Lattice Definition and 437 Threads

Ultra cold atom is achieved by laser cooling. For optical lattice, it is achieved by the interference of counter-propagating laser beams. What is the relation between Ultra-cold atom and optical lattice? Why do people load Ultra-cold atom in optical lattice? Thank you for your answer.

Homework Statement A two-dimensional rectangular crystal has a unit cell with sides a 6.28Å and b 3.14Å. A beam of monochromatic neutrons of wavelength 5.0 Å is used to examine the crystal. Using either the Laue condition for diffraction or Bragg's Law, determine whether it would be...

In elementary particle theory, professor Susskind encourages us to think of space-time as divided into a lattice of cells. We use annihilation and creation operators in the Lagrangian to consume a particle in a cell and to create a new particle in an adjacent cell. Repeated application of...

Hello! Long time lurker, first time poster. This is the first of a couple of questions which has totally stumped me, although I have a feeling it's easier than it first seems. Homework Statement A particle is initially located at one of two atoms. The particle is subject to Hhop , a...

Hi, In my book it says that it is difficult to determine the lattice energy of NaCl so they use the Haber cycle which applies Hess' law. Lattice is the energy change when a solid ionic substance separates into ions in gas phase. We could simply increase tempetrature until NaCl breaks down...

My question is at here: abstract algebra - Use a subgroup lattice to compute a normalizer - Mathematics Thank you!

This is from Molecular Driving Forces, 2nd Ed. 5.3: Calculating the entropy of mixing. Consider a lattice with N sites and n green particles, and another lattice with M sites and m red particles. These lattices cannot exchange particles. This is state A. (a) What is the total number of...

Dear experts, I'm not familiar with crystal structure theory. I'm seek expertise to figure out space groups in 2 dimensions Bravais lattice of the attached structures. In the figure, red and greens dots represent different atoms. I'll greatly appreciate your help. Struture 1...

Homework Statement Sodium transforms from bcc to hcp at about T=23K. Assuming that the density remains fixed and the c/a ratio is ideal (1.633), calculate the hcp lattice constant a, given that the lattice constant a'=4.23 Angstrom in the cubic phase Homework Equations I can't find any...

Given a circle centered at the origin, how can one prove that the limit of the quotient of the number of lattice points on the circle over the radius goes to zero as radius goes to infinity?

I got a bunch of questions about reciprocal lattice, I start with this one: In an x-ray experiment: For one specific orientation of your incident beam on your real lattice, only a portion of the points of your reciprocal lattice will become visible as your diffraction pattern right? See my...

Homework Statement Given the following thermodynamic data, calculate the lattice energy of CaBr2(s) caculate the lattice enegy: (A) Δ°Hf CaBr2(s) = -675 kJ/mol (B) Δ°Hf Ca(g) = 179 kJ/mol (C) Δ°Hf Br(g) = 112 kJ/mol (D) 1st ionization energy of Ca = 590 kJ/mol (E) 2nd ionization...

Homework Statement For a lattice with a two atoms basis, the two dispersion relations valid for Ka = ±∏ w2 = 2C/M2 and w2 = 2C/M1 Show that under these conditions the lattice acts as two independent lattices (one lattice per each atom) with one of the lattices moving while the other is...

Homework Statement Suppose an ideal bose gas sees a periodic potential with a period a in both x and y directions. Its eigenstates are altered from the free-particle form. The lowest band has energies \epsilon_\vec{k}=2t(2-cos(k_xa)-cos(k_ya)) where t is an energy scale that depends on the...

Is there a nice closed-form for this?

Hi, I just started self studying solid state and I'm having trouble figuring out what the hamiltonian for a square lattice would be when considering the Heisenberg interaction. I reformulated the dot product into 1/2( Si+Si+δ+ +Si+δ+S-- ) + SizSi+δz and use Siz = S-ai+ai Si+ =...

Does any circle having irrational radius have no lattice points on its boundary ? Extended question: Is there any way to determine the number of lattice points lying on the boundary of a given circle ? *The centres of these circles are all (0,0) *

I find the expression: "In general, one can expand the atomic displacements in terms of all the lattice wave modes (resembles a Fourier series expansion)" at: https://courses.cit.cornell.edu/ece407/Lectures/handout17.pdf But I have not found the expression in any other literature. (In fact...

Hi guys, sorry as this is probably a silly question. This isn't homework, but it's something I'm confused about in my GCSE course. If a lattice of ions can't conduct electricity when solid, then why can a wire (composed of these lattices (I think?)) conduct electricity? The electrons in a...

Hi, I'm looking for an aerodynamic code to model a transonic (say around M=0.8) wing for some basic structural sizing and performance estimation. I'm hoping to use the MATLAB based VLM code Tornado. It has an inbuilt Prandtl-Glauert correction option. I realize that this is technically...

Bear with me (Two part question), In the ideal case, an electron in a lattice under the influece of a static force will undergo bloch oscillations. A simple hamiltonian for this system would be: H=H° +Fx and V(x+d)=V(x) If I used the kronig-Penney Model would I be able to derive...

Homework Statement NaCl is a simple cubic lattice, with the Na and Cl atoms alternating positions. Assuming that the atoms are hard spheres with nearest neighbors touching, what is the lattice constant of NaCl? (The effective radius of Na is 1.0 angstroms, and the effective radius of Cl is 1.8...

Hi, i would ask you an opinion about a (maybe stupid) doubt. Let us think of a 1D lattice whose sites distant from each other "a"; a plane wave in the lattice is given by e^{ikja} where k is the momentum and j an integer label for each site. Now, we modify the lattice in this way: between...

Homework Statement Draw the position of the atoms in the two neighboring planes of the GaAs crystal perpendicular to vector [010]. Find the type of the lattice and the basis of 2D crystal which is made by singling out those two neighboring layers from 3D lattice. Homework Equations...

Homework Statement Calculate magnetisation for partition function ##Z=12+4\cosh (8\beta J)## for Ising model 2x2 lattice.Homework Equations F=-k_BTln Z M(H,T)=-\frac{\partial}{\partial H}(\frac{F}{k_BT}) The Attempt at a Solution For me it looks that magnetisation is zero. By just doing the...

http://books.google.rs/books?id=vrcHC9XoHbsC&pg=PA252&lpg=PA252&dq=Nolting+Finite+Ising+lattice&source=bl&ots=5uRHp0iALf&sig=_YBUSvbCBbhNQJ5Zu1go9AsEkM8&hl=sr&sa=X&ei=y_E4UIEyyobiBPvFgMgM&ved=0CC0Q6AEwAA#v=onepage&q=Nolting%20Finite%20Ising%20lattice&f=false A finite lattice X with so...

I am studying Solid state physics from kittel and I am stuck at the following equation. I can see that the exponential term turns to the kroneckler delta, but I don't understand how the integral gives the volume of the specimen, Ω? What am I not seeing? ∫d3x f(x)eiK.x = \sum aG∫d3x ei(K+G).x =...

I have heard generally that it is possible to put different physical theories on a lattice and after renormalization get the same continuum theory. I mean, different lattice theories that lead to the same continuum theory. Is this true for, say, qcd, or other particle theories? Are there...

I know that accelerating electrons in a solid are responsible for the emission, absorption and reflection of light. However, what role do the lattice vibrations play? These oscillating atoms are charge distributions and should emit radiation too, right? As far as I can remember, the...

Homework Statement Hi guys, I don't reach the correct answer to an exercise. I'm following Ashcroft's book. I must find that the reciprocal of the bcc Bravais lattice is a fcc one and the reciprocal of the fcc Bravais lattice is a bcc one. Homework Equations If a_1, a_2 and a_3 are...

Homework Statement There are Cl+ ions at the corners of a cube of side a = .4nm and a Cs- ion at the center. a) What is the net force on the Cs- ion? b) What is the electric field at the center of the cube cause by all of the Cl ions? c) What is the electric potential at that point...

Homework Statement Calculate the theoretical lattice energy for MgF2 (Born-Landé equation) Ionic radius Mg+2 (coordination number 6) = 86 pm Ionic radius F- (coordination number 3) = 116 pm Madelung constant = 2.408 n = 7 Homework Equations The Attempt at a Solution I'm...

I'm not a physicist, but I always thought that the rest mass of the electron was a physical constant and its apparent mass was only affected by relativistic effects. This abstract discusses heavy electrons in a Kondo lattice. In what sense are these electrons "heavy"? At low temperatures, they...

My professor gave me data points representing living cells on a rectangular plane and was told to analyze their spatial pattern, i.e., do the date points on the finite plane have a tendency to be clustered, random, or dispersed. I successfully accomplished this for points on a continuous plane...

Hi there, I know that primitive cell is not unique and there are more than one way to define the primitive vectors but my question is when we said "primitive vectors" do we have to construct the Bravais lattice with choosing a proper basis first? My reasoning is suppose the crystal consist of...

Hi there, I am reading the book "Condensed Matter Physics" second edition by Michael P. Marder. It stated in page 9 that one basis of the the honeycomb lattice is \vec{v}_1 = a [0 \ 1/(2\sqrt{3})], \qquad \vec{v}_2 = a [0 \ -1/(2\sqrt{3})] which is based on figure 1.5(B) in page...

Do theories of quantum gravity require that space-time is a lattice instead of a continuum? I guess this question has been addressed elsewhere, but I would appreciate hearing different points of view. Please dummy down the responses so a philosopher can understand it.

Homework Statement given the following position vector: R = (10n1 + 9n2 + 19n3)(a/10) x + 6(n2+n3)(a/5) y + 2(n3)a z where n1, n2 and n3 are integers Find the primitive lattice vectors. Homework Equations any position vector of a lattice point is of the type R= c1 a1 + c2 a2 + c3 a3; and...

[FONT="Times New Roman"]I need to derive the lattice parameter in terms of the Zn-S separation distance, l. I looked up the value and I've found it to be a = \frac{4}{\sqrt{3}}l The way that I started my derivation was saying that each tetrahedron has a sulfide ion in the center, so then we...

Homework Statement A 1-D lattice consists of a linear array of N particles (N>>1) interacting via spring-like nearest neighbor forces. The normal node frequencies are given by \omega_n=\omega_0\sqrt{\,\,2-2\cos\left(2\pi n/N\right)} where \omega_0 is a constant and n an integer ranging...

How can I help my students to comprehend/understand the concept of reciprocal lattice (pictorially) and Brillouin zone?

I'm reading about symmetries in QM in "Geometry of quantum theory" by Varadarajan. In one of the proofs, he refers to theorem 2.1, which is stated without proof. He says that the theorem is proved in "Linear algebra and projective geometry" by Baer. That isn't very helpful, since he doesn't even...

The number of lattice point in FCC? Hi, I am having a trouble to figure the number of lattie point in FCC structure out. My textbook said simple cubic has 1 lattice point, BCC has 2 points, and FCC has 4 points. However there is no further explanation or figures. I am a kind of understand...

the 10 X 20 lattice game has the following rules: - two players alternate picking points (x,y) in the plane. the points must have integer coordinates(lattice points) and we must have 1 ≤ x ≤ 10 1 ≤ y ≤ 20 - first player must begin from (1,1). that is, player 1 can choose any point with one...

Who can tell me the concept of optical lattice and quantum dot? Or give me an advice of some thesis? Thank you very much.

What decides that which salt will take up which crystal lattice? Some salts have cubic lattice , some have hexagonal , some have orthorhombic - but what factor decides which crystal system the salt will take over. Most of the examples i have seen consist of cubic lattice system. Is it becasue...

Homework Statement In a simple cubic lattice of spacing 0.2nm a phonon traveling in the {1 0 0} direction with wavelength 0.42nm collides with another phonon of the same wavelength which is traveling in the {1 1 0} direction. Draw a reciprocal space diagram to show the magnitude and...

Homework Statement Place the following in order of decreasing magnitude of lattice energy. KF, MgS, RbI I'm not really sure how to do this without looking up the lattice energy values with each. And I don't think that is what our teacher wants us to do

Hello I am looking to learn about Lattice Gauge Theory. I am already understand the general theory, (that is, defining fermions and gauge fields on lattice sites and links, respectively), but am having trouble intuiting the results of such calculations. As an example, the following is a...

can anyone tell me why we use reciprocal lattice for understanding the diffraction of X rays from crystal? thanks in advance :)