LATTICE EQUILIBRIUM THEORY AND SIZE EFFECTS FOR BOSONS IN A BOUNDED HARMONIC POTENTIAL

2006 ◽  
Vol 20 (02) ◽  
pp. 151-179 ◽  
Author(s):  
S. LUMB ◽  
S. K. MUTHU ◽  
K. K. SINGH
Keyword(s):  
Harmonic Oscillator ◽  
Size Effects ◽  
General Structure ◽  
Energy Levels ◽  
Ideal Gas ◽  
Harmonic Potential ◽  
Thermodynamic Quantities ◽  
Self Consistent ◽  
Spatial Size ◽  
Crossover Parameter

Effects of finite spatial size of boson assemblies in traps are studied in a self-consistent lattice theory by modeling the trap as a bounded harmonic potential of size R0. The thermodynamic quantities exhibit scaling and crossover from ideal gas behaviour at small (R0/a0) to that appropriate to an unbounded harmonic potential at large (R0/a0) with a crossover parameter [Formula: see text], a0 being the harmonic oscillator length, and τ denoting the dimensionless thermal energy. The numerical results obtained earlier by computing the energy levels of the bounded harmonic oscillator fit the general structure predicted by the theory very well. For a1>10, the spatial size effects are negligible but for a1<10 they become appreciable and experimentally measurable in suitably designed traps. At low temperatures the self consistent cell size is found to be about 2.5a0 implying that the condensate is essentially a single coherent state contained in the central cell.

scholarly journals The ultra-violet spectrum of magnesium hydride. 1.—The band at λ 2430

1929 ◽  
Vol 122 (790) ◽  
pp. 442-455 ◽  
Keyword(s):  
Fine Structure ◽  
General Structure ◽  
Energy Levels ◽  
Visible Region ◽  
Ultra Violet ◽  
Present Theory ◽  
Magnesium Hydride ◽  
Electronic Energy ◽  
Band Spectra ◽  
Electronic Energy Levels

The system of bands in the visible region of the emission spectrum of magnesium hydride is now well known. The bands with heads at λλ 5622, 5211, 4845 were first measured by Prof. A. Fowler, who arranged many of the strongest lines in empirical series for identification with absorption lines in the spectra of sun-spots. Later, Heurlinger rearranged these series in the now familiar form of P, Q and R branches, and considered them, with the OH group, as typical of doublet systems in his classification of the fine structure of bands. More recently, W. W. Watson and P. Rudnick have remeasured these bands, using the second order of a 21-foot concave grating, and have carried out a further investigation of the fine structure in the light of the present theory of band spectra. Their detection of an isotope effect of the right order of magnitude, considered with the general structure of the system, and the experimental work on the production of the spectrum, seems conclusive in assigning these bands to the diatomic molecule MgH. The ultra-violet spectrum of magnesium hydride is not so well known. The band at λ 2430 and the series of double lines in the region λ 2940 to λ 3100, which were recorded by Prof. Fowler in 1909 as accompanying the group of bands in the visible region, appear to have undergone no further investigation. In view of the important part played by hydride band spectra in the correlation of molecular and atomic electronic energy levels, it was thought that a study of these features might prove of interest in yielding further information on the energy states of the MgH molecule. The present paper deals with observations on the band at λ 2430; details of an investigation of the other features of the ultra-violet spectrum will be given in a later communication.

VIBRATIONAL ENERGIES OF MEMBERS IN STRUCTURAL NETWORKS FITTED WITH TUNED VIBRATION ABSORBERS

2006 ◽  
Vol 06 (02) ◽  
pp. 269-284 ◽  
Author(s):  
SUNNY K. GEORGE ◽  
K. SHANKAR
Keyword(s):  
Energy Level ◽  
Vibrational Energy ◽  
General Structure ◽  
Energy Levels ◽  
Complex Structure ◽  
Input Power ◽  
Vibration Absorbers ◽  
Tuned Vibration Absorbers ◽  
Vibrational Energies ◽  
Structural Networks

The distribution of vibrational energy in members of a complex structure with tuned absorbers attached at the joints and subjected to dynamic loading is studied. The concept of power flows through the structure is used to determine the time-averaged energy levels of each member in the structure. The power flows are calculated using the time-averaged product of force and velocity at the input and coupling points (joints) of a general structure made of axially vibrating rods. The receptance approach is used to calculate the coupling forces and velocities in the structure. By balancing the input power against the dissipated powers, the time-averaged energy levels in members are determined. The main criteria studied here is the reduction in the frequency-averaged vibrational energy level of a member when an absorber is attached, expressed as a percentage compared to the case where there are no absorbers. The concept is first illustrated with a simple model of 2 axially vibrating rods with an absorber attached to the joint. Next, a more complex structure comprising 8 rods with arbitrary orientations and several absorbers attached to junctions is studied. The effect of activating absorbers at various locations on reducing the energy levels of certain members is examined. It is possible to estimate the usefulness of the absorber with respect to any member by determining the percentage reduction of energy level for that member.

Small is different

2021 ◽  
pp. 81-93
Author(s):  
Adrian P Sutton
Keyword(s):  
Crystal Structure ◽  
Electronic Structure ◽  
Catalytic Activity ◽  
Giant Magnetoresistance ◽  
Energy Levels ◽  
Exclusion Principle ◽  
Thermodynamic Quantities ◽  
Discrete Energy ◽  
Size Dependent ◽  
The World

As the size of a material decreases to the nanoscale its properties become size-dependent. This is the world of nanoscience and nanotechnology. At the nanoscale the crystal structure may change and thermodynamic quantities such as the melting point also change. Changes in the catalytic activity and colour of nanoparticles suspended in a liquid indicate changes to the electronic structure. Quantum dots have discrete energy levels that can be modelled with the particle-in-a-box model. Excitons may be created in them using optical illumination, and their decay leads to fluorescence with distinct colours. The classical and quantum origins of magnetism are discussed. The origin of magnetoresistance in a ferromagnet is described and related to the exclusion principle. The origin of the giant magnetoresistance effect and its exploitation in nanotechnology is outlined.

scholarly journals Geometric Models of the Relativistic Harmonic Oscillator

1997 ◽  
Vol 12 (20) ◽  
pp. 3545-3550 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Harmonic Oscillator ◽  
Finite Number ◽  
Continuous Spectrum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Energy Spectra ◽  
De Sitter ◽  
Geometric Models ◽  
Relativistic Harmonic Oscillator ◽  
Quantum Models

A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1 + 1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.

scholarly journals Fast calculation of plasma prominent atomic magnitudes by using a new analytical potential for excited configurations

2002 ◽  
Vol 20 (1) ◽  
pp. 139-144 ◽  
Author(s):  
R. RODRÍGUEZ ◽  
J.G. RUBIANO ◽  
J.M. GIL ◽  
P. MARTEL ◽  
E. MÍNGUEZ
Keyword(s):  
Ground State ◽  
Energy Levels ◽  
Analytical Models ◽  
Special Importance ◽  
Fast Calculation ◽  
Transition Energies ◽  
Analytical Potential ◽  
Self Consistent ◽  
Total Energies

In this work, a new analytical potential for studying ions in excited configurations is presented, which is built up from a parametric potential for ions in a ground state. It is used to calculate atomic magnitudes of special importance in plasmas such as total energies, energy levels, and transition energies, for ions in excited configurations. The results are successfully compared with those obtained with both self-consistent or analytical models.

scholarly journals Statistical problem of ideal gas in general two-dimensional regions

2014 ◽  
Vol 29 (02) ◽  
pp. 1450243 ◽  
Author(s):  
Ci Song ◽  
Wen-Du Li ◽  
Pardon Mwansa ◽  
Ping Zhang
Keyword(s):  
Perturbation Theory ◽  
Conformal Mapping ◽  
Ideal Gas ◽  
Mapping Method ◽  
Numerical Results ◽  
Statistical Problem ◽  
Thermodynamic Quantities ◽  
Two Dimensional ◽  
Conformal Mapping Method

In this paper, based on the conformal mapping method and the perturbation theory, we develop a method to solve the statistical problem within general two-dimensional regions. We consider some examples and the numerical results and fitting results are given. We also give the thermodynamic quantities of the general two-dimensional regions, and compare the thermodynamic quantities of the different regions.

Sign in / Sign up

Export Citation Format

Share Document