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

Research proposal for the Hadean-Eoarchean geological research in the Eoarchean high-grade orthogneiss, Mount Sones, Endarby Land, Antarctica

The Tenth Symposium on Polar Science/Special session: [S] Future plan of Antarctic research: Towards phase X of the Japanese Antarctic Research Project (2022-2028) and beyond, Tue. 3 Dec. / Entrance Hall (1st floor) at National Institute of Polar Research (NIPR

Hydrogen and oxygen isotope ratios of thermal waters of Okayama Prefecture, Japan

Hydrogen and oxygen isotope rations of thermal waters from 46 spas in Okayama Prefecture range from -62.6 to -29.2% in δD and from -10.0 to -4.4% in δ18O, respectively. The isotope rations indicate that all but one of the thermal water in Okayama prefecture are meteoric in origin. The Ofuku thermal water is the only exception, which is probably a mixture of seawater and meteoric water with the ratio of about 1. Sulfur isotope rations of dissolvel sulfate in the thermal waters range from -6.2 ti 59.3% in δ34S. The high δ34S values observed in some thermal waters may be due to bacterial reduction of sulfate

Criteria for the Scaling Up of Mixing Vessels

There are several concepts for the scaling up of mixing vessels. They are neither consistent nor conclusive. The authors propose an idea that the selection must be made depending upon the mixing objects. The classification of the types of scaling up is as follows : (1) Similarity for power requirement. Power requirement is correlated by Reynolds-, Froude- and Weber-numbers. The latter two are negligible in an ordinary correlation. (2) Similarity for mixing velocity of homogeneous liquid phase. The authors conclude that the similarity in blending speed is obtained by equal impeller speeds. (3) Similarity for heat and mass transfer on the fixed surface. Rushton et al. proposed the method of scaling-up by the following equation. (n₂/n₁)=(D₁/D₂)⁽²ˣ⁻¹⁾/ˣ This criterion should be limited in the case of the heat and mass transfer on a fixed surface. (4) Similarity for suspension of solid particles, dispersion of gas and liquid, and mass transfer on dispersed objects. The authors support the criterion of equal power per unit volume proposed by W.Büche

Feedback control of quantum entanglement in a two-spin system

A pair of spins is the most simple quantum system that can possess entanglement, a non-classical property playing an essential role in quantum information technologies. In this paper, feedback control problems of the two-spin system conditioned on a continuous measurement are considered. In order to make some useful formulas in stochastic control theory directly applicable, we first derive a two-dimensional description of the system. We then prove that a feedback controller stabilizes an entangled state of the two spins almost globally with probability one. Furthermore, it is shown that another entangled state, which corresponds to a non-equilibrium point of the dynamics, is stabilized via feedback in the sense that the expectation of the distance from the target can be made arbitrarily small

Flow Patterns of Liquid in a Cylindrical Mixing Vessel without Baffles

The velocity distribution of agitated liquid in a cylindrical mixing vessel was measured by using a set of pitot tubes, the construction of which is shown in Fig. 2. Some of the experimental results are shown in Figs. 4, 5, 6, 7, 8, 9 and 10. As a result, the flow patterns in an agitated vessel were made clear and it was ascertained that, in addition to the primary circulation flow around the impeller axis, there was a secondary circulation of liquid ensued by the discharge flow from the tip of an impeller as shown in Figs. 8 and 10. Integrating the measured velocity distributions, the discharge flow rates of impellers were determined and the discharging performance of various impellers (refer to Table 1) was compared in connection with the power consumption. Dimensionless factor, Nq₁, was defined and was called the coefficient of discharge. The ratio, Np/Nq₁ in Table 3, corresponds to the relative power required for a unit quantity of discharge. Furthermore, the power consumption in the neighbourhood of an impeller (Nᴘᵢₘₚ), in other words, in the cylindrical domain (refer to hatched region in Fig. 14) was calculated and compared with that consumed in the outer region of the vessel as shown in Table 4. It is concluded that the improvement in the discharging capacity can be accomplished to some extent by the proper design of an impeller ; however, the fundamental improvement must rely upon some other method