Quantum Machine Learning
In dealing with NP hard problems which posses extremely rough "energy" landscapes, ordinary machine learning techniques such as gradient descent and linear regression can be very inefficient as they tend to get stuck in local minima. Powerful physics-inspired solvers such as PT, SA and SQA are then used to alleviate this shortcoming. Potential quantum computers like D-wave are used to examine quantum advantage in machine learning application.
Physics of Spin Glasses
Disordered and frustrated systems such as spin glasses and electron glasses are among well studied yet less understood problems in the context of statistical mechanics. Frustration leads to enormous complexity of the phase space of such systems,. Hence their study of calls for novel analytical methods such as the Parisi replica technique as well as advanced numerical algorithms like Parallel Tempering (PT), Population Annealing (PA) .
Quantum Enhanced Qptimization
The rapid progress in the filed of quantum computing in recent years prompted the need for demonstrating "quantum advantage" over classical computers. This requires on one hand designing in particular optimization problems that are small in scale yet hard enough for the state of art classical solvers and on the other hand developing better classical algorithms inspired by quantum mechanics.
Nonlinear Dynamics and Chaos
The dynamics of many complex physical systems like atmosphere and non-laminar fluids exhibit nonlinear behaviors such as period doubling and extreme sensitivity to initial conditions. Using the techniques of the chaos theory like time series and Lyapunov exponents, one can tune the parameters of the model in a way that chaotic regions are avoided and the system operates in a predictable fashion.
QCD is an elegant theory that describes the physics of strong force on a group theoretical ground. The SU(3) gauge theory governs the dynamics of quarks and gluons which leads to the interesting phenomenon of asymptotic freedom meaning that at low energy the subatomic material is strongly binding where perturbative methods cannot be utilized. Many features of QCD such as axial anomaly and color confinement can be studied using effective theories of QCD.
Almost 100 years after Einstein introduced the general theory of relativity, new features are still found in this theory. Physics of black holes in particular is of great significance as it is closely related to many other areas of high energy physics such as gauge/gravity duality as well as information theory. The search for the ultimate theory of quantum gravity is still at its infancy. Numerous challenges such as non-renormalizablity, the problem of time and background dependency plague the development of QG.