Abstract:
For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.

Abstract:
The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current $J$ to the chemical potential difference $\Delta \mu$ between right-going and left-going particles. It is shown that both $J$ and $\Delta \mu$ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.

Abstract:
Measurement and fluctuations are closely related to each other in quantum mechanics. This fact is explicitly demonstrated in the case of a quantum non-demolition photodetector which is composed of a double quantum-wire electron interferometer.

Abstract:
We describe the fundamental equations for description of electron-photon interactions in insulating nanostructures. Since the theory for the nanostructures are based on the theory for the bulk crystals, we shall describe elements of the theory for the bulk crystals \cite{knox}-\cite{b2} in the first three subsections. It is important in discussions on optical phenomena that both the envelope function and the Wannier functions (or, equivalently, cell-periodic parts of the Bloch functions) should be taken into account. The theory for the nanostructure is discussed in the fourth subsection. In the final subsection, we briefly mention quantum optics in nanostructures.

Abstract:
We derive universal properties of nonlinear response functions of nonequilibrium steady states. In particular, sum rules and asymptotic behaviors are derived. Their consequences are illustrated for nonlinear optical materials and nonlinear electrical conductors.

Abstract:
Quantum information theory is closely related to quantum measurement theory because one must perform measurement to obtain information on a quantum system. Among many possible limits of quantum measurement, the simplest ones were derived directly from the uncertainty principles. However, such simple limits are not the only limits. I here suggest a new limit which comes from the forms and the strengths of the elementary interactions. Namely, there are only four types of elementary interactions in nature; their forms are determined by the gauge invariance (and symmetry breaking), and their coupling constants (in the low-energy regime) have definite values. I point out that this leads to a new fundamental limit of quantum measurements. Furthermore, this fundamental limit imposes the fundamental limits of getting information on, preparing, and controlling quantum systems.

We develop a new
technique to measure the exact upper diameters of trees that is comparatively
simple and inexpensive. We can measure the diameters of entire tree trunks
efficiently and with high precision. The system uses a digital camera with a
~15 - 30× telephoto lens to take a photograph that can be used for measuring the
diameter of the upper part of a comparatively slender tree trunk. Since this
method requires a measuring distance and the height of the target point in the
image, a range finder capable of measuring angles was combined with the main
digiscoping system. A range finder sensor uses a laser and makes a 360 degree
angle of observation possible. The diameter of a target position of the
objective tree can be obtained by measuring the digital image using image
editing software and calculations from spreadsheet software. We focus on the
Japanese cedar species in the southwestern part of Japan. Photographic
measurements were obtained prior to thinning. The estimates that we obtained
largely agree with the true measurements of all trees. With regard to the
estimated accuracy of all measured trees, the maximum error ratio was 7.0%
(1.45 cm), with a ~2% - 4% error for most of the estimated results. Although
the absolute value of the estimation error was 1.87 cm (5.3%) at the maximum
(9.87 m in height and 35.5 cm in diameter), an estimation accuracy of <1 cm
was reproduced in almost all measurements except for the extreme hypertrophy
portion by butt swelling.

Abstract:
We derive general properties, which hold for both quantum and classical systems, of response functions of nonequilibrium steady states. We clarify differences from those of equilibrium states. In particular, sum rules and asymptotic behaviors are derived, and their implications are discussed. Since almost no assumptions are made, our results are applicable to diverse physical systems. We also demonstrate our results by a molecular dynamics simulation of a many-body interacting system.

Abstract:
We derive an effective 1D theory from the Hamiltonian of the 3D system which consists of a mesoscopic conductor and reservoirs. We assume that the many-body interaction have the same magnitude in the conductor as that in the reservoirs, in contrast to the previous theories which made the ad hoc assumption that the many-body interaction were absent in the reservoirs. We show the following: (i) The effective potentials of impurities and two-body interaction for the 1D modes become weaker as $x$ goes away from the conductor. (ii) On the other hand, the interaction between the 1D and the reservoir modes is important in the reservoir regions, where the reservoir modes excite and attenuate the 1D modes through the interaction. (iii) As a result, the current $\hat I_1$ of the 1D modes is not conserved, whereas the total current $\hat I$ is of course conserved. (iv) For any steady state the total current $\bra I \ket$, its equilibrium fluctuation $\bra \delta I^2 \ket^{eq}$ at low frequency, and non-equilibrium fluctuation $\bra \delta I^2 \ket^{noneq}$ at low frequency, of the original system are independent of $x$, whereas $\bra \delta I^2 \ket^{eq}$ and $\bra \delta I^2 \ket^{noneq}$ at higher frequencies may depend on $x$. (v) Utilizing this property, we can evaluate $\bra I \ket$, $\bra \delta I^2 \ket^{eq}$, and $\bra \delta I^2 \ket^{noneq}$ at low frequency from those of the 1D current $\hat I_1$. (vi) In general, the transmittance $T$ in the Landauer formula should be evaluated from a single-body Hamiltonian which includes a Hartree potential created by the density deformation which is caused by the external bias.

Abstract:
We consider generation of an electrical pulse by an optical pulse in the ``virtual excitation'' regime. The electronic system, which is any electro-optic material including a quantum well structure biased by a dc electric field, is assumed to be coupled to an external circuit. It is found that the photon frequency is subject to an extra red shift in addition to the usual self-phase modulation, whereas the photon number is conserved. The Joule energy consumed in the external circuit is supplied only from the extra red shift.