Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session V43: Wave Chaos: Theory and ApplicationsFocus

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Sponsoring Units: GSNP Chair: Gabriele Gradoni, University of Nottingham Room: 346 
Thursday, March 17, 2016 2:30PM  2:42PM 
V43.00001: Modeling Transmission Line Networks Using Quantum Graphs Trystan Koch, Thomas Antonsen Quantum graphsone dimensional edges, connecting nodes, that support propagating Schr\"odinger wavefunctionshave been studied extensively as tractable models of wave chaotic behavior (Smilansky and Gnutzmann 2006, Berkolaiko and Kuchment 2013). Here we consider the electrical analog, in which the graph represents an electrical network where the edges are transmission lines (Hul et. al. 2004) and the nodes contain either discrete circuit elements or intricate circuit elements best represented by arbitrary scattering matrices. Including these extra degrees of freedom at the nodes leads to phenomena that do not arise in simpler graph models. We investigate the properties of eigenfrequencies and eigenfunctions on these graphs, and relate these to the statistical description of voltages on the transmission lines when driving the network externally. The study of electromagnetic compatibility, the effect of external radiation on complicated systems with numerous interconnected cables, motivates our research into this extension of the graph model. [Preview Abstract] 
Thursday, March 17, 2016 2:42PM  2:54PM 
V43.00002: Experimental Study of Quantum Graphs with Microwave Networks Ziyuan Fu, Trystan Koch, Thomas Antonsen, Edward Ott, Steven Anlage An experimental setup consisting of microwave networks is used to simulate quantum graphs. The networks are constructed from coaxial cables connected by T junctions. The networks are built for operation both at room temperature and superconducting versions that operate at cryogenic temperatures. In the experiments, a phase shifter is connected to one of the network bonds to generate an ensemble of quantum graphs by varying the phase delay. The eigenvalue spectrum is found from Sparameter measurements on oneport graphs. With the experimental data, the nearestneighbor spacing statistics and the impedance statistics of the graphs are examined. It is also demonstrated that timereversal invariance for microwave propagation in the graphs can be broken without increasing dissipation significantly by making nodes with circulators. Random matrix theory (RMT) successfully describes universal statistical properties of the system. [Preview Abstract] 
Thursday, March 17, 2016 2:54PM  3:06PM 
V43.00003: Controlling and enhancing high frequency collective electron dynamics in superlattices by chaosassisted miniband transport Mark Fromhold, Mark Greenaway, Natalia Alexeeva, Alexander Balanov, Oleg Makarovsky, Amalia Patane, Marat Gaifullin, Feo Kusmartsev We show in both measurements and calculations that a tilted magnetic field can transform the structure and THz dynamics of charge domains in a biased semiconductor superlattice (SL) [1]. In SLs, at critical field values, when the Bloch frequency equals the cyclotron frequency corresponding to the magnetic field component along the SL axis, the semiclassical electron motion changes abruptly from localized stable trajectories to unbounded chaotic paths, which propagate rapidly through the SL. This delocalisation of the electron creates a series of sharp resonant peaks in drift velocityfield characteristics, which were detected in previous DC currentvoltage measurements. We show that these additional peaks can create multiple propagating charge domains, shaped by both the strength and tilt angle of the magnetic field. As a result, the tilted magnetic field generates AC currents whose magnitude and frequencies are far higher than with no magnetic field applied. Chaosassisted singleelectron transport induced by the interplay between cyclotron and Bloch motion therefore provides a mechanism for controlling the collective dynamics of miniband electrons, and thus enhancing the high frequency response of SLs. References: [1] N. Alexeeva et. al. Phys. Rev. Lett. 109, 024102 (2012) [Preview Abstract] 
Thursday, March 17, 2016 3:06PM  3:42PM 
V43.00004: Statistical Model of Wave Transport in Systems with Coexisting Chaotic and Regular Phase Space Regions. Invited Speaker: Edward Ott We study the statistics of the inputoutput properties of wave systems in which ray trajectories that are regular and chaotic coexist (i.e., `mixed systems'). The transport is expressed as a summation over eigenmodes (energy states) where the eigenmodes can typically be classified as either regular or chaotic.. By appropriate characterization of regular and chaotic contributions, we obtain predictions for the transport as characterized by impedance or scattering matrices. We test these predictions by comparison with numerical calculations for a specific example. [Collaborators: M.J. Lee, T.M. Antonsen, and K. Ma] [Preview Abstract] 
Thursday, March 17, 2016 3:42PM  3:54PM 
V43.00005: Radiation of complex and noisy sources within enclosures Gabriele Gradoni, Stephen Creagh, Gregor Tanner Predicting the radiation of complex electromagnetic sources inside semiopen cavities and resonators~with arbitrary geometry is a challenging topic~both for~physics and for~engineering.~We have exploited a PerronFrobenius operator to propagate fieldfield correlation functions of complex and extended sources in freespace.~The formula is based on a phasespace picture of the electromagnetic field, using the Wigner distribution function,~and~naturally captures evanescent as well as diffracted waves. This approach can be extended to study the propagation of correlation functions within cavities, with the raydynamical map given by the geometry of the cord connecting a point of the boundary to another. While ray methods provide an efficient way to predict average values of the correlation matrix elements, the use of random matrix theory approaches allows efficient characterisation of statistical fluctuations around these averages. Universal relations are derived and tested in the presence of dissipation for quantum maps and billiard systems. The use of this formalism is discussed in the contexts of open systems with surface roughness.~The~theory and achieved results are of interest~in the simulation of nextgeneration of wireless communications. [Preview Abstract] 
Thursday, March 17, 2016 3:54PM  4:06PM 
V43.00006: FDTD simulations of the losses in complex electromagnetic cavities Franco Moglie, Luca Bastianelli, Valter Mariani Primiani The simulations of complex electromagnetic cavities like reverberation chambers (RC) require a massive parallel computer to accurately account the complex three dimensional geometry. A parallel finitedifference timedomain (FDTD) code optimized for a massive parallel computer could lose its efficiency if the losses are concentrated in some part of the computation volume. For example, the simulation of the finite conductivity of the cavity metallic walls requires a significant overcharge for the computer processors that handle the boundary part of the global computational domain. Our inhouse parallel FDTD code replaces the volumetric losses in every cell of the grid instead of the Ohmic losses on the walls. In this contribution, we evaluate the difference in the field distribution inside the cavity due to this replacement. Moreover, we compare the common RC statistics like the number of stirrer uncorrelated positions and the field uniformity, and the resources required for the two methods are reported and discussed. Finally, the numerical results will be compared with the measurements of the RC in our laboratory with a volume of 60 m$^3$ and plated steel walls in the frequency range 0.21.0 GHz, that includes the transition from the undermoded to the overmoded region. [Preview Abstract] 
Thursday, March 17, 2016 4:06PM  4:18PM 
V43.00007: Conductance and Transmittance of waves through a chaotic cavity (or, equivalently, quantum dot) results in regularization of tunneling rates Louis Pecora, Dong Ho Wu, Christopher Kim Tunneling rates in closed, double well quantum or wave systems in two dimensions or higher are radically different between wells with classically regular or chaotic behavior [1]. Wells with regular dynamics have tunneling rates that fluctuate by several orders of magnitude as a function of energy or frequency. Wells with chaotic dynamics have fluctuations smaller than one order of magnitude (a regularization of the fluctuations). We examine a more realistic experimental system, a single well with two channels with tunneling barriers at their junctions with the wells. Former theories for conductance in quantum dots will not apply here. We developed a theory, which uses proper boundary conditions at the barriers and yields the scattering matrix. Results show that the transmission rates fluctuate by orders of magnitude in the regularshaped well, but are greatly reduced (regularized) for the chaoticshaped well. We will show experimental results that test these theoretical findings for microwave transmission through a chaoticshaped cavity, which is made of copper and has two ports with tunneling barriers. [1] Chaos regularization of quantum tunneling rates, L. M. Pecora, H. Lee, DH. Wu, T. Antonsen, MJ. Lee, and E. Ott, Phys. Rev. E 83, 065201(R) (2011) [Preview Abstract] 
Thursday, March 17, 2016 4:18PM  4:30PM 
V43.00008: Time Reversed Electromagnetics as a Novel Method for Wireless Power Transfer Anu Challa, Steven M. Anlage Taking advantage of raychaotic enclosures, time reversal has been shown to securely transmit information via shortwavelength waves between two points, yielding noise at all other sites. In this presentation, we propose a method to adapt the signalfocusing technique to electromagnetic signals in order to transmit energy to portable devices. Relying only on the timereversal invariance properties of waves, the technique is unencumbered by the inverselyproportionaltodistance path loss or precise orientation requirements of its predecessors, making it attractive for power transfer applications. We inject a short microwave pulse into a complex, wavechaotic chamber and collect the resulting long timedomain signal at a designated transceiver. The signal is then time reversed and emitted from the collection site, collapsing as a timereversed replica of the initial pulse at the injection site. When amplified, this reconstruction is robust, as measured through metrics of peaktopeak voltage and energy transfer ratio. We experimentally demonstrate that time reversed collapse can be made on a moving target, and propose a way to selectively target devices through nonlinear timereversal. [Preview Abstract] 
Thursday, March 17, 2016 4:30PM  4:42PM 
V43.00009: Enhancement of coherent terahertz beam with chaotic electrodes in a photoconductive antenna Dong Ho Wu, Benjamin Graber, Louis Pecora, Christopher Kim We investigated terahertz beam emission from photoconductive antennas containing various shapes of electrodes. With a pair of curved (e.g. concave shape) electrodes it appears that electrons (mostly thermal electrons) follow chaotic trajectories, which keep the electrons away from the surface plasma so that the surface plasma can coherently oscillates without being disrupted by thermal electrons, resulting a slightly increased coherent terahertz power. For an emitter with a pair of ripple electrodes, the classical Poincare surface section map using Birkoff coordinate tends to exhibit chaotic sea and KAM islands if the ripple amplitude becomes comparable to the electrode gap, indicating considerable electron bunching in between the ripple electrodes. Our data show that, when the bunched electrons are stimulated by terahertz pulses, the emitter produces additional spontaneous coherent terahertz beams, which is known as Dicke effect. We will discuss details of our experiments and results. [Preview Abstract] 
Thursday, March 17, 2016 4:42PM  4:54PM 
V43.00010: Numerical and experimental studies of the elastic enhancement factor of 2D open systems Leszek Sirko, Ma{\l}gorzata Bia{\l}ous, Vitalii Yunko, Szymon Bauch, Micha{\l} {\L}awniczak We present the results of numerical and experimental studies of the elastic enhancement factor $W$ for microwave rough and rectangular cavities simulating twodimensional chaotic and partially chaotic quantum billiards in the presence of moderate absorption strength. We show that for the frequency range $\nu =15.018.5$ GHz, in which the coupling between antennas and the system is strong enough, the values of $W$ for the microwave rough cavity lie below the predictions of random matrix theory and on average they are above the theoretical results of V. Sokolov and O. Zhirov, Phys. Rev. E, {\bf 91}, 052917 (2015). We also show that the enhancement factor $W$ of a microwave rectangular cavity coupled to the external channels via microwave antennas, simulating a partially chaotic quantum billiard [1], calculated by applying the PotterRosenzweig model with $\kappa=2.8\pm 0.5$ is close to the experimental one. Our numerical and experimental results suggest that the enhancement factor can be used as a measure of internal chaos which can be especially useful for systems with significant openness or absorption. [1] M. {\L}awniczak, M. Bia{\l}ous, V. Yunko, S. Bauch, and L. Sirko, Phys. Rev. E {\bf 91}, 032925 (2015). [Preview Abstract] 
Thursday, March 17, 2016 4:54PM  5:06PM 
V43.00011: Light transport in dense composite media: role of nearfield coupling Roxana Rezvani Naraghi, Sergey Sukhov, Juan José Sáenz, Aristide Dogariu In scattering media, optical waves comprise both homogeneous and evanescent components. At very high concentrations of scatterers, particles are located in close proximity and interact through evanescent near fields. Thus, in this regime the energy is not only carried by propagating waves but it also evolves through evanescent coupling between individual scatterers. We have shown that in dense composite media additional transmission channels open because of these nearfield interactions between close proximity scatters and, consequently, a new regime of transport emerges. This is clearly beyond simple descriptions of scatterers acting independently of their environment and framed in terms of farfield characteristics such as Mie crosssections. We will show that, because in the dense media the energy can transfer through both diffusion and evanescent channels, the total transmittance is $T=T_{CS} +T_{NF} =1 \mathord{\left/ {\vphantom {1 {L(l_{CS}^{\ast } +l_{NF}^{\ast } )}}} \right. \kern\nulldelimiterspace} {L(l_{CS}^{\ast } +l_{NF}^{\ast } )}.$ Correcting the total transmission in this manner is appealing because it is done in terms of physically meaningful and measurable quantities such a nearfield (NF) scattering crosssection $\sigma_{NF} $. [Preview Abstract] 
Thursday, March 17, 2016 5:06PM  5:18PM 
V43.00012: Complexity of knotting in chaotic 3D eigenfunctions Alexander Taylor, Mark Dennis Quantised vortices occur generically in disordered 3D complex scalar fields, forming a geometrically complex and statistically random large scale tangle even in systems with very different origins of complexity such as turbulent superfluids, optical volume speckle, the quantum eigenfunctions of chaotic 3D cavities, and liquid crystal phases. Although all such systems are random and fractal on large scales [1], it has previously been established that topological measures such as the probability of vortices knotting or linking with one another are sensitive to the local physics. We use the wave chaos as a universal model system with just one physical lengthscale, the wavelength, beyond which its vortices are Brownian. To access finitevolume realisations of wavefields, vortices are traced numerically in three different random degenerate eigenfunction systems, each approximating the random isotropic limit but with different constraints and symmetries that significantly impact topological statistics even at high energies. By a simple mode counting argument, we observe that the probability of a generic eigenfunction containing a knotted vortex line reaches 50\% by around its 10003000th mode.\\[0pt] [1] A J Taylor and M R Dennis, \emph{J Phys A} \textbf{47} 465101 (2014) [Preview Abstract] 
Thursday, March 17, 2016 5:18PM  5:30PM 
V43.00013: Supersymmetric sigma model of disordered, isotropic, elastic media Douglas Photiadis The supersymmetry method proposed by Efetov in 1983 has been enormously successful at describing a broad range of phenomena involving disorder, providing a framework for understanding and going beyond the successes of random matrix theory and allowing a calculation of the slowing of diffusion as the Anderson transition is approached. The original model described the propagation of a scalar wave in a disordered medium, and subsequent work extended these ideas to classical waves, optical or elastic, with the approximation that the wave propagation can be similarly described by a scalar theory. Such a theory cannot however account correctly for scattering between different polarizations. A direct attempt to derive a supersymmetric model describing elastic waves results in a nonrenormalizable field theory, and poses substantial difficulties. We have obtained a supersymmetric sigma model by considering the dual model which describes a generalized superstress field. The model enables one to fully account for the different wave types and polarizations in the medium. We will present our recent results in this area, including model predictions for the obtained diffusion constants, and the effects of renormalization to first order. [Preview Abstract] 
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