English
Emergent anyons in quantum Hall physics
Post-edited
Auteurs : Rougerie, Nicolas (Auteur de la Conférence)
CIRM (Editeur )
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
35Q40 - PDEs in connection with quantum mechanics
35Q55 - NLS-like equations (nonlinear Schrödinger)
81S05 - Canonical quantization, commutation relations and statistics
81V70 - Many-body theory; quantum Hall effect
82B10 - Quantum equilibrium statistical mechanics (general)
CIRM (Editeur )
Résumé :
Anyons are by definition particles with quantum statistics different from those of bosons and fermions. They can occur only in low dimensions, 2D being the most relevant case for this talk. They have hitherto remained hypothetical, but there is good theoretical evidence that certain quasi-particles occuring in quantum Hall physics should behave as anyons.
I shall consider the case of tracer particles immersed in a so-called Laughlin liquid. I will argue that, under certain circumstances, these become anyons. This is made manifest by the emergence of a particular effective Hamiltonian for their motion. The latter is notoriously hard to solve even in simple cases, and well-controled simplifications are highly desirable. I will discuss a possible mean-field approximation, leading to a one-particle energy functional with self-consistent magnetic field.
Keywords : mathematical physics; many-body quantum mechanics; anyons; fractional quantum Hall effect; quantum statistics; Laughlin state; mean-field approximation
Codes MSC : I shall consider the case of tracer particles immersed in a so-called Laughlin liquid. I will argue that, under certain circumstances, these become anyons. This is made manifest by the emergence of a particular effective Hamiltonian for their motion. The latter is notoriously hard to solve even in simple cases, and well-controled simplifications are highly desirable. I will discuss a possible mean-field approximation, leading to a one-particle energy functional with self-consistent magnetic field.
Keywords : mathematical physics; many-body quantum mechanics; anyons; fractional quantum Hall effect; quantum statistics; Laughlin state; mean-field approximation
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
35Q40 - PDEs in connection with quantum mechanics
35Q55 - NLS-like equations (nonlinear Schrödinger)
81S05 - Canonical quantization, commutation relations and statistics
81V70 - Many-body theory; quantum Hall effect
82B10 - Quantum equilibrium statistical mechanics (general)
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 04/05/16 Date de captation : 19/04/16 Sous collection : Research talks arXiv category : Mathematical Physics ; Analysis of PDEs Domaine : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Durée : 00:56:09 Audience : Researchers Download : https://videos.cirm-math.fr/2016-04-19_Rougerie.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : Spectral theory of novel materials / Théorie spectrales des nouveaux matériauxOrganisateurs de la rencontre : Exner, Pavel ; Kotani, Motoko ; Kuchment, Peter ; Zagrebnov, Valentin A. Dates : 18/04/16 - 22/04/2016 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1399.html
Données de citation
DOI : 10.24350/CIRM.V.18961603Citer cette vidéo: Rougerie, Nicolas (2016). Emergent anyons in quantum Hall physics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18961603 URI : http://dx.doi.org/10.24350/CIRM.V.18961603 |
Voir aussi
- [Multi angle] Twisted equivariant $\mathrm{K}$-theory and topological phases / Auteur de la Conférence Kubota, Yosuke.
- [Multi angle] Overdamping in gyroscopic systems composed of high-loss and lossless components / Auteur de la Conférence Figotin, Alexander.
- [Multi angle] Gysin maps and bulk-edge correspondence / Auteur de la Conférence Matsuo, Shinichiroh.
- [Multi angle] Topological nature of the Fu-Kane-Mele invariants / Auteur de la Conférence De Nittis, Giuseppe.
Bibliographie
- Arovas, D., Schrieffer, J.R., & Wilczek, F. (1984). Fractional statistics and the quantum Hall effect. Physical Review Letters, 53(7), 722-723 - http://dx.doi.org/10.1103/PhysRevLett.53.722
- Cooper, N.R., & Simon, S.H. (2015). Signatures of fractional exclusion statistics in the spectroscopy of quantum Hall droplets, Physical Review Letters, 114, 106802 - http://dx.doi.org/10.1103/PhysRevLett.114.106802
- Forte, S. (1991). Berry's phase, fractional statistics and the Laughlin wave function. Modern Physics Letters A, 6(34), 3152-3162 - http://dx.doi.org/10.1142/S021773239100364X
- Laughlin, R.B. (1983). Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Physical Review Letters, 50(18), 1395-1398 - http://dx.doi.org/10.1103/PhysRevLett.50.1395
- Laughlin, R. B. (1999). Nobel lecture: Fractional quantization. Reviews of Modern Physics, 71(4), 863-874 - http://dx.doi.org/10.1103/RevModPhys.71.863
- Lundholm, D., & Solovej, J. P. (2013). Local exclusion principle for identical particles obeying intermediate and fractional statistics. Physical Review A, 88, 062106 - http://dx.doi.org/10.1103/PhysRevA.88.062106
- Lundholm, D., & Solovej, J. P. (2013). Hardy and Lieb-Thirring inequalities for anyons. Communications in Mathematical Physics, 322(3), 883-908 - http://dx.doi.org/10.1007/s00220-013-1748-4
- Lundholm, D., & Rougerie, N. (2015). The average field approximation for almost bosonic extended anyons. Journal of Statistical Physics, 161(5), 1236-1267 - http://dx.doi.org/10.1007/s10955-015-1382-y
- Lundholm, D., & Rougerie, N. (2016). Emergence of fractional statistics for tracer particles in a Laughlin liquid.
- Myrheim, J. (1999). Anyons. In A. Comtet, T. Jolicoeur, S. Ouvry, & F. David (Eds.), Aspects topologiques de la physique en basse dimension (pp. 265-413). Les Ulis: EDP Sciences - http://dx.doi.org/10.1007/3-540-46637-1_4
- Ouvry, S. (2007). Anyons and lowest Landau level anyons. In B. Duplantier, J.-M. Raimond, & V. Rivasseau (Eds.), The Spin (pp. 77-107). Basel: Birkhäuser - http://dx.doi.org/10.1007/978-3-7643-8799-0_3
- Stormer, H.L., Tsui, D.C., & Gossard, A.C. (1999). The fractional quantum Hall effect. Reviews of Modern Physics, 71(2), S298-S305 - http://dx.doi.org/10.1103/RevModPhys.71.S298
- Wilczek, F. (1990). Fractional statistics and anyon superconductivity. Singapore: World Scientific - http://www.worldscientific.com/worldscibooks/10.1142/0961
- Zhang, Y., Sreejith, G.J., Gemelke, N.D., & Jain, J.K. (2014). Fractional angular momentum in cold atom systems. Physical Review Letters, 113, 160404 - http://dx.doi.org/10.1103/PhysRevLett.113.160404
