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Quantum Dissipation and Decoherence of Collective Telefon 08 21/598-32 34 Prof

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N§ MAI %NRAISONDU -OBILITÏ DÏMÏNAGEMENT E DU3ERVICEDELA RENCONTREDÏTUDIANTS !UPROGRAMMERENCONTREDÏTU TAIRE ÌL5,0!JOUTERÌ COMMUNICATION DIANTSETDENSEIGNANTS CHERCHEURS LACOMPÏTENCEDISCIPLINAIREETLIN ETDENSEIGNANTS LEPROCHAIN CHERCHEURSDANSLE VISITEDUCAMPUS INFORMATIONSSUR GUISTIQUE UNE EXPÏRIENCE BINATIO LES ÏCHANGES %RASMUS3OCRATES NALEETBICULTURELLE TELESTLOBJECTIF BULLETIN DOMAINEDESSCIENCESDE ENTRELES&ACULTÏSDEBIOLOGIEDES DECETTECOLLABORATIONNOVATRICEEN DINFORMATIONS LAVIE5,0 5NIVERSITËT DEUX UNIVERSITÏS PRÏSENTATION DE BIOLOGIEBIOCHIMIE PARAÔTRA DES3AARLANDES PROJETS DE RECHERCHE EN PHARMA LEMAI COLOGIE VIROLOGIE IMMUNOLOGIE ET #ONTACTS 5NE PREMIÒRE RENCONTRE AVAIT EU GÏNÏTIQUEHUMAINEDU:(-" &ACULTÏDESSCIENCESDELAVIE LIEU Ì 3AARBRàCKEN EN MAI $R*OERN0àTZ #ETTERENCONTRE ORGANISÏEÌLINI JPUETZ IBMCU STRASBGFR SUIVIEENFÏVRIERPARLAVENUE TIATIVEDU$R*0àTZETDU#ENTRE #ENTREDELANGUES)," Ì 3TRASBOURG DUN GROUPE DÏTU DELANGUESDEL)NSTITUT,E"ELCÙTÏ #ATHERINE#HOUISSA DIANTS ET DENSEIGNANTS DE LUNI STRASBOURGEOIS DU 0R - 3CHMITT BUREAU( VERSITÏ DE LA 3ARRE ,A E ÏDITION CÙTÏ SARROIS SINSCRIT DANS LE CATHERINECHOUISSA LABLANG ULPU STRASBGFR LE MAI PERMETTRA CETTE CADREDESÏCHANGESENTRELESDEUX FOISAUXSTRASBOURGEOISDEDÏCOU FACULTÏS VISANT Ì LA MISE SUR PIED ;SOMMAIRE VRIR LES LABORATOIRES DU :ENTRUM DUN CURSUS FRANCO ALLEMAND EN FàR(UMANUND-OLEKULARBIOLOGIE 3CIENCES DE LA VIE 5NE ÏTUDIANTE !CTUALITÏS :(-" DEL5NIVERSITÏDELA3ARRE DE L5,0 TERMINE ACTUELLEMENT SA IMPLANTÏS SUR LE SITE DU #(5 DE LICENCE, ÌL5D3 DEUXÏTUDIANTS /RGANISATION 3AARBRàCKEN (OMBURG SARROISPASSERONTLANNÏEUNIVERSI INSTITUTIONNELLE 0ERSONNELS &ORMATION 2ECHERCHE )54 #ULTURE SCIENTIFIQUE *OURNÏEi-ANAGEMENT ÌÏVALUERDANSLENTREPRISELESRIS DECONSIGNERLERÏSULTATDELÏVALUA QUES POUR LA SÏCURITÏ ET LA SANTÏ TIONDESRISQUESSURUNDOCUMENT 2ELATIONS DELASANTÏETDELASÏCURITÏ INTERNATIONALES ENMAINTENANCEw DES TRAVAILLEURS #ETTE RECHERCHE UNIQUEÌTENIRÌJOUR DESRISQUESÏVENTUELSETLEURÏVA -ULTIMÏDIA LUATION SETRADUITNOTAMMENTPAR -AINTENANCE ,EDÏPARTEMENT'ÏNIEINDUSTRIEL 6IEÏTUDIANTE LANALYSEDESPROCÏDÏSDEFABRICA !VEC UNE OCCURRENCE DE MALADIE MAINTENANCE ENCOLLABORATIONAVEC TION DES ÏQUIPEMENTS DE TRAVAIL PROFESSIONNELLE Ì FOIS PLUS !GENDA L!SSOCIATION FRAN AISE DES INGÏ DES SUBSTANCES OU PRÏPARATIONS ÏLEVÏE QUE LA MOYENNE ET UNE SCIENTIFIQUE NIEURSETRESPONSABLESDEMAINTE CHIMIQUES DE LAMÏNAGEMENT DES DURÏE DINCAPACITÏ TEMPORAIRE !CTIONSOCIALE NANCE ORGANISEUNEJOURNÏESURLE LIEUXDETRAVAILOUDESINSTALLATIONS LIÏEAUXACCIDENTSDEJOURS LES ETCULTURELLE i-ANAGEMENTDELASANTÏETDELA ARTICLE, DUCODEDUTRA MÏTIERS DE LA MAINTENANCE DANS SÏCURITÏENMAINTENANCEwLEJEUDI )NFOSPRATIQUES VAIL 5N NOUVEL i ARTICLE 2 LINDUSTRIE SE RÏVÒLENT BIEN PLUS MAIÌL)54,OUIS0ASTEUR wDUCODEDUTRAVAILNOVEMBRE EXPOSÏSAUXACCIDENTSETAUXMALA ALLÏED!THÒNESÌ3CHILTIGHEIM RENFORCE LA PRÏVENTION DES DIESPROFESSIONNELLESQUELESAUTRES RISQUESPROFESSIONNELSENINSTITUANT MÏTIERS #EST CE QUI RESSORT DE 3ANTÏETSÏCURITÏ LOBLIGATION POUR TOUT EMPLOYEUR LÏTUDERÏALISÏEPARL!&)-DANSLA ,ECODEDUTRAVAILOBLIGELESEMPLOYEURS Prof. G.-L. Ingold Institut für Physik Universität Augsburg 86135 Augsburg Prof. Dr. Gert-Ludwig Ingold · · · Institut für Physik An den Universität Augsburg Dekan der Mathematisch-Naturwissenschaftlichen Universitätsstraße 1 86135 Augsburg Fakultät Quantum dissipation and decoherence of collective Telefon 08 21/598-32 34 Prof. Dr. Siegfried Horn excitations in metallic nanoparticlesTelefax 08 21/598-32 22 [email protected] im Hause www.physik.uni-augsburg.de/theo1/ingold — Guillaume Weick — 26. April 2006 Doktorprüfung Guillaume Weick Sehr geehrter Herr Dekan, A dissertation submitted to Universit´eLouis Pasteur, Strasbourg I Herr Guillaume Weick hat in den letzten drei Jahren u&nter der Betreuung von Prof. Jalabert in Strasbourg (Frankreich) und mir seinUniversit¨atAugsburge Doktorarbeit angefertigt. Grundlage hierfür ist eine Vereinbarung der Universitat Augsbuforrg theund degreesder Univ of ersité Louis Pasteur über ein binationales PromotionsvDocteurerfahren, dedie l’Universit´eLouisvom Rektor, Pr Pasteur,of. Bottk Strasbourge, am 27.10.2003 I unterzeichnet wurde. (Sp´ecialit´e: Physique de la mati`erecondens´ee) Im Herbst diesen Jahres soll nun die Doktorprüfung stattfi& nden. In diesem Zusammen- hang möchte ich um die Genehmigung der nacDoktorhste derhend Naturwissenschaftenaufgeführten Prüfungskommissi- on bitten, die bereitsdervon Mathematisch-Naturwissenschaftlichendem zuständigen Gremium an der ULP Fakult¨atderStrasbour Universit¨atAugsburgg akzeptiert wurde: Thesis defence in Strasbourg, 22 September 2006 in front of the jury comprising Gutachter Frankreich Dr. Jean-Yves Bigot Supervisor ULP: Prof. Rodolfo A. Jalabert (IPCMS, Strasbourg) Institut de PhysiquSupervisore et Chimie Augsburg:de StrasbouProf.rg Gert-Ludwig Ingold (Institut f¨urPhysik, Augsburg) 23, rue du Loess Referees: Dr. Jean-Yves Bigot (IPCMS, Strasbourg) BP 43 Prof. Ulrich Eckern (Institut f¨ur Physik, Augsburg) ´ F-67034 Strasbourg Cedex 2 Prof. Eric Suraud (IRSAMC, Toulouse) Examiner: Prof. Hermann Grabert (Physikalisches Institut, Freiburg) Prof. Dr. Éric Suraud Invited member: Dr. Dietmar Weinmann (IPCMS, Strasbourg) Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes 118, route de Narbonne F-31062 Toulouse Gutachter Deutschland Prof. Dr. Ulrich Eckern Institut für Physik Universität Augsburg Universitätsstraße 1 86135 Augsburg A` Caroline Contents Remerciements (acknowledgments in French) ix Summary xi R´esum´e xv 1 Introduction 19 1.1 Surface plasmon excitation . 22 1.1.1 Mie theory . 24 1.1.2 Spill-out effect . 26 1.2 Surface plasmon linewidth and quantum size effects . 28 1.2.1 Free path effect . 28 1.2.2 Linear response theory . 28 1.2.3 Random phase approximation . 31 1.2.4 Time-dependent local density approximation . 32 1.2.5 Approach of this thesis . 35 1.3 Time-resolved pump-probe spectroscopy . 35 1.4 Outline of this thesis . 40 2 Metallic nanoparticles: A model system 43 2.1 Electronic Hamiltonian within the jellium model . 43 2.1.1 Single-particle confinement . 44 2.1.2 Separation into collective and relative coordinates . 45 2.1.3 Alternative derivation of the coupling Hamiltonian . 47 2.2 Mean-field approximation and second quantization procedure . 50 2.2.1 Center-of-mass Hamiltonian . 50 2.2.2 Hamiltonian of the relative coordinates . 50 2.2.3 Coupling between center-of-mass and relative-coordinate systems 52 2.3 External driving field . 53 2.4 Conclusion for Chapter 2 . 54 3 Dynamics of the surface plasmon excitation 55 3.1 Reduced density-matrix description of the electronic center of mass . 55 3.1.1 Free evolution of the center of mass . 56 3.1.2 Effect of the external driving field . 64 3.2 Two-level system approach . 66 3.2.1 Analytical solutions of the Bloch equations without detuning . 69 v Contents 3.2.2 Numerical solutions of the Bloch equations in presence of detuning 73 3.2.3 Estimation of the saturation parameter in typical experiments . 74 3.3 Conclusion for Chapter 3 . 75 4 Lifetime of the surface plasmon excitation 77 4.1 Dipole matrix element from single-particle self-consistent states . 78 4.2 Semiclassical low-temperature expansion . 81 4.3 Shell effects and nonmonotonic behavior of the plasmon linewidth . 91 4.4 Conclusion for Chapter 4 . 94 5 Frequency of the surface plasmon excitation 95 5.1 Spill-out-induced frequency shift . 96 5.1.1 Mean-field approximation . 96 5.1.2 Semiclassical low-temperature expansion for the number of spill- out electrons . 98 5.1.3 Number of spill-out electrons: semiclassics vs. LDA . 101 5.1.4 Redshift of the surface plasmon resonance . 102 5.2 Environment-induced frequency shift . 105 5.3 Conclusion for Chapter 5 . 109 6 Time evolution of the optical transmission in a pump-probe configuration 111 7 Double plasmon excitation and ionization in metallic clusters 115 7.1 Second plasmon decay: Landau damping . 116 7.2 Second plasmon decay and ionization . 121 7.3 Conclusion for Chapter 7 . 127 8 Surface plasmon linewidth with an inhomogeneous dielectric environment 129 8.1 Surface plasmon linewidth with a soft self-consistent potential . 133 8.1.1 Semiclassical dipole matrix element with spherical symmetry . 135 8.1.2 Surface plasmon rate with a slope for the self-consistent field . 138 8.2 Steepness of the self-consistent potential with a dielectric mismatch . 140 8.2.1 First case: d = m = =1......................141 8.2.2 Second case: d = m = 6=1 ....................142 8.2.3 Third case: d 6= m ..........................143 8.3 Surface plasmon linewidth with a dielectric mismatch . 143 8.4 Conclusion for Chapter 8 . 144 9 Concluding remarks and outlook 147 9.1 Summary . 147 9.2 Outlook and future perspectives . 151 vi Contents A Three-level system 155 A.1 Rabi oscillations of a three-level system . 157 A.2 Three-level system with additional damping mechanisms . 159 A.2.1 Stationary solutions for the case γ1 = γ2 = 0 (no additional damp- ing constants) . 159 A.2.2 Stationary solutions for the three-level system with additional dampings . 160 B Semiclassical physics 163 B.1 Quantum propagator . 164 B.2 Feynman’s path integrals . 164 B.3 Semiclassical approximation of the propagator and of the Green function 165 B.3.1 Free propagator and van Vleck’s approximation . 165 B.3.2 Gutzwiller’s approximation to the propagator and the Green func- tion — Semiclassical expansions . 166 B.4 Semiclassical density of states: Gutzwiller’s trace formula . 170 C Semiclassics with radial symmetry 173 C.1 Langer modification and partial density of
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  • Nonequilibrium Fluctuation-Dissipation Inequality and Nonequilibrium

    Nonequilibrium Fluctuation-Dissipation Inequality and Nonequilibrium

    PHYSICAL REVIEW E 88, 012102 (2013) Nonequilibrium fluctuation-dissipation inequality and nonequilibrium uncertainty principle C. H. Fleming and B. L. Hu Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA Albert Roura Max-Planck-Institut fur¨ Gravitationsphysik (Albert-Einstein-Institut), Am Muhlenberg¨ 1, 14476 Golm, Germany (Received 16 January 2013; revised manuscript received 7 May 2013; published 3 July 2013) The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature, and often in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a nonequilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Instead of being proportional, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations vanish at zero temperature. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, in both its microscopic origins and its influence upon systems. Moreover, it is shown that there is a coupling-dependent nonequilibrium fluctuation-dissipation relation that determines the nonequilibrium uncertainty relation of linear systems in the weak-damping limit. DOI: 10.1103/PhysRevE.88.012102 PACS number(s): 05.30.−d, 03.65.Yz, 05.40.−a I. INTRODUCTION instantaneous, but where there is nonlocal damping: The fluctuation-dissipation relation (FDR) is a fundamental t m x¨(t) + 2 dτ γ(t − τ) x˙(τ) − F (x) = ξ(t), (4) relation in nonequilibrium statistical mechanics, dating back to −∞ Einstein’s Nobel Prize-winning work on Brownian motion [1] and Nyquist’s seminal work on electronic conductivity [2].