Lattice Definition and 437 Threads

I'm applying to grad school this year and I'm thinking I might be interested in exploring lattice gauge theory. Honestly, I don't know very much about the subject but it sounds very interesting to me. Does anybody know which schools have lattice gauge theory and which schools are really good...

Can someone explain to me how the concept of particle is defined in lattice QCD? Here are the reasons why it seems problematic to me: 1) Lattice QCD is based on functional-integral formulation of QFT, which does not contain any operators in the Hilbert space. In particular, it does not contain...

When designing a core lattice, which one of the thermal-hydraulics and neutronics consideration are important?

I have a Hilbert space H; given a closed subspace U of H let PU denote the orthogonal projection onto U. I also have a lattice L of closed subspaces of H, such that for all U and U' in L, PU and PU' commute. The problem is to find an orthonormal basis B of H, such that for every element b of B...

Given an n dimensional integer lattice, is it possible to certify a vector as being a shortest one in time polynomial in n? If we then fix the dimension n, is it possible to certify the shortest-ness in time strictly less than O(k^n) where k is the length of the largest basics vector?

What are the methods or steps of drawing reciprocal lattice?

Can somebody explain me how can we visualise reciprocal lattice of a crystal lattice. Also what do we mean by wavevectors of a reciprocal lattice. What is its physical significance?

It is a common theme among background independent quantum gravity theories that there should be some sort of discretization, or fuzziness, of the spacetime manifold occurring on Planckian scales. It has occurred to me that if we take this discretization to consist of a lattice of sorts, might...

here is a question on reciprocal lattices that I am stuck on for a simple cubic lattice, the unit cell is defined by a1=a(1,0,0) a2 = a(0,1,0) a3 = a(0,0,1), demonstrate that the reciprocal lattice of its reciprocal lattice is the original crystal lattice.From what I've found, i think the...

Homework Statement Hi Say I have a 5x5 lattice, where each entry (or we can call it site) contains the number 1. Now, on the lattice we have a function g(R), which is equal to the number on the site. In this case g(R)=1 for all sites (here R is a vector from the point (3,3), which denotes the...

hello how can I find the angles between the tetahedral bonds of a diamond lattice & what are the direction cosines of the nearest-neighbor bonds with the atom at the origin along the x, y, z axes ?

Homework Statement Show that the reciprocal cubic of cubic lattice is also cubic. Homework Equations cos\alpha*=\frac{cos\beta cos\gamma-cos\alpha}{sin\beta sin\gamma} cos\beta*=\frac{cos\alpha cos\gamma-cos\beta}{sin\alpha sin\gamma} cos\gamma*=\frac{cos\alpha...

S= \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} for simple cubic I= \begin{bmatrix} -\frac{a}{2} & \frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & -\frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & \frac{a}{2} & -\frac{a}{2} \end{bmatrix}...

I am somewhat distracted so this post will not be what it should, given that GAP is one of my interests. For those who don't already know: GAP is a powerful open source software package for computational algebra, especially computational group theory and allied subjects. This long running...

Homework Statement As a part of a lab report, I need to calculate the distance of the (111) planes of an FCC lattice made out of spheres with diameter D. Homework Equations The Attempt at a Solution The course assistant has given me the value of \frac{\sqrt{6}}{3}D. I can...

What is the basic idea behind lattice theory or computer-based QFT calculations? For example, take a scalar field, and the functional path integral: W[J(x)]=\int [d\phi(x)]e^{i\int \mathcal L \mbox{ }d^4x+i\int J(x)\phi(x)d^4x} W[J] is the starting point for all types of...

can someone please tell me what actually is lattice enthalpy. Is it energy released when one mole of bonds are broken or the energy released when one of an ionic compound is broken into the constituents? So do we write U or 2U in the born habber cycle of MgCl2?

Homework Statement I'm trying to figure out the lattice parameter, c, of the HCP crystal structure. Here are a couple links showing the structure...

Hi guys I have the Hamiltonian, which describes my lattice of NxN metal atoms, and their mutual coupling. What I need is the density of states of this lattice, and I am quite sure that there is a way to find it from my Hamiltonian; I just need to find out how. What I thought was that I can...

Will anyone give me an explanation helping me understanding it?

I studied in AMO physics. nowaday, I study about BEC. I'm wonder, Difference between 1D lattice and 2D lattice on BEC. In the web, they just explain what they do using that. Maybe just short word, or sentence, give me a huge knowledge. Thanks you, and Have a nice day!

My understanding is that the folks who do particle mass calculations using the formalism of a lattice get results that fit measured values well without using a Higgs field. Is this correct? If so, do we have any use for and/or reason to believe in the Higgs field/particle?

Dear Friends, I read some articles about alloys. Most articles have a table listing lattice parameters (a,b,c-axis) and unit cell volumes. But they never explain how those data come from. How do we get those data? By comparing XRD images with PDF databases? Or by calculation? Example...

Metals with what type of crystal lattice less prone to brittle fracture? Why?

Homework Statement An element crystalises in a face-centred cubic lattice with a basis group of two atoms at 000 and 1/4 1/4 1/4. The lattice constant is 3.55Angstroms. i) what is the separation of nearest neighbor atoms ii) how many nearest and second nearest neighbors does each atom...

Homework Statement What is the lattice energy of KI? Given the information below. Heat of formation for KI = -328 kJ/mol Heat of sublimation for K = 89.20 kJ/mol Ionization energy for K = 419 kJ/mol Bond dissociation energy for I2 = 149 kJ/mol Electron affinity for I = - 295...

Homework Statement What is the lattice energy of LiI? Given the information below. Heat of formation for LiI = -270 kJ/mol Heat of sublimation for Li = 159.40 kJ/mol Ionization energy for Li = 520 kJ/mol Bond dissociation energy for I2 = 149 kJ/mol Electron affinity for I = -...

In a math contest, the question goes somehow like this: A lattice point is a point wherein the value of (x,y) is an integer. Determine the total number of lattice points in a circle which has a radius of 6 and the its center is at the origin. Any one knows the solution or shortcut for this?

Homework Statement If a_1 a_2 a_3 are the unit vectors of a real space lattice, then the so-called “reciprocal lattice” is defined by the unit vectors b_1 b_2 b_3 where: b_1 = \frac{2\pi a_2 \times a_3}{a_1 \cdot a_2 \times a_3} b_2 = \frac{2\pi a_3 \times a_1}{a_1 \cdot a_2 \times...

1. Homework Statement Using the powder XRD data below, show that the substance has a face centred cubic structure. (xray lamda = 0.154056 nm) Peak No.------2(theta) 1 -------------38.06 2 -------------44.24 3 -------------64.34 4 -------------68.77 5 -------------73.07 2...

Homework Statement Using the powder XRD data below, show that the substance has a face centred cubic structure. (xray lamda = 0.154056 nm) Peak No.------2(theta) 1 -------------38.06 2 -------------44.24 3 -------------64.34 4 -------------68.77 5 -------------73.07 Homework...

Dispersion relation and lattice constants I need to be able to calculate the period (which I believe is the lattice constant) for a 1D crystal given the energy wavevector relation. Is this possible? I also have to find the Bravais lattice of a 2D crystal give a similar relation. What is it...

Can EM waves falling on a solid contribute towards lattice vibrations? If yes, then i)when is the energy used in lattice vibrations, ii)when is it used in excitation of electron into higher energy level, and finally, iii)when is the energy utilized for slight vibration of the electron...

f(\vec{r}) = f(\vec{r}+\vec{T}) \vec{T}= u_{1} \vec{a_{1}} + u_{2} \vec{a_{2}}+u_{3} \vec{a_{3}} u_{1},u_{2},u_{3} are integers. f(\vec{r}+\vec{T})= \sum n_{g} e^{(i\vec{G}.(\vec{r}+\vec{R}) )}= f(\vec{r}) e^{i\vec{G}.\vec{R} }= 1 \vec{G}.\vec{R} = 2\pi m we call...

In the article "The Lattice Theory of Quark Confinement", by Claudio Rebbi (Scientific American) there is a graphic representing the chromoelectric field. The caption reads: "Chromoelectric field is a gauge field similar in principle to the electromagnetic field but more complicated...

Can entangled protons be maintained in a crystal lattice for an indefinite period of time? The following papers seem to support this contention. I need the help of the Forum’s readers to critique this research and the assertions the authors are making. Dr. Francois Fillauxa and Dr Alain...

Hello, I know that Wen might be able to get W Z gauge bosons and chiral neutrinos using his lattice bosonic models he is unable to get chiral interactions using standard bosonic lattice on minkowski space. If instead he used Connes' noncommutative space would he be able to get chiral...

Hi all My book says: "The reason that phonons on a lattice do not carry momentum is that a phonon coordinate (except for wavevector K=0) involves relative coordinates of the atoms". I can't quite figure this statement out. I understand the words, but I cannot see why it is an...

Do yoh have some nice picture to show why the primitive vectors of basic cubic lattice are \vec{a}_1=\frac{a}{2}(-\vec{e}_x+\vec{e}_y+\vec{e}_z) \vec{a}_2=\frac{a}{2}(\vec{e}_x-\vec{e}_y+\vec{e}_z) \vec{a}_3=\frac{a}{2}(\vec{e}_x+\vec{e}_y-\vec{e}_z) Thanks!

Hello, I would like to know how the lattice diffusion is done & why is it temperature dependent? I have tried googling Lattice diffusion several times, but I couldn't find any complete online reading/video... Your contributions will be highly appreciated.

Why the name Reciprocal lattice ?? Is it because the dimensions get bigger & we are able to understand the structure on a macro level & removing the infinities that occur in h, k, l plane system ??

Hi Well I have been thinking of this quite sometime, but i really dint know anyone who could answer my question. We all know that may elements exist in the form of crystals e.g. Si, Cu etc. And they have very specific crystal structure like Diamond for Si and face centered for Cu. Can we...

(nevermind, answered my own question after spending the time to type this up!) Hi, I was flipping through Hilbert's Geometry and the Imagination, and in it, he includes a proof of Leibniz' series ( pi/4 = 1 - 1/3 + 1/5 - 1/7 + ... ) which is carried out by estimating the area of a circle at...

Homework Statement I do not understand the following statement (Please, see the attachment): "C4 has trivial subgroups and only one cyclic subgroup of 2 elements, namely <b>. This is because both a and c can be verified to be generators of C4." The Attempt at a Solution The notation...

i have one problem on atomic radius. i read (http://en.wikipedia.org/wiki/Atomic_radius) the artical and try to understand it but i don't found any formula for it. The problem is: if the lattice parameter of alpha iron is 286 pm (Pico meter),what is its atomic radius? here we have only one...

need help working out this problem. if you have a simple cubic lattice characterised using x-ray diffraction with a wavelegth of 1.6\dot{A}. The main peak in the scan is (222) and the angle is 32 degrees. By using braggs law to find the lattice constant do you just sub in the values and solve...

Is there any lattice model for String Theory? If there is such models, can anyone any good literature? Many Thanks.

I have three primitive vectors a1,a2,a3 for the body-centered cubic (bcc) Bravais can be chosen as a1=ax a2=ay a3=(a/2)(x+y+z) or, for instance, as b1=(a/2)(y+z-x) b2=(a/2)(z+x-y) b3=(a/2)(x+y-z) where x,y,z are unit vectors. Now I should show that any vector of the form...

I am reading a paper right now on lattice QCD that presents a "method that improves the cooling method and constructs an improved topological charge operator based on the product of link variables forming rectangular Wilson loops." Unfortunately I...

What is the difference between a boolean algebra and a complete lattice? What are their similarities?