fermionische

Fermionische is not a standard English term, but in some German-language or cross-linguistic physics literature it may be used to refer to concepts, models, and phenomena pertaining to fermions—particles with half-integer spin that obey Fermi-Dirac statistics and the Pauli exclusion principle. In English, the corresponding adjective is fermionic. The term can appear in discussions of quantum many-body theory, solid-state physics, and quantum information when the emphasis is on fermionic degrees of freedom.

The core idea behind fermionische concepts is that the quantum states of systems of identical fermions are described by antisymmetric wavefunctions with respect to particle exchange. In the second-quantization formalism, fermions are represented by creation and annihilation operators satisfying anticommutation relations. Exchanging two fermions multiplies the state by minus one, and this antisymmetry enforces the Pauli exclusion principle, which forbids more than one fermion from occupying the same quantum state.

Applications of fermionic models span many areas: electrons in atoms and solids, the physics of ultracold fermionic atoms, neutron stars, and superconductivity in certain limits. In quantum information and simulation, fermionic modes provide a framework for studying many-body dynamics and for mapping fermionic problems onto quantum circuits or classical simulations using Jordan-Wigner or Bravyi-Kitaev transformations.

Fermionische concepts are distinct from other particle statistics such as anyons, which arise in two-dimensional systems and exhibit fractional statistics. Related topics include Fermi-Dirac statistics, the Pauli exclusion principle, and second quantization.