en>Duoduoduo: symmetry of presentation

2013-09-10T17:49:05Z

symmetry of presentation

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	~~Hello~~. ~~Allow me introduce~~ the ~~writer~~. ~~Her name~~ is ~~Emilia Shroyer but~~ it~~'s not~~ the ~~most female name out there~~. ~~South Dakota~~ is where ~~I've usually been living~~. ~~I utilized~~ to ~~be unemployed but now I am~~ a ~~librarian~~ and the ~~salary~~ has ~~been really satisfying~~. ~~To do aerobics~~ is a ~~thing~~ that ~~I'm totally addicted to~~.<br><br>~~Take~~ a ~~look~~ at ~~my website~~ [~~http:~~//~~www~~.~~gaysphere~~.~~net~~/~~blog~~/~~167593 www~~.~~gaysphere~~.~~net~~]		[[Superfluidity]] and [[superconductivity]] are macroscopic manifestations of [[quantum mechanics]]. There is considerable interest, both theoretical and practical, in these quantum [[phase transition]]s. There has been a tremendous amount of work done in the field of phase transitions and critical phenomenon in two dimensions.<ref>David Thouless: Condensed Matter Physics in Less Than Three dimensions. Ch. 7. The New Physics, Paul Davies, ed. Cambridge.</ref> Much of the interest in this field is because as the number of dimensions increases, the number of exactly solvable models diminishes drastically. In three or more dimensions one must resort to a mean field theory approach. The theory of superfluid transitions in two dimensions is known as the [[Berezinsky-Kosterlitz-Thouless transition\|Kosterlitz-Thouless]] (KT) theory. The 2D [[XY model]] - where the order parameter is characterized by an amplitude and a phase - is the [[universality class]] for this transition.

			==Experimental methods==

			In looking at [[phase transition]]s in thin films, specifically [[helium]], the two main experimental signatures are the [[superfluid]] fraction and [[heat capacity]]. If either of these measurements were to be done on a superfluid film in a typical open container, the film signal would be overwhelmed by the background signal from the container. Therefore, when studying superfluid films, it is of paramount importance to study a system of large surface area as to enhance the film signal.
			There are several ways of doing this. In the first, a long thin strip of material such as [[PET film (biaxially oriented)\|PET film]] is rolled up into a "jelly roll" configuration. The result is a film that is a long continuous plane, referred to as a planar film.<ref>D. J. Bishop, J. D. Reppy. Study of the Superfluid Transition in Two-Dimensional <sup>4</sup>He films. Phys. Rev. Lett. 40, 1727(1978)</ref> A second way is to have a highly porous material such as porous gold, [[Vycor]], or [[Aerogel]]. This results in a multiply connected film where the substrate is much like Swiss cheese with the holes interconnected.<ref>J. E. Berthold, D. J. Bishop, J. D. Reppy. Superfluid Transition of <sup>4</sup>He Films Adsorbed on Porous Vycor Glass. Phys. Rev. Lett. 39, 348(1977)</ref> These porous materials all have an extremely high surface area to volume ratio. A third method is to separate two extremely flat plates by a thin spacer, again resulting in a large surface area to volume ratio.
			{\| class="wikitable"
			\|-
			! Material
			! Surface area (m<sup>2</sup>/g)
			! Pore Size (nm)
			\|-
			! Vycor Glass
			\| 250
			\| 4
			\|-
			! Porous gold
			\| 100-200
			\| 100
			\|-
			! Aerogel
			\| 200-1000
			\| 20
			\|}

			<gallery>
			Image:Porous_Gold_10micron.jpg\|SEM image of porous gold, 10 micrometres square
			</gallery>
			One can measure the superfluid response of the film by measuring the [[moment of inertia]]. An indispensable tool for this is the Torsional Oscillator, and early design was first used by Andronikashvili to detect superfluid in bulk fluid <sup>4</sup>He and later modified by John Reppy and co-workers at Cornell in the 1970s. In the torsional oscillator, the experimental volume is suspended by a torsion rod and made to oscillate at resonance via capacitive coupling with a fin or pair of fins, depending on the configuration (shown below in grey). When part of the film becomes superfluid, it no longer has any viscosity and will remain at rest in the lab frame, lowering the moment of inertia of the cell. Recall that the resonant period of a torsional oscillator is <math>2\pi\sqrt{m/k}</math>. Therefore, lowering the moment of inertia reduces the resonant period of the oscillator. By measuring the period drop as a function of temperature, and total loading of the film from the empty cell value, one can deduce the fraction of the film that has entered the superfluid state. A typical set of data clearly showing the superfluid decoupling in helium films is shown in ref. 2.

			<gallery>
			Image:TOwhitebackground.svg\|Torsional Oscillator with single fin configuration
			</gallery>
			A typical torsional oscillator has a resonant frequency on the order of 1000 Hz. This corresponds to a maximum velocity of the substrate of micrometres per second. The critical velocity of helium films is reported to be on the order of 0.1 m/s . Therefore, in comparison to the critical velocity, the oscillator is almost at rest. To probe theories of dynamical aspects of thin film phase transitions one must use an oscillator with a much higher frequency. The [[quartz crystal microbalance]] provides just such a tool having a resonant frequency of about 10 kHz. The operating principles are much the same as for a torsional oscillator. When the thin film is adsorbed onto the surface of the crystal, the resonant frequency of the quartz crystal drops. As the crystal is cooled through the superfluid transition, the superfluid decouples and the frequency increases.<ref>M Hieda, A. C. Clark, M. H. W. Chan. Quartz crystal microbalance study of superfluid <sup>4</sup>He films on gold and porous gold surfaces. ''[[Journal of Low Temperature Physics]]'' 134, 91(2004)</ref>

			==Some results==

			The KT theory has been confirmed in a set of experiments by Bishop and Reppy in planar films, i.e. Helium films on mylar . Specifically, they found that the transition temperature scaled with film thickness and the superfluid transition is found in films as thin as 5% of a monolayer. More recently, it has been found that near the transition temperature when the correlation lengths exceed any relevant length scale in the system, a multiply connected film will behave as a 3D system near its critical point.<ref>M. H. W. Chan, K. I. Blum, S. Q. Murphy, G. K. S. Wong, J. D. Reppy. Phys. Rev. Lett. 61, 1950(1988)</ref>

			==See also==
			* [[Superfluid]]
			* [[Bose–Einstein condensate]]
			* [[Superconductivity]]
			* [[Quantum vortex]]
			* [[Supersolid]]
			* [[Phase Transition]]

			==Notes==
			{{reflist}}

			==References==
			* M. H. W. Chan, A. W. Yanof, J. D. Reppy. Superfluidity of thin <sup>4</sup>He films. Phys. Rev. Lett. 32, 1347(1974)

			==External links==

			<!--Categories-->
			[[Category:Condensed matter physics]]

en>Giftlite: /* Proof */ +.

2012-08-13T17:05:38Z

Proof: +.

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Hello. Allow me introduce the writer. Her name is Emilia Shroyer but it's not the most female name out there. South Dakota is where I've usually been living. I utilized to be unemployed but now I am a librarian and the salary has been really satisfying. To do aerobics is a thing that I'm totally addicted to.<br><br>Take a look at my website [http://www.gaysphere.net/blog/167593 www.gaysphere.net]

British flag theorem - Revision history

en>Duoduoduo: symmetry of presentation

en>Giftlite: /* Proof */ +.