n-Particle Quantum Statistics on Graphs

Harrison, J. M.; Keating, Jon P; Robbins, Jonathan M; Sawicki, Adam

doi:10.1007/s00220-014-2091-0

Cited by 34 publications

(61 citation statements)

References 18 publications

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“…The main advantage of this approach is that it allows to easily predict the results of many complex calculations. The method recovers all the known results concerning (co)homology groups of graph configuration spaces [14,23]. Its application to higher (co)homology groups, however, still requires considerable development.…”

Section: Introductionmentioning

confidence: 58%

“…Recently the idea of Leinaas and Myrheim has been explored in the setting of graphs [14]. In particular, the authors of [14] showed that particles constrained to move on a graph can exhibit even more exotic forms of anyons.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the authors of [14] showed that particles constrained to move on a graph can exhibit even more exotic forms of anyons. In fact, this previous work was based on the simplest topological information about graph configuration spaces, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Describing the remaining groups is an open problem. The authors of [14,23] proposed a method for calculation of homology groups that combines tools from algebraic topology and graph theory with a set of combinatorial relations derived from the analysis of certain small canonical graphs. The main advantage of this approach is that it allows to easily predict the results of many complex calculations.…”

Section: Introductionmentioning

confidence: 99%

“…on a graph. The approach taken in [14] enabled identification of the key topological determinants of the quantum statistics on graphs.…”

mentioning

confidence: 99%

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Torsion in Cohomology Groups of Configuration Spaces

Maciążek

Sawicki

2017

Acta Phys. Pol. A

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An important and surprising discovery in physics in the last fifty years is that if quantum particles are constrained to move in two rather than three dimensions, they can in principle exhibit new forms of quantum statistics, called anyons. Although anyons were initially only a theoretical concept, they quickly proved to be useful in explaining one of the most significant discoveries of condensed matter physics in the last century, i.e. fractional quantum Hall effect. Recently, it was shown that particles constrained to move on a graph can exhibit even more exotic forms of quantum statistics, depending on the topology of the graph. In this paper we discuss what possible new quantum signatures of topology may arise when one takes into account more complex topological information, called higher (co)homology groups, which may also be associated with graph configuration spaces. In particular we focus on the significance of a torsion component.

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Section: Introductionmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…on a graph. The approach taken in [14] enabled identification of the key topological determinants of the quantum statistics on graphs.…”

mentioning

confidence: 99%