Confined One Dimensional Harmonic Oscillator as a Two-Mode System

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in any other way. An alternative to casting the problem in terms of one or the other basis set consists of using an "oblique" basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful. Keywords: one-dimensional harmonic oscillator, particle in a box, exactly solvable models, two-mode system, oblique basis states, perturbation theory, coherent states, adiabatic mixing.Comment: 11 pages and 9 figures; Submitted to American Journal of Physic

Local Single- and Two-Phase Heat Transfer from an Impinging Cross-Shaped Jet

Local single- and two-phase heat transfer distributions are measured under a confined impinging jet issuing from a cross-shaped orifice. Spatially resolved temperature maps and convection coefficients resulting from the impinging flow are obtained via infrared imaging of a thin-foil heat source. The cooling patterns in single- and two-phase operation are explained by an accompanying numerical investigation of the fluid flow issuing from the orifice; computed velocity magnitudes and turbulence intensities are presented. In single-phase operation, the coolest surface temperatures correspond to areas with high liquid velocities. High velocities and developing turbulence are also shown to increase convective heat transfer along the diagonal outflow directions from the impinging jet. During two-phase transport, boiling preferentially begins in regions of low velocity, providing enhanced heat transfer in the areas least affected by the impingement. The cross-shaped orifice achieves local heat transfer coefficients that exceed the stagnation-point value of a circular jet of equivalent open orifice area by up to 1.5 times, while resulting in an increased pressure drop only 1.1 times higher than that of the circular jet

Efimov states and their Fano resonances in a neutron-rich nucleus

Asymmetric resonances in elastic n+$^{19}$C scattering are attributed to Efimov states of such neutron-rich nuclei, that is, three-body bound states of the n+n+$^{18}$C system when none of the pairs is bound or some of them only weakly bound. By fitting to the general resonance shape described by Fano, we extract resonance position, width, and the "Fano profile index". While Efimov states have been discussed extensively in many areas of physics, there is only one very recent experimental observation in trimers of cesium atoms. The conjunction that we present of the Efimov and Fano phenomena may lead to experimental realization in nuclei.Comment: 4 double-column pages, 3 figure

A Tomographic-PIV Investigation of Vapor-Induced Flow Structures in Confined Jet Impingement Boiling

Tomographic particle image velocimetry (PIV) is used to study the effect of confinement gap height on the liquid flow characteristics in jet impingement boiling. This first application of tomographic PIV to flow boiling is significant given the complexity of confined two-phase jet impingement. A jet of subcooled wa- ter at a Reynolds number of 5,0 0 0 impinges onto a circular heat source undergoing boiling heat transfer at a constant heat input. Confinement gap heights of 8, 4, and 2 jet diameters are investigated. A visual hull method is used to reconstruct the time-varying regions of the vapor in the flow. The vapor motion is found to govern the liquid flow pattern and turbulence generation in the confinement gap. Time-averaged velocities and regions of turbulent kinetic energy in the liquid are highest for a confinement gap height of 8 jet diameters, with lower velocity magnitude and turbulence being observed for the smaller spac- ings. Coherent vortical structures identified with the λ2 -criterion are found to occur most frequently near the moving vapor interface. The most intense regions of turbulent kinetic energy do not coincide with the location of coherent structures within the flow. Irrotational velocity fluctuations in the liquid phase caused by vapor bubble pinch-offare the primary cause of the high turbulent kinetic energy measured in these regions. At a gap height of H / d = 2 the vapor plume is constrained as it grows from the heat source, causing bulk flow oscillations in the downstream region of the confinement gap

Algebraic characterization of X-states in quantum information

A class of two-qubit states called X-states are increasingly being used to discuss entanglement and other quantum correlations in the field of quantum information. Maximally entangled Bell states and "Werner" states are subsets of them. Apart from being so named because their density matrix looks like the letter X, there is not as yet any characterization of them. The su(2) X su(2) X u(1) subalgebra of the full su(4) algebra of two qubits is pointed out as the underlying invariance of this class of states. X-states are a seven-parameter family associated with this subalgebra of seven operators. This recognition provides a route to preparing such states and also a convenient algebraic procedure for analytically calculating their properties. At the same time, it points to other groups of seven-parameter states that, while not at first sight appearing similar, are also invariant under the same subalgebra. And it opens the way to analyzing invariant states of other subalgebras in bipartite systems.Comment: 4 pages, 1 figur

SASE FEL Storage Ring

We explore the possibility of operating a SASE FEL with a Storage Ring. We use a semi-analytical model to obtain the evolution inside the undulator by taking into account the interplay on the laser dynamics due to the induced energy spread and to the radiation damping. We obtain the Renieri's limit for the stationary output power and discuss the possibility of including in our model the effect of the beam instabilities.Comment: 5 page

Anomalous Elasticity of Polymer Cholesterics

We show that polymer cholesterics have much longer pitches than comparable short molecule cholesterics, due to their anomalous elasticity. The pitch $P$ of a chiral mixture with concentration $c$ near the racemic (non-chiral) concentration $c^*$ diverges like $\vert c-c^*\vert^{-\nu}$ with $\nu=1.43 \pm 0.04$ (for short molecule cholesterics $\nu=1$). The short molecule law is recovered for polymers of finite molecular length $\ell$ once the pitch is longer than a length that diverges like $\ell^\gamma$ with $\gamma=0.67 \pm 0.01$. Our predictions could be tested by measurements of the pitch in DNA.Comment: 12 pages, Plain TeX, (1 postscript figure, compressed, uuencoded and appended to paper), minor corrections, IASSNS-HEP-94/4

Pair creation: back-reactions and damping

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back-reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period tau_pl. Allowing for collisions, these oscillations are damped on a time-scale, tau_r, determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless tau_r >> tau_pl and tau_pl approx. 1/Lambda_QCD approx 1 fm/c.Comment: 16 pages, 6 figure, REVTEX, epsfig.st