Four problems in non-equilibrium statistical physics are investigated: 1. The
thermodynamics of single-photon gas; 2. Energy of the ground state in Multi-electron
atoms; 3. Energy state of the H2 molecule; and 4. The Condensation behavior in N
weakly interacting Boson gas.
In the single-photon heat engine, we have derived the equation of state similar
to that in classical ideal gas and applied it to construct the Carnot cycle with a single
photon, and showed the Carnot efficiency in this single-photon heat engine.
The energies of the ground state of multi-electron atoms are calculated using the
modi ed Bohr model with a shell structure of the bound electrons. The di erential
Schrodinger equation is simpli ed into the minimization problem of a simple energy
functional, similar to the problem in dimensional scaling in the H-atom. For the
C-atom, we got the ground state energy -37:82 eV with a relative error less than 6
%.
The simplest molecular ion, H+
2 , has been investigated by the quasi-classical
method and two-center molecular orbit. Using the two-center molecular orbit derived
from the exact treatment of the H+
2 molecular ion problem, we can reduce the number
of terms in wavefunction to get the binding energy of the H2 molecule, without using
the conventional wavefunction with over-thousand terms. We get the binding energy
for the H2 with Hylleraas correlation factor 1 + kr12 as 4:7eV, which is comparable
to the experimental value of 4:74 eV.
Condensation in the ground state of a weakly interacting Bose gas in equilibrium
is investigated using a partial partition function in canonical ensemble. The recursive
relation for the partition function developed for an ideal gas has been modi ed to
be applicable in the interacting case, and the statistics of the occupation number in
condensate states was examined. The well-known behavior of the Bose-Einstein Condensate
for a weakly interacting Bose Gas are shown: Depletion of the condensate
state, even at zero temperature, and a maximum
uctuation near transition temperature.
Furthermore, the use of the partition function in canonical ensemble leads to
the smooth cross-over between low temperatures and higher temperatures, which has
enlarged the applicable range of the Bogoliubov transformation. During the calculation,
we also developed the formula to calculate the correlations among the excited
states.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-05-8007 |
| Date | 2010 May 1900 |
| Creators | Kim, Moochan |
| Contributors | Scully, Marlan |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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