Bulletin of the American Physical Society
Fall 2009 Meeting of the Four Corners Section of the APS
Volume 54, Number 14
Friday–Saturday, October 23–24, 2009; Golden, Colorado
Session H6: Solitons and Quantum Dynamics |
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Chair: Lincoln Carr, Colorado School of Mines Room: Hill Hall 204 |
Saturday, October 24, 2009 11:20AM - 11:32AM |
H6.00001: Soliton solutions to the nonlinear Schr\"odinger equation Samuel Rivera Solitary wave (soliton) solutions are considered for the nonlinear Schr\"odinger equation $iu_t+u_{xx}+2|u|^2u=0.$ Their physical importance is studied, and a Mathematica program is presented producing such soliton solutions and their updated animations. [Preview Abstract] |
Saturday, October 24, 2009 11:32AM - 11:44AM |
H6.00002: Rotons and Slitons in a Magnetic Cactus: Dynamical Phyllotaxis Cristiano Nisoli, Nathaniel Gabor Phyllotaxis, the study of mathematical patterns in the arrangement of leaves on stems, spines on cacti, petals on flowers, et cetera, fascinated mankind since the dawn of times. Similar patterns emerge in the the statics of simple physical systems. Here we reproduce experimentally the striking number-theoretical patterns found in the phyllotaxis of living beings in the statics of a simple mechanical apparatus. Then we show that its dynamics reveal unusual excitations beyond botany: multiple classical rotons and a large family of interconverting topological solitons. Applications at different scales and in different areas of physics are proposed and discussed. \\[4pt] [1] C. Nisoli {\it et al}, Phys. Rev. Lett. {\bf 102}, 186103 (2009).\\[0pt] [2] C. Nisoli Phys. Rev. E {\bf 80}, 026110 (2009). [Preview Abstract] |
Saturday, October 24, 2009 11:44AM - 11:56AM |
H6.00003: Observation of Chaotic Solitons in Magnetic Film-Based Feedback Rings Zihui Wang, Aaron Hagerstrom, Wei Tong, Mingzhong Wu, Richard Eykholt, Boris Kalinikos Chaos and solitons are two important branches of nonlinear science. Usually one believes that chaos and solitons have no direct relation per se. Recent simulations, however, have indicated the existence of solitons that exhibit chaotic behavior with time. This presentation reports the first experimental observation of chaotic solitons. The experiments were carried out with a magnetic film strip-based feedback ring. At some ring gain level, the ring eigenmode with the lowest decay rate is self-generated and one obtains a continuous spin wave. A further increase in the ring gain leads to the generation of additional modes through a 4-wave process. In the time domain, this corresponds to the formation of a single spin wave pulse that circulates in the ring. At some higher gain level, this pulse develops into a chaotic soliton -- a soliton pulse whose amplitude changes with time in a chaotic manner. The pulse has a hyperbolic secant shape and a flat phase profile across the pulse width, which are the signatures of solitons. The overall time-domain signal resulting from the circulation of the pulse exhibits a finite correlation dimension and a positive Lyapunov exponent, which are evidence of chaotic motion. [Preview Abstract] |
Saturday, October 24, 2009 11:56AM - 12:08PM |
H6.00004: Non-strange chaotic attractors equivalent to their templates John Starrett We construct systems of three autonomous first order differential equations with bounded two dimensional attracting sets $M$. The flows on $M$ are chaotic and have one dimensional Poincar\'{e} sections diffeomorphic to unimodal maps of the interval. Because the attractors are two dimensional rather than fractal, they are topologically equivalent to the templates of suspended horseshoes. These systems and their attractors are useful as simplified models of solutions to chaotic systems -- for instance, the attractor of the cubic system is equivalent to the template of the parametrically forced pendulum. Thus, we are able to relate the well known dynamics of, say, the cubic map to the periodic orbit set of the forced pendulum. [Preview Abstract] |
Saturday, October 24, 2009 12:08PM - 12:20PM |
H6.00005: Excitation of Chaotic Surface Spin Waves in Magnetic Film Feedback Rings through Three-Wave Processes Aaron Hagersrom, Mingzhong Wu, Richard Eykholt Surface spin waves in magnetic thin films can undergo three-wave splitting and confluence processes. In a splitting process, a surface spin wave produces two volume spin waves at about half of its frequency. In a confluence process, two half-frequency volume waves interact to produce a surface wave. This presentation reports the excitation of chaotic surface spin waves in magnetic thin film-based active feedback rings through these three-wave nonlinear interactions. Previous work has demonstrated such chaotic excitation in feedback rings. Neither the development of spectral modes nor the fractal dimensions of chaotic signals, however, have been reported. Experiments were performed with a 5 $\mu$m-thick yttrium iron garnet film and a static magnetic field of about 120 Oe. At some ring gain level, a single ring eigenmode was excited. As the gain was increased, one observed the excitation of additional modes, an increase in the frequency spacing between these modes, a period-doubling bifurcation, and the onset of chaos. One also observed a shift of the main mode to lower frequencies with increasing the gain. The correlation dimensions of the chaotic signals were found to be in the 2-4 range. It was also found that the correlation dimension increases with the ring gain. [Preview Abstract] |
Saturday, October 24, 2009 12:20PM - 12:32PM |
H6.00006: Open Source TEBD: software for entangled quantum many-body dynamics Michael Wall, Lincoln Carr Matrix product state (MPS) based methods have proven in recent years to be the most efficient means of studying strongly correlated one dimensional systems. Among these methods is time-evolving block decimation (TEBD), which allows for studies of entangled quantum many-body dynamics in situations that may be far from equilibrium. Open Source TEBD is an open source effort which aims at making this algorithm available to a wider audience. In this talk I will discuss the conceptual and theoretical background of TEBD and MPS based methods in general, demonstrate the capabilities of the software package, and discuss future prospects for the open source effort. [Preview Abstract] |
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