Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement

From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4. This fundamental lower-bound may become bigger when taking the structure and quality of a specific measurement apparatus into account. In this paper, we consider a particle subjected to a linear dynamics that is continuously monitored with efficiency $\eta\in(0,1]$. It is then clarified that the above Heisenberg uncertainty relation is replaced by \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4\eta if the monitored system is unstable, while there exists a stable quantum system for which the Heisenberg limit is reached.Comment: 4 page

Intrinsic double-peak structure of the specific heat in low-dimensional quantum ferrimagnets

Motivated by recent magnetic measurements on A3Cu3(PO4)4 (A=Ca,Sr) and Cu(3-Clpy)2(N3)2 (3-Clpy=3-Chloropyridine), both of which behave like one-dimensional ferrimagnets, we extensively investigate the ferrimagnetic specific heat with particular emphasis on its double-peak structure. Developing a modified spin-wave theory, we reveal that ferromagnetic and antiferromagnetic dual features of ferrimagnets may potentially induce an extra low-temperature peak as well as a Schottky-type peak at mid temperatures in the specific heat.Comment: 5 pages, 6 figures embedded, Phys. Rev. B 65, 214418 (2002