Classical and thermodynamic limits for generalised quantum spin systems

Masanori Ohya, Dėnes Petz

P Lslash ugiewicz, Robert Olkiewicz

Environmentally induced classical properties in quantum spin systems in the thermodynamic limit are discussed. In particular, it is shown that such a system, subjected to a specific interaction with another quantum system, may be described for all practical purposes as a classical dynamical system. This provides an alternative approach to the classical ℏ → 0 limit for the emergence of reversible classical evolution from dissipative quantum dynamics.

Lenart Zadnik, Kemal Bidzhiev, Maurizio Fagotti

We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of ``local'' macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.

Élliott H. Lieb

Тамара Грава, Alice Guionnet, Karol Kajetan Kozlowski +1 more

This work establishes a large deviation principle for the spectral measure of the Lax matrix associated to the periodic Toda chain of $N$ particles, subject to a generalised Gibbs measure. This large deviation principle is governed by a rate function which can be regarded as a generalisation of the free energy of the system. Such a large deviation principle is proven both for the model when the momentum is constrained to be zero and when it is allowed to fluctuate. Moreover, the large deviation principle is proven directly at the level of the representation of the generalised Gibbs partition function given in terms of the variables realising the classical separation of variables, \textit{i.e.} rectifying the equations of motion. As such, this work paves the way towards the computation of the thermodynamic limit of dynamical correlation functions in the Toda chain subject to generalised Gibbs ensemble statistics.

Élliott H. Lieb