Luca Ciandrini

The role of the particles' stepping cycle in an ASEP: A model of mRNA translation

One of the most important steps of protein synthesis is the translation of the messenger RNA (mRNA). During this process, macromolecules known as ribosomes translate the genetic information encoded by the triplets of nucleotides (codons) of the mRNA, and assemble proteins amino acid by amino acid. Several ribosomes may simultaneously translate the same messenger. Like goods waiting on a production line, ribosomes can queue on the track influencing the protein production rate.

We use a general approach to study mRNA translation by means of statistical-mechanical models based on the Totally Asymmetric Simple Exclusion Process (TASEP), which considers ribosomes as a one-dimensional driven lattice gas. To achieve a better understanding of the underlying biological processes and to compare the theoretical predictions with experimental results, we include in the model the two fundamental steps of the ribosomeÕs biochemical cycle [PRE 81, 051904 (2010)].

Benjamin Doyon

Exact low-energy results for non-equilibirum steady states

Let two large quantum systems prepared at different temperatures come into contact and evolve unitarily. After a large enough time, a non-equilibrium steady state will exist whereby energy flows from one system to the other. I will explain how to describe the steady state, and mention some low-energy universal properties of the energy current. For effectively one-dimensional systems, I will explain exact results from Conformal Field Theory for the energy current and its fluctuations (the full-counting statistics: all large-time energy-transfer cumulants). This is based on works with Denis Bernard.

Martin Evans

Exact solution of a nonequilibrium model: the asymmetric exclusion process

The asymmetric exclusion process models the stochastic transport of a conserved quantity (mass, cars, molecular motors etc) through an open system. Since a current of mass always flows, the system is out of equilibrium but will nevertheless attain a nonequilibrium stationary state in the long time limit. In this talk I will give an overview of how the stationary state can be solved exactly by a matrix product ansatz and discuss the resulting phase diagram. I shall also discuss generalisations to multispecies systems.

Fabian Essler

Bethe Ansatz Results for the Open PASEP

The partially asymmetric exclusion process with open boundaries can be mapped onto a spin-1/2 Heisenberg XXZ chain with non-diagonal boundary conditions. The latter is solvable by Bethe Ansatz. I summarize how to to determine the finite-size scaling of the spectral gap, which characterizes the approach to the stationary state. I then discuss how to obtain the statistics of current fluctuations from the exact solution.

Thomas Gasenzer

Dynamics of ultracold atomic gases in one spatial dimension

Ultracold atomic gases allow a particularly clean experimental access to study the dynamics of many-body quantum systems out of equilibrium. Quantum gases with contact interactions "living" in one spatial dimension can be described by analytically integrable equations of motion. This implies more conserved quantities than energy and particle number and thus suggests that thermalisation of such a gas driven out of equilibrium may not be granted. In the talk I will discuss available methods to study the equilibration dynamics of one-dimensional gases and aim at giving an account of the understanding and of open problems concerning equilibration and thermalisation of such systems.

Des Johnston

Lattice Paths and the PASEP

We discuss the equivalence of the (non-equilibrium) partially asymmetric exclusion process, or PASEP, with an (equilibrium) model of weighted lattice paths. Methods borrowed from combinatorialists, including continued fraction expansions of generating functions, are useful for understanding these.

Kirone Mallick

Current fluctuations in the exclusion process

The asymmetric simple exclusion process is a model used as a template to study various aspects of non-equilibrium statistical physics. It appears as a building block in more realistic descriptions for low-dimensional transport with constraints. In the steady state, a non-vanishing current is carried through the system. The statistical properties of this current are archetypal observables for non-equilibrium behaviour. It this talk, we explain how to derive the full statistics of the current in the ASEP. We present exact combinatorial formulas valid for all system sizes and all values of the system parameters. Our results are obtained using integrability techniques borrowed from the theory of quantum integrable systems such as the Bethe Ansatz and the Matrix Product Representation.

Pierre van Moerbeke

Non-intersecting Brownian Motions, Domino Tilings and Critical Processes

I will give an overview of recent results on edge behaviors of non-intersecting random processes, when the number of particles gets very large. These processes have given rise to Airy and Pearcey processes and variations thereof; they are related to the boundary points of the region swept out by the process in space-time. The boundary points can be generic, a cusp or a tacnode. The latter has given rise to a new "universal" process. Very recently, it has also appeared in the context of domino tiling problems.

Francesco Turci

TASEPs in the presence of a localized dynamical constraint

Production of proteins is carried out through the transport of ribosomes along RNA templates, involving a complex machinery. In particular, riboswitches, which are RNA secondary structures, can activate or deactivate ribosome transport, hence protein synthesis, according to their conformation (unfolded or folded) and their state (bonded or not to a ribosome). We present a simplified model of such a dynamical process, based on a modified version of TASEP (Totally Asymmetric Exclusion Process) with periodic boundary conditions. We describe in detail the current-density relation, as well as the density profiles, which can be quantitatively explained by a mean-field model valid for a large range of parameters. However, if the blocking rate of the riboswitch is large, and in the case of small systems, interesting phenomena emerge: the transport is characterized by temporal intermittency and long-range correlations, giving rise to an increase of the current at large densities. This effect could be of biological relevance and highlights the complex dynamical role of riboswitches.