The Resolvent Algebra for Oscillating Lattice Systems: Dynamics, Ground and Equilibrium States
- 89 Downloads
Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of such systems acts on the resolvent algebra by automorphisms and there exists a (in any regular representation) weakly dense subalgebra on which this action is pointwise norm continuous. Based on this observation, equilibrium (KMS) states as well as ground states are constructed, which are shown to be regular. It is also indicated how to deal with singular interactions and non-harmonic oscillations.
Unable to display preview. Download preview PDF.
- 1.Albeverio, S., Kondratiev, Y., Kozitsky, Y., Röckner, M.: The Statistical Mechanics of Quantum Lattice Systems: A Path Integral Approach. EMS Tracts Math 8 (2009)Google Scholar
- 8.Buchholz, D., Grundling, H.: Quantum systems and resolvent algebras. In: Blanchard, P., Fröhlich, J., (eds.) The Message of Quantum Science: Attempts Towards a Synthesis. Lect. Notes Phys. 899, pp. 33–45. Springer, Berlin (2015)Google Scholar
- 10.Kanda, T., Matsui, T.: KMS states of weakly coupled anharmonic crystals and the resolvent CCR algebra. e-print arXiv:1601.04809
- 13.Nachtergaele, B., Schlein, B., Sims, R., Starr, S., Zagrebnov, V.A.: On the existence of the dynamics for anharmonic quantum oscillator systems. Rev. Math. Phys. 22, 207–231 (2010)Google Scholar
- 14.Nachtergaele, B., Sims, R.: On the dynamics of lattice systems with unbounded on-site terms in the Hamiltonian. e-print arXiv:1410.8174v1