start date: any time (but see the prereqs below)
duration: approx. one year (with an option to continue)
location: Faculty of Physics, Sofia University, 5 James Bourchier Blvd, 1164 Sofia, Bulgaria (EU)
advisor: Marin Bukov, PhD
Motivated bachelor and master students (including visiting and Erasmus students) are encouraged to inquire about possibilities to participate in the research projects of the group by sending an email to mgbukov(AT)phys.unisofia.bg. Research projects will naturally lead to a bachelor or master thesis, and may result in publications in peerreviewed journals. We have both analytical and numerical projects, depending on the student’s interest, but most projects involve a mixture of both to a certain extent. Students are encouraged to check out previous research projects and the corresponding publications to get an idea about possible topics of research; we particuarly encourage students to suggest their own research projects within the research interests of the group. Motivated students are welcome to start working on a project any time during their studies (no need to wait until the last semester).
Master Research Prerequisites
Deep understanding in one or more of the following topics, plus excellent understanding of the bachelor research prereqs^{1}. We are happy to provide students with reading materials, in case they need to refresh their knowledge.
 quantum manybody systems: Bogoliubov theory, BCS theory, quantum Ising and Heisenberg models, Hubbard models
 quantum simulators: ultracold atoms, Rydberg atoms, trapped ions, superconducting qubits, NV centers, etc.
 quantum computing: quantum gates, digital and analog quantum computing, Qiskit library, etc.
 condensed matter theory: band structure, acoustic and optical phonons, magnetism, condensed matter/statistical field theory (Green’s functions, Dyson equation, self energy, Feynman diagrams, Renormalization group, etc.)
 nonequilibrium dynamics: quantum quenches, periodically driven (Floquet) systems, eigenstate thermalization hypothesis, random matrix theory, equilibration and thermalization, Anderson and manybody localization, etc.
 computational physics: exact diagonalization, variational Monte Carlo, matrix product states, DMRG, etc.
 machine learning: unsupervised learning, reinforcement learning
Bachelor Research Prerequisites
Deep understanding of at least one of the three basic physics courses. We are happy to provide students with reading materials, in case they would like to refresh their knowledge.
 theoretical mechanics: coupled linear and nonlinear oscillators, Hamiltonian and Lagrangian formalism, phase space, Liouville’s theorem, etc.
 quantum mechanics: twolevel system, quantum harmonic oscillator, creation and annihilation operators, hydrogen atom, timedependent and timeindependent perturbation theory, angular momentum and spin, quantum entanglement, adiabatic theorem
 statistical mechanics: ensemble theory, partition functions, free energy, classical Ising model, phase transitions and critical phenomena
Suggestions for Bachelor Thesis Topics:
1) Symmetry breaking in correlated optimization landscapes (quantum mechanics)
Symmetrybreaking is a fundamental phenomenon which occurs across phyics: from condensedmatter systems to quantum field theory. Recently, it was discovered that symemtry breaking also occurs in the control landscapes, although it remains unclear what triggers it in this case. The goal of this project is to construct a toy model for the symemtrybreaking transition known from twoqubit control.
2) Fundamental nature of control phase transitions (statistical mechanics)
In much the same way phases of matter determine the properties of solidstate materials and quantum matter, control phases are believed to contain information about the properties of control problems (quantum and classical). The goal of this project is to determine whether control phase transitions are intrinsically equilibrium or nonequilibrium.
3) Control Phase Transitions in Classical ManyBody Systems (classical mechanics)
Control phase transitions were first established in quantum systems. However, they also exist in classical models. This project aims at studying the control properties of the classical XYmodel.

Math, Computer Science, and Chemistry majors are also welcome to join the group, but be prepared to work hard to catch up with the physics material. ↩