{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T15:56:03Z","timestamp":1765554963786,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T00:00:00Z","timestamp":1611273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We theoretically investigate the evolution of the peak height of energy-resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor equal to two. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energies. We investigate this quantity assuming a short-range capacitive coupling between the edges. Moreover, we also phenomenologically take into account the possibility of energy dissipation towards additional degrees of freedom\u2014both linear and quadratic\u2014in the injection energy. Through a comparison with recent experimental data, we rule out the non-dissipative case as well as a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate for describing the behavior of the quasi-particle peak at short enough propagation lengths.<\/jats:p>","DOI":"10.3390\/e23020138","type":"journal-article","created":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T11:13:53Z","timestamp":1611314033000},"page":"138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Electronic Wave-Packets in Integer Quantum Hall Edge Channels: Relaxation and Dissipative Effects"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4218-9326","authenticated-orcid":false,"given":"Giacomo","family":"Rebora","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Genova, Via Dodecaneso 33, 16146 Genova, Italy"},{"name":"SPIN-CNR, Via Dodecaneso 33, 16146 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dario","family":"Ferraro","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Genova, Via Dodecaneso 33, 16146 Genova, Italy"},{"name":"SPIN-CNR, Via Dodecaneso 33, 16146 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2553-5883","authenticated-orcid":false,"given":"Ramiro H.","family":"Rodriguez","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7ois D.","family":"Parmentier","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrice","family":"Roche","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maura","family":"Sassetti","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Genova, Via Dodecaneso 33, 16146 Genova, Italy"},{"name":"SPIN-CNR, Via Dodecaneso 33, 16146 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1126\/science.1141243","article-title":"An on-demand coherent single-electron source","volume":"316","author":"Berroir","year":"2007","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1142\/S0217984911026772","article-title":"Electron quantum optics in quantum Hall edge channels","volume":"25","author":"Grenier","year":"2011","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/andp.201300181","article-title":"Electron quantum optics in ballistic chiral conductors","volume":"526","author":"Bocquillon","year":"2014","journal-title":"Ann. Phys. (Berl.)"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1600531","DOI":"10.1002\/pssb.201600531","article-title":"Electronic quantum optics beyond the integer quantum Hall effect","volume":"254","author":"Ferraro","year":"2017","journal-title":"Phys. Status Solidi B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1600621","DOI":"10.1002\/pssb.201600621","article-title":"Electron quantum optics as quantum signal processing","volume":"254","author":"Roussel","year":"2017","journal-title":"Phys. Status Solidi B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1600650","DOI":"10.1002\/pssb.201600650","article-title":"Levitons for electron quantum optics","volume":"254","author":"Glattli","year":"2017","journal-title":"Phys. Status Solidi B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"056503","DOI":"10.1088\/1361-6633\/aaa98a","article-title":"Coherent control of single electrons: A review of current progress","volume":"81","author":"Glattli","year":"2018","journal-title":"Rep. Prog. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1038\/177027a0","article-title":"Correlation between photons in two coherent beams of light","volume":"177","author":"Twiss","year":"1956","journal-title":"Nature (Lond.)"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2044","DOI":"10.1103\/PhysRevLett.59.2044","article-title":"Measurement of subpicosecond time intervals between two photons by interference","volume":"59","author":"Hong","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"196803","DOI":"10.1103\/PhysRevLett.108.196803","article-title":"Electron Quantum Optics: Partitioning Electrons One by One","volume":"108","author":"Bocquillon","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1126\/science.1232572","article-title":"Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources","volume":"339","author":"Bocquillon","year":"2013","journal-title":"Science"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1038\/nature12713","article-title":"Minimal excitation states for electron quantum optics using levitons","volume":"502","author":"Dubois","year":"2013","journal-title":"Nature (Lond.)"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6854","DOI":"10.1038\/ncomms7854","article-title":"Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization","volume":"6","author":"Freulon","year":"2015","journal-title":"Nat. Comm."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"115311","DOI":"10.1103\/PhysRevB.94.115311","article-title":"Decoherence and relaxation of a single electron in a one-dimensional conductor","volume":"94","author":"Marguerite","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1103\/PhysRevLett.49.405","article-title":"Quantized Hall Conductance in a Two-Dimensional Periodic Potential","volume":"49","author":"Thouless","year":"1982","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1038\/nnano.2012.28","article-title":"Electrical control of a solid-state flying qubit","volume":"7","author":"Yamamoto","year":"2012","journal-title":"Nat. Nanotechnol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"125432","DOI":"10.1103\/PhysRevB.89.125432","article-title":"Theoretical, numerical, and experimental study of a flying qubit electronic interferometer","volume":"89","author":"Bautze","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3844","DOI":"10.1038\/ncomms4844","article-title":"Dynamical control of interference using voltage pulses in the quantum regime","volume":"5","author":"Gaury","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1002\/1521-3978(200009)48:9\/11<771::AID-PROP771>3.0.CO;2-E","article-title":"The Physical Implementation of Quantum Computation","volume":"48","year":"2000","journal-title":"Fortschritte Der Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"046802","DOI":"10.1103\/PhysRevLett.112.046802","article-title":"Interactions and Charge Fractionalization in an Electronic Hong-Ou-Mandel Interferometer","volume":"112","author":"Wahl","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"166403","DOI":"10.1103\/PhysRevLett.113.166403","article-title":"Real-Time Decoherence of Landau and Levitov Quasiparticles in Quantum Hall Edge Channels","volume":"113","author":"Ferraro","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"155302","DOI":"10.1103\/PhysRevB.98.155302","article-title":"Taming electronic decoherence in one-dimensional chiral ballistic quantum conductors","volume":"98","author":"Cabart","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"035426","DOI":"10.1103\/PhysRevB.98.035426","article-title":"Probing interactions via non-equilibrium momentum distribution and noise in integer quantum Hall systems at \u03bd = 2","volume":"98","author":"Acciai","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"245310","DOI":"10.1103\/PhysRevB.101.245310","article-title":"Collisional interferometry of levitons in quantum Hall edge channels at \u03bd = 2","volume":"101","author":"Rebora","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"205409","DOI":"10.1103\/PhysRevB.91.205409","article-title":"Single quasiparticle and electron emitter in the fractional quantum Hall regime","volume":"91","author":"Ferraro","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"076801","DOI":"10.1103\/PhysRevLett.118.076801","article-title":"Minimal Excitations in the Fractional Quantum Hall Regime","volume":"118","author":"Rech","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"245415","DOI":"10.1103\/PhysRevB.95.245415","article-title":"Minimal excitation states for heat transport in driven quantum Hall systems","volume":"95","author":"Vannucci","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"075401","DOI":"10.1103\/PhysRevB.98.075401","article-title":"Crystallization of levitons in the fractional quantum Hall regime","volume":"98","author":"Ronetti","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1140\/epjst\/e2018-800074-1","article-title":"Hong-Ou-Mandel characterization of multiply charged Levitons","volume":"227","author":"Ferraro","year":"2018","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"205406","DOI":"10.1103\/PhysRevB.99.205406","article-title":"Hong-Ou-Mandel heat noise in the quantum Hall regime","volume":"99","author":"Ronetti","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"125451","DOI":"10.1103\/PhysRevB.86.125451","article-title":"Signatures of Wigner correlations in the conductance of a one-dimensional quantum dot coupled to an AFM tip","volume":"86","author":"Cavaliere","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"206402","DOI":"10.1103\/PhysRevLett.115.206402","article-title":"Fractional Wigner crystal in the Helical Luttinger Liquid","volume":"115","author":"Crepin","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"115417","DOI":"10.1103\/PhysRevB.94.115417","article-title":"Thermal effects on the Wigner localization and Friedel oscillations in many-electron nanowires","volume":"94","author":"Cavaliere","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"085122","DOI":"10.1103\/PhysRevB.94.085122","article-title":"Out-of-equilibrium density dynamics of a quenched fermionic system","volume":"94","author":"Porta","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_35","first-page":"113","article-title":"Edge physics in two-dimensional topological insulators","volume":"39","author":"Dolcetto","year":"2016","journal-title":"Riv. Del Nuovo C."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"035308","DOI":"10.1103\/PhysRevB.77.035308","article-title":"Quantum detection of electronic flying qubits in the integer quantum Hall regime","volume":"77","author":"Degiovanni","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"012108","DOI":"10.1103\/PhysRevA.97.012108","article-title":"Application of path-integral quantization to indistinguishable particle systems topologically confined by a magnetic field","volume":"97","author":"Jacak","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1038\/nphys1429","article-title":"Non-equilibrium edge-channel spectroscopy in the integer quantum Hall regime","volume":"6","author":"Altimiras","year":"2009","journal-title":"Nat. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"056803","DOI":"10.1103\/PhysRevLett.105.226804","article-title":"Energy Relaxation in the Integer Quantum Hall Regime","volume":"105","author":"Altimiras","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"121302(R)","DOI":"10.1103\/PhysRevB.81.121302","article-title":"Plasmon scattering approach to energy exchange and high-frequency noise in \u03bd = 2 quantum Hall edge channels","volume":"81","author":"Degiovanni","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"041311(R)","DOI":"10.1103\/PhysRevB.81.041311","article-title":"Interaction-induced edge channel equilibration","volume":"81","author":"Lunde","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"106403","DOI":"10.1103\/PhysRevLett.109.106403","article-title":"Relaxation in Driven Integer Quantum Hall Edge States","volume":"109","author":"Kovrizhin","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1038\/ncomms2788","article-title":"Separation of neutral and charge modes in one-dimensional chiral edge channels","volume":"4","author":"Bocquillon","year":"2013","journal-title":"Nat. Commun."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2426","DOI":"10.1038\/s41467-020-16331-4","article-title":"Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid","volume":"11","author":"Rodriguez","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_45","unstructured":"Goremykina, A.S., Borin, A., and Sukhorukov, E.V. (2019). Heat current in a dissipative quantum Hall edge. arXiv."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3915","DOI":"10.1038\/s41467-019-11888-1","article-title":"Auger-spectroscopy in quantum Hall edge channels and the missing energy problem","volume":"10","author":"Fischer","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1080\/00018739500101566","article-title":"Topological orders and edge excitations in fractional quantum Hall states","volume":"44","author":"Wen","year":"1995","journal-title":"Adv. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"093032","DOI":"10.1088\/1367-2630\/14\/9\/093032","article-title":"Environmental induced renormalization effects in quantum Hall edge states","volume":"14","author":"Braggio","year":"2012","journal-title":"New J. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"045322","DOI":"10.1103\/PhysRevB.78.045322","article-title":"Dephasing in the electronic Mach-Zehnder interferometer at filling factor \u03bd = 2","volume":"78","author":"Levkivskyi","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"035421","DOI":"10.1103\/PhysRevB.93.035421","article-title":"Relaxation of an electron wave packet at the quantum Hall edge at filling factor \u03bd = 2","volume":"93","author":"Slobodeniuk","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"014","DOI":"10.21468\/SciPostPhys.3.2.014","article-title":"Interaction effects in a multi-channel Fabry-Perot interferometer in the Aharonov-Bohm regime","volume":"3","author":"Ferraro","year":"2017","journal-title":"Sci. Post Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"035420","DOI":"10.1103\/PhysRevB.93.035420","article-title":"Robust quantum coherence above the Fermi sea","volume":"93","author":"Tewari","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"115418","DOI":"10.1103\/PhysRevB.97.115418","article-title":"Coherence recovery mechanisms of quantum Hall edge states","volume":"97","author":"Goremykina","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"241307(R)","DOI":"10.1103\/PhysRevB.80.241307","article-title":"Decoherence and relaxation of single-electron excitations in quantum Hall edge channels","volume":"80","author":"Degiovanni","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"013012","DOI":"10.1088\/1367-2630\/12\/1\/013012","article-title":"Neutral modes\u2019 edge state dynamics through quantum point contacts","volume":"12","author":"Ferraro","year":"2010","journal-title":"New J. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/2\/138\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:14:08Z","timestamp":1760159648000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/2\/138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,22]]},"references-count":55,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["e23020138"],"URL":"https:\/\/doi.org\/10.3390\/e23020138","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,1,22]]}}}