An Expression of the Ground State Energy of the Spin-Boson Model(Recent Trends in Infinite Dimensional Non-Commutative Analysis)

Masao Hirokawa

Masao Hirokawa

Tohru Koma, Bruno Nachtergaele

We review recent results on interface ground states of quantum spin systems.

Herbert E. Spohn

Volkmar Liebscher

Based on certain conditional expectations leading to conditional local states we provide a Gibbs Theory analogous to $[20, 21]$ .As example, we look at specifications corresponding to coherent states and the ideal Bose gas.

Luigi Accardi, Sergei Vladimirovich Kozyrev, Igor Vasil'evich Volovich

We consider the stochastic limit of the standard non relativistic QED (but our results also hold for the polaron interaction of a particle with a Boson field).Extending the Fock case results of $[\mathrm{A}\mathrm{c}\mathrm{L}\mathrm{u}92]$ , we take the initial state of the field to be a Gibbs state at a given temperature.We show that a new algebra, with commutation relations depending on the temperature and acting on a Hilbert module, emerges.This algebra, that we call the Hot Ree Algebra, generalizes the QED Hilbert module algebra in the sense of $[\mathrm{A}\mathrm{c}\mathrm{L}\mathrm{u}\mathrm{v}_{0}97\mathrm{C}]$ and [Ske96] and therefore also the Ree (or Boltzmannian) algebra.It is interesting to notice that, when the module structure is neglected, the algebra we find is precisely the algebra that was found in the singleton independence central limit theorem of $[\mathrm{A}\mathrm{h}_{0}98\mathrm{a}],$ $[\mathrm{A}\mathrm{h}_{0}98\mathrm{b}]$ .So the present result also gives a natural physical interpretation for that algebra.