Fermi-Pasta-Ulam Physics with Nanomechanical Graphene Resonators: Intrinsic Relaxation and Thermalization from Flexural Mode Coupling

Abstract

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. We find the thermalization rate Γ to be independent of radius and scaling as Γ ∼ T * / 2 pre , where T * and pre are effective resonator temperature and prestrain.Advances in fabrication techniques enable production and characterization of one and two dimensional nanoscale mechanical resonators [1][2][3][4]. In particular, carbon-based resonators are considered to be promising for many applications due to their low mass and high quality factors (Q-factors) [5][6][7][8]. It is also known that these systems display strongly nonlinear behavior [4,9], which makes them interesting for investigations of nonlinear dynamics. The nonlinearities lead to a coupling between the vibrational modes [10,11]. This coupling allows for intermodal energy-transfer, which facilitates the redistribution of energy initially localized in a single mode.In this respect, the mode-coupling provides a dissipation channel for the fundamental mode (FM) dynamics. In contrast to other dissipation mechanisms previously studied in nanomechanical resonators [12][13][14][15][16][17], this is a fundamental intrinsic mechanism and therefore constitutes a lower limit on the relaxation rate of the FM. At finite temperatures, the effect of the mode couplings will be two-fold. First, they give rise to fluctuations in the resonator strain leading to dephasing or spectral broadening of the resonator [18]. Second, as we show in this Letter, they allow for energy redistribution among the modes. To distinguish the two effects we consider a ringdown setup, where the total energy of the resonator is conserved and the evolution of the spectral distribution of energy is monitored. This allows us to access the dynamics of the FM energy.The process of thermalization in a system of nonlinearly coupled oscillators was originally considered by Fermi, Pasta and Ulam (FPU) in their famous computer experiment in 1955 [19,20], and spawned an impressive amount of research that eventually resulted in the development of chaos theory [21] and the discovery of solitons [22]. For the FPU problem, it is known that above a certain critical energy density, energy initially fed into the FM is quickly redistributed among all modes, and the system approaches a thermal state. This threshold is connected to the onset of widespread chaos in the mode dynamics [20,21] and the stability of localized modes ("qbreathers") [23,24]. In recent years, the consensus has been reached that the main features observed in the FPU problem are not specific to the original model Hamiltonian [25,26]. A natural question, which is still under debate [27], is whether those f...

Diffusion-induced dissipation and mode coupling in nanomechanical resonators

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Strain-dependent damping in nanomechanical resonators from thin MoS2 crystals

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