A semiclassical study of the Jaynes-Cummings model

We consider the Jaynes-Cummings model of a single quantum spin $s$ coupled to a harmonic oscillator in a parameter regime where the underlying classical dynamics exhibits an unstable equilibrium point. This state of the model is relevant to the physics of cold atom systems, in non-equilibrium situations obtained by fast sweeping through a Feshbach resonance. We show that in this integrable system with two degrees of freedom, for any initial condition close to the unstable point, the classical dynamics is controlled by a singularity of the focus-focus type. In particular, it displays the expected monodromy, which forbids the existence of global action-angle coordinates. Explicit calculations of the joint spectrum of conserved quantities reveal the monodromy at the quantum level, as a dislocation in the lattice of eigenvalues. We perform a detailed semi-classical analysis of the associated eigenstates. Whereas most of the levels are well described by the usual Bohr-Sommerfeld quantization rules, properly adapted to polar coordinates, we show how these rules are modified in the vicinity of the critical level. The spectral decomposition of the classically unstable state is computed, and is found to be dominated by the critical WKB states. This provides a useful tool to analyze the quantum dynamics starting from this particular state, which exhibits an aperiodic sequence of solitonic pulses with a rather well defined characteristic frequency.Comment: pdfLaTeX, 51 pages, 19 figures, references added and improved figure captions. To appear in J. Stat. Mec

Innovative experiences in teaching conservation. Involving communities’ interests on preservationtopics by fast investigations and social media dissemination

Since 2019, the authors carried out a didactical experience trough the Preservation Studio workshop in the historical center of Vimercate, a town in the north east area of Milan, implementing a convention agreement between the Municipality and the Atheneum. The convention was arranged in order to set the relationship between the three academic courses of the Politecnico di Milano and the administration of Vimercate, supporting the teaching staff by providing ac- cessibility to various services and some public properties located in the city-cen- ter. Thanks to this kind of agreement, the courses could be supported in their activities by document centers, public associations and the members of the local community, while the teaching staff offered a constant sharing of the main activ- ities by social media and periodical disseminations through public lectures. After maturing several years of didactical workshops on the main buildings of the his- torical center of Vimercate, this paper shows the results collected with the stu- dios: the active class strategies, the on-site survey campaigns, the evolution of the results observed by year after year inspections, ND testing activities and local community involvement. The impact coming from the researches developed by the preservation classes and specific in depth studies realized by graduation thesis showed an increasing participation of the community to the topics connected to the city center: from conservation policies to future uses, historical buildings reached the attention of the people through the development of a new sensibility and perception of new values associated to the local architectural heritage

Hamiltonian solutions of the 3-body problem in (2+1)-gravity

We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.Comment: 25 pages, no figure. v2: some calculation details removed to make the paper more concise (see v1 for the longer version), minor correction in a formula in the section on quantization, references added; results and conclusions unchange