Negative feedback amplifier - Revision history

en>Brews ohare: /* Signal flow analysis */ Reword

2015-01-07T16:36:37Z

Signal flow analysis: Reword

← Older revision		Revision as of 18:36, 7 January 2015
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en>Johnuniq: Reverted edits by 27.251.177.99 (talk) to last version by 24.181.113.138

2014-02-06T07:19:31Z

Reverted edits by 27.251.177.99 (talk) to last version by 24.181.113.138

← Older revision		Revision as of 09:19, 6 February 2014
Line 1:		Line 1:
	~~{{Refimprove\|date=January 2013}}~~		There is nothing to write about myself really.<br>Nice to be here and a member of wmflabs.org.<br>I just wish I'm useful in some way here.<br><br>My blog - [http://hemorrhoidtreatmentfix.com/internal-hemorrhoids internal hemorrhoids]
	~~{{Condensed matter physics\|expanded=States of matter}}~~
	~~A '''Fermi gas'''~~ is an ensemble of a large number of [[fermions]]. Fermions, named after [[Enrico Fermi]], are [[subatomic particle\|particles]] that obey [[Fermi–Dirac statistics]]. These statistics determine the energy distribution of fermions in a Fermi gas in [[thermal equilibrium]], and is characterized by their [[number density]], [[temperature]], and the set of available energy states.

	By the [[Pauli exclusion principle]], no [[quantum state]] can be occupied by more than one fermion with an identical set of [[quantum number]]s. Thus a noninteracting Fermi gas, unlike a [[Bose gas]], is prohibited from condensing into a [[Bose-Einstein condensate]], although interacting Fermi gases might.<~~ref~~>[http://www.conferences.uiuc.edu/bcs50/PDF/Jin.pdf]</ref> The total energy of the Fermi gas at [[absolute zero]] is larger than the sum of the single-particle [[ground state]]s because the Pauli principle implies a sort of interaction or pressure that keeps fermions separated and moving. For this reason, the [[pressure]] of a Fermi gas is non-zero even at zero temperature, in contrast to that of a classical ideal gas. This so-called [[degeneracy pressure]] stabilizes a [[neutron star]] (a Fermi gas of neutrons) or a [[white dwarf]] star (a Fermi gas of electrons) against the inward pull of [[gravity]], which would ostensibly collapse the star into a [[Black Hole]]. Only when a star is sufficiently massive to ~~overcome the degeneracy pressure can it collapse into a singularity.~~

	~~It is possible to define a [[Fermi temperature]] below which the gas can~~ be ~~considered degenerate (its pressure derives almost exclusively from the Pauli principle). This temperature depends on the mass of the fermions~~ and the [[density of states\|density of energy states]]. For metals, the electron gas's Fermi temperature is generally many thousands of [[kelvin]]s, so in human applications they can be considered degenerate. The maximum energy of the fermions at zero temperature is called the [[Fermi energy]]. The Fermi energy surface in [[momentum space]] is known as the [[Fermi surface]].

	~~==Ideal Fermi gas==~~
	~~{{seealso\|free electron model}}~~
	~~An ideal Fermi gas or free Fermi gas is a [[Mathematical model\|physical model]] assuming~~ a ~~collection~~ of ~~non-interacting fermions~~. ~~It is the [[quantum mechanics\|quantum mechanical]] version of an [[ideal gas]], for the case of fermionic particles~~. ~~The behavior of electrons in a [[white dwarf]] or [[neutron]]s~~ in a [[neutron star]] can be approximated by treating them as an ideal Fermi gas. Something similar can be done for periodic systems, such as electrons moving in the [[crystal structure\|crystal lattice]] of [[metal]]s and [[semiconductor]]s, using the so-called ''quasi-momentum'' or ''crystal momentum'' ([[Bloch wave]]). Since interactions are neglected by definition, the problem of treating the equilibrium properties and dynamics of an ideal Fermi gas reduces to the study of the behavior of single independent particles. As such, it is still relatively tractable and forms the starting point for more advanced theories that deal with interactions, e.g., using the [[perturbation theory (quantum mechanics)\|perturbation theory]].

	Assuming that the concentration of fermions does not change with temperature, then the [[total chemical potential]] ''µ'' ([[Fermi level]]) of the three dimensional ideal Fermi gas is related to the zero temperature [[Fermi energy]] ''E''<~~sub~~>F<~~/sub~~> ~~by the following expansion (assuming <math>kT \ll E_F</math>):~~
	:~~<math>\mu = E_0 + E_F \left[ 1- \frac{\pi ^2}{12} \left(\frac{kT}{E_F}\right) ^2 - \frac{\pi^4}{80} \left(\frac{kT}{E_F}\right)^4 + \cdots \right] <~~/~~math>~~
	~~where ''E''<sub>0<~~/~~sub> is the potential energy per particle, ''k'' is the [[Boltzmann constant]] and ''T'' is [[temperature]]~~.

	~~Hence, the [[~~internal ~~chemical potential]], ''µ''~~-''E''<sub>0</sub>, is approximately equal to the Fermi energy at temperatures that are much lower than the characteristic Fermi temperature ''E<sub>F</sub>''/''k''. The characteristic temperature is on the order of 10<sup>5</sup> [[kelvin\|K]] for a metal, hence at room temperature (300 K), the Fermi energy and internal ~~chemical potential are essentially equivalent.~~

	~~==References==~~
	~~{{reflist}}~~

	~~==See also==~~
	* [[Fermi liquid]]
	* [[Bose gas]]
	* [[Free electron model]]
	* [[Gas in a box]]

	~~{{DEFAULTSORT:Fermi Gas}}~~
	~~[[Category:Ideal gas]]~~
	~~[[Category:Fermi–Dirac statistics]~~]

24.181.113.138 at 20:57, 27 November 2013

2013-11-27T20:57:57Z

← Older revision		Revision as of 22:57, 27 November 2013
Line 1:		Line 1:
			{{Refimprove\|date=January 2013}}
			{{Condensed matter physics\|expanded=States of matter}}
			A '''Fermi gas''' is an ensemble of a large number of [[fermions]]. Fermions, named after [[Enrico Fermi]], are [[subatomic particle\|particles]] that obey [[Fermi–Dirac statistics]]. These statistics determine the energy distribution of fermions in a Fermi gas in [[thermal equilibrium]], and is characterized by their [[number density]], [[temperature]], and the set of available energy states.

			By the [[Pauli exclusion principle]], no [[quantum state]] can be occupied by more than one fermion with an identical set of [[quantum number]]s. Thus a noninteracting Fermi gas, unlike a [[Bose gas]], is prohibited from condensing into a [[Bose-Einstein condensate]], although interacting Fermi gases might.<ref>[http://www.conferences.uiuc.edu/bcs50/PDF/Jin.pdf]</ref> The total energy of the Fermi gas at [[absolute zero]] is larger than the sum of the single-particle [[ground state]]s because the Pauli principle implies a sort of interaction or pressure that keeps fermions separated and moving. For this reason, the [[pressure]] of a Fermi gas is non-zero even at zero temperature, in contrast to that of a classical ideal gas. This so-called [[degeneracy pressure]] stabilizes a [[neutron star]] (a Fermi gas of neutrons) or a [[white dwarf]] star (a Fermi gas of electrons) against the inward pull of [[gravity]], which would ostensibly collapse the star into a [[Black Hole]]. Only when a star is sufficiently massive to overcome the degeneracy pressure can it collapse into a singularity.

	~~Marketing video was an absolutely new point years ago. One needed~~ to ~~spend~~ a ~~large amount to produce it~~. ~~Now~~ the ~~approach are at your hand~~, ~~it is possible to conserve~~ the ~~total amount that was once invested as there~~'s ~~sharp successful~~ of the ~~press~~. ~~Media have already developed communication network and there are various sources to emphasize ads~~. ~~Only at that current moment if you wish you can come into close contact with online marketing inside~~ a ~~minute with~~ the ~~assistance~~ of ~~new technologies~~.~~<br><br>Attempt To visit their workplace so that you understand that they've~~ a ~~center~~ in ~~place which~~ can ~~support your electronic advertising needs~~. ~~Understanding how to hire~~ the ~~right electronic marketing organization will help change Your Online marketing into a profit~~-~~making software~~. ~~Verify~~ the ~~awards~~ and ~~honors won by~~ the ~~companies as which will chat a whole lot about their function. Attempt To check them giving smaller tasks prior to making a yearly contract with them.<br><br>It's important to make certain~~ the ~~SEO service you use does not make use~~ of ~~any blackhat SEO practices~~. ~~Black-hat SEO does~~ more ~~harm than good~~. ~~Sooner or later~~, ~~searchengines punish and will see your website~~. ~~You ought to stick~~ with ~~whitehat SEO~~ the ~~results tend~~ to ~~be long-lasting and because it is much better or even permanent.~~<br><br><br><br>~~Commit at least a few momemts if you are new going through these details. Show patience when the posts are humanly permitted since approval can take many days.~~<br><br>~~Gone will be~~ the ~~days when selling your goods~~ and ~~services online means splitting your pockets~~. ~~You can simply promote product awareness~~, ~~Today and you can popularize your website even if you do not have a single dime to spare to your marketing expense. As long as you understand how to utilize various~~ [~~http://www.linkedin.com/pub/jordan-kurland/a/618/581 Jordan Kurland~~] ~~instruments~~, it'~~s highly probable that you will flourish in the online industry right away.~~<br><br>~~You should be marketing online. Use what you may must market online. You should be using PPC to obtain consumers. Pay Per Click~~ is ~~one of many best ways~~ to ~~get people who~~ are ~~searchign for appropriate keywords to visit your website. PPC is easy with a few of~~ the ~~energetic ads and other items Google has devote AdWords reports.~~<br><br>~~Next time you enter a search term in your search engine and get redirected to your site, notice the ads that appear~~ on the ~~sides, top or bottom~~ of the page. If they are related from what you've looked for, then the marketer almost certainly uses the contextual form of advertising, which involves browsing this content and search phrases to generate relevant and related ads.<br><br>~~You can get started quickly by reading posts on setting up your sales station~~, ~~learning~~ the ~~tricks about keywords~~ and ~~how to influence them for your company. After you get that down, you can give attention to how exactly to market~~.		It is possible to define a [[Fermi temperature]] below which the gas can be considered degenerate (its pressure derives almost exclusively from the Pauli principle). This temperature depends on the mass of the fermions and the [[density of states\|density of energy states]]. For metals, the electron gas's Fermi temperature is generally many thousands of [[kelvin]]s, so in human applications they can be considered degenerate. The maximum energy of the fermions at zero temperature is called the [[Fermi energy]]. The Fermi energy surface in [[momentum space]] is known as the [[Fermi surface]].

			==Ideal Fermi gas==
			{{seealso\|free electron model}}
			An ideal Fermi gas or free Fermi gas is a [[Mathematical model\|physical model]] assuming a collection of non-interacting fermions. It is the [[quantum mechanics\|quantum mechanical]] version of an [[ideal gas]], for the case of fermionic particles. The behavior of electrons in a [[white dwarf]] or [[neutron]]s in a [[neutron star]] can be approximated by treating them as an ideal Fermi gas. Something similar can be done for periodic systems, such as electrons moving in the [[crystal structure\|crystal lattice]] of [[metal]]s and [[semiconductor]]s, using the so-called ''quasi-momentum'' or ''crystal momentum'' ([[Bloch wave]]). Since interactions are neglected by definition, the problem of treating the equilibrium properties and dynamics of an ideal Fermi gas reduces to the study of the behavior of single independent particles. As such, it is still relatively tractable and forms the starting point for more advanced theories that deal with interactions, e.g., using the [[perturbation theory (quantum mechanics)\|perturbation theory]].

			Assuming that the concentration of fermions does not change with temperature, then the [[total chemical potential]] ''µ'' ([[Fermi level]]) of the three dimensional ideal Fermi gas is related to the zero temperature [[Fermi energy]] ''E''<sub>F</sub> by the following expansion (assuming <math>kT \ll E_F</math>):
			:<math>\mu = E_0 + E_F \left[ 1- \frac{\pi ^2}{12} \left(\frac{kT}{E_F}\right) ^2 - \frac{\pi^4}{80} \left(\frac{kT}{E_F}\right)^4 + \cdots \right] </math>
			where ''E''<sub>0</sub> is the potential energy per particle, ''k'' is the [[Boltzmann constant]] and ''T'' is [[temperature]].

			Hence, the [[internal chemical potential]], ''µ''-''E''<sub>0</sub>, is approximately equal to the Fermi energy at temperatures that are much lower than the characteristic Fermi temperature ''E<sub>F</sub>''/''k''. The characteristic temperature is on the order of 10<sup>5</sup> [[kelvin\|K]] for a metal, hence at room temperature (300 K), the Fermi energy and internal chemical potential are essentially equivalent.

			==References==
			{{reflist}}

			==See also==
			* [[Fermi liquid]]
			* [[Bose gas]]
			* [[Free electron model]]
			* [[Gas in a box]]

			{{DEFAULTSORT:Fermi Gas}}
			[[Category:Ideal gas]]
			[[Category:Fermi–Dirac statistics]]

en>Johnuniq: Reverted edits by 14.97.217.107 (talk) to last version by Johnuniq

2012-08-21T23:14:11Z

Reverted edits by 14.97.217.107 (talk) to last version by Johnuniq

New page

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