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    Wyświetlanie 1-12 z 12
    Tytuł:
    Edge Switching Transformations of Quantum Graphs
    Autorzy:
    Aizenman, M.
    Schanz, H.
    Smilansky, U.
    Warzel, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030017.pdf
    Data publikacji:
    2017-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    05.45.Mt
    02.10.Ox
    Opis:
    Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schrödinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by {Eₙ}^{∞}ₙ₌₁ and {Ẽₙ}^{∞}ₙ₌₁ correspondingly, are level-2 interlaced, so that Eₙ-₂ ≤ Ẽₙ ≤ Eₙ₊₂. The proofs are guided by considerations of the quantum graphs' discrete analogs.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 6; 1699-1703
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Geometric properties of quantum graphs and vertex scattering matrices
    Autorzy:
    Kurasov, P.
    Nowaczyk, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255512.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    scattering theory
    quantum graphs
    matching (boundary) conditions
    Opis:
    Differential operators on metric graphs are investigated. It is proven that vertex matching (boundary) conditions can be successfully parameterized by the vertex scattering matrix. Two new families of matching conditions are investigated: hyperplanar Neumann and hyperplanar Dirichlet conditions. Using trace formula it is shown that the spectrum of the Laplace operator determines certain geometric properties of the underlying graph.
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 295-309
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Inverse Problems for Quantum Graphs: Recent Developments and Perspectives
    Autorzy:
    Kurasov, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/1492443.pdf
    Data publikacji:
    2011-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Nk
    73.63.-b
    85.35.-p
    Opis:
    An introduction into the area of inverse problems for the Schrödinger operators on metric graphs is given. The case of metric finite trees is treated in detail with the focus on matching conditions. For graphs with loops we show that for almost all matching conditions the potential on the loop is not determined uniquely by the Titchmarsh-Weyl function. The class of all admissible potentials is characterized.
    Źródło:
    Acta Physica Polonica A; 2011, 120, 6A; A-132-A-141
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Inverse Problem for Quantum Graphs with One Cycle
    Autorzy:
    Kurasov, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/1585121.pdf
    Data publikacji:
    2009-11
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Nk
    73.63.-b
    85.35.-p
    Opis:
    Quantum graphs having one cycle are considered. It is shown that if the cycle contains at least three vertices, then the potential on the graph can be uniquely reconstructed from the corresponding Titchmarsh-Weyl function (Dirichlet-to-Neumann map) associated with graph's boundary, provided certain non-resonant conditions are satisfied.
    Źródło:
    Acta Physica Polonica A; 2009, 116, 5; 765-771
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Experimental Study of Quantum Graphs with Simple Microwave Networks: Non-Universal Features
    Autorzy:
    Fu, Z.
    Koch, T.
    Antonsen, T.
    Ott, E.
    Anlage, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030007.pdf
    Data publikacji:
    2017-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    Quantum graphs
    universal fluctuations
    impedance
    random coupling model
    microwave graphs
    Opis:
    Quantum graphs provide a setting to test the hypothesis that all ray-chaotic systems show universal wave chaotic properties. Here, an experimental setup consisting of a microwave coaxial cable network is used to simulate quantum graphs. The networks which are large compared to the wavelength, are constructed from coaxial cables connected by T junctions. The distributions of impedance statistics are obtained from experiments on an ensemble of tetrahedral networks. The random coupling model (RCM) is applied in an attempt to uncover the universal statistical properties of the system. Deviations from RCM predictions have been observed in that the statistics of diagonal and off-diagonal impedance elements are different. It is argued that because of the small finite-size quantum graphs utilized here there will be non-universal results.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 6; 1655-1660
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pseudo-Orbit Expansion for the Resonance Condition on Quantum Graphs and the Resonance Asymptotics
    Autorzy:
    Lipovský, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/1189973.pdf
    Data publikacji:
    2015-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    03.65.Ge
    03.65.Nk
    02.10.Ox
    Opis:
    In this note we explain the method how to find the resonance condition on quantum graphs, which is called pseudo-orbit expansion. In three examples with standard coupling we show in detail how to obtain the resonance condition. We focus on non-Weyl graphs, i.e. the graphs which have fewer resonances than expected. For these graphs we explain benefits of the method of "deleting edges" for simplifying the graph.
    Źródło:
    Acta Physica Polonica A; 2015, 128, 6; 968-973
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Surgery of Graphs: M-Function and Spectral Gap
    Autorzy:
    Kurasov, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030010.pdf
    Data publikacji:
    2017-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    quantum graphs
    spectral theory
    Opis:
    We discuss behaviour of the spectral gap for quantum graphs when two metric graphs are glued together. It appears that precise answer to this question can be given using a natural generalisation of the Titchmarsh-Weyl M-functions.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 6; 1666-1671
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Experimental Determination of the Autocorrelation Function of Level Velocities for Microwave Networks Simulating Quantum Graphs
    Autorzy:
    Ławniczak, M.
    Borkowska, A.
    Hul, O.
    Bauch, S.
    Sirko, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/1492514.pdf
    Data publikacji:
    2011-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    05.45.Mt
    03.65.Nk
    Opis:
    The autocorrelation function c(x) of level velocities is studied experimentally. The measurements were performed for microwave networks simulating quantum graphs. One and two ports measurements of the scattering matrix Ŝ necessary for determining c(x) were realized for the networks possessing 5 and 6 vertices, respectively. The network with six vertices was fully connected. In the case of the networks with five vertices, additionally to the fully connected configuration, we measured the networks without the bond connecting input/output vertices. The obtained experimental results besides the autocorrelation function of level velocities, also the nearest-neighbor spacing distribution and parametric velocities distribution are compared to the predictions of random matrix theory and numerical results.
    Źródło:
    Acta Physica Polonica A; 2011, 120, 6A; A-185-A-190
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Torsion in Cohomology Groups of Configuration Spaces
    Autorzy:
    Maciążek, T.
    Sawicki, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030016.pdf
    Data publikacji:
    2017-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    Quantum graphs
    quantum statistics
    vector bundles
    homology groups
    Opis:
    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.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 6; 1695-1698
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On reflectionless equi-transmitting matrices
    Autorzy:
    Kurasov, P.
    Ogik, R.
    Rauf, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/255075.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    quantum graphs
    vertex scattering matrix
    equi-transmitting matrices
    Opis:
    Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.
    Źródło:
    Opuscula Mathematica; 2014, 34, 3; 483-501
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of Missing Level Statistics for Microwave Networks Simulating Quantum Chaotic Graphs Without Time Reversal Symmetry - the Case of Randomly Lost Resonances
    Autorzy:
    Ławniczak, M.
    Białous, M.
    Yunko, V.
    Bauch, S.
    Dietz, B.
    Sirko, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030011.pdf
    Data publikacji:
    2017-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    05.40.-a
    05.45.Mt
    05.45.Tp
    03.65.Sq
    Opis:
    We present experimental and numerical studies for level statistics in incomplete spectra obtained with microwave networks simulating quantum chaotic graphs with broken time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the nearest-neighbor spacing distribution, the spectral rigidity and the average power spectrum are in good agreement with theoretical predictions for incomplete sequences of levels of systems with broken time reversal symmetry.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 6; 1672-1676
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional Revival of Threshold Graphs Under Laplacian Dynamics
    Autorzy:
    Kirkland, Steve
    Zhang, Xiaohong
    Powiązania:
    https://bibliotekanauki.pl/articles/31552789.pdf
    Data publikacji:
    2020-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Laplacian matrix
    spectral decomposition
    quantum information transfer
    fractional revival
    Opis:
    We consider Laplacian fractional revival between two vertices of a graph $X$. Assume that it occurs at time \(\tau\) between vertices 1 and 2. We prove that for the spectral decomposition \(L=∑_{r=0}^qθ_rE_r\) of the Laplacian matrix $L$ of $X$, for each $r = 0, 1, . . ., q$, either $E_re_1 = E_re_2$, or $E_re_1 = −E_re_2$, depending on whether \(e^{i\tauθ_r}\) equals to 1 or not. That is to say, vertices 1 and 2 are strongly cospectral with respect to $L$. We give a characterization of the parameters of threshold graphs that allow for Laplacian fractional revival between two vertices; those graphs can be used to generate more graphs with Laplacian fractional revival. We also characterize threshold graphs that admit Laplacian fractional revival within a subset of more than two vertices. Throughout we rely on techniques from spectral graph theory.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 2; 585-600
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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