A note on the time evolution of generalized coherent states

I consider the time evolution of generalized coherent states based on non-standard fiducial vectors, and show that only for a restricted class of fiducial vectors does the associated classical motion determine the quantum evolution of the states. I discuss some consequences of this for path integral representations.Comment: 9 pages. RevTe

On the Groenewold-Van Hove problem for R^{2n}

We discuss the Groenewold-Van Hove problem for R^{2n}, and completely solve it when n = 1. We rigorously show that there exists an obstruction to quantizing the Poisson algebra of polynomials on R^{2n}, thereby filling a gap in Groenewold's original proof without introducing extra hypotheses. Moreover, when n = 1 we determine the largest Lie subalgebras of polynomials which can be unambiguously quantized, and explicitly construct all their possible quantizations.Comment: 15 pages, Latex. Error in the proof of Prop. 3 corrected; minor rewritin

Nanomechanics of a Hydrogen Molecule Suspended between Two Equally Charged Tips

Geometric configuration and energy of a hydrogen molecule centered between two point-shaped tips of equal charge are calculated with the variational quantum Monte-Carlo (QMC) method without the restriction of the Born-Oppenheimer (BO) approximation. Ground state nuclear distribution, stability, and low vibrational excitation are investigated. Ground state results predict significant deviations from the BO treatment that is based on a potential energy surface (PES) obtained with the same QMC accuracy. The quantum mechanical distribution of molecular axis direction and bond length at a sub-nanometer level is fundamental for understanding nanomechanical dynamics with embedded hydrogen. Because of the tips' arrangement, cylindrical symmetry yields a uniform azimuthal distribution of the molecular axis vector relative to the tip-tip axis. With approaching tips towards each other, the QMC sampling shows an increasing loss of spherical symmetry with the molecular axis still uniformly distributed over the azimuthal angle but peaked at the tip-tip direction for negative tip charge while peaked at the equatorial plane for positive charge. This directional behavior can be switched between both stable configurations by changing the sign of the tip charge and by controlling the tip-tip distance. This suggests an application in the field of molecular machines.Comment: 20 pages, 10 figure

Supersymmetry in Thermo Field Dynamics

By considering the enlarged thermal system including the heat bath, it is shown that this system has supersymmetry which is not broken at finite temperature. The super algebra is constructed and the Hamiltonian is expressed as the anti-commutator of two kinds of super charges. With this Hamiltonian and the thermal vacuum $\mid 0(\beta)>$, this supersymmetry is found to be preserved.Comment: 12 pages, Latex fil

Boxfishes (Teleostei: Ostraciidae) as a model system for fishes swimming with many fins: kinematics

Swimming movements in boxfishes were much more complex and varied than classical descriptions indicated. At low to moderate rectilinear swimming speeds (<5 TL s^(-1), where TL is total body length), they were entirely median- and paired-fin swimmers, apparently using their caudal fins for steering. The pectoral and median paired fins generate both the thrust needed for forward motion and the continuously varied, interacting forces required for the maintenance of rectilinearity. It was only at higher swimming speeds (above 5 TL s^(-1)), when burst-and-coast swimming was used, that they became primarily body and caudal-fin swimmers. Despite their unwieldy appearance and often asynchronous fin beats, boxfish swam in a stable manner. Swimming boxfish used three gaits. Fin-beat asymmetry and a relatively nonlinear swimming trajectory characterized the first gait (0–1 TL s^(-1)). The beginning of the second gait (1–3 TL s^(-1)) was characterized by varying fin-beat frequencies and amplitudes as well as synchrony in pectoral fin motions. The remainder of the second gait (3–5 TL s^(-1)) was characterized by constant fin-beat amplitudes, varying finbeat frequencies and increasing pectoral fin-beat asynchrony. The third gait (>5 TL s^(-1)) was characterized by the use of a caudal burst-and-coast variant. Adduction was always faster than abduction in the pectoral fins. There were no measurable refractory periods between successive phases of the fin movement cycles. Dorsal and anal fin movements were synchronized at speeds greater than 2.5 TL s^(-1), but were often out of phase with pectoral fin movements

Hydrodynamic stability of swimming in ostraciid fishes: role of the carapace in the smooth trunkfish Lactophrys triqueter (Teleostei: Ostraciidae)

The hydrodynamic bases for the stability of locomotory motions in fishes are poorly understood, even for those fishes, such as the rigid-bodied smooth trunkfish Lactophrys triqueter, that exhibit unusually small amplitude recoil movements during rectilinear swimming. We have studied the role played by the bony carapace of the smooth trunkfish in generating trimming forces that self-correct for instabilities. The flow patterns, forces and moments on and around anatomically exact, smooth trunkfish models positioned at both pitching and yawing angles of attack were investigated using three methods: digital particle image velocimetry (DPIV), pressure distribution measurements, and force balance measurements. Models positioned at various pitching angles of attack within a flow tunnel produced well-developed counter-rotating vortices along the ventro-lateral keels. The vortices developed first at the anterior edges of the ventro-lateral keels, grew posteriorly along the carapace, and reached maximum circulation at the posterior edge of the carapace. The vortical flow increased in strength as pitching angles of attack deviated from 0°, and was located above the keels at positive angles of attack and below them at negative angles of attack. Variation of yawing angles of attack resulted in prominent dorsal and ventral vortices developing at far-field locations of the carapace; far-field vortices intensified posteriorly and as angles of attack deviated from 0°. Pressure distribution results were consistent with the DPIV findings, with areas of low pressure correlating well with regions of attached, concentrated vorticity. Lift coefficients of boxfish models were similar to lift coefficients of delta wings, devices that also generate lift through vortex generation. Furthermore, nose-down and nose-up pitching moments about the center of mass were detected at positive and negative pitching angles of attack, respectively. The three complementary experimental approaches all indicate that the carapace of the smooth trunkfish effectively generates self-correcting forces for pitching and yawing motions — a characteristic that is advantageous for the highly variable velocity fields experienced by trunkfish in their complex aquatic environment. All important morphological features of the carapace contribute to producing the hydrodynamic stability of swimming trajectories in this species

Flow Patterns Around the Carapaces of Rigid-bodied, Multi-propulsor Boxfishes (Teleostei: Ostraciidae)

Boxfishes (Teleostei: Ostraciidae) are rigid-body, multi-propulsor swimmers that exhibit unusually small amplitude recoil movements during rectilinear locomotion. Mechanisms producing the smooth swimming trajectories of these fishes are unknown, however. Therefore, we have studied the roles the bony carapaces of these fishes play in generating this dynamic stability. Features of the carapaces of four morphologically distinct species of boxfishes were measured, and anatomically-exact stereolithographic models of the boxfishes were constructed. Flow patterns around each model were investigated using three methods: 1) digital particle image velocimetry (DPIV), 2) pressure distribution measurements, and 3) force balance measurements. Significant differences in both cross-sectional and longitudinal carapace morphology were detected among the four species. However, results from the three interrelated approaches indicate that flow patterns around the various carapaces are remarkably similar. DPIV results revealed that the keels of all boxfishes generate strong longitudinal vortices that vary in strength and position with angle of attack. In areas where attached, concentrated vorticity was detected using DPIV, low pressure also was detected at the carapace surface using pressure sensors. Predictions of the effects of both observed vortical flow patterns and pressure distributions on the carapace were consistent with actual forces and moments measured using the force balance. Most notably, the three complementary experimental approaches consistently indicate that the ventral keels of all boxfishes, and in some species the dorsal keels as well, effectively generate self-correcting forces for pitching motions—a characteristic that is advantageous for the highly variable velocity fields in which these fishes reside