Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption

Hul, Oleh; Tymoshchuk, Oleg; Bauch, Szymon; Koch, Peter; Sirko, Leszek

doi:10.1088/0305-4470/38/49/003

Cited by 72 publications

(65 citation statements)

References 34 publications

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“…The mathematical equivalence of spectra of twodimensional quantum billiards and flat microwave resonators is used to experimentally explore a variety of quantum chaotic phenomena in closed [22,23,54,55] and open systems [56][57][58][59][60][61][62]. Here, we use the data measured for a microwave billiard in the shape of a classically chaotic tilted-stadium billiard; see Refs.…”

Section: Comparison With Microwave Datamentioning

confidence: 99%

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

et al. 2017

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The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. We thus eventually fully solve a problem which already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

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Section: Comparison With Microwave Datamentioning

confidence: 99%

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

et al. 2017

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“…Scattering theory is needed to understand experiments in a wide range of fields [3], including nuclear, atomic and molecular physics, as well as mesoscopic ballistic devices and even classical wave systems such as microwave and elastomechanical billiards, and most recently wireless communication [3,4,5,6,7,8,9,10,11,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Scattering theory still poses challenges, we recently solved one of those by calculating tthe distribution of the off-diagonal scattering matrix elements.…”

Section: Introductionmentioning

confidence: 99%

Exact results for chaotic scattering and experimental validation

Guhr

2017

AIP Conference Proceedings

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Abstract. As scattering experiments are the key tool to obtain information on nuclei and other quantum systems, the foundations of scattering theory were laid already a long time ago. Compound nucleus scattering prompted the study of generic statistical features. In the Heidelberg approach, those are taken into account by assuming that the reaction zone is fully quantum chaotic. Later on, this approach turned out to be applicable to a large variety of systems on different scales, including classical wave systems. For a long time, the distribution of the off-diagonal scattering-matrix elements resisted analytical treatment. In two recent studies [1, 2], we fully solved this problem and we also carried out a comparison with data from microwave experiments. Some comment are made on our very recent results for the cross-section distributions.

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“…In mathematical physics the Dirac oscillator has become a paradigm for the realization of covariant quantum models and it has found applications both in nuclear [23][24][25] and subnuclear [26,27] physics as well as in quantum optics [28][29][30]. Very recently a one dimensional version of the Dirac oscillator has been realised experimentally [31] for the first time with realistic prospects to realise in the near future the two dimensional version of the Dirac oscillator which may be feasible using networks of microwave coaxial cables [32][33][34]. It is interesting to note that a further interaction in the form of a homogeneous magnetic field can still be incorporated in the Dirac oscillator keeping the system still exactly solvable [28,[35][36][37][38] and this combined system has quite interesting properties.…”

Section: Introductionmentioning

confidence: 99%

Re-entrant phase transitions in non-commutative quantum mechanics

Panella

Roy

2016

J. Phys.: Conf. Ser.

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Abstract. We discuss the (2+1)-dimensional Dirac oscillator in a magnetic field in non commutative quantum mechanics. The system is known to be characterised by a left rightchiral phase transition in ordinary Quantum mechanics. We show that the momentum noncommutativity shifts the know phase transition while the space non commutativity introduces a new right-left chiral quantum phase transition giving rise to the intriguing phenomenon of re-entrant phase transition observed in condensed matter as well as in black hole physics. IntroductionOn the basis that both string theory and quantum gravity indicate that space-time can be non-commutative [1-4] several quantum mechanical systems have been studied by a number of authors to determine the role of noncommutativity parameters on a variety of physical observables [5][6][7][8][9][10][11][12][13][14].The Dirac oscillator on the other hand is one of the very few relativistic systems which is exactly solvable [15][16][17][18][19][20][21][22]. In mathematical physics the Dirac oscillator has become a paradigm for the realization of covariant quantum models and it has found applications both in nuclear [23][24][25] and subnuclear [26,27] physics as well as in quantum optics [28][29][30]. Very recently a one dimensional version of the Dirac oscillator has been realised experimentally [31] for the first time with realistic prospects to realise in the near future the two dimensional version of the Dirac oscillator which may be feasible using networks of microwave coaxial cables [32][33][34]. It is interesting to note that a further interaction in the form of a homogeneous magnetic field can still be incorporated in the Dirac oscillator keeping the system still exactly solvable [28,[35][36][37][38] and this combined system has quite interesting properties. In some recent papers it has been shown that for this combined system there is a chirality phase transition if the magnitude of the magnetic field either exceeds or is less than a critical value B cr (which also depends on the oscillator strength) [39,40]. A consequence of this chirality phase transition is that the spectrum is different for B > B cr and B < B cr , B being the magnetic field strength.Our objective here is to analyse the same system, a 2D Dirac oscillator within a constant magnetic field, but in the framework of non-commutative space and momentum coordinates. It will be shown that in this case the critical value of the magnetic field depends not only on the oscillator strength but on the non-commutativity parameters as well. The interesting feature which we would like to emphasise, is that beside the two left-and right-chiral phases present also in the commutative case, in the non-commutative scenario there appear also a new third

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Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption

Cited by 72 publications

References 34 publications

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

Exact results for chaotic scattering and experimental validation

Re-entrant phase transitions in non-commutative quantum mechanics

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