Let ##\mathscr{L_H}## be the usual lattice of subspaces of Hilbert space ##\mathscr{H}##, where for ##p,q\in\mathscr{H}## we write ##p\leq q## iff ##p## is a subspace of ##q##. Then, as discussed by, e.g., Beltrametti&Cassinelli https://books.google.com/books?id=yWoq_MRKAgcC&pg=PA98, this...
If propositions ##p,q\in{\mathscr L}_{\mathcal H}## (i.e., the lattice of subspaces of ##\mathcal H##) are incompatible, then ##\hat p\hat q\neq\hat q\hat p##. But since it's a lattice, there exists a unique glb ##p\wedge q=q\wedge p##. How are they mathematically related?
In particular, I...
hi guys
our solid state physics professor introduced to us this new concept of reciprocal lattice , and its vectors in k space ( i am still an undergrad)
i find these concepts some how hard to visualize , i mean i don't really understand the k vector of the wave it elf and what it represents...
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...
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...
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...
Hi PhysicsForums,
I have a pretty basic question about extracting physical parameters from lattice QCD simulations. As described in "Quantum Chromodynamics on the Lattice" by Gattringer and Lang, it seems we should be able to extract the static quark/anti-quark potential by considering the...
Homework Statement
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I'm trying to write a program for caclulating Green's function using Monte Carlo method (Metropolis algorithm) in scalar field theory with a potential λφ4 in 4D. I'm writing it in python.
N_t, N_x, N_y, N_z - total number of lattice sites in each directions.
Field...
Homework Statement
A triangular lattice of lattice spacing ##a=2 ## angstroms is irradiated with x-rays at time zero of wavelength 20 angstroms at an incident angle of ##\alpha =135##.
1) What is the maximum wavelength of the incident x-rays?
2) What is the scattering angle ##\Omega## for...
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...
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...
Hamiltonian of tight binding model in second quantization is given as H = -t \sum_{<i,j>} a_i^{\dagger} a_j
After changing basis it is H = \sum_{\vec{k}} E_{\vec{k}} a_{\vec{k}}^{\dagger} a_{\vec{k}}
where E_{\vec{k}} = -t \sum_{\vec{b}} e^{i \vec{k} \cdot \vec{b}}
where \vec{b} is a nearest...
Hi there, I'm currently working on a relatively simple code to do some lattice simulations. I have access to a computing cluster at school and have been learning how to use OpenMP to parallelize my code (each node has 16 cores). I'm currently not planning to use MPI.
My main question is...
Hello!
When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components
k_x = \displaystyle \frac{\pi}{L_x}p
k_y = \displaystyle \frac{\pi}{L_y}q
k_z = \displaystyle \frac{\pi}{L_z}r...
Hey
could anyone please explain how you go about drawing a reciprocal lattice? For example a 2d rectangular lattice to it's reciprocal form?
Also... I don't know if this is correct but if you have a 2d rectangular lattice with lattice vectors L=n1a1 + n2a2
would the reciprocal lattice...
Hi. What are superconductor ions? Are they naturally occurring ions inside the lattice structure of a superconductor when it's manufactured or are they ions introduced artificially to a superconductor's lattice ? And do the ions have spin?
Hi. I'm wondering if anyone has any info on "quark seeding" like:
Is it possible to dope the crystal lattice of a solid material by replacing electrons with quarks ?
Homework Statement
What is the area of the primitive cell for the lattice shown below? The nearest neighbor separation is "a."
Homework Equations
Here's the lattice we were given on our handout, and I have added the lines to indicate the square lattice (in red), the basis (in purple), and...
I understand that the lattice energy is the energy released when an solid ionic compound forms or it is the energy required to separate completely a mole of a solid ionic compound into its gaseous ions. So is second definition the same thing as vaporizing an ionic compound and so we can...
Peierls distortion states that for a 1 dimensional polymer (like polyacyteline) with lattice spacing a they should have a half-filled conduction band, why?
And how does changing the lattice space to 2a cause it to form an energy gap? In my mind it should be the same as the first case...
A Bloch wave has the following form..
## \Psi_{nk}(r)=e^{ik\cdot r}u_{nk}(r)##
The ##u_{nk}## part is said to be periodic in real space. But what about reciprocal space? I've had a hard time finding a direct answer to this question, but I seem to remember reading somewhere that the entire...
I'm confused as to how the Born-Landé equation can be extrapolated to find the electrostatic potential for an ionic lattice without halving it, as each interaction is otherwise counted twice.
As I understand it, and according to Wikipedia, the electric potential energy in a charge configuration...
I'm reading M. Omar Ali's Elementary Solid State Physics and in it, in Subsection 1.4 The Fourteen Bravais Lattices and the Seven Crystal Systems he says that "..., but one cannot place many such pentagons side by side so that they fit tightly and cover the whole area. In fact, it can be...
Homework Statement
If there are a large number of ions oscillating in a straight line, we can pick the nth one oscillating about its equilibrium a*n. The potential of the entire lattice is then U = 0.5*K[u(an)-u([n+1]a)]^2 - summed over all n. How do I use Force = -dU/du(an) to derive that...
Background information:
The wave function for an electron in a crystal lattice is modeled by a Bloch wave. A Bloch wave is a function with the periodicity of the lattice multiplied times a complex exponential function. This exponential function has a wave vector k, called the crystal momentum...