G.Salerno et al. Eqs.(15)-(16)are found.In particular,the complex hop- SCHERMANN J.P.,Phrys.Reo.Lett.,24(1970)861 PeapitndeoftheBHnodelmrepodsotheco [2]DUNLAP D.H.and KENKRE V.M.,Phys.Rev.B,34 (1986) plex coupling the pen the drA/h des [3]IGNATOV A.A.and ROMANOV Y.A.,Phys.Status Solidi B, An on-site interaction term analo HOLTHAUS M.P .,69(1992）35 gous to the U term in Eq.(19)directly appears when the 的NELDTEF anh ulums is t o account be (0-(4 .Rep.,3041998)22g t has b ed in the M g R.B.,NIu Q. m2e pendulums corresponds to a att the cal la worth 0101 (n)t tential that is typically used for this pose in ultracold 040 atom experiments [9,11,15,16]can only provide modu- 12 lation amplitude that are l AMPINI D. MORSCH O.and ARIMONDO E.,.Ret.A, d [13 VEISS C.and HOLTHAUS M.,Phys.Red will be very useful in view of generating synthetic gauge field configurations in our mechanical system. Final r remarks and m4 [15)ZE ESINTA LIGNTER H.CIAMPINI D.MORSCHO.and WEINBERG M.,HAUKE P. effects in a clas ums on 25304 press the coupling between the two pendulums,while e dynamical is ion allows to is ate the s ext our rest 00n d dent frequency.for instance temporally modulated RLC [20]HAUKE electric circuits K.LEWENSTEIN M.and ECKARDT A. rom e poi of view of funda ntal physics,the analogous to the Peierls phase of Bose-Hubbard mod- ed-matter physics.In analogy at Ph insulation,new ,9(2013)738 [22 AIDE expecte 8530 dulums.Further exciting developments in nonlinear 23)M e as a result of the intrinsic [24]LONGHIS.,MARA Plrys.Rev.Le we to Ni gno,Andre AMEIT A ,496(2013)196 edge partial financial su ort from ERC via the QGBE [26] M andrmPini NJ.,MIGDALL A.and TAYLOR [27]BUTIKOV E. .Pys,69(2001)75 hods of Classical Mechanics [291 [1]HAROCHE S.,COHEN-TANNOUDJI C.,AUDOIN C.and 0(A and ROMANB.m P P-6G. Salerno et al. Eqs. (15)-(16) are found. In particular, the complex hop￾ping amplitude of the BH model corresponds to the com￾plex coupling between the pendulums, J e iφij ↔ Ω eff ij : the non-trivial Peierls phase φij = R ri rj dr · A/~ describ￾ing the effect of an external vector potential acting on the quantum particles [32] corresponds to a non-trivial phase of the Ω eff ij coupling. An on-site interaction term analo￾gous to the U term in Eq. (19) directly appears when the anharmonicity of the pendulums is taken into account be￾yond the linearized motion Equations (1)-(4). The modulation scheme that has been envisaged in the present Letter for coupled pendulums corresponds to a temporal modulation of the on-site energies of the BH lattice. There is however one crucial difference worth noting: while the global shaking of the optical lattice po￾tential that is typically used for this purpose in ultracold atom experiments [9, 11, 15, 16] can only provide modu￾lation amplitudes that are linearly dependent on the site position [30], systems of pendulums allow for an individ￾ual addressing of each single pendulum. This freedom will be very useful in view of generating synthetic gauge field configurations in our mechanical system. Final remarks and conclusions. – Inspired by analo￾gous quantum effects, in this Letter we have theoretically studied dynamical localization and dynamical isolation effects in a classical system of two coupled pendulums when a temporally periodic modulation of the oscillation frequencies is applied to them. The dynamical decou￾pling effect can be used in mechanical engineering to sup￾press the coupling between the two pendulums, while the dynamical isolation allows to isolate the system from external forces. Of course, our results are valid for cou￾pled oscillators of any physical nature with a time depen￾dent frequency, for instance temporally modulated RLC electric circuits. From the point of view of fundamental physics, the non-trivial coupling phase between the pendulums is analogous to the Peierls phase of Bose-Hubbard mod￾els of quantum condensed-matter physics. In analogy to orbital magnetism and topological insulation, new in￾triguing phenomena are expected to appear in multi￾dimensional lattices of many temporally modulated pen￾dulums. Further exciting developments in nonlinear physics are expected to arise as a result of the intrinsic anharmonicity of pendulums. ∗ ∗ ∗ We are grateful to Nicola Pugno, Andr´e Eckardt and Jean Dalibard for stimulating discussions. 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