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Cited by 6 publications
References 58 publications
Dynamic fluctuations of current and mass in nonequilibrium mass transport processes
We study steady-state dynamic fluctuations of current and mass in several variants of random average processes on a ring of L sites. These processes violate detailed balance in the bulk and have nontrivial spatial structures: their steady states are not described by the Boltzmann–Gibbs distribution and can have nonzero spatial correlations. Using a microscopic approach, we exactly calculate the second cumulants, or the variance, ⟨ Q i 2 ( T ) ⟩ c and ⟨ Q sub 2 ( l , T ) ⟩ c , of cumulative (time-integrated) currents up to time T across the ith bond and across a subsystem of size l (summed over bonds in the subsystem), respectively. We also calculate the (two-point) dynamic correlation function of the subsystem mass. In particular, we show that, for large L ≫ 1 , the second cumulant ⟨ Q i 2 ( T ) ⟩ c of the cumulative current up to time T across the ith bond grows linearly as ⟨ Q i 2 ⟩ c ∼ T for initial times T ∼ O ( 1 ) , subdiffusively as ⟨ Q i 2 ⟩ c ∼ T 1 / 2 for intermediate times 1 ≪ T ≪ L 2 , and then again linearly as ⟨ Q i 2 ⟩ c ∼ T for long times T ≫ L 2 . The scaled cumulant lim l → ∞ , T → ∞ ⟨ Q sub 2 ( l , T ) ⟩ c / 2 l T of current across the subsystem of size l and up to time T converges to the density-dependent particle mobility χ ( ρ ) when the large subsystem-size limit is taken first, followed by the large-time limit; when the limits are reversed, it simply vanishes. Remarkably, regardless of the dynamical rules, the scaled current cumulant D ⟨ Q i 2 ( T ) ⟩ c / 2 χ L ≡ W ( y ) as a function of scaled time y = D T / L 2 can be expressed in terms of a universal scaling function W ( y ) , where D is the bulk-diffusion coefficient; interestingly, the intermediate-time subdiffusive and long-time diffusive growths can be connected through a single scaling function W ( y ) . The power spectra for current and mass are also exactly characterized by the respective scaling functions. Furthermore, we provide a microscopic derivation of equilibrium-like Green–Kubo and Einstein relations that connect the steady-state current fluctuations to an ‘operational’ mobility (i.e. the response to an external force field) and mass fluctuation, respectively.
Dynamic fluctuations of current and mass in nonequilibrium mass transport processes
We study steady-state dynamic fluctuations of current and mass in several variants of random average processes on a ring of L sites. These processes violate detailed balance in the bulk and have nontrivial spatial structures: their steady states are not described by the Boltzmann–Gibbs distribution and can have nonzero spatial correlations. Using a microscopic approach, we exactly calculate the second cumulants, or the variance, ⟨ Q i 2 ( T ) ⟩ c and ⟨ Q sub 2 ( l , T ) ⟩ c , of cumulative (time-integrated) currents up to time T across the ith bond and across a subsystem of size l (summed over bonds in the subsystem), respectively. We also calculate the (two-point) dynamic correlation function of the subsystem mass. In particular, we show that, for large L ≫ 1 , the second cumulant ⟨ Q i 2 ( T ) ⟩ c of the cumulative current up to time T across the ith bond grows linearly as ⟨ Q i 2 ⟩ c ∼ T for initial times T ∼ O ( 1 ) , subdiffusively as ⟨ Q i 2 ⟩ c ∼ T 1 / 2 for intermediate times 1 ≪ T ≪ L 2 , and then again linearly as ⟨ Q i 2 ⟩ c ∼ T for long times T ≫ L 2 . The scaled cumulant lim l → ∞ , T → ∞ ⟨ Q sub 2 ( l , T ) ⟩ c / 2 l T of current across the subsystem of size l and up to time T converges to the density-dependent particle mobility χ ( ρ ) when the large subsystem-size limit is taken first, followed by the large-time limit; when the limits are reversed, it simply vanishes. Remarkably, regardless of the dynamical rules, the scaled current cumulant D ⟨ Q i 2 ( T ) ⟩ c / 2 χ L ≡ W ( y ) as a function of scaled time y = D T / L 2 can be expressed in terms of a universal scaling function W ( y ) , where D is the bulk-diffusion coefficient; interestingly, the intermediate-time subdiffusive and long-time diffusive growths can be connected through a single scaling function W ( y ) . The power spectra for current and mass are also exactly characterized by the respective scaling functions. Furthermore, we provide a microscopic derivation of equilibrium-like Green–Kubo and Einstein relations that connect the steady-state current fluctuations to an ‘operational’ mobility (i.e. the response to an external force field) and mass fluctuation, respectively.
Time-dependent properties of run-and-tumble particles. II. Current fluctuations
No abstract
Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
No abstract
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