Quantum field theory on quantum graphs and application to their conductance
arXiv:0901.2431 · doi:10.1088/1751-8113/42/29/295205
Abstract
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized star product approach. We give several examples and show how they generalize some of the scattering matrices computed in the mathematical or condensed matter physics litterature. Then, we apply the construction for the calculation of the conductance of graphs, within a small distance approximation. The consistency of the approximation is proved by direct comparison with the exact calculation for the `tadpole' graph.
32 pages; misprints in tree graph corrected; proofs of consistency and unitarity added
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Cited by in corpus (11)
- Non-equilibrium Steady States of Quantum Systems on Star Graphs
- Quantum wire junctions breaking time reversal invariance
- Quantum Fields on Star Graphs with Bound States at the Vertex
- Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
- Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs
- Direct computation of scattering matrices for general quantum graphs
- Unitary equivalence between the Green's function and Schrödinger approaches for quantum graphs
- Off-critical Luttinger Junctions
- Quantum Wire Network with Magnetic Flux
- Scattering matrices in the sl(3) twisted Yangian
- Quantum graph vertices with minimal number of passbands