Quantum fields on star graphs with bound states at the vertex
- Institute for High Energy Phenomenology, Newman Laboratory of Elementary Particle Physics, Cornell University, Ithaca, New York 14853 (United States)
- Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica dell'Universita di Pisa, Largo Pontecorvo 3, 56127 Pisa (Italy)
- Laboratoire de Physique Theorique d'Annecy-le-Vieux (LAPTH), UMR5108, CNRS, Universite de Savoie, 9, Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex (France)
We investigate the propagation of a massless scalar field on a star graph, modeling the junction of n quantum wires. The vertex of the graph is represented by a pointlike impurity (defect), characterized by a one-body scattering matrix. The general case of off-critical scattering matrix with bound and/or antibound states is considered. We demonstrate that the contribution of these states to the scalar field is fixed by causality (local commutativity), which is the key point of our investigation. Two different regimes of the theory emerge at this stage. If bound sates are absent, the energy is conserved and the theory admits unitary time evolution. The behavior changes if bound states are present because each such state generates a kind of damped harmonic oscillator in the spectrum of the field. These oscillators lead to the breakdown of time-translation invariance. In both regimes we investigate in this framework the electromagnetic conductance of the Luttinger liquid on the quantum wire junction. We derive an explicit expression for the conductance in terms of the scattering matrix and show that antibound and bound states have a different impact, giving rise to oscillations with exponentially damped and growing amplitudes, respectively.
- OSTI ID:
- 21335928
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 3; Other Information: DOI: 10.1063/1.3318159; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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