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2 Acta Physica Polonica A

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Torsion in Cohomology Groups of Configuration Spaces

100%

Maciążek T. , Sawicki A.

Acta Physica Polonica A

2017

tom 132

nr 6

1695-1698

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.

Isoscattering Microwave Networks - The Role of the Boundary Conditions

70%

Ławniczak M. , Bauch S. , Sawicki A. , Kuś M. , Sirko L.

nr 6

1078-1081

The recent paper by Hul et al. (Phys. Rev. Lett. 109, 040402 (2012)}, see Ref. [7]) addresses an important mathematical problem whether scattering properties of wave systems are uniquely connected to their shapes? The analysis of the isoscattering microwave networks presented in this paper indicates a negative answer to this question. In this paper the sensitivity of the spectral properties of the networks to boundary conditions is tested. We show that the choice of the proper boundary conditions is extremely important in the construction of the isoscattering networks.