TY - JOUR

T1 - Energy Current Cumulants in One-Dimensional Systems in Equilibrium

AU - Dhar, Abhishek

AU - Saito, Keiji

AU - Roy, Anjan

N1 - Funding Information:
We are grateful to Bernard Derrida and Henk van Beijeren for their many valuable suggestions and critical comments on the manuscript. A. D. acknowledges support from UGC-ISF Indo-Israeli research Grant No. 6-8/2014 (IC) and the Grant EDNHS ANR-14-CE25-0011 of the French Ministry of Education. K. S. was supported by JSPS (No. 26400404). We thank the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the initiation of this work. We thank the NESP program (ICTS/Prog-NESP/2015/10) at the International Centre for Theoretical Sciences, TIFR, where this work was largely completed.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/5/31

Y1 - 2018/5/31

N2 - A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.

AB - A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.

UR - http://www.scopus.com/inward/record.url?scp=85048176555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048176555&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.120.220603

DO - 10.1103/PhysRevLett.120.220603

M3 - Article

C2 - 29906157

AN - SCOPUS:85048176555

VL - 120

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 22

M1 - 220603

ER -