Research

Selected Research Projects

Current work centered on spin probability currents, interacting quantum systems, and the astrophysical dynamics of supermassive black-hole binaries. My main orientation is quantum theory, with active interest in condensed matter, gravitation/cosmology, and high-energy physics.

One-dimensional cross section of spin and orbital probability currents

Bachelor's Thesis: Spin Probability Currents in Hall Systems and Bose-Einstein Condensates

Bachelor's thesis · 2026

This work studies the physical relevance of spin probability currents, which are often neglected because they do not affect the continuity equation. In the fundamental Hall state, the spin current cancels the orbital contribution and recovers the classical Hall effect.

Focus: interaction-driven breaking of the spin-orbital cancellation in Bose-Einstein condensates.
Methods: Hall-state analysis, condensate modeling, total-current predictions, and comparison with measurable observables.
Output: implications for the Aharonov-Bohm effect, vortex formation, and the threshold magnetic field for vortex generation.

Numerical frame of a supermassive black-hole binary inspiral

Solving the Final Parsec Problem with Self-Interacting Dark Matter

IAC internship · 2026

Theoretical review developed during my IAC internship around the proposal by Alonso-Alvarez et al. that self-interacting dark matter can solve the Final Parsec Problem.

Focus: how a thermalized SIDM core may replenish the dark-matter spike around a supermassive black-hole binary.
Methods: review of the SIDM mechanism, dynamical-friction estimates, and interpretation of CDM spike depletion.
Output: explanation of dynamical friction as the averaged effect of many microscopic gravitational slingshots.

Landau-level diagram for charged quantum states in a magnetic field

From Schrödinger to Dirac: Gauge Invariance, Landau Quantization, and Probability Currents. Minimal Coupling, Gauge Invariance & Landau Levels

Research notes · 2025

How EM fields enter quantum dynamics: canonical → minimal coupling, U(1) gauge transformations, and spectra in uniform fields.

Focus: electromagnetic coupling in non-relativistic and relativistic quantum dynamics.
Methods: gauge transformations, Landau quantization, and probability-current derivations.
Output: structured report connecting minimal coupling to physical spectra and current densities.

Spatial symmetry diagram for conserved quantities in the Pauli equation

Symmetries of the Pauli Equation: Noether Currents and Conservation Laws Spin SU(2), Magnetic Interactions & Conserved Quantities

Research notes · 2025

Spin rotations, Space-time translations, generators/commutators and constants of motion in the Pauli Hamiltonian.

Focus: symmetry structure of the Pauli Hamiltonian and its conserved quantities.
Methods: generators, commutators, Noether-current reasoning, and magnetic-interaction analysis.
Output: report on spin SU(2), spatial symmetries, and conservation laws.

Reports

Selected Reports

Spin Probability Currents

Bachelor's thesis report on spin and orbital probability currents in Hall systems and interacting condensates.

Open report

Final Parsec Problem & SIDM

IAC internship report on SIDM, dynamical friction, dark-matter spike replenishment, and SMBH binary hardening.

Open report

Electromagnetism in Quantum Mechanics

Notes on minimal coupling, gauge invariance, Landau quantization, and probability currents.

Open report

Symmetries of the Pauli Equation

Notes on spin rotations, conserved quantities, Noether currents, and magnetic interactions.

Open report