Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator

A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved. The solution yields the spectral resolution of the Liouvillian, that is, all eigenvalues and eigenprojections are obtained. This spectral resolution is discussed in depth in the context of the biorthogonal system and the rigged Hilbert space, and the contribution of each eigenprojection to expectation values of physical quantities is revealed. We also construct the ladder operators of the Liouvillian, which clarify the structure of the spectral resolution.Comment: 22pages, no figure; title changed, minor corrections, references added; minor correction

On unilateral contact problems with friction for an elastic body with cracks (Analysis of inverse problems through partial differential equations and related topics)

This expository article deals with contact problems with friction for a linearized (visco) elasticity in two dimension, which are arising from a wide variety of phenomena in mechanical engineering and concerning with some inverse problems and control problems. Contact conditions for cracks are so-called non-penetration conditions defined as unilateral conditions on the displacements of bodies to exclude nonphysical phenomenon such as mutual penetration of crack faces, see [11] for the details. In the present paper, mathematical results obtained in [9] and [5] are introduced and moreover, dynamic unilateral contact problems are discussed

Free energy density for mean field perturbation of states of a one-dimensional spin chain

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy

Thermoelectric phase diagram of the SrTiO3-SrNbO3 solid solution system

Thermoelectric energy conversion - the exploitation of the Seebeck effect to convert waste heat into electricity - has attracted an increasing amount of research attention for energy harvesting technology. Niobium-doped strontium titanate (SrTi1-xNbxO3) is one of the most promising thermoelectric material candidates, particularly as it poses a much lesser environmental risk in comparison to materials based on heavy metal elements. Two-dimensional electron confinement, e.g. through the formation of superlattices or two-dimensional electron gases, is recognized as an effective strategy to improve the thermoelectric performance of SrTi1-xNbxO3. Although electron confinement is closely related to the electronic structure, the fundamental electronic phase behavior of the SrTi1-xNbxO3 solid solution system has yet to be comprehensively investigated. Here, we present a thermoelectric phase diagram for the SrTi1-xNbxO3 (0.05 =< x =< 1) solid solution system, which we derived from the characterization of epitaxial films. We observed two thermoelectric phase boundaries in the system, which originate from the step-like decrease in carrier effective mass at x ~ 0.3, and from a local minimum in carrier relaxation time at x ~ 0.5. The origins of these phase boundaries are considered to be related to isovalent/heterovalent B-site substitution: parabolic Ti 3d orbitals dominate electron conduction for compositions with x < 0.3, whereas the Nb 4d orbital dominates when x > 0.3. At x ~ 0.5, a tetragonal distortion of the lattice, in which the B-site is composed of Ti4+ and Nb4+ ions, leads to the formation of tail-like impurity bands, which maximizes the electron scattering. These results provide a foundation for further research into improving the thermoelectric performance of SrTi1-xNbxO3.Comment: 20 pages, 6 figure

Gastric Metastasis from a Primary Renal Leiomyosarcoma

Primary leiomyosarcoma of the kidney is rare. Here we report a case of metastasis of this tumor to the stomach. A 73-year-old man visited our hospital suffering from general weakness and intermittent tarry stools. He had undergone right nephrectomy for renal leiomyosarcoma 2 years previously. There had been no local recurrence or distant metastasis in the 2-year follow-up period. Endoscopy revealed two submucosal tumors in the stomach. These tumors were diagnosed histologically as leiomyosarcoma and distal gastrectomy was performed. Subsequent histochemical staining confirmed the diagnosis of gastric metastasis from renal leiomyosarcoma. The patient died due to metastases to the liver and bone 9 months after the operation. To the best of our knowledge, this is the first report of gastric metastasis from primary renal leiomyosarcoma

Microstructures and Thermoelectric Properties of Sintered Misfit-Layered Cobalt Oxide

Misfit-layered cobalt oxide Ca3Co4O9 is considered to be a prospective material for thermoelectric conversion. The thermoelectric properties are anisotropic owing to its anisotropic crystal structure. The crystal has preferred thermoelectric properties along the a-b plane. Therefore, the thermoelectric properties are improved and controlled by the degree of orientation of the sintered sample. In the present work, Sr-doped misfit cobalt oxide Ca2.7Sr0.3Co4O9 was prepared by solid-phase reaction, followed by uniaxial compression molding and sintering at 1173 K. The Seebeck coefficient α, electrical resistivity ρ, and dimensionless figure of merit ZT were measured as a function of the compression pressure applied in the uniaxial molding. α, ρ, and ZT as functions of the degree of orientation and the relative density are experimentally clarified and explained by calculations using the compound model