Graph Theory in Physics

In General > s.a. [graph theory]; quantum systems.
@ And quantum mechanics: Ettinger & Hoyer qp/99 [graph isomorphisms].
@ Lagrangian systems: Novikov & Schvarts RMS(99)mp/00.
@ Discretized field theories: Kan & Shiraishi JMP(05)ht/04 [QED, divergences]; > s.a. lattice field theory.
@ Quantum mechanics on graphs: Barra & Gaspard PRE(02)cm/01; Blümel et al qp/02 [regular, math foundations]; Bolte & Harrison JPA(03) [form factor, spin]; Blasiak & Horzela a0710 [graph operator algebras]; > s.a. Cellular Automaton.
@ Graph evolution models: Markopoulou & Prémont-Schwarz a0805 [conserved topological defects].
@ Related topics: Barra & Gaspard PRE(01) [classical dynamics]; Fiorenza ACS(06)m.CT/02 [sums over graphs]; Giorda & Zanardi qp/03, qp/03 [bosonic, entanglement and tunneling]; Procacci & Scoppola mp/05 [random cluster model]; Reidys DM(08) [sequential dynamical systems]; > s.a. entanglement [graph states].
> Specific models: see discrete geometry [gravity]; Polymers; supersymmetric theories; toda lattice.

Statistical Models > s.a. game theory; stochastic processes.
@ Random walks: Watrous cs.CC/98-in; Burioni & Cassi JPA(05) [rev]; > s.a. diffusion, random processes.
@ Quantum walks: Farhi & Gutmann PRA(98); Aharonov et al qp/00-in; Kendon IJQI(06)qp/03 [discrete t]; Montanaro qp/05; Osborne qp/06 [approximate locality].
@ Transport: Muelken & Blumen PRE(06)qp [quantum vs classical percolability].
@ Random graphs, evolution: Barbosa et al PhyA(04) [directed]; Lee et al NPB(04) [as Potts model]; Lushnikov JPA(05); Finkel ht/06-in [local moves and lqg]; Turova JSP(06) [phase transitions]; > s.a. discrete geometry, ising model, networks.
@ Fields on graphs: Häggström AAP(00) [percolation, phase transitions].
@ Thermodynamics on graphs: Burioni et al JPA(00) [spectral partitions into subgraphs]; Majka & Wislicki PhyA(04) [communication networks].
@ Quantum field theory on graphs: Cimasoni & Reshetikhin a0704 [from dimer model].

Operators
@ General references: Requardt mp/00 [spectral analysis and Connes distance]; Kostrykin & Schrader JMP(01)mp/00 [scattering matrices].
@ Schrödinger operator: Novikov RMS(97)mp/00; Kostrykin & Schrader JPA(00)mp, RVMP(00)mp [1D]; Gutkin & Smilansky JPA(01) [spectrum determines graph uniquely].
@ Laplacian: Forman Top(93) [determinant]; Akkermans et al AP(00) [spectral determinant]; Khorunzhy & Vengerovsky mp/00 [random graph]; Requardt JPA(02)mp/01 [Dirac operator and Connes metric]; Dean JPA(02) [density of states]; Kenyon mp/02; Hashimoto et al JMP(03) [large graph, spectral distribution]; Dorogovtsev et al PhyA(04) [random, spectrum]; Braunstein et al AC(06)qp/04 [as a density matrix]; Khorunzhiy et al AAP(06)mp/05 [random graph, tails of spectra]; Müller & Stollmann mp/05 [on supercritical bond-percolation graphs]; Kostrykin & Schrader mp/06 [inverse scattering]; Hu DM(07) [eigenvalues, and adjacency matrix]; Elon a0804 [statistical approach].
@ Dirac operator: Bolte & Harrison JPA(03) [spectral statistics].

Other Concepts > see decoherence, spin models [graph states]; phase transition.

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