Keywords

foundations of quantum mechanics
entanglement
open systems
decoherence
foundations of statistical mechanics
deformations of algebraic structures
Clifford algebras in electrodynamics
Riemann hypothesis and physics

Research topics

Mathematical aspects of the classical and quantum theoretical physics, in particular: mathematical foundations of quantum mechanics and statistical mechanics; theory of open systems and decoherence; theory of quantum deformations; differential forms and Clifford algebras in classical electro-dynamics; relations between number theory and quantum physics.

Research subjects

Foundations of quantum mechanics: quantum logics, structure of lattices, causal structures and causal logics.

Theory of entanglement and quantum information theory: entanglement of quantum states, measures of entanglement, evolution of entanglement in quantum systems.

Theory of open systems: dynamic semigroups in quantum optics, decoherence, entanglement of open systems, diffusions on manifolds.

Foundations of statistical mechanics: application of methods of functional analysis to precise studies of phase transitions in classical and quantum continuous systems.

Theory of quantum deformations: deformations of classical algebraic structures and Lie algebras.

Differential forms and Clifford algebras in classical electrodynamics: premetric formulation of classical electrodynamics.

Studies on the relation between Riemann hypothesis and quantum mechanics (conjecture of Polya-Hilbert).

Grants

• Research subjects: “Theory of entanglement” and
• “Theory of open systems” are realized in the framework of Polish scientific network: Laboratory of Physical Foundations of information processing.

Top publications

• Ph. Blanchard, R. Olkiewicz, „Decoherence Induced Continous Pointer States”, Phys. Rev. Lett. 90, 010493(2003).
• W. Cegła, J. Florek, „Orthomodular Lattices Generated by Graphs of Functions”, Commun. Math. Phys. 259, 363(2005).
• Ł. Derkacz, L. Jakóbczyk, „Quantum Interference and Evolution of Entanglement in a System of Three-level Atoms”, Phys. Rev. A 74, 032313(2006).
• Ł. Derkacz, L. Jakóbczyk, „Entanglement Versus Etropy for a Class of Mixed Two-Qutrit States“,Phys. Rev. A 76, 042304(2007).
• M. Gorzelańczyk, „Positive Operators in Statistical Mechanics of Continuous Systems”, J. Funct. Anal. 239, 683(2006).
• P. Ługiewicz, R. Olkiewicz, „Classical Properties of Infinite Quantum Systems”, Commun. Math. Phys. 239, 241(2003).
• P. Ługiewicz, B. Zegarliński, „Coercive Inequalities for Hoermander Type Generator in Infinite Dimensions”, J. Funct. Anal. 247, 438(2007).
• M. Mozrzymas, „Tensor Operators and Wigner-Eckart Theorem for the Quantum Superalgebra
• Uq[osp(1| 2)]”, J. Phys. A 37, 9515(2004).
• A. Odlyzko, M. Rubinstein, M. Wolf, „Jumping Champions“, Experimental Mathematics, 8, 107(1999).
• R. Olkiewicz, B. Zegarliński, “Hypercontractivity in Noncommutative Lp Spaces”, J. Funct. Anal. 161, 246(1999).

Collaboration

• Imperial College, London, Great Britain – B. Zegarliński
• Uniwersity of Bielefeld, Germany – Ph. Blanchard
• Uniwersity of Gdańsk, Poland – W.A. Majewski
• Wrocław University of Economics, Poland – J. Florek