Student seminar topics (for students of University of Ljubljana, Faculty of Mathematics and Physics)

1. Strongly correlated electrons in a small Hubbard cluster
   The goal is to understand how electron repulsion suppresses charge fluctuations and produces magnetic correlations. Exact diagonalization of a two-site model and a small chain, assisted by SNEG, provides a concrete introduction to the physics underlying Mott insulators.

2. From the Cooper-pair box to the transmon
   The goal is to explore how charging energy and Josephson tunnelling determine the quantum states of a superconducting circuit. Numerical diagonalization can show how the spectrum, charge sensitivity, and transition strengths change between the Cooper-pair-box and transmon regimes. Reference.

3. Solving a quantum impurity one energy scale at a time
   The goal is to understand the central idea of Wilson’s numerical renormalization group: resolving successively lower energy scales through iterative diagonalization. The NRG_SIAM examples provide a practical route to studying energy-level flows and the accuracy of numerical approximations.

4. Automating quantum calculations with symbolic algebra
   The goal is to learn how computers manipulate fermionic, bosonic, and spin operators using SNEG. A focused project could automate the derivation of an effective spin Hamiltonian and compare its predictions with exact diagonalization of the original electronic model.

5. Finding signals, drift, and noise in experimental data
   The goal is to learn how spectral analysis, autocorrelation, and Allan deviation distinguish periodic signals, random fluctuations, and slow drift. Using TSRhythms with simulated or measured data, one can determine when averaging improves a measurement and when drift limits its precision.

6. Quantum interference in coupled quantum dots
   The goal is to investigate how interference between electron paths produces asymmetric resonances and can suppress electrical conductance. A simple two-dot model provides an accessible starting point, with electron interactions as a possible extension. Reference.

7. Why does the resistivity of a bad metal keep increasing?
   The goal is to investigate what controls electrical resistivity when the usual picture of long-lived electron quasiparticles becomes unreliable. Using simple spectral functions and the bubble code, one can separate the effects of spectral broadening, finite bandwidth, and thermal occupation.

8. From a single magnetic impurity to a correlated material
   The goal is to understand how dynamical mean-field theory represents a lattice through an impurity embedded in a self-consistent environment. Using DMFT_NRG_KLM, a focused numerical study can follow how changing electron filling modifies the spectrum of a Kondo lattice.

9. Creating atomic jets by shaking a quantum gas
   The goal is to explore how periodic modulation of atomic interactions ejects matter-wave jets from a soliton. A one-dimensional simulation can determine how the jet velocities and emission threshold depend on modulation frequency and amplitude. Reference.

10. Programming precise pulse sequences for quantum experiments
    The goal is to understand how an FPGA coordinates digital signals for experimental control. Using PulsePins, a project could implement a sequence for triggering instruments or controlling external devices, then measure its timing accuracy and synchronization.

11. Fractional powers emerging from a superconducting gap edge
    The goal is to understand why an energy shift can scale as a fractional power of coupling strength, rather than following ordinary perturbation theory. A discrete level coupled to a continuum with a singular density of states provides a simple model for deriving and testing this behaviour. Reference.

12. Electron tunnelling that exchanges energy with its environment
    The goal is to investigate how an electromagnetic environment changes tunnelling by absorbing or supplying energy. Starting with a junction coupled to one oscillator, one can calculate photon-assisted features in the current and examine how they evolve with temperature. Reference.

13. When the Hall coefficient stops counting electrons
    The goal is to examine how Fermi-surface geometry changes the relation between Hall response and carrier density. A two-dimensional tight-binding band allows one to calculate the Hall coefficient across a change in Fermi-surface topology and compare it with the actual electron concentration.

14. Encoding a quantum impurity on qubits
    The goal is to map a small fermionic impurity Hamiltonian onto qubit operators and understand where fermionic exchange signs enter the encoding. A classical quantum-circuit simulator can then test the mapped model and estimate the resources needed for its time evolution.

15. Freezing tunnelling with a periodic drive
    The goal is to investigate how periodic modulation can suppress tunnelling even though the two sites remain coupled. A driven two-site model allows direct time evolution to be compared with an effective Floquet Hamiltonian and reveals where the high-frequency approximation fails.

16. Sound horizons in a flowing quantum gas
    The goal is to explore what happens to a small density disturbance when a condensate flows through a region faster than its local sound speed. Extending a one-dimensional GPE Ljubljana simulation can reveal wave blocking and mode conversion at an acoustic horizon.

17. Direct microwave sampling and the useful side of aliasing
    The goal is to understand how a microwave signal can be digitized through deliberate bandpass sampling and digital frequency conversion. A simulated receiver can establish the roles of Nyquist-zone selection, filtering, and clock jitter, with a possible RFSoC implementation.