# Research

In this page, I write some stories of my research experiences and what I purse doing in the near future.

Mostly I am interested in statistical physics and thermodynamics of systems. In the context of theoretical physics, thermodynamics is important because it has survived the two great revolutions: Einstein’s general relativity and quantum mechanics. Therefore, perhaps the laws of thermodynamics have a deep reason for obeying by physical systems.

The main quantity which has an important role in thermodynamics is entropy. The definition of entropy varies depending on the system and scale under study. For example, the Gibbs entropy for the systems with statistical properties, the von-Neumann entropy for the information-theoric systmes, and so on. But all of these entropies have a key property: non-negativity. In other words, there is no any system that tries to violate the second law of thermodynamics: from black holes to nano-scaled systems.

When analyzing such entropies, you must use a variety of tools and methods depending on what system you are working with. Condensed matter physicists are more likely study crystals, lattices and magnetic systems with high-level techniques using symmetries and orders. Also, most fundamnetal laws in particle physics are based on symmetries and their consequences as well. But in constrast, there are crazy magnetic systmes in which they do not respect to any obvious symmetry, for example spin glasses. In this case, spins have quenched random interactions and even they can be long-range. Consequently, most of previous techniques are not going to work with these new models.

So how we can study thermodynamic features of spin glasses? The advent of some statistical physicists (such as G. Parisi) in early 1970’s helped the context of physics to develop new methods and techniques in order to obtain a more rigorous results about validation of the second law and the non-negativity of entropy.

But this is not the end-point. Thermodynamics tell us more than these laws. Mostly we know basic terms of defnition for a phase: just like vapor (gas), liquid, and solid. In magnetic systmes, especially ones that have more complex properties, i.e., spin glasses, the consistency of the number of phases and the transitions between them is an open problem! This problem cannot be solved except by studying the physics of complex systems.

Indeed, my main approach of studying physics is studying thermodynamic properties of disorderd systems in both classical and quantum regimes.