#PhysicsFactlet: The "Ashcroft/Mermin Project"
I will try to (likely very slowly) go through the classic textbook "Solid State Physics" by Ashcroft and Mermin and make one or more animation/visualization per chapter.
This will (hopefully) help people digest the topic and/or be useful to lecturers who are teaching about it. As with all my animations, feel free to use them.
The idea is that the animations are a companion to the book, so I will give only very brief explanations here.
#PhysicsFactlet: The "Ashcroft/Mermin Project"
Chapter 1: The Drude Theory of metals
Electrons in a metal are accelerated by an electric field, but they keep bouncing on the metal defects/impurities. The resulting diffusion-like motion produces a roughly steady current.
#PhysicsFactlet: The "Ashcroft/Mermin Project"
Chapter 2: Sommerfeld model
Electrons in a metal can be approximated as a Fermi gas, where only one electron can occupy a given state. At low temperature most of them are difficult to excite, because there is no free state available.
#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices
A Bravais lattice is an infinite array of points generated by discrete translations, so that every point can be written as a (integral) linear combination of the basis vectors.
#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices
The "Wigner-Seitz" primitive cell is the region of space that is closer to a given point in the lattice. It has the advantage of being a primitive cell with the same symmetries as the Bravais lattice.
#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices
Once we have the Bravais lattice, we can fully describe a crystal structure by specifying how the atoms are arranged around the lattice points (i.e. the "basis").
Not a #PhysicsFactlet, but a full beginner-friendly tutorial on how to use speckle correlations for imaging through a scattering medium, complete with a step-by-step guide on how to set up your first experiment and analyse the data: https://arxiv.org/abs/2404.14088
Through the years I made a LOT of scientific visualizations (#PhysicsFactlet), and lately I ran out of steam.
To get some motivation back I decided to go through a standard undergrad Physics textbook and try to create as many visualizations as I can for it.
Should I go for:
#PhysicsFactlet
Common misunderstanding about #Entropy: the two configurations below have exactly the same entropy, and in both cases the entropy is zero (as you know exactly where each dot is, so there is only one possible microstate they can be in).
#PhysicsFactlet
A quantum simple pendulum.
The pendulum position is spread out, with opacity here being proportional to the probability that the pendulum is at that position at a given time. The average position of the quantum dynamics is the same as the classical pendulum dynamics (Ehrenfest theorem).
Technicalities: I used the Crank-Nicholson method to evolve the system in time. This is a 1D problem, and the only variable I considered was the angle, with the initial state being a Gaussian.
#PhysicsFactlet
The Lorenz system is a common example of chaotic dynamics and of a strange attractor.
Points with very similar initial conditions initially evolve very similarly to each other, until their trajectories diverge from each other, and start moving on a "butterfly"-shaped fractal. #Physics#Chaos
#PhysicsFactlet
A microscope makes an image bigger than the object, i.e. it magnifies it. A telescope makes an image smaller than the object, i.e. it demagnifies it.
Which is good because you want your image of a star to be smaller than a star 🙃 #Optics#ITeachPhysics
#PhysicsFactlet
In the limit of small oscillations, a simple pendulum is isochronous, meaning that its period doesn't depend on how wide the oscillations are.
Once the oscillations get too big, the period starts growing, until they stop looking sinusoidal altogether. #ITeachPhysics#Physics
#PhysicsFactlet
If you sample N points uniformly on the unit sphere, take for each the halfway point to the north pole of the sphere, and then project is on the x-y plane, you obtain N points sampled uniformly on the unit disk.
#PhysicsFactlet:
Signals (e.g. light) move at a finite speed, so there is a time lag between when they are emitted and when they are detected. If the source is moving, the detector will "see" the signal that was emitted at a previous time, not the signal that is being emitted right now, and this time lag can change with time in a complicated way.
(Notice that, as the source is always moving slower than the signal, the detector sees the signals in the same order they were emitted.) #Physics#ITeachPhysics#Electrodynamics#Optics#Relativity
"The Royal Swedish Academy of Sciences has decided to award the 2023 #NobelPrize in Physics to Pierre Agostini, Ferenc Krausz and Anne L’Huillier “for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter.” " https://www.nobelprize.org/prizes/physics/2023/summary/
This year #NobelPrize in #Physics has been awarded for the work done in generating attosecond laser pulses, and their use to study electron dynamics.
Let me try to give you a lay-person explanation of what that means and why anybody should care.
Imagine you have a box containing a pendulum. You can't see inside, but you can both push the pendulum, and measure how it makes the box shake. Your goal is to find out what the properties of the pendulum are. If you could open the box you could just measure how heavy and long the pendulum is, and you would have mostly everything you need, but you can't. You can push the pendulum, but how should you push it to be able to gain any information?
The pendulum is a relatively simple object, and if left to its own device what it likes to do is to oscillate. If nobody touches it, it will stay still at its rest position, but if you push it, it will start oscillating, and it will tend to oscillate at its own "natural frequency", which define a preferred time scale for the pendulum: its period (the fact that a pendulum likes to always oscillate with its own period is why we can use them as clocks).
If we push the pendulum too slowly, we won't ever see this oscillation, as the pendulum will just follow your push. So we have to push it quickly (ideally a "kick"), let it oscillate how it likes to oscillate, measure how the box is shaking due to this oscillation, and we are done.
For a normal pendulum this is easy to do, but what if we want to measure something smaller and faster?
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#PhysicsFactlet
Most optical media can be approximated as a collection of dipoles which, when excited by an external field, will oscillate and radiate.
Usually they will oscillate independently from each other, with the total radiated power increasing linearly with the number of dipoles.
But if they all oscillate in phase the emission will interfere constructively, with the total radiated power increasing quadratically with the number of dipoles (superradiance).
Conversely, if they oscillate out of phase the emission will interfere destructively (subradiance). #Physics#Optics#QuantumMechanics#AtomicPhysics
Just made this (as a variation on an old animation) for a talk, so why not show it here?
(hand-coded) finite element simulation of a pulse hitting a disordered medium and being scattered around. #PhysicsFactlet#ITeachPhysics#Physics#Optics
#PhysicsFactlet
In the past I have made a number of threads on Xwitter giving brief explanations of bits of Physics. I now need a less volatile place where to keep them, so I started to copy-paste them into my personal page. I assume it will take me forever to transfer even just a small part of them, but here is a starting point: https://jacopobertolotti.com/LagrangianIntro.html
#PhysicsFactlet
Does a chaotic system always behave chaotically?
Not really, as many chaotic systems have a subset of possible initial conditions that lead to a quasi-periodic motion.
As an example, below are two sets (black and orange) of 20 double pendula each, all with the same initial energy, and each group starting with very similar initial conditions.
The first group (black) spread out a little bit with time, but nearby initial conditions keeps evolving into nearby dynamics, which is typical of integrable systems.
On the other hand the pendula in the second group (orange) also starts with similar initial condition, but after a short transient evolve each very differently from each other, which is a mark of a chaotic system. #Physics#Visualization#Chaos
#PhysicsFactlet
Can shadows move faster than light?
Not really. There is nothing moving sideways, so nothing is moving faster than light (which, incidentally, mean you can't use shadows to communicate faster than light).
But the edges of the projection of the shadow can indeed appear to move arbitrarily fast. #ITeachPhysics#Visualization#Physics#Optics
#PhysicsFactlet
Magnetic hysteresis: In a ferromagnet the equilibrium configuration is with all magnetic moments aligned with each other. If we want to flip them, we need to flip all of them at the same time, which requires a stronger field than if the moments were independent, resulting in the characteristic hysteresis loop.
(Simulation done by numerically solve the Landau–Lifshitz equation with a tiny bit of noise added to speed the process up on a square grid of magnetic moment with periodic boundary conditions.)