The excitation spectrum for a Bose gas with repulsive and attractive interactions
Helium 2 elementary excitation spectrum derived microscopically for realistic interatomic potential
Brown, G. V.↗
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Excitation spectrum for a Bose gas with repulsive core and attractive well.
He II excitation spectrum for interparticle potential using pair Hamiltonian with repulsive core and attractive well
Brown, G. V.↗
Collisional spin transfer in an atomic heteronuclear spinor Bose gas
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Fang Fang↗
Hard-sphere fluid in infinite dimensions
The exact Mayer series is derived for the pressure, density, and equation of state of a hard-sphere fluid in the limit of infinite space dimensions D. The Mayer series can be analytically continued into the full (cut) activity plane, and there is no sign of a phase transition. The quantum-mechanical system is also treated. For D = infinity, the fluid behaves like an ideal Bose gas and undergoes a Bose-Einstein condensation.
Wyler, D.↗
Fast Rotating Scalar and Multi-component Bose Gases
We show that in the limit of large angular momentum, many equilibrium and dynamical phenomena of scalar and multi-component Bose gases can be accounted for by approximating the system to reside in an effective lowest Landau level. This method explains the origin of the mysterious stripe formation in fast rotating Bose gas recently observed at JILA, and accounts for all the dynamical details observed in this experiment. To further demonstrate the usefulness of this method, we present its predictions of the interference patterns of two vortex lattices, and rich vortex lattice structures in multi-component Bose gases.
Ho, TIn-Lun Jason↗
Quantum principles and free particles
The quantum principles that establish the energy levels and degeneracies needed to evaluate the partition functions are explored. The uncertainty principle is associated with the dual wave-particle nature of the model used to describe quantized gas particles. The Schroedinger wave equation is presented as a generalization of Maxwell's wave equation; the former applies to all particles while the Maxwell equation applies to the special case of photon particles. The size of the quantum cell in phase space and the representation of momentum as a space derivative operator follow from the uncertainty principle. A consequence of this is that steady-state problems that are space-time dependent for the classical model become only space dependent for the quantum model and are often easier to solve. The partition function is derived for quantized free particles and, at normal conditions, the result is the same as that given by the classical phase integral. The quantum corrections that occur at very low temperatures or high densities are derived. These corrections for the Einstein-Bose gas qualitatively describe the condensation effects that occur in liquid helium, but are unimportant for most practical purposes otherwise. However, the corrections for the Fermi-Dirac gas are important because they quantitatively describe the behavior of high-density conduction electron gases in metals and explain the zero point energy and low specific heat exhibited in this case.
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Bose-einstein condensation in narrow channels.
Bose-Einstein gas model to investigate transition temperature of liquid helium in narrow channels
TEMPERATURE MEASUREMENT↗
Equilibrium polymerization on the equivalent-neighbor lattice
The equilibrium polymerization problem is solved exactly on the equivalent-neighbor lattice. The Flory-Huggins (Flory, 1986) entropy of mixing is exact for this lattice. The discrete version of the n-vector model is verified when n approaches 0 is equivalent to the equal reactivity polymerization process in the whole parameter space, including the polymerized phase. The polymerization processes for polymers satisfying the Schulz (1939) distribution exhibit nonuniversal critical behavior. A close analogy is found between the polymerization problem of index the Schulz r and the Bose-Einstein ideal gas in d = -2r dimensions, with the critical polymerization corresponding to the Bose-Einstein condensation.
Kaufman, Miron↗
Dehydration kinetics and thermochemistry of selected hydrous phases, and simulated gas release pattern in carbonaceous chondrites
As part of our continued program of study on the volatile bearing phases and volatile resource potential of carbonaceous chondrite, results of our experimental studies on the dehydration kinetics of talc as a function of temperature and grain size (50 to 0.5 microns), equilibrium dehydration boundary of talc to 40 kbars, calorimetric study of enthalpy of formation of both natural and synthetic talc as a function of grain size, and preliminary results on the dehydration kinetics of epsomite are reported. In addition, theoretical calculations on the gas release pattern of Murchison meteorite, which is a C2(CM) carbonaceous chondrite, were performed. The kinetic study of talc leads to a dehydration rate constant for 40-50 microns size fraction of k = (3.23 x 10(exp 4))exp(-Q/RT)/min with the activation energy Q = 376 (plus or minus 20) kJ/mole. The dehydration rate was found to increase somewhat with decreasing grain size. The enthalpy of formation of talc from elements was measured to be -5896(10) kJ/mol. There was no measurable effect of grain size on the enthalpy beyond the limits of precision of the calorimetric studies. Also the calorimetric enthalpy of both synthetic and natural talc was found to be essentially the same, within the precision of measurements, although the natural talc had a slightly larger field of stability in our phase equilibrium studies. The high pressure experimental data the dehydration equilibrium of talc (talc = enstatite + coesite + H2O) is in strong disagreement with that calculated from the available thermochemical data, which were constrained to fit the low pressure experimental results. The calculated gas release pattern of Murchison meteorite were in reasonable agreement with that determined by stepwise heating in a gas chromatograph.
Bose, Kunal↗
A Coupled Plasma Dynamics and Gas Flow Model for Semiconductor Processing
A continuum modeling approach by self-consistently coupling plasma dynamics and gas flow will be presented for the analysis of high density plasma reactors. Experimental data shows that gas flow distribution affects the etch rate uniformity even at low pressures (6-20 mTorr) and flow rates (20-70 sccm). This study will investigate the effects of gas flow and gas energy on bulk plasma densities and temperatures using a continuum model. The model solves multidimensional equations of mass balance for neutrals and ions, gas momentum, separate energy equations for electrons and neutrals and Maxwell's equations for power coupling. A test case of N2 plasma in a 300mm TCP etch reactor, for which hybrid model and Langmuir probe data are available, is chosen for this analysis. Our preliminary results show that modeling gas flow and energy improves the predictions of electron density and its spatial variation in the reactor when compared with the experimental data. The aim of this study is to identify the operating conditions for the TCP reactor when a self-consistent modeling of gas flow is important.
Bose, Deepak↗
Modeling Growth of Nanostructures in Plasmas
As semiconductor circuits shrink to CDs below 0.1 nm, it is becoming increasingly critical to replace and/or enhance existing technology with nanoscale structures, such as nanowires for interconnects. Nanowires grown in plasmas are strongly dependent on processing conditions, such as gas composition and substrate temperature. Growth occurs at specific sites, or step-edges, with the bulk growth rate of the nanowires determined from the equation of motion of the nucleating crystalline steps. Traditional front-tracking algorithms, such as string-based or level set methods, suffer either from numerical complications in higher spatial dimensions, or from difficulties in incorporating surface-intense physical and chemical phenomena. Phase field models have the robustness of the level set method, combined with the ability to implement surface-specific chemistry that is required to model crystal growth, although they do not necessarily directly solve for the advancing front location. We have adopted a phase field approach and will present results of the adatom density and step-growth location in time as a function of processing conditions, such as temperature and plasma gas composition.
Hwang, Helen H.↗
Predictive Modeling in Plasma Reactor and Process Design
Research continues toward the improvement and increased understanding of high-density plasma tools. Such reactor systems are lauded for their independent control of ion flux and energy enabling high etch rates with low ion damage and for their improved ion velocity anisotropy resulting from thin collisionless sheaths and low neutral pressures. Still, with the transition to 300 mm processing, achieving etch uniformity and high etch rates concurrently may be a formidable task for such large diameter wafers for which computational modeling can play an important role in successful reactor and process design. The inductively coupled plasma (ICP) reactor is the focus of the present investigation. The present work attempts to understand the fundamental physical phenomena of such systems through computational modeling. Simulations will be presented using both computational fluid dynamics (CFD) techniques and the direct simulation Monte Carlo (DSMC) method for argon and chlorine discharges. ICP reactors generally operate at pressures on the order of 1 to 10 mTorr. At such low pressures, rarefaction can be significant to the degree that the constitutive relations used in typical CFD techniques become invalid and a particle simulation must be employed. This work will assess the extent to which CFD can be applied and evaluate the degree to which accuracy is lost in prediction of the phenomenon of interest; i.e., etch rate. If the CFD approach is found reasonably accurate and bench-marked with DSMC and experimental results, it has the potential to serve as a design tool due to the rapid time relative to DSMC. The continuum CFD simulation solves the governing equations for plasma flow using a finite difference technique with an implicit Gauss-Seidel Line Relaxation method for time marching toward a converged solution. The equation set consists of mass conservation for each species, separate energy equations for the electrons and heavy species, and momentum equations for the gas. The sheath is modeled by imposing the Bohm velocity to the ions near the walls. The DSMC method simulates each constituent of the gas as a separate species which would be analogous in CFD to employing separate species mass, momentum, and energy equations. All particles including electrons are moved and allowed to collide with one another with the stipulation that the electrons remain tied to the ions consistent with the concept of ambipolar diffusion. The velocities of the electrons are allowed to be modified during collisions and are not confined to a Maxwellian distribution. These benefits come at a price in terms of computational time and memory. The DSMC and CFD are made as consistent as possible by using similar chemistry and power deposition models. Although the comparison of CFD and DSMC is interesting, the main goal of this work is the increased understanding of high-density plasma flowfields that can then direct improvements in both techniques. This work is unique in the level of the physical models employed in both the DSMC and CFD for high-density plasma reactor applications. For example, the electrons are simulated in the present DSMC work which has not been done before for low temperature plasma processing problems. In the CFD approach, for the first time, the charged particle transport (discharge physics) has been self-consistently coupled to the gas flow and heat transfer.
Hash, D. B.↗
Impact of Gas Heating in Inductively Coupled Plasmas
Recently it has been recognized that the neutral gas in inductively coupled plasma reactors heats up significantly during processing. The resulting gas density variations across the reactor affect reaction rates, radical densities, plasma characteristics, and uniformity within the reactor. A self-consistent model that couples the plasma generation and transport to the gas flow and heating has been developed and used to study CF4 discharges. A Langmuir probe has been used to measure radial profiles of electron density and temperature. The model predictions agree well with the experimental results. As a result of these comparisons along with the poorer performance of the model without the gas-plasma coupling, the importance of gas heating in plasma processing has been verified.
Hash, D. B.↗
Generation of a Cold Atom Beam from a Pyramidal Magneto-Optical Trap
Techniques to generate cold atom beams are of great interest in a variety of applications, from atomic frequency standards and atom optics to experimental studies of Bose-Einstein condensation. Cold atom beams have been produced by slowing thermal atomic beams using the Zeeman-slowing technique or chirped lasers, or using laser-cooling techniques to extract a slow atomic beam from the background gas in a low-pressure vapor cell. These laser-cooling techniques include "atomic funnels" or two-dimensional magneto-optical traps, as well as a variation of the conventional vapor cell magneto-optical trap called the "low-velocity intense source" (LVIS). Variations of the LVIS have been realized with unique trap geometries such as conical or pyramidal mirror traps. The present work implements a simple and robust design based on the pyramidal trap geometry and allows use of a single large diameter (<less than or = 20 cm) laser beam to obtain large capture rates of atoms from the background vapor. The four 45 deg mirrors are truncated just before the apex of the pyramid, and the 1 sq cm region at the center of the incident laser beam is retro-reflected by lambda /4 plate with a high-reflectance gold coating on the second surface. A small (1 mm diameter) hole in this retro-optic forms an extraction column for the atoms while maintaining a low conductance between the source region and an adjacent UHV chamber.
Kohel, J.↗
NASA Tech Briefs, February 2003
opics covered include: Integrated Electrode Arrays for Neuro-Prosthetic Implants; Eroding Potentiometers; Common/Dependent-Pressure-Vessel Nickel-Hydrogen Batteries; 120-GHz HEMT Oscillator With Surface-Wave-Assisted Antenna; 80-GHz MMIC HEMT Voltage-Controlled Oscillator; High-Energy-Density Capacitors; Microscale Thermal-Transpiration Gas Pump; Instrument for Measuring Temperature of Water; Improved Measurement of Coherence in Presence of Instrument Noise; Compact Instruments Measure Helium-Leak Rates; Irreversible Entropy Production in Two-Phase Mixing Layers; Subsonic and Supersonic Effects in Bose-Einstein Condensate; Nanolaminate Mirrors With "Piston" Figure-Control Actuators; Mixed Conducting Electrodes for Better AMTEC Cells; Process for Encapsulating Protein Crystals; Lightweight, Self-Deployable Wheels; Grease-Resistant O Rings for Joints in Solid Rocket Motors; LabVIEW Serial Driver Software for an Electronic Load; Software Computes Tape-Casting Parameters; Software for Tracking Costs of Mars Projects; Software for Replicating Data Between X.500 and LDAP Directories; The Technical Work Plan Tracking Tool; Improved Multiple-DOF SAW Piezoelectric Motors; Propulsion Flight-Test Fixture; Mechanical Amplifier for a Piezoelectric Transducer; Swell Sleeves for Testing Explosive Devices; Linear Back-Drive Differentials; Miniature Inchworm Actuators Fabricated by Use of LIGA; Using ERF Devices to Control Deployments of Space Structures; High-Temperature Switched-Reluctance Electric Motor; System for Centering a Turbofan in a Nacelle During Tests; Fabricating Composite-Material Structures Containing SMA Ribbons; Optimal Feedback Control of Thermal Networks; Artifacts for Calibration of Submicron Width Measurements; Navigating a Mobile Robot Across Terrain Using Fuzzy Logic; Designing Facilities for Collaborative Operations; and Quantitating Iron in Serum Ferritin by Use of ICP-MS.
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Plasma Reactor Modeling and Validation Experiments
Plasma processing is a key processing stop in integrated circuit manufacturing. Low pressure, high density plum reactors are widely used for etching and deposition. Inductively coupled plasma (ICP) source has become popular recently in many processing applications. In order to accelerate equipment and process design, an understanding of the physics and chemistry, particularly, plasma power coupling, plasma and processing uniformity and mechanism is important. This understanding is facilitated by comprehensive modeling and simulation as well as plasma diagnostics to provide the necessary data for model validation which are addressed in this presentation. We have developed a complete code for simulating an ICP reactor and the model consists of transport of electrons, ions, and neutrals, Poisson's equation, and Maxwell's equation along with gas flow and energy equations. Results will be presented for chlorine and fluorocarbon plasmas and compared with data from Langmuir probe, mass spectrometry and FTIR.
Meyyappan, M.↗
Thermodynamics and statistical mechanics
The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.
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Experiments with Ultracold Quantum-degenerate Fermionic Lithium Atoms
Experimental methods of laser and evaporative cooling, used in the production of atomic Bose-Einstein condensates have recently been extended to realize quantum degeneracy in trapped Fermi gases. Fermi gases are a new rich system to explore the implications of Pauli exclusion on scattering properties of the system, and ultimately fermionic superfluidity. We have produced a new macroscopic quantum system, in which a degenerate Li-6 Fermi gas coexists with a large and stable Na-23 BEC. This was accomplished using inter-species sympathetic cooling of fermionic 6Li in a thermal bath of bosonic Na-23. We have achieved high numbers of both fermions (less than 10(exp 5) and bosons (less than 10(exp 6), and Li-6 quantum degeneracy corresponding to one half of the Fermi temperature. This is the first time that a Fermi sea was produced with a condensate as a "refrigerator".
Ketterle, Wolfgang↗