Graph Theory in Physics| Graph Theory in Physics |
In General
> s.a. graph theory / quantum systems.
@ General references: Estrada a1302-ch [introduction];
Jouneghani et al IJTP(14)-a1309 [review of quantum graphical models].
@ Lagrangian systems: Novikov & Schvarts RMS(99)mp/00.
@ Discretized field theories: Kan & Shiraishi JMP(05)ht/04 [QED, divergences];
Fedorov a1809 [conservation laws];
Padmanabhan & Sugino a2104 [Abelian gauge theory, anyons];
> s.a. lattice field theory.
@ Quantum mechanics on graphs: Ettinger & Hoyer qp/99 [graph isomorphisms];
Barra & Gaspard PRE(02)cm/01;
Blümel et al qp/02 [regular, mathematical foundations];
Bolte & Harrison JPA(03) [form factor, spin];
Błasiak & Horzela a0710
≠ Błasiak et al JPCS(10) [graph operator algebras];
Pavičić et al JMP(10)-a1004 [graph approach to quantum systems];
Harrison et al PRS(11) [particle statistics];
Mintchev JPA(11)-a1106 [non-equilibrium steady states on star graphs];
Ionicioiu & Spiller PRA(12)-a1110 [mapping graphs to quantum states];
> s.a. cellular automaton; spin models [graph states].
@ Graph evolution models: Dadic & Pisk IJTP(79);
Markopoulou & Prémont-Schwarz CQG(08)-a0805 [conserved topological defects];
Rath & Toth EJP(09)-a0808 [random graphs and self-organized critical state];
Grindrod & Higham PRS(10);
Arrighi & Dowek a1202 [causal dynamics];
Arrighi & Martiel PRD(17)-a1607 [Quantum Causal Graph Dynamics];
Kelly et al CQG(19)-a1901 [self-assembly of space, based on the Ollivier curvature].
@ Related topics:
Barra & Gaspard PRE(01) [classical dynamics];
Fiorenza ACS(06)m.CT/02 [sums over graphs];
Giorda & Zanardi PRA(03)qp,
EPL(04)qp/03 [bosonic, entanglement and tunneling];
Procacci & Scoppola CPAA-mp/05 [random cluster model];
Reidys DM(08) [sequential dynamical systems];
Cornelissen & Marcolli JGP(13) [graph reconstruction and quantum statistical mechanics];
Cabello et al PRL(14)-a1401 [graph invariants and quantum correlations];
Arrighi et al a2010 [quantum superpositions];
> s.a. entangled systems [graph states];
Virial Expansion.
> Specific models: see Anderson
Localization; discrete geometry models [gravity, quantum graphity];
Polymers; supersymmetric theories;
toda lattice.
Statistical Models
> s.a. networks [entropy]; game theory;
phase transitions; Power-Law Distribution;
stochastic processes.
@ Random walks:
Watrous cs.CC/98-in;
Burioni & Cassi JPA(05) [rev];
Mendonça PRE(11)-a1106 [cover time];
Arendt & Jost a1203/EPJB [multiple-agent consensus problem];
> s.a. diffusion; green functions;
random processes.
@ Quantum walks: Farhi & Gutmann PRA(98);
Aharonov et al qp/00-proc;
Kendon IJQI(06)qp/03 [discrete time];
Montanaro QIC(07)qp/05;
Osborne PRL(08)qp/06 [approximate locality];
Kargin JPA(10) [bounds on the mixing time];
Higuchi et al JMI-a1207 [discrete-time evolution operators].
@ 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);
Turova JSP(06) [phase transitions];
> s.a. ising model; networks;
types of graphs.
@ Emergence of continuum geometry: Bombelli et al CQG(09)-a0905 [manifolds from graphs in lqg];
Conrady JSP(11)-a1009 [emergence of 2D space];
Chen & Plotkin PRD(13)-a1210 [and emergent manifolds];
Tee EPJC(21)-a1909 [new Hamiltonian with enhanced locality, and matter];
Pugliese a2007.
@ Quantum-gravity motivated:
Finkel ht/06-conf [local moves and lqg];
Kelly et al a2102 [graph regularisation of Euclidean gravity];
> s.a. discrete geometry models.
@ Fields on graphs: Häggström AAP(00) [percolation, phase transitions];
Gobron a1312
[Pfaffian representations of Ising partition function, non-planar graphs];
> s.a. entanglement entropy; wave equation.
@ 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 CMP(08)-a0704 [from dimer model].
Operators
@ General references: Requardt mp/00/JPA [spectral analysis and Connes distance];
Kostrykin & Schrader JMP(01)mp/00 [scattering matrices].
@ 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 JFA(07)mp/05 [on supercritical bond-percolation graphs];
Kostrykin & Schrader mp/06 [inverse scattering];
Hu DM(07) [eigenvalues, and adjacency matrix];
Elon JPA(08)-a0804 [statistical approach];
Schrader JPA(09) [Klein-Gordon and wave equation];
Keller & Lenz a1101;
Haeseler et al a1103 [infinite graphs];
Bauer et al a1211 [spectrum];
Majid JGP(13) [non-commutative geometry and canonical edge Laplacian];
Anantharaman a1512 [on large graphs, quantum ergodicity];
> s.a. types of graphs [random].
@ Laplacian, bounds on eigenvalues: Das & Guo DM(13) [for the second power of a graph];
Charles et al DM(13) [and non-positive eigenvalues of the adjacency matrix].
@ Schrödinger operator: Novikov RMS(97)mp/00;
Kostrykin & Schrader JPA(00)mp,
RVMP(00)mp [1D];
Gutkin & Smilansky JPA(01) [the spectrum determines the graph uniquely].
@ Other operators: Bolte & Harrison JPA(03) [Dirac operator, spectral statistics];
Exner a1205-fs [momentum operators];
Dahlberg & Wehner PTRS(18)-a1805 [single-qubit operations on graph states].
Quantum Graphs
* Idea: A quantum graph is a graph
considered as a (singular) one-dimensional variety and equipped with a second-order
differential Hamiltonian H (a "Laplacian") with suitable conditions
at the vertices; They are commonly used as models of complex quantum systems, for
example molecules, networks of wires, and states of condensed matter.
@ General references: Dabaghian & Blümel PRE(03)qp,
JETPL(03)qp,
qp/03 [analytically solvable];
Schmidt et al JPA(03) [Green functions];
Kurasov & Nowaczyk JPA(05) [inverse spectral problem];
Fulling m.SP/05-conf [local spectral density and vacuum energy];
Exner et al RVMP(07) [random potential, localization];
Fulling et al JPA(07)-a0708 [index theorems];
Kuchment in(08)-a0802 [rev];
Weaver a1506 [as quantum relations];
Andrade et al PRP(16)-a1601 [Green's function approach];
Berkolaiko a1603 [elementary intro].
@ And other physics: Dabaghian et al JETPL(01)qp [and chaos];
Tanner qp/05 [and quantum random walks].
@ Spectral properties: Barra & Gaspard JSP(00)qp [level spacing distribution];
Kuchment JPA(05)mp/04;
Gavish & Smilansky JPA(07)-a0807 [spectral theory and length spectrum];
Berkolaiko & Liu a1601 [simplicity of eigenvalues and non-vanishing of eigenfunctions].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 26 apr 2021