TY - JOUR
T1 - Transport, correlations, and chaos in a classical disordered anharmonic chain
AU - Kumar, Manoj
AU - Kundu, Anupam
AU - Kulkarni, Manas
AU - Huse, David A.
AU - Dhar, Abhishek
N1 - Funding Information:
We thank F. Huveneers and W. De Roeck for many useful discussions and for pointing out errors in an earlier analysis. We also thank C. Dasgupta for useful discussions. Manoj Kumar would like to acknowledge support from an ICTS postdoctoral fellowship and the Royal Society–SERB Newton International fellowship (NIF\R1\180386). A.K. acknowledges support from a DST grant under Project No. ECR/2017/000634. M.K. gratefully acknowledges the Ramanujan Fellowship (SB/S2/RJN-114/2016), Early Career Research Award (ECR/2018/002085), and Matrics Grant (MTR/2019/001101) from the Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India. A.D. and A.K. would like to acknowledge support from the project 5604-2 of the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). A.D., A.K., and M.K. acknowledge support of the Department of Atomic Energy, Government of India, under Project No. 12-R&D-TFR-5.10-1100 and would also like to acknowledge the ICTS program on “Thermalization, Many body localization and Hydrodynamics (Code: ICTS/hydrodynamics2019/11)” for enabling crucial discussions related to this work. D.A.H. is supported in part by a Simons Fellowship and by (USA) DOE Grant No. DE-SC0016244. The numerical simulations were performed on a Mario HPC at ICTS-TIFR and a Zeus HPC of Coventry University.
Funding Information:
We thank F. Huveneers and W. De Roeck for many useful discussions and for pointing out errors in an earlier analysis. We also thank C. Dasgupta for useful discussions. Manoj Kumar would like to acknowledge support from an ICTS postdoctoral fellowship and the Royal Society SERB Newton International fellowship (NIF\R1\180386). A.K. acknowledges support from a DST grant under Project No. ECR/2017/000634. M.K. gratefully acknowledges the Ramanujan Fellowship (SB/S2/RJN-114/2016), Early Career Research Award (ECR/2018/002085), and Matrics Grant (MTR/2019/001101) from the Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India. A.D. and A.K. would like to acknowledge support from the project 5604-2 of the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). A.D., A.K., and M.K. acknowledge support of the Department of Atomic Energy, Government of India, under Project No. 12-R&D-TFR-5.10-1100 and would also like to acknowledge the ICTS program on 'Thermalization, Many body localization and Hydrodynamics (Code: ICTS/hydrodynamics2019/11)' for enabling crucial discussions related to this work. D.A.H. is supported in part by a Simons Fellowship and by (USA) DOE Grant No. DE-SC0016244. The numerical simulations were performed on a Mario HPC at ICTS-TIFR and a Zeus HPC of Coventry University.
Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/8
Y1 - 2020/8
N2 - We explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size N, disorder strength Δ, and temperature T. The conductivity κN, obtained for finite length (N), saturates to a value κ∞>0 in the large N limit, for all values of disorder strength Δ and temperature T>0. We show evidence that for any Δ>0 the conductivity goes to zero faster than any power of T in the (T/Δ)→0 limit, and find that the form κ∞∼e-B|ln(CΔ/T)|3 fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be κN<κ∞ due to boundary resistance when the bulk conductivity is high (the weak disorder case), or κN>κ∞ due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.
AB - We explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size N, disorder strength Δ, and temperature T. The conductivity κN, obtained for finite length (N), saturates to a value κ∞>0 in the large N limit, for all values of disorder strength Δ and temperature T>0. We show evidence that for any Δ>0 the conductivity goes to zero faster than any power of T in the (T/Δ)→0 limit, and find that the form κ∞∼e-B|ln(CΔ/T)|3 fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be κN<κ∞ due to boundary resistance when the bulk conductivity is high (the weak disorder case), or κN>κ∞ due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.
UR - http://www.scopus.com/inward/record.url?scp=85091192815&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85091192815&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.102.022130
DO - 10.1103/PhysRevE.102.022130
M3 - Article
C2 - 32942452
AN - SCOPUS:85091192815
SN - 2470-0045
VL - 102
JO - Physical Review E
JF - Physical Review E
IS - 2
M1 - 027302
ER -