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Many Body Physics

# The Hitchhiker’s Guide to Many Body Physics

Science can be sometimes daunting for the unexperienced. Have you ever seen a scientific talk, or read a paper? There tends to be a lot of jargon flying around, circling the speaker to then buzz aggressively around the audience before it goes out the windows into the oblivion of the coffee break. This is our guide help you wizz through the jargon-jungle.

Scientific jargon is a necessary evil for us.

It allows us to focus a lot of meaning into a short word, and to be able to convey these meanings quickly to our peers. Imagine if we had to describe every formula and result every time. A lot of scientists, including Newton, had to do this due to a lack of good mathematical jargon. However, if we want to communicate science out of the cluster, it can become a bit cumbersome, and jargon will show us its other — evil and confusing — face. But don’t worry, this is why we have compiled here our 100% jargon-free explanations for several concepts fundamental for physics, with a focus on our favourite part, many body physics.

(Words you can find in the dictionary are bold).

Charge. For this entry you probably have already an intuition. You remember charge from electromagnetic scenarios, right? That intrinsic property of matter which differentiates between two otherwise equal ones, and tells them if they attract — or repel — each other. Well, in physics, it is a more general concept, related to the mathematical virtues of the underlying microscopic theory. Charges don’t need to be positive and negative, and for example, in the theory of nuclear interactions, three different kind of charges (not two) are needed to create a neutral system.

Condensed Matter Physics. This is the field of study where people take lots of the basic constituents studied in particle physics and look at how one can describe the properties of the resulting blobs of stuff. These blobs can be pieces of solid, magnets, polymers, you name it! And we can calculate them directly from the microscopic interaction between the fundamental constituents (also see microscopic theory). Interestingly, a lot of unexpected things happen when doing that due to the phenomenon of emergence.

Emergence. The phenomenon that when you put together lots of the same which you think you know very well and as a result something totally unexpected and different happens. For example, take lots of carbon atoms, some water molecules and, if you do it exactly right, you can create a human. While this is a quite extreme example, in many body physics this can be understood on a fundamental level and is truly what makes this field of study interesting and exciting. If you only want to read one scientific paper in your life, then make it this one: Phil Anderson’s beautiful description of emergence in “More is different”.

Energy. It is the quantity that measures how hard it is for a system to perform a movement, or physical process. In the case of kinetic energy — the energy of movement — it measures how much effort you make to stop the object. In the case of potential energy — the energy of eventuality — it measures the amount of movement you can get if freed from those constraints.

Interactions. In any model or theory of the real world, you need to know how the pieces of your system talk to each other, or interact. The way you can write the formulas describing your system down depends a lot on the system and framework, but there should always be parts describing these interactions. Normally, these will be mediated by one or more quantities which determine the interaction strength. These are called couplings. Electricity’s couplings are (electric) charges and Newtonian Gravity is mediated by masses.

Kinetic Theory. A framework were the fundamental components of the system are taken to behave like billiard balls. That is little points that bounce or scatter from each other, or, in other words, quasiparticles (find out more about them in next week’s blog post!). How they bounce from each other has to be established from an underlying microscopic theory.

Many Body Problem. A to solve a physical problem, you need to know two things: the number and identity of its smallest pieces, and the rules that apply to their interactions. So once you know that you are set, right? Not really. This may be true for a couple of particles, like the sun and the earth (while ignoring the other planets), but for more things involved, the mathematics of the problem can and will get very, very hairy. This problem, with the accusing tone of hardness and solving impossibility gets then a new name, a Many Body problem (check out our following posts to see how can we fix this problem).

Microscopic Theory. Imagine you have a system which has a set of rules. Then, you find out that those rules actually came from how the smallest pieces of the system behave. This second set of rules defines the microscopic theory of the first one. For example, electromagnetism and quantum mechanics are the microscopic theory of chemistry. Kinetic theory is the microscopic theory of fluid mechanics. In that sense, psychology is the microscopic theory of the social sciences. How the “bigger picture” arises from the microscopic theory is what we call emergence.

Momentum. It is the amount of inertia something carries. That means that the more momentum, the harder it is to stop it. For a single particle it is given by its speed and its mass. The more of any of those two ingredients, the harder it is to stop it.

Particle Physics. The study of the most fundamental quantities we know of, point particles. There is a whole zoo of particles inside the standard model of particle physics, which describes all matter around us in terms of these fundamental particles and four forces, which mediate interactions between them. One example for such a particle is the electron, the forces are electromagnetism, the weak and strong nuclear force (we will describe those at some point) and gravitation.

Point particle. A point particle is an object which has no spatial extent, regardless of any other physical context or properties. So, basically, a dot. It may be a green dot, or a red dot, or even a charged dot, but it has still got to be a dot. This is a good approximation for the fundamental particles like electrons or the now famous Higgs Boson. They can behave classically — like tiny billiard balls — or quantumly (See Quantum Mechanics below) depending on the context.

Quantum Field Theories. The generalization of Quantum Mechanics for objects which do have spatial extent. These are called Quantum Fields. The rules of Quantum Mechanics apply, like Heisenberg’s Principle. In Quantum Field Theory, point particles are nothing else than excitations of a quantum field (imagine the field being the surface of a pond — a particle would be the excitation you create by throwing a stone into the pond).

Quantum Mechanics. This is the funny way in which particles behave at very small scales. It means particles start behaving like waves. This means they can interfere with each other without having to crash like billiard balls. Sort of what waves do in a pond when you throw two stones at the same time. Quantum Mechanics also means that some quantities can’t be measured to arbitrary precision at the same time. This is called Heisenberg’s Uncertainty Principle. So, what does that mean? For example, the better we know where an electron is, the less we can know its speed (and you can’t make this better by buying a better speed-o-meter)!

Scattering. Imagine two point particles which are freely moving around, but steadily approach each other. At some point, they are going to feel the presence of each other and interact, changing the course of movement of each other. In many body physics jargon, they have scattered. The simplest example would be two billiard balls hitting each other. On a fundamental level, this scattering has to happen via exchange of a force carrier. For example, two electrons scatter by exchanging a photon, the base constituent of light and the force carrier of the electromagnetic force.

Temperature. You probably have some sense or another for what temperature is. Something which measures how “cold” or “hot” something is. But what does this mean on a microscopic level? One picture is the one given below — it is a measure for how quickly the particles in a gas move on average. In a solid, particles can of course not move, so there it is a measure for how quickly the atoms wiggle around their normal position. There is an absolute zero for temperature in this way to view it — when particles don’t move, temperature is zero. But there are actually systems in which temperature can become negative! If you want to find out more about it, readthis excellent FAQ from the people who have actually realized negative temperatures in experiment. Moreover, there are circumstances in which temperature is not even a usefull notion! This is exactly the case if there is no thermal equilibrium (and we will come back to what exciting things happen then in the future).

(Thermal) equilibrium. Strictly speaking, thermal equilibrium simply means that we can assign a temperature to something. More usefully, it means that there are no macroscopic differences between different parts of a system/material. Equilibrium also means that nothing changes over time. Everything just stays as it is. Quite importantly, all of these notions only deal with the macroscopic properties of a material. Microscopically, there is of course a lot of movement going on, for example in the air around you the oxygen molecules move around like crazy! But the law of large numbers means that the fluctuations between different parts and over time are negligibly small and so we can describe the whole thing as one bulk. The miracle of statistical physics is that we can then forget about all those gazillions of particles and their complicated interactions and describe the gas with just a handful of numbers such as temperature and pressure. Thermodynamics (the part of physics dealing with thermal equilibrium) is therefore a classic example as an emergent theory and statistical physics (the part of physics dealing with many particles) is its microscopic theory.

This post originally appeared on manybodyphysics.com, our new blog revolving around everything involving the science of many (quantum) things interacting with each other.

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## More from Many Body Physics

We are three enthusiastic young researchers trying to spread our fascination for the strange phenomena of interacting quantum matter into the world. Our second shared feat is a hobbyist’s interest in the Arts of different denominations. This project is about marrying those two.

## Alex Schuckert

Trying to make sense of quantum physics with the help of green tea.