Lattice Definition and 437 Threads

Hi everyone, even before addressing the following points I have a serious issue in understandig the text of the Exercise.My idea was to model this system with a lattice gas. Given that each site can host 2 atoms I have 3 possibilities for each site: I'll call'em ##S_{11} S_{00}## and ##...

may someone explain to me or show me the steps of how equations 7a, 7b, 7c were determined from equations 5 and 6

Hello, i am new in condensed matter physics and studying the article 'Engineering artificial graphene in a two-dimensional electron gas' (Gibertini et al., 2009). I read a lot about bloch theorem lately and i got the main idea but still i don't understand the component of the equation. In the...

Hello, everyone. :) All I could gather is that, if I'm correct, lattices are spans of the column vectors of the matrix within the "LAT()" notation and the X and Y occurrences are unit placeholders (such as the pixel unit (since this is in the context of image processing)). And, as an attempt...

Hi, I don't understand why the author in calculating the expression for the specific heat, divides by ##1/V## (the total volume). Also, in calculating the fraction of modes with frequency in the range ##v##, ##v+dv## he divides by ##V## (eq. 2.65, 2.67) Thanks, Ric

I have been encountering "zero lattice element hit" when I try to run it in MCNP5. The input file is provided below. The square lattice runs fine, but the hexagonal does not. Hope someone can help me here. Thank you.

Hi, I'm a bit confused about Bloch functions. This is what, I think, I understood: can someone please tell me what's wrong? From Bloch's theorem we know that the wave-function of an electron inside a periodical lattice can be written as ##ψ_k(r)=u_k(r)e^{ik⋅r}##. We hope that far from a lattice...

Can anyone confirm the claim on this site that n is greater or equal to 23 when Theta is 90 degrees and t is 3? My calculations indicate that the argument of arccosine in the numerator has to be very close to 1, but the numerator of the argument (k_laset+t) is 3.1 whereas the denominator...

Is a photon simply a propagating vibration of the spacetime lattice similar to gravitational waves but at a different wavelength and amplitude, and the electron that creates it plucks a single lattice string rather than a bunch? Therefore it has no mass and travels differently through spacetime...

I have two question about a exemple given in the Sakurai's quantum mechanics book, section 4.3. Let's consider an electron in a periodic potential ##V(x + a) = V(x)##, that has the form of a wave. We will take the potential to go to infinity between two latteces sites, such that its form change...

Usually the truth values of propositions of a logic are structured into a lattice, with 0 (False) on (say) the bottom and 1(True) on (say) the top, and the connecting lines being implication. In paraconsistent logics, there is at least one node which is not implied by 0. Can one safely say that...

In question (a) Calculate the average position ? https://en.wikipedia.org/wiki/Expected_value#Finite_case ##<x> =\sum x_ip_i## I saw the answer and wondered. ## \bar{x} = <x> = \sum_{n=0}^{N} \frac{N!}{n!(N-n)!} x_n p^n q^{N-n}## so ##x_n = (2n-N)a## a is lattice constant why x_n = (2n-N)a ...

I'm given to understand that perturbation methods don't work in QCD because the coupling constant is too large. So they use supercomputers to calculate equations at various points on a lattice. Does this lattice method still take into account the virtual gluons that we might see in perturbation...

Hi all, I am having trouble understanding the some ideas presented in some notes I've been reading, help is greatly appreciated! I've uploaded screenshots of the material I'm referring to below, the last two images are what I'm mainly referencing, and the first few are to provide context...

Hi, I am trying to build a honeycomb structure in MCNP. The code is given below. Hexagonal lattice 1 0 -1 -19 29 fill=1 imp:n=1 2 1 -2.26 -10 11 -12 13 -14 15 u=1 lat=2 imp:n=1 3 0 1:19:-29 imp:n=0 1 c/z 50 50 200 19 pz 31 29 pz -31 10 px 1 11 px -1 12 p 1...

There is a proposal for a generalized lattice standard model by Juven Wang and Xiao-Gang Wen. Could this be correct? I've put this under BTSM because it also mentions grand unified models. https://arxiv.org/abs/1809.11171 A Non-Perturbative Definition of the Standard Models Juven Wang...

In case of simple cubic lattice relative magnetization is given by \sigma=1-\frac{1}{S}\frac{v}{(2\pi)^3}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\mbox{d} k_x\mbox{d} k_y\mbox{d}k_z(\mbox{e}^{\frac{E(\vec{k})}{kT}}-1)^{-1}...

Homework Statement Prove that the set of all subgroups of a group ##G## is a lattice with respect to the partial order relation given by containment. Note: You need not prove that containment is a partial order relation but you do need to prove that if ##H\leq G## and ##K\leq G## then there...

Dear experts, How should I compute the wind loads for a Shukhow tower, i.e. a circular cross-section steel lattice structure? The structural members should be rectangular or circular. I´ve been checking EUROCODEs EN 1991-1-4 (2005) and EN 1993-3-1 (2006) without success. Is there any other...

Mathematicians, I summon thee to help me identify which field deals with this stuff. I come here not as a physicist but as a sunday programmer trying to solve some numerical problems. I set out to model a lattice version of a smooth space. A discretization procedure not uncommon in physics, but...

Hi everyone, I need a little help understanding how periodic reciprocal space applies to the Debye model for solids. Many thanks in advance! If we start with the general derivation of a dispersion relation for a 1D system, with atoms coupled by springs, one gets the following relation $$\omega...

I think the title sums up pretty well my doubts. I learned QFT from Peskin and Schroeder and other common sources, all implicitly defined QFT at zero temperature. Then I started learning about lattice QCD, how to define the action, how to find continuum limits, the importance of the dependence...

Greetings, for a Monte Carlo simulation of N hard spheres, I want to set up the initial configuration as a fcc lattice. I am thinking about how to do it most efficiently. Here is the lattice structure: The 3 lattice vectors, each one pointing to a different type of the 12 nearest neighbors...

In lattice diagram, if the voltage wave is generated at Junction that there is an overhead transmission line before it, will the wave be in two directions with the same magnitude, or one in neglected ? Picture may illustrate .

Homework Statement Homework EquationsThe Attempt at a Solution Attempted in the picture

Recently I found an experiment done by Prof. Sila Beane. In this experiment he simulates a tiny porportion of the universe using a QCD Lattice where spacetime is a discrete lattice. He inputs the GZK cutoff point of a cosmic ray into the lattice and what happens is, the result is that the...

Hello people, I have 3 questions related to the mean speed of electrons in a period potential /lattice. I've read Ashcroft and Mermin's page 139 as well as the Apendix E. From what I understood, if one applies the momentum operator on the wavefunction of a Bloch electron, one doesn't get a...

Mossbauer spectroscopy is an example of a nuclear (de)excitation coupling to a lattice phonons Are there any other examples of this phenomena ?

Hi all Decided to post in 'beyond standard model' because lattice gauge theories are usually used to explore these models. Hope that's all right. So in lattice simulations, phase transitions in beta mass plane seem to have an important meaning. I understand phase transitions from a...

So I made this diagram of the order imposed on the set of topologies on a 3 point set. Each small circle is a topology with the circle elements being the open sets. The larger circles join isomorphic topologies together. The ordering was messy when I tried to draw inclusion from each topology to...

The electron gyromagnetic ratio of 1.0011596522 is computed using perturbation method and Feynman diagrams that is said to produce a value to better than one part in 10^10, or about three parts in 100 billion. Does the nonperturbative lattice QFT also able to compute it? What is the counterpart...

Homework Statement I am not sure I understand how did they solve question (b). Here's the solution to question (b): Homework EquationsThe Attempt at a Solution For the first approximation I plugged everything to the identity in (a) and indeed got the approximation as it's written in the...

Dear All I would like to understand a paper for Xiao-Gang Wen " A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model" . Can anyone help me by suggesting another reference that is a little bit easier. Thank you

Hello, My question is very simple but I do not have a lot of experience with simulation. I want to write some code to simulate a lattice with boundary conditions and then I will perform calculations with the Hubbard model to find different kinds of properties of interest. I would like to know...

Homework Statement When calculating the Fourier coefficients of the potential of the following lattice (the potential is a sum of deltas at the atom sites): I get the wrong coefficients if I choose the following primitve cell, with primitve vectors a1,a2: And the right coefficients if I...

Hello everyone. I'm working on a program to solve 2D Ising model of magnetic materials, using a system with 10x10 spins for simplicity at a temperature of 1E-8 K. I'm using this parameters to get a faster result of m=1 and guarantee it is correct. but... For now i already pass 300 Monte Carlo's...

I have a question about reciprocal lattice of graphene. When we see LEED pattern, we can know that reciprocal lattice of graphene is honeycomb. But how can we know theorically that it is honeycomb? Hexagonal lattice or other bravais lattice has just lattice vectors which don`t contain baises. So...

Homework Statement Homework Equations I'm not sure. The Attempt at a Solution I started on (i) -- this is where I've gotten so far. I am asked to compute the Fourier transform of a periodic potential, ##V(x)=\beta \cos(\frac{2\pi x}{a})## such that...

Homework Statement ##\Omega = {nw_1+mw_2| m,n \in Z} ## ##z_1 ~ z_2 ## is defined by if ##z_1-z_2 \in \Omega ## My notes say ##z + \Omega## are the cosets/ equivalence classes , denoted by ##[z] = {z+mw_1+nw_2} ## Homework Equations above The Attempt at a Solution So equivalance classe...

Homework Statement Hi I am looking at the proof attached for the theorem attached that: If ##s \in R##, then ##\sum'_{w\in\Omega} |w|^-s ## converges iff ##s > 2## where ##\Omega \in C## is a lattice with basis ##{w_1,w_2}##. For any integer ##r \geq 0 ## : ##\Omega_r := {mw_1+nw_2|m,n \in...

I need details on this topic ,this is my assignment but my solid state physics is not so good,and don't know much about it but i have to do this assignment ,i have material on reciprocal lattice but for only including in assignment ,not for my understanding,so i directly need any material on...

From Courant's Differential and Integral Calculus p.13, In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral. Proof: Let ##A=(0,0)...

This is schematic band structure for the dxz and dyz orbitals using a 2D square Fe lattice. What is the location in the Brillouin zone of the hole-like Fermi surface and the electron-like Fermi surface?

Hi everyone, I plan to do a simulation of a Boltzmann equation with experimentally known scattering between two particles. Initially I intend to incorporate the scattering into the collision integral and use Lattice Boltzmann Equation (LBE) afterwards. But I only see LGBK (DnQb) which requires...

Homework Statement 1. For a simple cubic lattice with a lattice constant of a, the energy band can be expressed as:E = Acos(kxa)cos(kya)cos(kza) + B. (a) Suppose the effective mass for the electron at conduction band is m* = -ħ2/2a2, find A. Homework EquationsThe Attempt at a Solution I...

Hi everyone, I've been given a problem where I have to index reflections from a cubic lattice, the procedure is simple enough but I'm getting a case where I get : h^2+k^2+l^2=7 I've taken to many books, but most either don't mention the topic or say they are simply 'forbidden' reflections. I...

I have a real hard time trying to imagine why a face centered cubic cell originates a Bravais lattice. Could you try to explain it? I have also been trying to figure out if a side-centered cell is a Bravais lattice as well. This cell is a simple cubic cell with additional point at the midpoints...

Can someone tell me that in bcc lattice why xrd 100 peak does not appear?

Hello everyone, I am not an expert in the topic so I apologize in advance if the question has an easy answer. I think it is well known that if we have a set of N vortices in a superfluid their mutual interaction is logarithmic. Meaning that if \vec x_n is the position of the n-th vortex, then...

How can i use F4 tally in hexagonal lattice geometry which composed of circular fuel assembly? For example one hexagonal lattice includes circle which is cell number 5 and another hexagonal lattice includes circle which is cell number 7 etc. I want to use all these cells in one f4 tally. Please...