1. Physics of solitons

• Theoretical studies on the influence of curvature of long and large-area Josephson Junctions on the dynamics of the fluxion and the creation of fluxions during the transition to the superconducting phase.
  Research project No. 2011/03/B/ST3/00448 NCN “Fluxion dynamics in a curved Josephson junction. ”
  (Project Manager : Tomasz Dobrowolski) read more…
• Topological defect production in spatially inhomogenous systems during second order phase transitions (in the context of phase transitions in condensed matter systems).Realized within the framework of the European Science Foundation in the international research program: “COSLAB – Cosmology in the Laboratory.”
• Creation of extended topological defects at early stages of evolution of the Universe.
• Applications of the geodesic deviation equation to testing sensitivity to initial conditions in Hamiltonian systems.

2. Theory of solid state physics

• Electronic structure of transition metal compounds of iron, lanthanides and uranium groups.
• Magnetism of transition-metal (iron, lanthanides and uranium) compounds.
• Strongly correlated electron systems.
• Physics of heavy-fermion intermetallics.
• Theory of magnetism and physics of low-dimensional systems.
• Theoretical description of the magnetic and electronic properties of transition metal compounds with 3d, 4f, 5f atoms.
• Explanation of the magnetic and electronic properties of 3d / 4f / 5f compounds in connection with the low-energy electron structure of paramagnetic ions.
• Multi-electron states of the paramagnetic atom in a solid in comparison to a free atom.
• The influence of relativistic effects on the electronic structure of 3d / 4f / 5f compounds.

Description of compounds at the atomic scale:
uranides (5f): UPd₂Al₃, Npd₂Al₃, UGa₂, NpGa₂
lanthanides (4f): ErNi₅, Ho₂Co₁₇, Nd₂Fe₁₄B, YbRh₂Si₂, PrO₂, PrRu₂Si₂, Dy₂Co₁₇, Nd₂CuO₄, Cs₂AgF₄, DyNi₅
3d compounds (3d): LaCoO₃, NiO, FeBr₂, FeO, Na₂V₃O₇, CoO, CoF₃

Scientific achievements:
Formulation of the Quantum Atomistic Solid-State Theory (QUASST) (worked out in times when the crystal field and the discrete electronic structure was very unpopular).
Eksperymetal and theoretical confirmation of the existence of discrete electronic structure in 3d oxides (LaCoO₃, NiO, FeO, CoO).
Physical importance of the crystal field and spin-orbit interactions in transition-metal compounds.
Original theory of heavy-fermion compounds (YbRh₂Si₂, UPd₂Al₃).

3. The theory of gravity

• The application of the Sikorski’s differential structures in the theory of singularities in the General Theory of Relativity.
• Application of soliton theory in chiral models and general relativity.
• Studies of the properties of cosmological models.
• Nonsymmetric gravity theory.
• Study of chronological structures.
• Geometric methods in studies of the stability of motion and chaos. Applications of the geodesic deviation equation to testing sensitivity to initial conditions in Hamiltonian systems.

4. Didactics of Physics

• Eyetracking in Research on Physics Education.
• Mobile technologies in science education.
• Neurodidactical approach to research on science education.