Condensed matter is basically chemistry but without reactions: you study a fixed state of matter, not a reaction in which compositions change with time.
Just like in chemistry, you end up getting some very well defined substance properties due to the incredibly large number of atoms.
Just like chemistry, the ultimate goal is to do de-novo computational chemistry to predict those properties.
And just like chemistry, what we can actually is actually very limited in part due to the exponential nature of quantum mechanics.
Also since chemistry involves reactions, chemistry puts a huge focus on liquids and solutions, which is the simplest state of matter to do reactions in.
Condensed matter however can put a lot more emphasis on solids than chemistry, notably because solids are what we generally want in end products, no one likes stuff leaking right?
But it also studies liquids, e.g. notably superfluidity.
One thing condensed matter is particularly obsessed with is the fascinating phenomena of phase transition.
If Ciro had had greater foresight, this might have been what he studied at university!
How are the bands measured experimentally?
Why are there gaps? Why aren't bands infinite? What determines the width of gaps?
- Applications of Quantum Mechanics by David Tong (2017) Chapter 2 "Band Structure"
Ciro Santilli distinctly remembers being taught that at basic electrical engineering school during Ciro Santilli's undergrad studies at the University of São Paulo.
It really allows you to do alternating current calculations much as you'd do DC calculations with resistors, quite poweful. It must have been all the rage in the 1950s.
The basis of 1970-20XX computers, gotta understand them I guess?
- "An introduction to superconductivity" by Alfred Leitner originally published in 1965, source: www.alfredleitner.com/
- Isotope effect on the critical temperature. hyperphysics.phy-astr.gsu.edu/hbase/Solids/coop.html mentions that:
If electrical conduction in mercury were purely electronic, there should be no dependence upon the nuclear masses. This dependence of the critical temperature for superconductivity upon isotopic mass was the first direct evidence for interaction between the electrons and the lattice. This supported the BCS Theory of lattice coupling of electron pairs.
- Actually goes into the equations.Notably, youtu.be/O_zjGYvP4Ps?t=3278 describes extremely briefly an experimental setup that more directly observes pair condensation.
- Cool CNRS video showing the condensed wave function, and mentioning that "every pair moves at the same speed". To change the speed of one pair, you need to change the speed of all others. That's why there's not energy loss.
andor.oxinst.com/learning/view/article/measuring-resistance-of-a-superconducting-sample-with-a-dry-cryostat Not a video, but well done, by Oxford Instruments.
Isn't that awesome!
The dream of course being room temperature and pressure superconductor.
Upside: superconducting above 92K, which is above the 77K of liquid nitrogen, and therefore much much cheaper to obtain and maintain than liquid helium.
Downside: it is brittle, so how do you make wires out of it? Still, can already be used in certain circuits, e.g. high temperature SQUID devices.
Discovered in 1988, the first high-temperature superconductor which did not contain a rare-earth element.
As of 2023 the most important ones economicaly were:
The main application is Magnetic resonance imaging. Both of these are have to be Liquid helium, i.e. they are not "high-temperature superconductor" which is a pain. One big strength they have is that they are metallic, and therefore can made into wires, which is crucial to be able to make electromagnetic coils out of them.
TODO, come on, Internet!
No, see: superconductor I-V curve.
- physics.stackexchange.com/questions/62664/how-can-ohms-law-be-correct-if-superconductors-have-0-resistivity on Physics Stack Exchange
Main theory to explain Type I superconductors very successfully.
TODO can someone please just give the final predictions of BCS, and how they compare to experiments, first of all? Then derive them.
High level concepts:
- the wave functions of pairs of electrons (fermions) get together to form bosons. This is a phase transition effect, thus the specific sudden transition temperature.
- the pairs form a Bose-Einstein condensate
- once this new state is reached, all pairs are somehow entangled into one big wave function, and you so individual lattice imperfections can't move just one single electron off trajectory and make it lose energy
A good summary from Wikipedia by physicist Andrew Whitaker:
at a junction of two superconductors, a current will flow even if there is no drop in voltage; that when there is a voltage drop, the current should oscillate at a frequency related to the drop in voltage; and that there is a dependence on any magnetic field
In 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling (1963, Prediction of the Josephson effect)".
In 1963 Philip W. Anderson and John M. Rowell published their paper that first observed the effect as Section "Possible new effects in superconductive tunnelling (1963, Prediction of the Josephson effect)".
Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:
As part of the course Anderson had introduced the concept of broken symmetry in superconductors. Josephson "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally."
The inaugural that predicted the Josephson effect.
Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.
Paywalled by Elsevier as of 2023 at: www.sciencedirect.com/science/article/abs/pii/0031916362913690
Paywalled by the American Physical Society as of 2023 at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.10.230
TODO understand the graphs in detail.
A reconstruction of their circuit in Ciro's ASCII art circuit diagram notation TODO:
There are not details of the physical construction of course. Reproducibility lol.
By looking at the Josephson equations, we see that a positive constant, then just increases linearly without bound.
Therefore, from the first equation: .
This meas that we can use a Josephson junction as a perfect voltage to frequency converter.
Wikipedia mentions that this frequency is , so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.
Also it is likely not going to be very useful for many practical applications in this mode.
An I-V curve can also be seen at: Figure 7. "Electron microscope image of a Josephson junction its I-V curve".
If you shine microwave radiation on a Josephson junction, it produces a fixed average voltage that depends only on the frequency of the microwave. TODO how is that done more preciesely? How to you produce and inject microwaves into the thing?
It acts therefore as a perfect frequency to voltage converter.
The Wiki page gives the formula: en.wikipedia.org/wiki/Josephson_effect#The_inverse_AC_Josephson_effect You get several sinusoidal harmonics, so the output is not a perfect sine. But the infinite sum of the harmonics has a fixed average voltage value.
And en.wikipedia.org/wiki/Josephson_voltage_standard#Josephson_effect mentions that the effect is independent of the junction material, physical dimension or temperature.
TODO understand how/why it works better.
Two equations derived from first principles by Brian Josephson that characterize the device, somewhat like an I-V curve:
Is a fixed characteristic value of the physical construction of the junction.
A function defined by the second of the Josephson equations plus initial conditions.
It represents an internal state of the junction.
A device that exhibits the Josephson effect.
TODO is there any relationship between this and the Josephson effect?
Experimental observation published as Experimental Evidence for Quantized Flux in Superconducting Cylinders.
This appears to happen to any superconducting loop, because the superconducting wave function has to be continuous.
Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43
The first published experimental observation of the magnetic flux quantum.
The paper that follows it in the journal is also of interest, "Theoretical Considerations Concerning Quantized Magnetic Flux In Superconducting Cylinders" by N. Byers and C. N. Yang, it starts:
In a recent experiment, the magnetic flux through a superconducting ring has been found to be quantized in units of ch/2e. Quantization in twice this unit has been briefly discussed by London' and by Onsager. ' Onsager' has also considered the possibility of quantization in units ch/2e due to pairs of electrons forming quasi-bosons.So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.
Dumping the fitures at: archive.org/details/experimental-evidence-for-quantized-flux-in-superconducting-cylinders One day we can also dump the paper scans when it goes into the public domain in 2056! Public domain scientific paper by year.
The inverse of the magnetic flux quantum.
The most practical/precise volt standard.
It motivated the definition of the ampere in the 2019 redefinition of the SI base units
Quick NIST article about it: www.nist.gov/news-events/news/2013/04/primary-voltage-standard-whole-world (archive)
Can be used as a very precise magnetometer.
Two parallel Josephson junctions.
In Ciro's ASCII art circuit diagram notation:
| +-+-+ | | X X | | +-+-+ |
TODO WTF is this? How is it built? What is special about it?
Mentioned a lot in the context of superconducting quantum computers, e.g. youtu.be/t5nxusm_Umk?t=268 from Video "Quantum Computing with Superconducting Qubits by Alexandre Blais (2012)",
www.youtube.com/watch?v=PbuiIhr0LVA 7 Different Types of Plastic and Their Uses by Orange Plastics Academy (2018) Does not mention packaging foams.
The wiki comments: en.wikipedia.org/w/index.php?title=Ferromagnetism&oldid=965600553#Explanation
The Bohr–van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.
Each point in the lattice has two possible states: TODO insert image.
As mentioned at: stanford.edu/~jeffjar/statmech/intro4.html some systems which can be seen as modelled by it include:
- the spins direction (up or down) of atoms in a magnet, which can undergo phase transitions depending on temperature as that characterized by the Curie temperature and an externally applied magnetic fieldNeighboring spins like to align, which lowers the total system energy.
- the type of atom at a lattice point in a 2-metal alloy, e.g. Fe-C (e.g. steel). TODO: intuition for the neighbour interaction? What likes to be with what? And aren't different phases in different crystal structures?
Also has some funky relations to renormalization TODO.
TODO what it means to solve an Ising model in general?
A tiny idealized magnet! It is a very good model if you have a small strong magnet interacting with objects that are far away, notably other magnetic dipoles or a constant magnetic field.
The intuition for the name is likely that "dipole" means "both poles are on the same spot".
Applications: produce high magnetic fields for
As of the early 2020s, superconducting magnets predominantly use low temperature superconductors Nb-Ti and Nb-Sn, see also most important superconductor materials, but there were efforts underway to create practical high-temperature superconductor-based magnets as well: Section "High temperature superconductor superconducting magnet (HTS magnet)".
- Magnetic resonance imaging, the most important commercial application as of the early 2020s
- more researchy applications as of the early 2020s:
Wikipedia has done well for once:
The current to the coil windings is provided by a high current, very low voltage DC power supply, since in steady state the only voltage across the magnet is due to the resistance of the feeder wires. Any change to the current through the magnet must be done very slowly, first because electrically the magnet is a large inductor and an abrupt current change will result in a large voltage spike across the windings, and more importantly because fast changes in current can cause eddy currents and mechanical stresses in the windings that can precipitate a quench (see below). So the power supply is usually microprocessor-controlled, programmed to accomplish current changes gradually, in gentle ramps. It usually takes several minutes to energize or de-energize a laboratory-sized magnet.
They became a major supplier for Magnetic resonance imaging applications.
Used to explain the black-body radiation experiment.
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of speciﬁc bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
TODO how can it be derived from theoretical principles alone? There is one derivation at; en.wikipedia.org/wiki/Planck%27s_law#Derivation but it does not seem to mention the Schrödinger equation at all.
- The Quantum Story by Jim Baggott (2011) page 10 mentions:
Early examples of such cavities included rather expensive closed cylinders made from porcelain and platinum.and the footnote comments:
The study of cavity radiation was not just about establishing theoretical principles, however. It was also of interest to the German Bureau of Standards as a reference for rating electric lamps.
- 1859-60 Gustav Kirchhoff demonstrated that the ratio of emitted to absorbed energy depends only on the frequency of the radiation and the temperature inside the cavity
- 1896 Wien approximation seems to explain existing curves well
- 1900 expriments by Otto Lummer and Ernst Pringsheim show Wien approximation is bad for lower frequencies
- 1900-10-07 Heinrich Rubens visits Planck in Planck's villa in the Berlin suburb of Grünewald and informs him about new experimental he and Ferdinand Kurlbaum obtained, still showing that Wien approximation is bad
- 1900 Planck's law matches Lummer and Pringsheim's experiments well. Planck forced to make the "desperate" postulate that energy is exchanged in quantized lumps. Not clear that light itself is quantized however, he thinks it might be something to do with allowed vibration modes of the atoms of the cavity rather.
- 1900 Rayleigh-Jeans law derived from classical first principles matches Planck's law for low frequencies, but diverges at higher frequencies.
Observation that all solids appear to have the same constant heat capacity per mole.
It can be seen as the limit case of an Einstein solid at high temperatures. At lower temperatures, the heat capacity depends on temperature.
Wikipedia mentions that it is completely analogous to Planck's law, since both are
The key advantages of lasers over other light sources are:
- it emits a very narrow range of frequencies (small linewidth), which for many purposes can be considered a single frequencyIt does however have a small range of frequencies. The smaller the range, the better the laser quality.
- it can be efficient collimated, while still emitting a lot of output power: Section "Why can't you collimate incoherent light as well as a laser?"
- can be phase and polarization coherent, though it is not always the case? TODO.
You could put an LED in a cavity with a thin long hole but then, most rays, which are not aligned with the hole, will just bounce inside forever producing heat.
So you would have a very hot device, and very little efficiency on the light output. This heat might also behave like a black-body radiation source, so you would not have a single frequency.
The opposite of elementary particle.
As a phisicist once amazingly put it in a talk Ciro watched:
It all depends on how much energy you have to probe nature with. Previously, we thought protons were elementary particles. But then we used more energy and found that they aren't.If some alien race had even less energy, they might not know about electrons at all, and could think that anyons are actually elementary.Being an "elementary particle" is always a possibly temporary label.
- When condensed matter physics became king by Joseph D. Martin (2019): physicstoday.scitation.org/doi/10.1063/PT.3.4110
- www.youtube.com/watch?v=RImqF8z91fU&list=PLtTPtV8SRcxi91n9Mni2xcQX4KhjX91xp Solid State Physics" course by Sergey Frolov taught at the University of Pittsburgh in the Fall 2015 semester
Affiliation: University of São Paulo.