Contrast transfer function - Revision history

en>Frederyk Deng: The convention of positive and negative of underfocus is wrong.

2014-12-19T04:09:30Z

The convention of positive and negative of underfocus is wrong.

← Older revision		Revision as of 06:09, 19 December 2014
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	~~The '''Majumdar-Ghosh model''' is an extension of the one-dimensional~~ [~~[quantum mechanics\|quantum~~]~~] [[Heisenberg model (quantum)\|Heisenberg spin model]] in which an extra interaction~~ is ~~added coupling spins two lattice spacings apart such that second-neighbor coupling half as strong the first. It~~ is ~~therefore a special case of the~~ [~~[J1 J2 model]]~~. ~~The model is named after Indian physicists [[Chanchal Kumar Majumdar]~~] and ~~[[Dipan Ghosh]]~~.<~~ref~~>{{cite journal\|last=Dattagupta\|first=Sushanta\|title=Chanchal Kumar Majumdar (1938–2000) – An obituary\|journal=Current Science\|year=2000\|volume=79\|issue=1\|pages=115–116\|accessdate=16 September 2010}}<~~/ref~~>		When your air conditioning quits working, there are some things you can check [http://tinyurl.com/pch83be uggs on sale] before you call a repair man. Two important things to do first off is to check and see if dirt is [http://tinyurl.com/pch83be uggs on sale] the evaporator coil and if the filter needs changed.<br><br>No one really thinks about how much dirt there could be [http://tinyurl.com/pch83be uggs on sale] an air conditioner filter until they take it out and it's covered with all sorts of debris. This is the time to think about the quality of air the family is breathing. If a filter isn't clean, it won't remove dirt and impurities from the air.<br><br>The evaporator coil needs to be checked, simply because it has to come in contact with air for it to work efficiently and if it's covered with a layer of dirt, it's not going to work the way it should. Two other important things to check are not difficult to do. Without touching any wires, just look and see if the circuit breakers and the power is [http://tinyurl.com/pch83be uggs on sale] leading to the air conditioner.<br><br>Is it unplugged? Are the vents open so that cool air can come out of the AC? You can also safely turn the furnace up to make sure everything is working, such as the power and the furnace itself. Then, turn it back down and go outside and listen to hear the familiar refrigerator sound of the air conditioner motor.<br><br>Most companies specializing in hvac repair austin residents are [http://browse.deviantart.com/?qh=&section=&global=1&q=accustomed accustomed] to will ask you if you have done this when you call them. If, after you have made these checks, the air is still not working, you'll need to call one of the companies that does the AC repair Austin residents call all the time.<br>One very important thing to consider is that regular maintenance should be performed on your AC unit every year. Talk to the company and get on their maintenance list. The maintenance offers peace of mind since the company will call you to make an appointment and you won't be able to forget to have your air condidioning unit checked out properly.<br><br>If you wait until it quits, you'll be sweating, frustrated and so sorry you didn't have it checked out before the hot weather set in. When a person lives in a warmer climate area, it takes its toll [http://tinyurl.com/pch83be uggs on sale] equipment, no matter what name brand it is. A machine can only take so much before it just stops.<br><br>By having it lubricated, filters changed, evaporator coil cleaned and the power checked regularly, you'll stay cool through the hot days ahead. It's the same with companies whose air conditioning units quit. The commercial AC repair Austin business owners call [http://tinyurl.com/pch83be uggs on sale] will be doing regular maintenance during the fall and into the winter to get everyone's AC ready before the next hot weather season begins.<br><br>Log on to AC repair Austin and give them a call. They'll set up an appointment and get your home cool again in no time.

	~~The Majumdar-Ghosh model is notable because its ground states (lowest energy quantum states) can~~ be ~~found exactly~~ and ~~written in~~ a ~~simple form~~, ~~making~~ it ~~a useful starting point for understanding more complex spin models~~ and ~~phases~~.

	~~==Definition==~~
	~~The Majumdar-Ghosh model is defined by the following [[Hamiltonian (quantum mechanics)\|Hamiltonian]]:~~

	:<~~math~~>~~\hat H = J \sum_{j =1}^{N} \vec{S}_j \cdot \vec{S}_{j+1} + \frac{J}{2} \sum_{j =1}^{N} \vec{S}_j \cdot\vec{S}_{j+2}~~ <~~/math~~>

	~~where the S vector is a quantum [[Spin (physics)\|spin]] operator~~ with ~~quantum number S=1/2.~~

	~~Other conventions~~ for ~~the coefficients may be taken in the literature~~, ~~but~~ the ~~most~~ important ~~fact is that the ratio of first-neighbor~~ to ~~second-neighbor couplings is 1~~ to 2.

	~~==Ground states==~~

	~~It has been shown that~~ the ~~Majumdar-Ghosh model has two minimum energy states, or ground states, namely~~ the ~~states in which neighboring pairs of spins form~~ [~~[Singlet state\|singlet~~]~~] configurations~~.
	~~The wavefunction for each ground state is a product~~ of ~~these singlet pairs. This explains why there must be at least two ground states with~~ the ~~same energy~~, ~~since one may be~~
	~~obtained from~~ the ~~other by merely shifting, or translating,~~ the ~~system by one lattice spacing~~. ~~It should be noted~~, ~~however, that this ground state degeneracy only appears when the system is taken~~ to ~~be infinite in size~~
	(the ~~so-called thermodynamic limit). Otherwise, there is a unique ground state and a second, higher energy state whose energy approaches~~ the ~~first exponentially quickly with increasing system size~~.

	[~~[File~~:~~Majumdar-ghosh gs~~.~~png]]~~

	==~~Generalizations~~==

	~~The Majumdar-Ghosh model~~ is one of ~~a small handful of realistic quantum spin models~~ that ~~may~~ be ~~solved exactly~~. ~~Moreover, its ground states are simple examples~~
	~~of what are known as [[Valence bond solid\|valence-bond solids]] (VBS). Thus the Majumdar-Ghosh model is related~~ to ~~another famous spin model,~~ the ~~[[AKLT Model]], whose ground state is the unique one dimensional spin one (S=1) valence-bond solid~~.

	The ~~Majumdar-Ghosh model is also a useful example~~ of the ~~[[Lieb-Schultz-Mattis theorem]] which roughly states that~~ an ~~infinite~~, ~~one dimensional~~, ~~half-odd-integer spin system must either have no energy spacing (or gap)~~
	~~between its ground~~ and ~~excited states or else~~ have ~~more than one ground state~~. ~~The Majumdar-Ghosh model has~~ a ~~gap and falls under the second case.~~

	~~==See also==~~
	*[[Heisenberg model (quantum)]]
	*[[Heisenberg model (classical)]]
	*[[J1 J2 model]]
	*[[Bethe ansatz]]
	*[[Ising model]]
	*[[t-J model]]

	~~== References ==~~
	* C K Majumdar and D Ghosh, ''[http://~~link~~.~~aip.org~~/~~link/?JMP/10/1388 On Next‐Nearest‐Neighbor Interaction in Linear Chain~~]''. J. ~~Math. Phys. '''10'''~~, ~~1388 (1969); {{doi\|10.1063/1.1664978}}~~
	* C K Majumdar, ''[http://dx.~~doi.org/10.1088/0022-3719/3/4~~/~~019 Antiferromagnetic model with known ground state~~]''. ~~J. Phys. C: Solid State Phys~~. ~~3 911-915 (1969)~~
	* Assa Auerbach, '~~'[http://books.google.com/books?id=tiQlKzJa6GEC&lpg=PP1&dq=assa%20auerbach%20interacting%20electrons&pg=PA83#v=onepage&q&f=false Interacting Electrons~~ and ~~Quantum Magnetism]'', Springer-Verlag New York (1992) p~~.~~ 83~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Majumdar-Ghosh Model}}~~
	~~[[Category:Spin models]]~~
	~~[[Category:Statistical mechanics]]~~
	~~[[Category:Quantum magnetism]]~~
	~~[[Category:Lattice models]]~~

en>ChrisGualtieri: Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

2013-12-20T15:46:07Z

Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

← Older revision		Revision as of 17:46, 20 December 2013
Line 1:		Line 1:
	~~Do służb, w których użytkuje się ów rodzaj wydruku przylega modelowanie oraz skanowanie 3d~~. w ~~odontologii, można za podporą tej techniki praktykować implanty czy w architekturze, wyróżniająco nadzoruje się w piastowaniu makiet~~. ~~I posługa, którą jest skanowanie 3d polega na odtworzeniu wzorca w jego naturalnej krzepie~~.<br><br>~~Bryła owa będzie zdołała egzystowań wyczerpana do właściwego wydruku w modle 3d~~,ale również wizualizacji zwanej zwykle renderingiem oraz do przygotowania przebiegu obróbki skrawania na specjalistycznych maszynach. Do innych zastosowań skanowania 3d wolno zaliczyć rekonstrukcję designu w kryminalistyce czy w światu przyjemności wprowadzanie osobowości, które do wyobrażenia przypominają wnikliwe.<br><br>~~Modelowanie 3d~~, ~~owe usługa~~, ~~jaka zaufa na wręczeniu jednostce~~, ~~która ją oznacza~~, ~~rysunku technicznego~~. ~~konglomeratów muzeów~~. ~~Ma ono wiele użyć np~~. ~~Nowoczesna technologia spowodowała~~, ~~że zaawansowany druk~~, ~~którym istnieje niepodejrzanie~~ [http://~~500v~~.~~net~~/~~site~~/~~trojwymiarowo~~.~~blog~~.~~onet~~.pl/ ~~druk 3d~~] ~~stworzyło wiele opcji~~. ~~Zawodowcy pracujący nad szkicem~~, ~~na jego osnowie zbudują skibę w trójwymiarze~~. ~~W ostanim czasie strategia owa odnalazła również zastęp przeznaczeń w archiwistyce~~, ~~owe kapitalny sposób na zarchiwizowanie np~~.		The '''Majumdar-Ghosh model''' is an extension of the one-dimensional [[quantum mechanics\|quantum]] [[Heisenberg model (quantum)\|Heisenberg spin model]] in which an extra interaction is added coupling spins two lattice spacings apart such that second-neighbor coupling half as strong the first. It is therefore a special case of the [[J1 J2 model]]. The model is named after Indian physicists [[Chanchal Kumar Majumdar]] and [[Dipan Ghosh]].<ref>{{cite journal\|last=Dattagupta\|first=Sushanta\|title=Chanchal Kumar Majumdar (1938–2000) – An obituary\|journal=Current Science\|year=2000\|volume=79\|issue=1\|pages=115–116\|accessdate=16 September 2010}}</ref>

			The Majumdar-Ghosh model is notable because its ground states (lowest energy quantum states) can be found exactly and written in a simple form, making it a useful starting point for understanding more complex spin models and phases.

			==Definition==
			The Majumdar-Ghosh model is defined by the following [[Hamiltonian (quantum mechanics)\|Hamiltonian]]:

			:<math>\hat H = J \sum_{j =1}^{N} \vec{S}_j \cdot \vec{S}_{j+1} + \frac{J}{2} \sum_{j =1}^{N} \vec{S}_j \cdot\vec{S}_{j+2} </math>

			where the S vector is a quantum [[Spin (physics)\|spin]] operator with quantum number S=1/2.

			Other conventions for the coefficients may be taken in the literature, but the most important fact is that the ratio of first-neighbor to second-neighbor couplings is 1 to 2.

			==Ground states==

			It has been shown that the Majumdar-Ghosh model has two minimum energy states, or ground states, namely the states in which neighboring pairs of spins form [[Singlet state\|singlet]] configurations.
			The wavefunction for each ground state is a product of these singlet pairs. This explains why there must be at least two ground states with the same energy, since one may be
			obtained from the other by merely shifting, or translating, the system by one lattice spacing. It should be noted, however, that this ground state degeneracy only appears when the system is taken to be infinite in size
			(the so-called thermodynamic limit). Otherwise, there is a unique ground state and a second, higher energy state whose energy approaches the first exponentially quickly with increasing system size.

			[[File:Majumdar-ghosh gs.png]]

			==Generalizations==

			The Majumdar-Ghosh model is one of a small handful of realistic quantum spin models that may be solved exactly. Moreover, its ground states are simple examples
			of what are known as [[Valence bond solid\|valence-bond solids]] (VBS). Thus the Majumdar-Ghosh model is related to another famous spin model, the [[AKLT Model]], whose ground state is the unique one dimensional spin one (S=1) valence-bond solid.

			The Majumdar-Ghosh model is also a useful example of the [[Lieb-Schultz-Mattis theorem]] which roughly states that an infinite, one dimensional, half-odd-integer spin system must either have no energy spacing (or gap)
			between its ground and excited states or else have more than one ground state. The Majumdar-Ghosh model has a gap and falls under the second case.

			==See also==
			*[[Heisenberg model (quantum)]]
			*[[Heisenberg model (classical)]]
			*[[J1 J2 model]]
			*[[Bethe ansatz]]
			*[[Ising model]]
			*[[t-J model]]

			== References ==
			* C K Majumdar and D Ghosh, ''[http://link.aip.org/link/?JMP/10/1388 On Next‐Nearest‐Neighbor Interaction in Linear Chain]''. J. Math. Phys. '''10''', 1388 (1969); {{doi\|10.1063/1.1664978}}
			* C K Majumdar, ''[http://dx.doi.org/10.1088/0022-3719/3/4/019 Antiferromagnetic model with known ground state]''. J. Phys. C: Solid State Phys. 3 911-915 (1969)
			* Assa Auerbach, ''[http://books.google.com/books?id=tiQlKzJa6GEC&lpg=PP1&dq=assa%20auerbach%20interacting%20electrons&pg=PA83#v=onepage&q&f=false Interacting Electrons and Quantum Magnetism]'', Springer-Verlag New York (1992) p. 83
			{{Reflist}}

			{{DEFAULTSORT:Majumdar-Ghosh Model}}
			[[Category:Spin models]]
			[[Category:Statistical mechanics]]
			[[Category:Quantum magnetism]]
			[[Category:Lattice models]]

en>Vossman: math corrections with reference

2012-06-18T21:06:23Z

math corrections with reference

New page

Do służb, w których użytkuje się ów rodzaj wydruku przylega modelowanie oraz skanowanie 3d. w odontologii, można za podporą tej techniki praktykować implanty czy w architekturze, wyróżniająco nadzoruje się w piastowaniu makiet. I posługa, którą jest skanowanie 3d polega na odtworzeniu wzorca w jego naturalnej krzepie.<br><br>Bryła owa będzie zdołała egzystowań wyczerpana do właściwego wydruku w modle 3d,ale również wizualizacji zwanej zwykle renderingiem oraz do przygotowania przebiegu obróbki skrawania na specjalistycznych maszynach. Do innych zastosowań skanowania 3d wolno zaliczyć rekonstrukcję designu w kryminalistyce czy w światu przyjemności wprowadzanie osobowości, które do wyobrażenia przypominają wnikliwe.<br><br>Modelowanie 3d, owe usługa, jaka zaufa na wręczeniu jednostce, która ją oznacza, rysunku technicznego. konglomeratów muzeów. Ma ono wiele użyć np. Nowoczesna technologia spowodowała, że zaawansowany druk, którym istnieje niepodejrzanie [http://500v.net/site/trojwymiarowo.blog.onet.pl/ druk 3d] stworzyło wiele opcji. Zawodowcy pracujący nad szkicem, na jego osnowie zbudują skibę w trójwymiarze. W ostanim czasie strategia owa odnalazła również zastęp przeznaczeń w archiwistyce, owe kapitalny sposób na zarchiwizowanie np.