arXiv subjects
Publications and source records attributed to G. Morandi.
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of Statistical Mechanics, i.e. that alternative Hamiltonian descriptions do lead to the same thermodynamical description of any physical system.
We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study the effect of degeneracies on geometric phases for three-level systems. This is shown to lead to a highly nontrivial generalization of the result for two-level systems in which degeneracy results in a "monopole" structure in parameter space. The rich structures that arise are related to the geometry of adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a three-level system is shown to lead to the known monopole structure.
We investigate both numerically and analytically the behaviour of a spin-1 antiferromagnetic (AFM) isotropic Heisenberg chain in an external magnetic field. Extensive DMRG studies of chains up to N=80 sites extend previous analyses and exhibit the well known phenomenon of the closure of the Haldane gap at a lower critical field H_c1. We obtain an estimate of the gap below H_c1. Above the lower critical field, when the correlation functions exhibit algebraic decay, we obtain the critical exponent as a function of the net magnetization as well as the magnetization curve up to the saturation (upper critical) field H_c2. We argue that, despite the fact that the SO(3) symmetry of the model is explicitly broken by the field, the Haldane phase of the model is still well described by an SO(3) nonlinear sigma-model. A mean-field theory is developed for the latter and its predictions are compared with those of the numerical analysis and with the existing literature.
We derive a path-integral expression for the effective action in the continuum limit of an AFM Heisenberg spin ladder with an arbitrary number of legs. The map is onto an $O(3)$ nonlinear $σ$-model (NL$σ$M) with the addition of a topological term that is effective only for odd-legged ladders and half-odd integer spins. We derive the parameters of the effective NL$σ$M and the behaviour of the spin gap for the case of even-legged ladders.
We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the saddle point approximation (SPA) for this problem. At the classical level we argue that exactness of the SPA stems from the fact that the dynamics (on the two--sphere $S^2$) of a classical spinning particle in a magnetic field is the reduction from $\br^4$ to $S^2$ of a linear dynamical system on $\br^4$. At the quantum level, however, and within the path integral approach, the restriction, inherent to the use of the SPA, to regular paths clashes with the fact that no regulators are present in the action that enters the path integral. This is shown to lead to a prefactor for the path integral that is strictly divergent except in the classical limit. A critical comparison is made with the various approaches to the same problem that have been presented in the literature. The validity of a formula given in literature for the spin propagator is extended to the case of motion in an arbitrary magnetic field.