- Open Access
Multiscale energy spreading in hard-particle chains
Phys. Rev. E 112, 014123 – Published 23 July, 2025
DOI: https://doi.org/10.1103/ddjx-d1dv
Abstract
We consider a one-dimensional array of particles interacting via an infinite well potential. We explore the properties of energy spreading from an initial state where only a group of particles has nonzero velocities, while others are at rest. We characterize anomalous diffusion of the active domain via moments and entropies of the energy distribution. Only in the special cases of a single-well potential (hard-particle gas) and when the distance between particles is half the potential width, does diffusion exhibit a single scale; otherwise, multiscale anomalous diffusion is observed.
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References (38)
- Thermal Transport in Low Dimensions. From Statistical Physics to Nanoscale Heat Transfer, edited by S. Lepri, Lecture Notes in Physics Vol. 921 (Springer, Heidelberg, 2016).
- R. Livi, Anomalous transport in low-dimensional systems: A pedagogical overview, Physica A 631, 127779 (2023).
- G. Benenti, D. Donadio, S. Lepri, and R. Livi, Non-Fourier heat transport in nanosystems, La Rivista del Nuovo Cimento 46, 105 (2023).
- S. Lepri, R. Livi, and A. Politi, On the anomalous thermal conductivity of one-dimensional lattices, Europhys. Lett. 43, 271 (1998).
- P. Cipriani, S. Denisov, and A. Politi, From anomalous energy diffusion to Lévy walks and heat conductivity in one-dimensional systems, Phys. Rev. Lett. 94, 244301 (2005).
- C. W. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl, Breakdown of Fourier's law in nanotube thermal conductors, Phys. Rev. Lett. 101, 075903 (2008).
- M. Upadhyaya and Z. Aksamija, Nondiffusive lattice thermal transport in Si-Ge alloy nanowires, Phys. Rev. B 94, 174303 (2016).
- A. Crnjar, C. Melis, and L. Colombo, Assessing the anomalous superdiffusive heat transport in a single one-dimensional pedot chain, Phys. Rev. Mater. 2, 015603 (2018).
- L. Yang, Y. Tao, Y. Zhu, M. Akter, K. Wang, Z. Pan, Y. Zhao, Q. Zhang, Y.-Q. Xu, R. Chen et al., Observation of superdiffusive phonon transport in aligned atomic chains, Nat. Nanotechnol. 16, 764 (2021).
- 50 Years Of Anderson Localization, edited by P. W. Anderson (World Scientific, Singapore, 2010).
- A. S. Pikovsky and D. L. Shepelyansky, Destruction of Anderson localization by a weak nonlinearity, Phys. Rev. Lett. 100, 094101 (2008).
- S. Flach, D. O. Krimer, and C. Skokos, Universal spreading of wave packets in disordered nonlinear systems, Phys. Rev. Lett. 102, 024101 (2009).
- S. Fishman, Y. Krivolapov, and A. Soffer, The nonlinear Schrödinger equation with a random potential: Results and puzzles, Nonlinearity 25, R53 (2012).
- S. Flach, Nonlinear lattice waves in random potentials, in Nonlinear Optical and Atomic Systems: At the Interface of Physics and Mathematics, edited by C. Besse and J.-C. Garreau, Lecture Notes in Mathematics Vol. 2146 (Springer, Cham, 2015), pp. 1–48.
- A. Pikovsky and S. Fishman, Scaling properties of weak chaos in nonlinear disordered lattices, Phys. Rev. E 83, 025201(R) (2011).
- S. Aubry, Diffusion without spreading of a wave packet in nonlinear random models, in Chaos, Fractals and Complexity, edited by T. Bountis, A. Provata, Y. Komminis, F. Vallianatos, and D. Kugiumtzis, Springer Proceedings in Complexity (Springer, Cham, 2023), pp. 3–36.
- Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, Observation of a localization transition in quasiperiodic photonic lattices, Phys. Rev. Lett. 103, 013901 (2009).
- M. Mulansky, K. Ahnert, and A. Pikovsky, Scaling of energy spreading in strongly nonlinear disordered lattices, Phys. Rev. E 83, 026205 (2011).
- M. Mulansky and A. Pikovsky, Energy spreading in strongly nonlinear disordered lattices, New J. Phys. 15, 053015 (2013).
- A. J. Martínez, P. G. Kevrekidis, and M. A. Porter, Superdiffusive transport and energy localization in disordered granular crystals, Phys. Rev. E 93, 022902 (2016).
- A. Ngapasare, G. Theocharis, O. Richoux, C. Skokos, and V. Achilleos, Chaos and anderson localization in disordered classical chains: Hertzian versus Fermi-Pasta-Ulam-Tsingou models, Phys. Rev. E 99, 032211 (2019).
- A. Pikovsky, Scaling of energy spreading in a disordered Ding-Dong lattice, J. Stat. Mech. (2020) 053301.
- E. Kim, A. J. Martínez, S. E. Phenisee, P. Kevrekidis, M. A. Porter, and J. Yang, Direct measurement of superdiffusive energy transport in disordered granular chains, Nat. Commun. 9, 640 (2018).
- L. Delfini, S. Denisov, S. Lepri, R. Livi, P. K. Mohanty, and A. Politi, Energy diffusion in hard-point systems, Eur. Phys. J.: Spec. Top. 146, 21 (2007).
- A. Politi, Heat conduction of the hard point chain at zero pressure, J. Stat. Mech. (2011) P03028.
- C. Mejía-Monasterio, A. Politi, and L. Rondoni, Heat flux in one-dimensional systems, Phys. Rev. E 100, 032139 (2019).
- G. Casati, Energy transport and the Fourier heat law in classical systems, Found. Phys. 16, 51 (1986).
- P. Grassberger, W. Nadler, and L. Yang, Heat conduction and entropy production in a one-dimensional hard-particle gas, Phys. Rev. Lett. 89, 180601 (2002).
- S. Lepri, R. Livi, and A. Politi, Too close to integrable: Crossover from normal to anomalous heat diffusion, Phys. Rev. Lett. 125, 040604 (2020).
- I. Aranson, M. Rabinovich, and L. S. Tsimring, Anomalous diffusion of particles in regular fields, Phys. Lett. A 151, 523 (1990).
- A. S. Pikovsky, Statistical properties of dynamically generated anomalous diffusion, Phys. Rev. A 43, 3146 (1991).
- P. Castiglione, A. Mazzino, P. Muratore-Ginanneschi, and A. Vulpiani, On strong anomalous diffusion, Physica D 134, 75 (1999).
- S. Chakraborti, S. Ganapa, P. L. Krapivsky, and A. Dhar, Blast in a one-dimensional cold gas: From newtonian dynamics to hydrodynamics, Phys. Rev. Lett. 126, 244503 (2021).
- P. I. Hurtado, Breakdown of hydrodynamics in a simple one-dimensional fluid, Phys. Rev. Lett. 96, 010601 (2006).
- F. Piazza and S. Lepri, Heat wave propagation in a nonlinear chain, Phys. Rev. B 79, 094306 (2009).
- S. Lepri, R. Schilling, and S. Aubry, Asymptotic energy profile of a wave packet in disordered chains, Phys. Rev. E 82, 056602 (2010).
- G. R. Lee-Dadswell, E. Turner, J. Ettinger, and M. Moy, Momentum conserving one-dimensional system with a finite thermal conductivity, Phys. Rev. E 82, 061118 (2010).
- Z. Gao, N. Li, and B. Li, Heat conduction and energy diffusion in momentum-conserving one-dimensional full-lattice ding-a-ling model, Phys. Rev. E 93, 022102 (2016).