Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries

Abstract

In this thesis, we consider one of the most popular models of non-equilibrium statistical physics: the Asymmetric Simple Exclusion Process, in which particles jump stochastically on a one-dimensional lattice, between two reservoirs at fixed densities, with the constraint that each site can hold at most one particle at a given time. This model has the mathematical property of being integrable, which makes it a good candidate for exact calculations. What interests us in particular is the current of particles that flows through the system (which is a sign of it being out of equilibrium), and how it fluctuates with time. We present a method, based on the "matrix Ansatz" devised by Derrida, Evans, Hakim and Pasquier, that allows to access the exact cumulants of that current, for any finite size of the system and any value of its parameters. We also analyse the large size asymptotics of our result, and make a conjecture for the phase diagram of the system in the so-called "s-ensemble". Finally, we show how our method relates to the algebraic Bethe Ansatz, which was thought not to be applicable to this situation.

198 pages, PhD thesis

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Cited by in corpus (7)

• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Learning nonequilibrium control forces to characterize dynamical phase transitions
• Markov duality and Bethe ansatz formula for half-line open ASEP
• Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• Pieri rules, vertex operators and Baxter Q-matrix
• Rare-event trajectory ensemble approach to study dynamical phase transitions in the zero temperature Glauber model