Teaching
Statistical Physics
Grading:
Final grades will be determined as: 40% Final Exam, 30% Midterm Exam, 30% Homework.
The course is awarded with the "NSYSU Excellent Teaching Award".
Description of the course for the prospective students:
Statistical Mechanics is the art of translating microscopic laws to macroscopic ones in order to understand nature from the macroscopic point of view.
In other words, Statistical Mechanics can be thought of as a dictionary between microscopic and macroscopic laws.
A simple example: Consider a box of ~10^23 particles with known properties and interactions under certain external conditions. How can we describe the physics in the box?
A way to answer this question would be to solve Schrödinger's equation for all the particles to find the corresponding wavefunctions (microscopic approach). This is computationally impossible. Even if we suppose we could do it we will still get a limited amount of information. For example, we would not directly know about the temperature of the gas, the color, or the pressure. To understand the physics in the box we use the methods of Statistical Mechanics, we apply statistical methods and probability theory to this large ensemble of particles.
Statistical Mechanics have a tremendously wide applicability. Some of the topics we will discuss in-depth and derive the required formalism to understand them in this course are:
What is the concept of temperature and how we define it?
What is the concept of entropy and how it is related to the arrow of time?
What is the relation between volume, pressure, and temperature in a gas? (Gas laws)
How much energy a hot object emits? (~Stefan-Boltzmann's law)
How much energy do you need to heat up an object? (~Dulong-Petit law)
What color is a hot object? (~Wien's displacement law)
Bonus-related question: Why the construction safety vests are all of the same yellow color?What is the Cosmic Microwave Background radiation?
Why paramagnetic materials when heated lose their properties? (~Curie's law)
Related question: Why magnets when heated above a critical temperature lose their magnetization? ( Curie Temperature)What is a phase transition in a physical system and when it occurs? (~Spin Lattice Models, Renormalization Group, Fixed Points)
How do the energy-based Neural Networks in Machine Learning work? (~Boltzmann Machines)
What is the Bose-Einstein Condensate state of matter and how is it formed? (~Bose-Einstein Statistics)
What is a white dwarf and why it exists? (~Fermi-Dirac Statistics)
Electromagnetism
Grading:
Final grades will be determined as: 40% Final Exam, 30% Midterm Exam, 30% Homework.
Description of the course for the prospective students:
In nature, there are four fundamental forces: the strong (binding nuclei together), the electromagnetic, the weak(radioactivity), and the gravitational. The electromagnetic and the gravitational are the forces we experience more often in our everyday lives. In fact, electromagnetic interactions are responsible for giving us the ability to observe anything around us through light propagation and its interactions. Electromagnetism plays a major role in technology and most of the natural phenomena we observe in everyday life. Moreover, the theory itself is elegant from the theoretical point of view and a necessary tool to understand nature. Understanding the electromagnetic theory, its structure, and its principles, is an essential groundwork for understanding the other forces.
Electro-magnetism is an example of "unification" of physical theories. Electricity and magnetism are two aspects of a single theory. Create an electric current(electricity) and bring close to it a magnetic compass(magnetism); you will notice that the magnetic compass needle is deflected. Alternatively, moving magnets generate electricity. Electricity and magnetism are therefore intertwined.
As a result, the equations that describe the theory should include both the electric and magnetic fields, so as to explain phenomena we just described. The equations that give a full description of the theory of electromagnetism are known as Maxwell equations. These are four coupled partial differential elegant equations of vectors, that describe the properties of the flows of the electric and magnetic fields respectively, and how the (time-dependent) magnetic and electric fields affect each other. To put it simply, any natural electromagnetic phenomenon can be understood by solving Maxwell's equations irrespective of how complicated it is.
Nevertheless, solving the Maxwell equations can be a very demanding task. We need to understand the mathematical beauty of these equations and how the symmetries can be used in order to simplify the equations and obtain solutions.
The purpose of this course is to introduce and study in-depth everything about Maxwell's equations. We will discuss why these equations fully describe electromagnetism, we will understand their geometric meaning, and we will learn how to take advantage of the symmetries in order to obtain their analytic solutions.