Bulletin of the American Physical Society
2006 37th Meeting of the Division of Atomic, Molecular and Optical Physics
Tuesday–Saturday, May 16–20, 2006; Knoxville, TN
Session S6: New Theoretical Methods and Nonlinear Dynamics |
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Chair: John Delos, College of William and Mary Room: Knoxville Convention Center 301C |
Friday, May 19, 2006 8:00AM - 8:12AM |
S6.00001: The sign and magnitude of some semiclassical Casimir energies Martin Schaden, Larry Spruch A transparent physical definition of finite Casimir energies based on universal subtractions in the spectral density is given. We estimate so defined Casimir energies by contributions due to classical periodic orbits. In semiclassical approximation the latter are dual variables to the mode frequencies. For manifolds without boundary the sign of the semiclassical contribution to the Casimir energy is related to optical properties of short periodic rays. We demonstrate the accuracy and simplicity of this semiclassical analysis on torii and spheres in various dimensions. The results are compared to those of zeta-function regularization. For manifolds with boundaries on which a massless scalar field satisfies certain conditions, semiclassical contributions to the Casimir energy due to periodic rays that lie entirely within the boundaries have to be included. The semiclassical Casimir energy of a parallelepiped in arbitrary dimensions for periodic, Neumann, Dirichlet, and metallic, boundary conditions on pairs of opposing surfaces is shown to be the Casimir energy obtained by more conventional methods; a simple semiclassical estimate of the electromagnetic Casimir energy of an ideal metallic spherical cavity is accurate to 1\%. It is finally shown how this semiclassical approach may be adapted to non- perturbatively include deviations from the ideal -- such as finite conductivity, surface roughness, and finite temperature. [Preview Abstract] |
Friday, May 19, 2006 8:12AM - 8:24AM |
S6.00002: Gaussian quantum operator representations for fermions Peter Drummond, Joel Corney We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behaviour in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas. These results are relevant to the well-known Fermi sign problem in dealing with many-body fermion calculations. [Preview Abstract] |
Friday, May 19, 2006 8:24AM - 8:36AM |
S6.00003: Atomic Spectral Methods for Molecular Electronic Structure Calculations Robert Hinde, Jerry Boatz, Peter Langhoff Progress is reported in development and implementation of atomic spectral methods for electronic structure and excitation-energy calculations on molecules and other atomic aggregates. The approach presented defers enforcement of wave function antisymmetry subsequent to construction of the Hamiltonian matrix in a formally complete atomic spectral-product basis, affording a number of conceptual and potential computational advantages over more conventional currently employed methods. Progress in implementation reported includes development of methods for isolating the totally antisymmetric representation of the aggregate symmetric group in the presence of non-Pauli states, avoidance of large-dimension Hamiltonian matrices and the attainment of closure by incorporation of explicitly antisymmetric atomic-pair information obtained from largely conventional diatomic calculations, and associated enforcement of appropriate wave function behavior in dissociation limits. These issues are illustrated with explicit calculations on simple diatomic and triatomic molecules and comparisons with results obtained for these systems using conventional electronic structure methods. [Preview Abstract] |
Friday, May 19, 2006 8:36AM - 8:48AM |
S6.00004: Monodromy? What's Monodromy? J.B. Delos, D. Sadovskii, B. Zhilinskii We say that a system exhibits \textit{monodromy} if we take the system around a closed loop in its parameter space, and we find that the system does not come back to its original state. Many systems have this property: atoms in a trap, a hydrogen atom in crossed fields, electronic states of H$_{2}^{+ }$, and vibrational states of CO$_{2}$. Imagine noninteracting classical particles moving in a two-dimensional circular box with a hard reflecting wall, and with a cylindrically-symmetric potential energy barrier: $\rho $ = (x$^{2}$+y$^{2})^{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }$ , [V($\rho )$ = -a $\rho ^{2}$/2, $\rho <$R], [V($\rho )$=infinity, $\rho $\underline {$>$}R]. Start all the particles moving on one line with angular momentum L=0, and with energy E$<$0. Then impose additional smooth forces and torques on the particles so that [L(t), E(t)] moves in a circle around the origin in the [L,E] plane. In other words, apply a torque to increase the angular momentum, then drive the particles to a higher energy (above the barrier), then reduce the angular momentum to a negative value, reduce the energy, and finally come back to the initial energy and angular momentum. Where in space do the particles end up? The answer is surprising. [Preview Abstract] |
Friday, May 19, 2006 8:48AM - 9:00AM |
S6.00005: The dynamic foundation of quantum mechanics V.J. Lee Quantum mechanics has been reinvented via mathematical incarnation of Newton's 2$^{nd}$ law in word for particle motion with an \textit{almost} \textit{nowhere} differentiable path. At \textit{almost every} radius vector$x$, the particle has a velocity \textbf{\textit{u}} in time forward and $\widetilde{u}$ in reversal. We formulate that$u=u_n +u_b $. The assumed stochastic radiation in vacuum causes that$\delta x_i \delta x_j =\delta _{ij} 2D\delta t\equiv \delta _{ij} \left( {\hbar \mathord{\left/ {\vphantom {\hbar m}} \right. \kern-\nulldelimiterspace} m} \right)\delta t$. That$\left[ {\left( {\partial \mathord{\left/ {\vphantom {\partial {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} \right)+u_n \cdot \nabla -iu_b \cdot \nabla -i\left( {\hbar \mathord{\left/ {\vphantom {\hbar {2m}}} \right. \kern-\nulldelimiterspace} {2m}} \right)\nabla ^2} \right]\left( {p_n -ip_b } \right)=K_n -iK_o $ emerges as the 2$^{nd}$ law; where $K_n $is an even function of time and $K_o $odd. Employing this law, we derive the Schr\"{o}dinger equation with the paradigm,$\left( {-i\hbar \nabla -qA} \right)\psi =\left( {p_n -ip_b } \right)\psi $, in pediatrician terms. Those $\nabla ^2\rho \left( {x_j } \right)=0$ specify$x_j \mbox{'s}$, where$p_b \mbox{'s}$are \textit{exactly} defined. For the case$A\equiv 0$, there are two pure cases: (a) $p_b $only; (b) $p_n $only. Miscategorization of$p_b $as$p_n $in quantum theory \textit{status quo} is revealed in (a). Energy is \textit{numerically} \textit{computed} at$x_j \mbox{'s}$, which explain atomic stability. That$p_n \cdot d=nh$ is the law of transmission of $p_n $ through crystal planes, is derived in (b). Summary also on web: http://mysite.verizon.net/vjtlee/ [Preview Abstract] |
Friday, May 19, 2006 9:00AM - 9:12AM |
S6.00006: Measurement of critical exponents at spontaneous symmetry breaking~in a parametrically excited magneto-optical trap Myoung-Sun Heo, Ki-Hwan Lee, Changil Ryoo, Dahyun Yum, Yonghee Kim, Kihwan Kim, Wonho Jhe While critical phenomena in equilibrium systems has been well known both in theory and in experiments, those studies in non-equilibrium or far-from-equilibrium systems are still challenging subjects. These have been studied in a number of systems. Laser cooled confined atoms also can be a good candidate since we are able to easily change its temperature and numbers. By parametrically modulating magneto-optical trap we have observed several interesting phenomena such as dynamic double well, Hopf bifurcation and spontaneous symmetry-breaking(SSB). Particularly SSB is approximately identified as Ising-like phase transition. We measured critical exponents relevant to this phase transition, varying the control parameter, the size of the system or total number. We also have observed SSB occurs, changing temperature by injecting resonant laser light. [Preview Abstract] |
Friday, May 19, 2006 9:12AM - 9:24AM |
S6.00007: Radiation-Pressure-Driven Micro-Mechanical Cavity and Emergence of Chaos Farhan Saif, Pierre Meystre In the presence of an optical field between its mirrors a high finesse micro-mechanical cavity acts as an oscillator driven by radition pressure force. We study the effect of radiation pressure force in two mirror cavity and three mirror cavity geometries. We explain the conditions which lead to a chaotic evolution of the micro mechanical oscillator. [Preview Abstract] |
Friday, May 19, 2006 9:24AM - 9:36AM |
S6.00008: Scaling in parameter dependence of decoherence of quantum systems far from their classically chaotic counterparts Arjendu Pattanayak, Arnaldo Gammal The behavior of the entropy for an open quantum system with a classically chaotic limit has been studied in some detail. It had been previously argued that the entropy production rate is (a) independent of $\hbar$ and(b) independent of $D$, the parameter denoting coupling to the environment and (c) equal to the sum of generalized Lyapunov exponents, modulo concerns about being 'near classical' and 'for D large enough'. However, there is little concrete evidence about this. We present results going well beyond earlier work on these issues. In particular, we consider how these results are altered by changing $\hbar$ as well as $D$, and show that there is a distinct transition from classical to quantum behavior in the entropy production rate, and that this transition depends on the composite parameter $\hbar^2/D$ [Preview Abstract] |
Friday, May 19, 2006 9:36AM - 9:48AM |
S6.00009: Chaos-induced pulse trains of cold atoms in a double Gaussian trap Kevin Mitchell In previous work, we predicted that a hydrogen atom, placed in parallel electric and magnetic fields, would ionize by emitting a train of electron pulses after an initial laser excitation. This pulse train results from chaos in the electron dynamics. Here we predict that an analogous pulse train can be measured using cold atoms in an optical dipole trap. We consider a trap potential realized by two overlapping Gaussian beams, forming a two-dimensional double well. The escape of atoms from the first well into the second is predicted to occur in pulses. The structure of these pulses bears the imprint of fractal structure that arises in the nonlinear dynamics of the trap. The underlying dynamics in this system is mathematically analogous to the dynamics of chaotic escape in many other physical systems, such as the ionization problem mentioned above. Thus, the double Gaussian trap could serve as a convenient experimental model for chaotic escape. [Preview Abstract] |
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