Dynamical fluctuations in the Riesz gas

Dandekar, Rahul; Krapivsky, P. L.; Mallick, Kirone

doi:10.1103/physreve.107.044129

Cited by 8 publications

(4 citation statements)

References 83 publications

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“…In the above equation we have used the fact that σ ρ 0 ,m 0 = 0 as is clear from equations ( 8) and (47). Equation ( 59) is a double integral and we can first compute the time integral.…”

Section: J Stat Mech (2023) 083208mentioning

confidence: 99%

“…As in the diffusive case, we analyze the case of uniform initial conditions, which is provided in equation (46). The zeroth-order equations provided in equation ( 29) admit the analytical solutions in equation (47). Substituting these solutions into the first-order equations for the conjugate fields yields…”

Section: Interacting Active Lattice Gas In the Zero-diffusion Limitmentioning

confidence: 99%

“…Subsequently, this was used to obtain a general expression for the variance of the current, starting from a flat initial condition [44], and to derive expressions for the higher-order cumulants [45]. Recently, the MFT equations for the SSEP have been exactly solved for annealed initial conditions [46], and the perturbative MFT approach has also been extended to long-range interactions [47].…”

Section: Introductionmentioning

confidence: 99%

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Current fluctuations in an interacting active lattice gas

Jose,

Dandekar,

Ramola

2023

J. Stat. Mech.

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We study the fluctuations of the integrated density current across the origin up to time T in a lattice model of active particles with hard-core interactions. This model is amenable to an exact description within a fluctuating hydrodynamics framework. We focus on quenched initial conditions for both the density and the magnetization fields and derive expressions for the cumulants of the density current, which can be matched with direct numerical simulations of the microscopic lattice model. For the case of uniform initial profiles, we show that the variance of the integrated current displays three regimes: an initial T rise with a coefficient given by the symmetric simple exclusion process, a cross-over regime where the effects of activity increase the fluctuations, and a large-time T behavior with a prefactor that depends on the initial conditions, the Péclet number, and the mean density of particles. Additionally, we study the limit of zero diffusion, where the fluctuations intriguingly exhibit a T 2 behavior at short times. However, at large times, the fluctuations still grow as T , with a coefficient that can be calculated explicitly. For low densities, we show that this coefficient can be expressed in terms of the effective diffusion constant D eff for non-interacting active particles.

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“…In the above equation we have used the fact that σ ρ 0 ,m 0 = 0 as is clear from equations ( 8) and (47). Equation ( 59) is a double integral and we can first compute the time integral.…”

Section: J Stat Mech (2023) 083208mentioning

confidence: 99%

Section: Interacting Active Lattice Gas In the Zero-diffusion Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Current fluctuations in an interacting active lattice gas

Jose,

Dandekar,

Ramola

2023

J. Stat. Mech.

Self Cite

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“…The quantity of interest is the total number of particles Q, passing into the half-infinite line (x > 0) up to time t. There have been many studies on the statistics of Q for different passive systems like non-interacting random walkers, symmetric simple exclusion process, and Kipnis-Marchioro-Presutti model, amongst others using analytical methods like Bethe ansatz, Green's function methods and macroscopic fluctuation theory [33][34][35][36][37][38][39]. The effect of initial conditions on active systems has been first analyzed systematically in [40] for noninteracting RTPs in one dimension where the exact expression for the variance of the integrated current Q in the annealed density and annealed magnetization setting was derived.…”

Section: Introductionmentioning

confidence: 99%

Effect of initial conditions on current fluctuations in non-interacting active particles

Jose,

Rosso,

Ramola

2024

J. Phys. A: Math. Theor.

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We investigate the effect of initial conditions on the fluctuations of the integrated density current across the origin (x = 0) up to a given time t in a one-dimensional system of non-interacting run-and-tumble particles. Each particle has initial probabilities f + and f − to move with an initial velocity +v and −v respectively, where v > 0. We derive exact results for the variance (second cumulant) of the current for quenched and annealed averages over the initial conditions for the magnetization and the density fields associated with the particles. We show that at large times, the variance displays a t behavior, with a prefactor contingent on the specific density initial conditions used. However, at short times, the variance displays either linear t or quadratic t 2 behavior, which depends on the combination of magnetization and density initial conditions, along with the fraction f + of particles in the positive velocity state at t = 0. Intriguingly, if f + = 0 , the variance displays a short time t 2 behavior with the same prefactor irrespective of the initial conditions for both fields.

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Full counting statistics of 1d short range Riesz gases in confinement

Kethepalli,

Kulkarni,

Kundu

et al. 2024

J. Stat. Mech.

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We investigate the full counting statistics of a harmonically confined 1d short range Riesz gas consisting of N particles in equilibrium at finite temperature. The particles interact with each other through a repulsive power-law interaction with an exponent k > 1 which includes the Calogero–Moser model for k = 2. We examine the probability distribution of the number of particles in a finite domain [ − W , W ] called number distribution, denoted by N ( W , N ) . We analyze the probability distribution of N ( W , N ) and show that it exhibits a large deviation form for large N characterized by a speed N 3 k + 2 k + 2 and by a large deviation function (LDF) of the fraction c = N ( W , N ) / N of the particles inside the domain and W. We show that the density profiles that create the large deviations display interesting shape transitions as one varies c and W. This is manifested by a third-order phase transition exhibited by the LDF that has discontinuous third derivatives. Monte–Carlo simulations based on Metropolis–Hashtings (MH) algorithm show good agreement with our analytical expressions for the corresponding density profiles. We find that the typical fluctuations of N ( W , N ) , obtained from our field theoretic calculations are Gaussian distributed with a variance that scales as N ν k , with ν k = ( 2 − k ) / ( 2 + k ) . We also present some numerical findings on the mean and the variance. Furthermore, we adapt our formalism to study the index distribution (where the domain is semi-infinite ( − ∞ , W ] ) , linear statistics (the variance), thermodynamic pressure and bulk modulus.

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Dynamical fluctuations in the Riesz gas

Cited by 8 publications

References 83 publications

Current fluctuations in an interacting active lattice gas

Current fluctuations in an interacting active lattice gas

Effect of initial conditions on current fluctuations in non-interacting active particles

Full counting statistics of 1d short range Riesz gases in confinement

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