We numerically investigate quantum quenches of a nonintegrable hard-core Bose-Hubbard model to test the accuracy of the microcanonical ensemble in small isolated quantum systems. We show that, in a certain range of system size, the accuracy increases
with the dimension of the Hilbert space $D$ as $1/D$. We ascribe this rapid improvement to the absence of correlations between many-body energy eigenstates as well as to the eigenstate thermalization. Outside of that range, the accuracy is found to scale as $1/sqrt{D}$ and improves algebraically with the system size.
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in the energ
y eigenbasis at each instant of time, meets the first two requirements and that the third requirement is satisfied if an arbitrary external operation is performed at typical times. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that the Hamiltonian dynamics restricts quantum trajectories under unitary evolution and that the external operation is performed without referring to any particular information about the microscopic state of the system.
By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH) which is considered to be a possible mechanism of
thermalization in isolated quantum systems. We find that the ETH in the weak sense holds in the thermodynamic limit even for an integrable system although it does not hold in the strong sense. Based on the result of the finite-size scaling analysis, we compare the contribution of the weak ETH to thermalization with that of yet another thermalization mechanism, the typicality, and show that the former gives only a logarithmic correction to the latter.
The AKARI All-Sky Catalogues are an important infrared astronomical database for next-generation astronomy that take over the IRAS catalog. We have developed an online service, AKARI Catalogue Archive Server (AKARI-CAS), for astronomers. The service
includes useful and attractive search tools and visual tools. One of the new features of AKARI-CAS is cached SIMBAD/NED entries, which can match AKARI catalogs with other catalogs stored in SIMBAD or NED. To allow advanced queries to the databases, direct input of SQL is also supported. In those queries, fast dynamic cross-identification between registered catalogs is a remarkable feature. In addition, multiwavelength quick-look images are displayed in the visualization tools, which will increase the value of the service. In the construction of our service, we considered a wide variety of astronomers requirements. As a result of our discussion, we concluded that supporting users SQL submissions is the best solution for the requirements. Therefore, we implemented an RDBMS layer so that it covered important facilities including the whole processing of tables. We found that PostgreSQL is the best open-source RDBMS products for such purpose, and we wrote codes for both simple and advanced searches into the SQL stored functions. To implement such stored functions for fast radial search and cross-identification with minimum cost, we applied a simple technique that is not based on dividing celestial sphere such as HTM or HEALPix. In contrast, the Web application layer became compact, and was written in simple procedural PHP codes. In total, our system realizes cost-effective maintenance and enhancements.
Regular arrays of InP nano pillars have been fabricated by low energy Electron Cyclotron Resonance (ECR) Ar+ ion irradiation on InP(111) surface. Several scanning electron microscopy (SEM) images have been utilized to invetsigate the width, height, a
nd orientation of these nano pillars on InP(111) surfaces. The average width and length of these nano-pillars are about 50 nm and 500 nm, respectively. The standing angle with respect to the surface of the nano-pillars depend on the incidence angle of the Ar ion irradiation during the fabrication process. Interestingly, the growth direction of the nano pillars are along the reflection direction of the ion beam and the standing angles are nearly same as the ion incidence angle with the surface normal. This nano-pillas are easily transferred from the InP surface to double sided carbon tape without any damage. High Resolution Transmission Electron Microscopy (HRTEM) study of single nano-pillar reveals that this nano-pillar are almost crystalline in nature except 2-4 nm amorphous layer on the outer surface. The transmission electron microscopy combined with energy-dispersive x-ray spectroscopy (TEM-EDS) analysis of these nano pillars exhibit that the ratio of In and P is little higher compared to the bulk InP.
We derive an upper bound on the difference between the long-time average and the microcanonical ensemble average of observables in isolated quantum systems. We propose, numerically verify, and analytically support a new hypothesis, eigenstate randomi
zation hypothesis (ERH), which implies that in the energy eigenbasis the diagonal elements of observables fluctuate randomly. We show that ERH includes eigenstate thermalization hypothesis (ETH) and makes the aforementioned bound vanishingly small. Moreover, ERH is applicable to integrable systems for which ETH breaks down. We argue that the range of the validity of ERH determines that of the microcanonical description.
