Quasiclassical methods for spin-charge coupled dynamics in low-dimensional systems [Elektronische Ressource] / Cosimo Gorini

Quasiclassical methods for spin-chargecoupled dynamicsin low-dimensional systemsCosimo GoriniLehrstuhl fu¨r Theoretische Physik II¨Universitat AugsburgAugsburg, April 2009SupervisorsPriv.-Doz. Dr. Peter SchwabInstitut fu¨r PhysikUniversita¨t AugsburgProf. Roberto RaimondiDipartimento di FisicaUniversita` degli Studi di Roma TreProf. Dr. Ulrich EckernInstitut fu¨r PhysikUniversita¨t AugsburgReferees: Prof. Dr. Ulrich EckernProf. Roberto RaimondiOral examination: 12/6/20093Mi scusi, dei tre telefoni qual e` quello con il tarapiotapioco che avverto lasupercazzola? . . . Dei tre . . .Conte MascettiMario Monicelli, Amici Miei, 1975Gib Acht auf dich, wenn du durch Deutschland kommst,die Wahrheit unter dem Rock.Galileo GalileiBertolt Brecht, Leben des Galilei, 1943God might have mercy, he won’t!Colonel Trautmann on John J. RamboRambo III, 1988Contents1 Introduction 71.1 Spintronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 The theoretical tools . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Enter the formalism 132.1 Green’s functions, contours and the Keldysh formulation . . . . . 132.1.1 Closed-time contour Green’s function and Wick’s theorem 152.1.2 The Keldysh formulation . . . . . . . . . . . . . . . . . . 182.2 From Dyson to Eilenberger . . . . . . . . . . . . . . . . . . . . . 192.2.1 Vector potential and gauge invariance . . . . . .