- Two-dimensional gas
A two-dimensional gas is a collection of N objects which are constrained to move in a planar or other two-
dimension al space in agas eous state. The objects can be:ideal gas elements such as rigid disks undergoingelastic collision s;elementary particle s, or any object inphysics which obeyslaws of motion . The concept of a two-dimensional gas is used either because: (a) the issue being studied actually takes place in two dimensions (as certain surface molecular phenomena); or, the two-dimensional form of the problem is more tractable than the analogous mathematically more complex three-dimension al problem.While
physicist s have studied simple two body interactions on a plane for centuries, the attention given to the two-dimensional gas (having many bodies in motion) is a 20th century pursuit. Applications have led to better understanding of gasthermodynamics , certainsolid state problems and several questions inquantum mechanics .Classical mechanics
Research at
Princeton University [C.M.Hogan, "Non-equilibrium statistical mechanics of a two-dimensional gas", Dissertation, Princeton University, Department of Physics, May 4, 1964] in the early 1960s posed the question of whether theMaxwell-Boltzmann statistics and other thermodynamic laws could be derived fromNewton ian laws applied to multi-body systems rather than through the conventional methods ofstatistical mechanics . While this question appears intractable from a three-dimensionalclosed form solution , the problem behaves differently in two-dimensional space. In particular an ideal two-dimensional gas was examined from the standpoint of relaxation time to equilibriumvelocity distribution given several arbitrary initial conditions of the ideal gas.Relaxation time s were shown to be very fast: on the order ofmean free time .In 1996 a computational approach was taken to the classical mechanics non-equilibrium problem of heat flow within a two-dimensional gas [D. Risso and P. Cordero, "Two-Dimensional Gas of Disks:
Thermal Conductivity ",Journal of Statistical Physics , volume 82, pages 1453-1466, (1996)] . This simulation work showed that for N>1500, good agreement with continuous systems is obtained.Electron gas
While the principle of the
cyclotron to create a two-dimensional array ofelectron s has existed since 1934, the tool was originally not really used to analyze interactions among the electrons (e.g. two-dimensionalgas dynamics ). An early research investigation to explore a two-dimensional electron gas [Walter Kohn, "Cyclotron Resonance and de Haas-van Alphen Oscillations of an Interacting Electron Gas",Physical Review 123, 1242–1244 (1961)] with respect tocyclotron resonance behavior and thede Haas-van Alphen effect . The investigator was able to demonstrate for a two-dimensional gas, the de Haas-van Alphenoscillation period is independent of the short-range electroninteraction s.Later applications to Bose gas
In 1991 a theoretical proof was made that a
Bose gas can exist in two dimensions [Vanderlei Bagnato and Daniel Kleppner. "Bose–Einstein condensation in low-dimensional traps",American Physical Society , 8 April, 1991] . In the same work an experimental recommendation was made that could verify the hypothesis.Experimental research with a molecular gas
Stranick used an ultrahigh
vacuum scanningmicroscope to image a two dimensionalbenzene gas layer in contact with a planar solid interface at 77kelvins [Stranick, S. J. ; Kamna, M. M. ; Weiss, P. S, "Atomic Scale Dynamics of a Two-Dimensional Gas-Solid Interface", Pennsylvania State University, Park Dept. of Chemistry, 3 June, 1994] . The experimenters were able to observe benzene molecules moving freely as a two-dimensional gas on the surface of Cu(III), to which a planar monomolecular film of solid benzene adhered. Thus the scientists could witness the equilibrium of the gas in contact with its solid state, even by observing transient migration and phase transition of individual benzene molecules.Implications for future research
A multiplicity of theoretical physics research directions exist for study via a two-dimensional gas. Examples of these are
*Complex
quantum mechanics phenomena, whose solutions may be more appropriate in a two-dimensional environment;
*Studies ofphase transition s (e.g. melting phenomena at a planar surface);
*Thin film phenomena such aschemical vapor deposition ;
*Surface excitations of a solid.References
ee also
*
Bose gas
*Fermi gas
*Melting point
*Optical lattice External links
* [http://citeseer.ist.psu.edu/lax95solution.html Riemann problems for a two-dimensional gas]
* [http://www.cec.uchile.cl/cinetica/papers/rc96.html Two-dimensional gas of disks]
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