Abstract
Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar--Parisi--Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114, 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.
Highlights
We study a model of particle transport on a lattice, uncovering a new scaling regime close to a dynamical phase transition (DPT) that is present in the model
In this paper we are interested in two aspects of the large deviation function (LDF): on a generic ground, we study the large deviations of current and activity in the SSEP and Asymmetric Simple Exclusion Process (ASEP) models, showing that there exists a correspondence allowing one to map the LDFs of K in the SSEP to that of Q in the ASEP, with well-chosen jump rates – and more generally to map the joint distribution of K and Q between two ASEPs with different jump rates
We study a consequence of this mapping for the large deviations of activity in the SSEP, by mapping these to the large deviations of the current in an ASEP. We infer from this mapping an almost complete picture of the large- but finite-L scaling governing the LDFs and DPT of the distribution of K in the SSEP; we show in particular that deviations beyond the diffusive (i.e. EW) scalings, are governed by KPZ scalings on one side of the DPT
Summary
Fluctuations in random processes are well described by the theory of large deviations, whenever a large-size and/or a large-time asymptotics naturally comes into play (see e.g. [1] for a review). In this paper we are interested in two aspects of the LDFs: on a generic ground, we study the large deviations of current and activity in the SSEP and ASEP models, showing that there exists a correspondence allowing one to map the LDFs of K in the SSEP to that of Q in the ASEP, with well-chosen jump rates – and more generally to map the joint distribution of K and Q between two ASEPs with different jump rates We show that this correspondence is valid for systems with periodic boundary conditions and for open systems in contact with reservoirs of particles. We show that the particle-hole symmetry breaking that occurs for the current LDF in the WASEP model can be mapped to a particle-hole symmetry breaking for the activity LDF, in another WASEP model
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