceland).

Jordan Moodie (Birmingham)

An exact power series representation of the Baker-Campbell-Hausdorff formula

The Baker-Campbell-Hausdorff formula, in various guises, is often thought of in the context of Lie groups and particle physics though more recently it has found use in quantum mechanics. For example, one could imagine evolving a system first by one Hamiltonian and then another, with the task being to find the Floquet Hamiltonian describing the overall operation. We believe it also occupies a natural space in statistical mechanics, where a transfer matrix may be re-imagined as the exponential of some free-energy operator. The existing formula is essentially a Taylor expansion in two variables which, in the quantum mechanics example, control the time each Hamiltonian is active for. There is a problem however; how should one truncate the expansion?
Unless both variables may be considered small this approach may not be fruitful. I will present recent work (arXiv:1807.07884) which exactly resums one of the variables in this double Taylor series, leaving a power series in the other. Closed form expressions for each coefficient will be found which generalise the first order term found by Campbell in the late 19th century. Practically, this result allows one to have one of the two aforementioned variables be large, opening up regions of phase-space previously inaccessible.

Peter Mühlbacher (Warwick)

Giant loops and percolation

The loop soups considered in this talk are probabilistic models on graphs with intimate connections to phenomena like Bose-Einstein condensation, correlation functions and other observables of certain quantum spin systems. They admit a natural comparison to an appropriately chosen percolation model which is expected to behave "the same way" on sufficiently well-connected graphs. If time permits a new proof for why this does not hold for graphs of uniformly bounded degree will be outlined.

Thomas Prellberg (Queen Mary)

Exact solution of pulled, directed vesicles with sticky walls in two dimensions

We analyse a directed lattice vesicle model incorporating both the binding-unbinding transition and the vesicle inflation-deflation transition. From the exact solution we derive the phase diagram for this model and elucidate scaling properties around the binding-unbinding critical point in this larger parameter space. We also consider how the phase diagram changes when a perpendicular force is applied to the end of a directed vesicle.
(with Aleks Owczarek)

Nathann Teixeira Rodrigues (Queen Mary)

On the special adsorption transition of interacting self-avoiding trails in two dimensions

We investigate the surface adsorption transition of interacting self-avoiding square lattice trails onto a straight boundary line. The character of this adsorption transition depends on the strength of the bulk interaction, which induces a collapse transition of the trails from a swollen to a collapsed phase, separated by a critical state. If the trail is in the critical state, the universality class of the adsorption transition changes; this is known as the special adsorption point. Using FlatPERM, a stochastic growth Monte Carlo algorithm, we simulate the adsorption of self-avoiding interacting trails on the square lattice using three different boundary scenarios which differ with respect to the orientation of the boundary and the type of surface interaction. We confirm the expected phase diagram, showing swollen, collapsed, and adsorbed phases in all three scenarios, and confirm universality of the normal adsorption transition at low values of the bulk interaction strength. Intriguingly, we cannot confirm universality of the special adsorption transition. In particular, we find two different values for the associated crossover exponent.
(Authors: Nathann T. Rodrigues, Thomas Prellberg and Aleks Owczarek)

Dominic Rose (Nottingham)

Spectral properties of simple classical and quantum reset processes

We study the spectral properties of classical and quantum Markovian processes that are reset at random times to a specific configuration or state with a reset rate that is independent of the current state of the system. We demonstrate that this simple reset dynamics causes a uniform shift in the eigenvalues of the Markov generator, excluding the zero mode corresponding to the stationary state, which has the effect of accelerating or even inducing relaxation to a stationary state. Based on this result, we provide expressions for the stationary state and probability current of the reset process in terms of weighted sums over dynamical modes of the reset-free process. We also discuss the effect of resets on processes that display metastability. We illustrate our results with two classical stochastic processes, the totally asymmetric random walk and the one-dimensional Brownian motion, as well as two quantum models: a particle coherently hopping on a chain and the dissipative transverse field Ising model, known to exhibit metastability.

Loredana Vasiloiu (Nottingham)

Enhancing correlation times for edge modes through dissipation in quantum spin models

Spin chains with open boundaries, such as the transverse field Ising model, can display coherence times for edge spins that diverge with the system size as a consequence of almost conserved operators, the so-called strong zero modes. I will discuss the fate of these coherence times when dynamics becomes dissipative [1]. While in general dissipation induces decoherence and loss of information, I will show that certain simple environments can actually enhance correlation times beyond those of the original unitary case. This allows to generalise the notion of strong zero modes to dissipative strong zero maps. Our results show how dissipation could, in principle, play a useful role in protocols for storing information in quantum devices. In addition, I will also discuss generalisation of strong zero modes to a class of Ising ladders with plaquette interactions for which the strong zero mode operators can be obtained exactly [2].
[1] Phys. Rev. B 98, 094308
[2] arXiv:1901.10211