10th Workshop on Quantum Chaos
and Localisation Phenomena
27 - 28 May 2021 - Warsaw, Poland
* Institute of Physics, Polish Academy of Sciences
* Center for Theoretical Physics, Polish Academy of Sciences
* Pro Physica Foundation
To assess achievements and to formulate directions of new research
on quantum chaos and localisation.
To bring together prominent experimental and theoretical physicists
who share a common interest in quantum
chaos and localisation phenomena.
Presentations will focus on the following topics:
Quantum chaos and nonlinear classical systems; Quantum and microwave billiards;
Quantum and microwave graphs;
Atoms in strong electromagnetic fields - experiment and theory;
Chaos vs. coherent effects in multiple scattering; Anderson localisation;
Random lasers; Quantum chaos and quantum computing; Entanglement and noise.
The 10th Workshop on Quantum Chaos and Localisation Phenomena
will be held from May 27 to May 28, 2021 on-line by ZOOM service.
It will be also live-streaming on YouTube.
Please disseminate information about the Workshop among your students, collaborators and colleagues who might be interested.
Registration and Abstract Submission: May 10, 2021
Manuscript submission to Acta Physica Polonica A: August 23, 2021
Conference fee to partially cover the Workshop organizing costs - speakers only:
• full: 340 PLN (75 Euro),
• for members of the Polish Physical Society: 200 PLN (45 Euro).
The payment should be transferred in Polish currency (złoty, PLN) or Euros
to the bank account:
Bank Gospodarstwa Krajowego
Account number for PLN: 89 1130 1017 0013 4373 9820 0025
Account number for Euros: PL 35 1130 1017 0013 4373 9820 0027
Instytut Fizyki PAN, Warszawa
All bank charges are on the account of the payer. Please include in the bank transfer documents the names
of the participants.
- The workshop's programme will consist of invited talks and poster contributions.
- The schedule of the Workshop:
- May 27, 9:30 - 18:00, CET: 12 lectures, 30 min. each
- May 28, 9:30 - 14:00, CET: 8 lectures, 30 min. each
Together 20 lectures.
The invited talks will be published in Acta Physica Polonica A.
We kindly ask invited speakers to prepare their manuscripts according to the guide to authors.
(Click twice on a name for more information)
Steven M. Anlage (University of Maryland, USA)
Affiliation: Department of Physics, University of Maryland, College Park, MD 20742-4111 USA
Title: Generalization of Wigner time delay to sub-unitary scattering systems
We introduce a complex generalization of Wigner time delay (τ) for subunitary scattering systems. Theoretical expressions for complex time delay asa function of excitation energy, uniform and non-uniform loss, and coupling, are given. We find very good agreement between theory and experimental data taken on microwave graphs containing an electronically variable lumped-losselement. We find that time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in Re[τ] and Im[τ] serves as a reliable indicator of the condition for Coherent Perfect Absorption (CPA). This work opens a new window on time delay in lossy systems and provides a means to identify the poles and zeros of the scatteringmatrix fromexperimentaldata. The results also enable a new approach to achieving CPA at an arbitrary energy/frequency in complex scattering systems. We also investigate the statistical properties of the complex time delay as a function of uniform attenuation, utilizing both theory and experiments on microwave graphs. This work is supported by AFOSR COE Grant No. FA9550-15-1-0171, NSF/DMR2004386, and ONR Grants N000141912481 and N000141912480.
Sergiy Denysov (Oslo Metropolitan University, Norway)
Affiliation: Department of Computer Science Oslo Metropolitan University Pilestredet 35 PS245 0166 Oslo, Norway
Title: Dissipative Quantum Chaos in Floquet Systems
Dissipative Quantum Chaos is an emerging theory with the agenda to relateopen quantum and classical dissipative systems and eventually provide us with a tool to determine whether the evolution of an open system is“chaotic” or “regular”. Spectral properties of generators of quantum Markovian evolution are important in this respect. So far the emphasiswas put on generators of the Gorini-Kossakowski-Sudarshan -- Lindblad (GKS-L) form. Universal features were fund and some new concept, likeComplex Spacing Ration, were developed by using the GKS-L framework. However, stationary GKS-L generators do not provide a straightforward wayto semiclassical chaotic regime; therefore it is hard to relate open quantum and dissipative classical system with chaotic dynamics. In thistalk I address another type of generator, the so-called Redfield generators, which emerge in the Floquet-Markov theory and allows for asemiclassical transition. I use a driven Duffing oscillator as a model to illustrate spectral properties of Redfield generators.
Barbara Dietz (Lanzhou University, China)
Affiliation: Theoretical Lanzhou Center for Theoretical Physics and the Gansu Provisional Key Laboratory of Theoretical Physics, Lanzhou University, 222 South Tianshui Road, Lanzhou, Gansu 730000, China
Title: Microwave photonic crystals, graphene- and honomebilliards with threefold symmetry: a comparison with nonrelativistic and relativistic quantum billiards
It was demonstrated recently  that the properties of the resonance frequenciesand electric field strength distributions of rectangular microwave photonic crystals obtained in superconducting measurements with flat resonatorscontaining metallic cylinders arranged on a triangular grid , are well described by the tight binding model of a finite-size honeycomb-kagome latticeof corresponding shape. They are referred to as Dirac and honome billiards, respectively. We investigate properties related to the band structure of a Diracbilliard with a threefold symmetric shape and compare them to those of the corresponding graphene and honome billiards and relativistic neutrino billiards.Generally, the eigenstates of threefold-symmetric systems can be classified according to their behavior under rotation by 2π/3 into singlets, that are rotationallyinvariant, and pairs of doublets. We reveal for the latter in graphene and honome billiards in momentum space a selective excitation of the two inequivalentDirac points. For the understanding of the symmetry related features, we extend known results for nonrelativistic quantum billiards and the associated semiclassical approach [3,4] to relativistic neutrino billiards. This work was supported by NNSF of China under Grant No. 11775100 and No.12047501.  W. Maimaiti, B. Dietz and A. Andreanov, Phys. Rev. B 102, 214301 (2020).  B. Dietz, T. Klaus, M. Miski-Oglu, and A. Richter, Phys. Rev. B 91, 035411 (2015). J. M. Robbins, Phys. Rev. A 40, 2128 (1989).  C. H. Joyner, S. Müller, and M. Sieber, J. Phys. A 45, 205102 (2012).
Thomas Dittrich (Universidad Nacional de Colombia Bogota, Colombia)
Affiliation: Departamento de Física, Universidad de los Andes, A. A. 4976, Santafé de Bogotá, Colombia
Title: Quantum chaos and quantum measurement – entropy production vs. unitary quantum dynamics
Quantum chaos and quantum measurement have one constitutive feature incommon: they capture information at the smallest scales to lift it to macroscopic observability. Fundamental bounds of the information content of closed quan- tum system with ﬁnite-dimensional Hilbert space their entropy production is exhausted in a ﬁnite time. Only in open systems where fresh entropy inﬁltrates from the environment, quantum dynamics (partially) recovers chaotic entropy production. Also in quantum measurements, a macroscopic apparatus observes a quantum system. Typically, notably in spin measurement, their results involve a com-ponent of randomness. The analogy with quantum chaos suggests that random outcomes of quantum measurements could, in a similar manner, reveal the en- tropy generated through the coupling to a macroscopic environment. Decoher- ence is required anyway to explain a crucial feature of quantum measurement, the collapse of the wavepacket. However, the subsequent step from a set of probabilities to deﬁnite individual measurement outcomes (the “second collapse”) still evades a proper understanding in microscopic terms and remains shrouded in concepts such as “quantum randomness”. Could this process be explained by the back action of the macroscopic apparatus on the measured system? To explore this hypothesis in the case of spin measurements, we adopt themodel of the measurement process proposed by Zurek and others, combined with a unitary approach to decoherence with heat baths comprising only a ﬁnite number N of modes, used in quantum chemistry and quantum optics. We ex- pect the dynamics of the measured spin for growing N to exhibit a scenario of increasingly irregular collapses and revivals: episodes of signiﬁcant spin polarization of increasing length alternating with spin ﬂips, determined by the initial condition of the apparatus. Preliminary analytical and numerical results con- ﬁrm our expectation. Complementing the quantum model, an analogous clas- sical system is presented: a particle, launched from the top of the barrier of a symmetric double-well potential, will fall into either well, depending on random impacts by ambient degrees of freedom.
Yan Fyodorov (Kings College London, UK)
Affiliation: Department of Mathematics, King's College London, London, UK
Title: Eigenfunction non-orthogonality in a single-channel chaotic scattering: non-perturbative RMT results
I will discuss distribution of diagonal non-orthogonality factors (also known as the Petermann factors, or eigenvalue condition numbers) characterizing eigenmodes in a single-channel wave-chaotic cavity. The results are obtained within RMT framework for the eﬀective Hamiltonian formalism for an arbitrary strength of coupling to continuum.
Sven Gnutzmann (University of Nottingham, UK)
Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
Title: The trace formula for quantum graphs with piecewise constant potentials and multi-mode quantum graphs
It is well known that one may deﬁne a unitary quantum map for quantumgraphs with free particle movement on all edges. This is a key ingredient in the derivation of the trace formula by Kottos and Smilansky. We will generalise this quantum map to the case of piecewise constant potentials. Due to the appearance of evanescent modes this is in general not a unitary map. We will show that there is however a reduced unitary map that only acts on the edges where the modes are propagating. We will use this to derive a trace formula and discuss some examples. The same technique may be applied to multi-mode quantum graphs which may be considered as a special case.
Thomas Guhr (Duisburg-Essen, Germany)
Affiliation: Fakulẗat f̈ur Physik, Universiẗat Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
Title: Non-stationarity and generic features in complex systems
Non-stationarity, i.e. the seemingly erratic change of important properties,is a characteristic feature of most complex systems. Equilibrium methods as in standard statistical mechanics do not apply, and new approaches are called for. We present two complementary approaches: ﬁrst, an analysis that identiﬁes diﬀerent operational states of complex systems and, second, a random matrix model explaining the heavy tails of multivariate amplitude distributions, i.e. the emergence of certain generic features. We illustrate our ﬁndings with examples from ﬁnance.
Boris Gutkin (Holon Institute of Technology, Israel)
Affiliation: Department of Applied Mathematics, Holon Institute of Technology, 58102 Holon, Israel
Title: Coupled cat maps as a toy model of many body quantum chaos
For decades, Arnold’s cat map served as a paradigm in classical and quan-tum chaos studies. I will discuss a natural extension of this model to many-body setting – a chain of cat maps linearly coupled by a nearest neighbor interaction. Despite of fully chaotic dynamics, the model turns out to be amenable to ana- lytical treatment due to the duality between its spatial and temporal dynamics. In particular, I will provide an explicit formula for correlations between local operators in suﬃciently long chains.
Liang Huang (Lanzhou University, China)
Affiliation: School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, China
Title: Quantization of states in complex soft-wall quantum billiards
Semiclassical quantization yields the exact eigenenergy spectrum for har-monic oscillators. How well it works for general conﬁnements with complex potentials that the classical dynamics varies drastically with energy? In this talk we will show an example of semiclassical quantization of a complicated conﬁnement potential. Despite the complexity in the classical dynamics, the semiclassical quantization works well for the scarring patterns around periodic orbits in this system even for low energy eigenstates. Particularly, unlike the hard-wall conﬁnement of the two-dimensional electron gas where the recurrent scarring patterns are equally spaced in square root of E, a general feature of the soft-wall conﬁnement is that the recurrent scarring patterns are equally spaced in E, which has been identiﬁed previously as a signature for relativistic billiards with hard-wall conﬁnements. The underlying mechanism here is the similarity of the potential proﬁle that the particle felt and that for a harmonic oscillator. These results could be exploited in understanding the measurements of the den- sity of states and transport properties in two dimensional electron gas systems with random long-range impurities.
Ulrich Kuhl (Université Côte d’Azur, CNRS, France)
Affiliation: Université Côte d’Azur, CNRS, Institut de Physique de Nice (InPhyNi), Ave. Joseph Vallot, 06108 Nice, France
Title: Microwave studies of the three chiral ensembles in chains of coupled dielectric resonators
Following a recently published work on chiral random matrix ensembles and their experimental realizations (Phys. Rev. Lett. 124, 116801 (2020)), the present work describes in more detail the obtained results and setup. The work will establish in detail the link between Random Matrix Theory (RMT) for sys- tems with a chiral symmetry and how to create them with a ﬁnite set of mi- crowave resonators. The ﬁnite systems from the experimental setup are compared to analytical results for ﬁnite-size systems.
Pavel Kurasov (Stockholm University, Sweden)
Affiliation: Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden
Title: On isospectral metric graphs
Isospectral standard Laplacians on metric graphs are studied. Different mechanisms behind isospectrality will be discussed.
Michał Ławniczak (Institute of Physics of the PAS, Warsaw, Poland)
Affiliation: Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46,02-668 Warszawa, Poland
Title: Euler characteristic of graphs and Fermi golden rule
We present theoretical, experimental and numerical studies of the Euler characteristic χ for simple quantum graphs simulated experimentally by micro-wave networks . The Euler characteristic χ is deﬁned as a diﬀerence between the number of graph vertices V and the number of its edges E. It also deﬁnes the Betti number β = 1 −χ of independent cycles in a graph. Thus, together with the total graph length L the Euler characteristic χ is the most important topological and geometrical characteristic of graphs. We show theoretically and conﬁrm experimentally that the Euler characteristic can be determined from a ﬁnite sequence of the lowest eigenenergies λ1, . . . , λN of a quantum graph, without the need for a visual inspection of the system. Thus, from a graph spectrum one can ﬁnd out what is the number of its vertices and edges, provided that the graph is fully connected, or that the graph is planar (β ≤ 3). We also present the experimental results of a Fermi golden rule study in the case of two- and ﬁve-edge quantum graphs simulated by microwave networks. A Fermi golden rule gives rates of decay of states obtained by perturbing embedded eigenvalues of graphs . Acknowledgments: This work was supported in part by the National Science Centre, Poland, Grant Nos. 2016/23/B/ST2/03979 and 2018/30/Q/ST2/00324, the Swedish Research Council (Grant No. D0497301), and the Center for Interdisciplinary Research (ZiF) in Bielefeld in the framework of the cooperation group on “Discrete and continuous models in the theory of networks”. J. L. was supported by the research programme “Mathematical Physics and Differential Geometry” of the Faculty of Science of the University of Hradec Králové. M. Ławniczak, P. Kurasov, S. Bauch, M. Białous, V. Yunko, and L. Sirko, Phys. Rev. E 101, 053320 (2020). M. Ławniczak, J. Lipovský, M. Białous, and L. Sirko, Phys. Rev. E 103, 032208 (2021).
Jiri Lipovsky (University of Hradec Kralove, Czech Republic)
Affiliation: Department of Physics, Faculty of Science, University of Hradec Králové, Czech Republic
Title: Graphs with preferred-orientation coupling and their spectral propertis
We investigate quantum graphs with the preferred-orientation couplingconditions suggested by Exner and Tater . In particular, we are interested in the high-energy limit of their spectra. These coupling conditions violate the time-reversal symmetry, for a particular energy, the particle approaching the vertex from a given edge leaves it through the neighbouring edge (for instance, to the left of the incoming edge) and this property is cyclical. It was previously shown that the vertex scattering matrix depends on the degree of the vertex; for an odd-degree vertex, the scattering matrix converges in the high-energy limit to the identity matrix, while even-degree vertices behave diﬀerently. This behaviour aﬀects the transport properties of these graphs.We study two models. The ﬁrst one is a ﬁnite graph consisting of edges of Platonic solids. We ﬁnd that the asymptotical distribution of the eigenvalues for the octahedron graph (having vertices with even degrees) is diﬀerent from the other Platonic solids (having vertices with odd degrees), for which the eigen- values approach the spectrum of the Neumann Laplacian on an interval. The second model consists of two types of inﬁnite lattices. For one of them, the transport at high energies is possible in the middle of the strip and is suppressed at the edges. For the other one, the transport is possible at the edge of the strip only.  P. Exner, M. Tater, Quantum graphs with vertices of a preferred orientation, Phys. Lett. A 382, 283–287 (2018). P. Exner, J. Lipovsky´, Spectral asymptotics of the Laplacian on Platonic solids graphs, J. Math. Phys. 60, 122101 (2019). P. Exner, J. Lipovsky´, Topological bulk-edge eﬀects in quantum graph transport, Phys. Lett. A 384, 126390 (2020).
Rafael Méndez (Universidad Nacional Autónoma de México, México)
Affiliation: Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México A.P. 20-364 62210 Cuernavaca, Morelos, México
Title: Emulating π orbitals in aromatic molecules using elastic waves: borazine
Mechanical waves have emerged as a paradigm of condensed matterphysics since with them many eﬀects of the latter can be emulated. Molecular π orbitals are of great interest in this area since they play a key role in electronic transport in 2D materials and aromatic molecules as benzene and borazine. Molecular π orbitals are of great interest in this area because they play a key role in the electronic transport of 2D materials and aromatic molecules such as benzene and borazine. In this work we show the design, construction and characterization of a mechanical structure, the artiﬁcial mechanical borazine, which emulates the π orbitals of the borazine. The structure consists of hexagonal res- onators, which act as artiﬁcial mechanical atoms coupled to each other through ﬁnite phononic crystals that act as artiﬁcial sigma bonds. When the resonant frequency of an artiﬁcial atom falls within the gap of the phononic crystal, the vibrations are trapped in it and interact weakly with neighboring atoms through evanescent Bloch waves. In this case, a tight-binding regime for mechanical waves emerge. Here these ideas are applied to emulate the π orbitals of bo- razine. The design relies on extensive ﬁnite element numerical simulations. The experimental results show an excellent agreement with both, the tight-binding formalism and with the numerical results. This work was supported by DGAPA-UNAM and CONACYT through projects PAPIIT-IN111021, and CB/284096, respectively.
Arkadiusz Orłowski (Warsaw University of Life Sciences - SGGW, Poland)
Affiliation: Institute of Information Technology, Warsaw University of Life Sciences – SGGW, Warsaw, Poland
Title: Simple approach to multiple scattering of waves from nontrivial media
Many interesting, subtle, and nontrivial eﬀects can be observed when clas-sical or quantum waves undergo multiple scattering. Depending on the size and structure of scattering media a plethora of phenomena can manifest themselves, including, but not restricted to, proximity resonances, coherent backscattering, strong (Anderson) localization, and others. Theoretical approaches to such ef- fects are often marred by inadequate descriptions of the scattering objects and too crude approximations made at the wave propagation level. Here some results concerning coherence eﬀects in multiple scattering are presented within a computational model that is extremely simple (although still realistic enough) at the level of the scattering medium description but which is exact at the wave propagation level. It is surprising how far one can go by modeling a scattering medium by discrete point-like dipoles and making no approximations to the wave propagation, thus describing scattering events in full generality within a given model. Apart from looking at the known examples from a diﬀerent perspective, some new results for both scalar and vector waves are given.
Tomaž Prosen (University of Ljubljana, Slovenia)
Affiliation: Department of Physics, Faculty of Mathematics and Physics, University ofLjubljana, Ljubljana, Slovenia
Title: Exactly solved models of chaotic many-body dynamics
One should be amazed with an unreasonable eﬀectiveness of random ma-trix theory to describe spectral ﬂuctuations in simple non-integrable many-body systems, say one dimensional spin 1/2 chains with local interactions. I will dis- cuss a class of Floquet (periodically driven) quantum spin chains – speciﬁcally, dual unitary Floquet circuits – where the random matrix result for the spectral form factor can be derived or even rigorously proven. Several other nontrivial exactly solvable features of the presented models, such as dynamical correlations or entanglement dynamics, will be discussed.
Gregor Tanner (University of Nottingham, UK)
Affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
Title: Quantum searching on Markov chains
I will give an introduction into the quantum search algorithms on Markovchains introduced by Szegedy about 15 years ago and highlight some recent developments culminating in a proof by Apers et al. published as a preprint in 2019 showing that a quantum search can ﬁnd a set of marked vertices quadratically faster (in units of the hitting time) for any reversible Markov chain. I will make some speculations about the underlying mechanisms for the search to work and critically discuss the use of the hitting time as a measure for the search time.
Bart Van-Tiggelen (Université Grenoble Alpes, France)
Affiliation: Université Grenoble Alpes, Centre National de la Recherche Scientifique, LPMMC, 38000 Grenoble, France
Title: Does Longitudinal Light Prevent Anderson Localization?
Recent numerical simulations demonstrated the absence of an Anderson transition when light propagates in a dense medium filled with electric dipoles. We present a transport theory in which longitudinal waves induce a novel transport channel. The mixing of this channel with the usual transverse channel imposes a minimum conductivity. https://arxiv.org/pdf/2012.11210
Jakub Zakrzewski (Jagiellonian University, Cracow, Poland)
Affiliation: Institute of Theoretical Physics, Jagiellonian University, Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
Title: Many-body localization without disorder
I will discuss aspects of nonergodic dynamics for spin chains (or their implementations as cold atoms in optical lattices) in disorder-free models: lattice with a constant tilt and/or strong (un-)harmonic binding.
Karol Życzkowski (Jagiellonian University, Cracow, Poland)
Affiliation: Department of Atomic Physics, Institute of Theoretical Physics, Jagiellonian University, Krakow, Poland
Title: Random generators of Markovian evolution: a quantum-classical transition by superdecoherence
Continuous-time Markovian evolution appears to be manifestly diﬀerentin classical and quantum worlds. We consider ensembles of random generators of N-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties . It is shown, how the two types of generators can be related by superdecoherence. In analogy with the mech- anism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolu- tion). By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. arXiv:2105.02369.
(Click twice on a name for more information and a file with poster)
Małgorzata Białous (Institute of Physics, PAS, Warsaw, Poland)
Affiliation: Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
Title: Investigations of the enhancement factor in an open wave chaotic system with time-reversal-invariance violation
We show experimentally and conﬁrm theoretically that above a certain sizeof time-reversal T -invariance violation the increase of the openness of a wave chaotic system can lead to an increase of the elastic enhancement factor. In the experiment a quantum billiard with partially violated time-reversal invariance, characterized by the T -invariance violation parameter ζ [0, 1] is simulated with a ﬂat quarter-bow-tie microwave cavity which contains two cylindrical ferrites that are magnetized by an external magnetic ﬁeld. The elastic enhance- ment factor FM (η, γ, ζ) is investigated as a function of internal absorption γ and openness η. In these investigations we focus on the frequency range of strongest T -invariance violation where the increase of the number of open chan- nels causes a boost of the elastic enhancement factor FM (η, γ, ζ) instead of the expected lowering [1,2]. This work was supported in part by the National Science Center, Poland, Grant No. UMO-2018/30/Q/ST2/00324. B.D. thanks the National Natural Science Foundation of China for ﬁnancial support through Grants No. 11775100, No. 11961131009, and No. 12047501. Supported by the 111 Project under Grant No. B20063. M. Białous, B. Dietz, and L. Sirko, Phys. Rev. E 102, 042206 (2020).  M. Białous, B. Dietz, and L. Sirko, Acta Phys. Pol. A 139, 462 (2021).
Lei Chen (University of Maryland, College Park, USA)
Affiliation: Department of Electrical and Computer Engineering, University of Maryland, 4150 Campus Dr., College Park, MD 20742-4111, USA
Title: Experimental demonstration of complex Wigner time delay in sub-unitary scattering systems
Wigner time delay has been appealing to physicists for its intuitive insights into the scattering properties of the complex scattering region. Here we developa complex generation of Wigner time delay in the sub-unitary scattering systems. By including both lumped and uniform loss and coupling eﬀects into the Scattering matrix, we model the complex time delay using the S-matrix zeros and poles, and establish connections between the time delay and Coherent Perfect Absorption (CPA). We demonstrate the idea of complex time delay in the sub-unitary scattering systems using a microwave graph experiment, and provide eﬀective methods for manipulating zeros and poles of the S-matrix. We also further investigate the statistical properties of the complex time delay as a function of uniform attenuation, utilizing both Random Matrix Theory (RMT) simulations and experiments on microwave graphs.
Shukai Ma (University of Maryland, College Park, USA)
Affiliation: Physics Department, University of Maryland, College Park
Title: Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs
The properties of chaotic systems have been studied extensively in diﬀerent dimensionalities. Common statistical tests include the eigenmode-spacingand eigenfnction analysis. However, the experimental studies of chaotic graph eigenfunctions are generally conﬁned to just the wavefunction values at the nodes, because 1D graphs are usually constructed with coaxial cables. In the meantime, recent studies reveal that the chaotic graphs face challenges from trapped modes, which may be better analyzed and understood with eigenfunction analysis tools. Here, we propose photonic crystal (PC) arrays as an al- ternative physical system for chaotic graph studies. The graph bonds realized with defect waveguides which can be modeled by the telegrapher’s equa- tion for parallel plate waveguides. We have numerically demonstrated an ensemble of such PC-graphs and conducted both eigenfunction amplitude and eigenmode-spacing studies, and these statistical properties are in good agree- ment with the GOE predictions. Diﬀerent methods are tested in order to measure the graph eigenfunction proﬁle. Our proposed system can be readily applied to other statistical studies, such as inverse participation ratio, as well as further experimental realizations.