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

Certifying isolated singular points and their multiplicity structure

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear instead of the quadratic increase of previous methods. The second construction gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root. We present a system of equations in the original variables plus a relatively small number of new vari-ables. We show that the roots of this new system include the original singular root but now with multiplicity one, and the new variables uniquely determine the multiplicity structure. Both constructions are "exact", meaning that they permit one to treat all conjugate roots simultaneously and can be used in certification procedures for singular roots and their multiplicity structure with respect to an exact rational polynomial system

Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice

Within the zero-temperature linear spin-wave theory we have investigated the effect of frustration and dimerization of a Heisenberg system with alternating spins $s_{1}$ and $s_{2}$ on one- and two-dimensional lattices. The combined effect most visibly appears in the elementary excitation spectra. In contrast to the ground state energy that decreases with dimerization and increases with frustration, the excitation energies are shown to be suppressed in energy by both dimerization and frustration. The threshold value of frustration that signals a transition from a classical ferrimagnetic state to a spiral state, decreases with dimerization, showing that dimerization further helps in the phase transition. The correlation length and sublattice magnetization decrease with both dimerization and frustration indicating the destruction of the long-range classical ferrimagnetic. The linear spin wave theory shows that in the case of a square lattice, dimerization initially opposes the frustration-led transition to a spiral magnetic state, but then higher magnitudes of lattice deformation facilitate the transition. It also shows that the transition to spiral state is inhibited in a square lattice beyond a certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure

First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field

First-order quantum correction to the Larmor radiation is investigated on the basis of the scalar QED on a homogeneous background of time-dependent electric field, which is a generalization of a recent work by Higuchi and Walker so as to be extended for an accelerated charged particle in a relativistic motion. We obtain a simple approximate formula for the quantum correction in the limit of the relativistic motion when the direction of the particle motion is parallel to that of the electric field.Comment: 12 pages, 2 figures, accepted for publication in Physical Review

Hybrid TLC-pair meter for the Sphinx Project

The chief aims in THE SPHINX PROJECT are research of super lepton physics and new detector experiments. At the second phase of THE SPHINX PROJECT, a hybrid TLC-PAIR METER was designed for measuring high energy neutrino sources (E upsilon * TeV), searching high energy muon sources (E mu TeV) and measuring muon group (E mu 1 TeV). The principle of PAIR METER has been already proposed. In this TLC-PAIR METER, electromagnetic shower induced by cosmic ray muons are detected using TL (Thermoluminescence) sheets with position counters