The spectrum of the Liouville–von Neumann operator in the Hilbert–Schmidt space
Copyright policy )The spectrum of the Liouville–von Neumann operator in the Hilbert–Schmidt space
The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.
- Angel Kanchev University of Ruse Bulgaria
- Wrocław University of Science and Technology Poland
- Vrije Universiteit Brussel Belgium
- Lomonosov Moscow State University Russian Federation
absolutely continuous spectrum, singular continuous spectrum, Liouvillian, Quantum dynamics and nonequilibrium statistical mechanics (general), Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), Spectrum, resolvent, Applications of operator theory in statistical physics, point spectrum, Hamiltonian
absolutely continuous spectrum, singular continuous spectrum, Liouvillian, Quantum dynamics and nonequilibrium statistical mechanics (general), Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), Spectrum, resolvent, Applications of operator theory in statistical physics, point spectrum, Hamiltonian
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).9 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!