# Current correlations, Drude weights and large deviations in a box–ball system

@article{Kuniba2022CurrentCD, title={Current correlations, Drude weights and large deviations in a box–ball system}, author={Atsuo Kuniba and Gr{\'e}goire Misguich and Vincent Pasquier}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2022}, volume={55} }

We explore several aspects of the current fluctuations and correlations in the box–ball system, an integrable cellular automaton in one space dimension. The state we consider is an ensemble of microscopic configurations where the box occupancies are independent random variables (i.i.d. state), with a given mean ball density. We compute several quantities exactly in such homogeneous stationary state: the mean value and the variance of the number of balls N t crossing the origin during time t…

## References

SHOWING 1-10 OF 39 REFERENCES

### Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents.

- PhysicsPhysical review letters
- 2016

A kinetic theory of elementary excitations is proposed and an exact expression for the expectation values of the charge currents in a generic stationary state is unveiled for the nonequilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain.

### Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz

- MathematicsNuclear Physics B
- 2018

### Ballistic transport in the one-dimensional Hubbard model: The hydrodynamic approach

- Physics
- 2017

We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, the complete kinematic data…

### Exact Anomalous Current Fluctuations in a Deterministic Interacting Model.

- PhysicsPhysical review letters
- 2022

We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function…

### Dynamics of the box-ball system with random initial conditions via Pitman's transformation

- Mathematics
- 2018

The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In this article, we study the BBS when started from a random…

### Fluctuations in Ballistic Transport from Euler Hydrodynamics

- Physics
- 2019

We propose a general formalism, within large-deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary…

### Generalized hydrodynamics in complete box-ball system for U q ( Ò sl n )

- Physics
- 2021

We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group Uq( sln). Compared with the conventional (n − 1)-color BBS,…

### Soliton Decomposition of the Box-Ball System

- MathematicsForum of Mathematics, Sigma
- 2021

Abstract The box-ball system (BBS) was introduced by Takahashi and Satsuma as a discrete counterpart of the Korteweg-de Vries equation. Both systems exhibit solitons whose shape and speed are…

### Generalized Hydrodynamic Limit for the Box–Ball System

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2020

We deduce a generalized hydrodynamic limit for the box-ball system, which explains how the densities of solitons of different sizes evolve asymptotically under Euler space-time scaling. To describe…

### Transport fluctuations in integrable models out of equilibrium

- PhysicsSciPost Physics
- 2020

We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous…