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Torsion in Cohomology Groups of Configuration Spaces

100%
Maciążek T., Sawicki A.
Acta Physica Polonica A
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2017
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vol. 132
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issue 6
1695-1698
EN
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.
2
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Basic set of experiments for determination of mechanical properties of sand

100%
Sawicki A., Mierczyński J.
Bulletin of the Polish Academy of Sciences: Technical Sciences
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2014
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issue 1
3
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Compaction and liquefaction of a sandy layer: simulation of shaking table experiments

100%
Sawicki A., Świdziński W.
Archives of Civil Engineering
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2013
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issue 4
4
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A study on liquefaction susceptibility of some soils from the coast of Marmara sea

100%
Sawicki A., Świdziński W.
Bulletin of the Polish Academy of Sciences: Technical Sciences
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2006
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vol. 54
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issue 4
5
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Note on the Role of Symmetry in Scattering from Isospectral Graphs and Drums

81%
Band R., Sawicki A., Smilansky U.
Acta Physica Polonica A
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2011
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vol. 120
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issue 6A
A-149-A-153
EN
We discuss scattering from pairs of isospectral quantum graphs constructed using the method described in the papers of Parzanchevski, Band and Ben-Shach. It was shown in the paper of Band et al. that scattering matrices of such graphs have the same spectrum and polar structure, provided that infinite leads are attached in a way which preserves the symmetry of isospectral construction. In the current paper we compare this result with the conjecture put forward by Okada et al. that the pole distribution of scattering matrices in the exterior of isospectral domains in ℝ^{2} is different.
6
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Isoscattering Microwave Networks - The Role of the Boundary Conditions

71%
Ławniczak M., Bauch S., Sawicki A., Kuś M., Sirko L.
Acta Physica Polonica A
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2013
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vol. 124
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issue 6
1078-1081
EN
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.
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