High-order symbolic strong-coupling expansion for the Bose-Hubbard model

Combining the process-chain method with a symbolized evaluation we work out in detail a high-order symbolic strong-coupling expansion (HSSCE) for determining the quantum phase boundaries between the Mott insulator and the superfluid phase of the Bose-Hubbard model for different fillings in hypercubic lattices of different dimensions. With a subsequent Pad{\'e} approximation we achieve for the quantum phase boundaries a high accuracy, which is comparable to high-precision quantum Monte-Carlo simulations, and show that all the Mott lobes can be rescaled to a single one. As a further cross-check, we find that the HSSCE results coincide with a hopping expansion of the quantum phase boundaries, which follow from the effective potential Landau theory (EPLT).Comment: 15 pages, 11 figures. For the latest version and more information see https://www.physik.uni-kl.de/eggert/papers/index.htm

Life Assessment of Railway Tunnel Lining Structure Based on Reliability Theory

The reliability of the tunnel lining during its service life has significance for tunnel safety management. To capture the performance of the lining under the effect of deterioration factors, the time-varying reliability theory was applied to predict the service life of the lining. The failure process of the lining structure under an erosion environment was analyzed. The limit state equations of the lining structure were established based on the durability criterion and the bearing capacity criterion, respectively. The time-varying reliability of the tunnel was calculated using the Monte-Carlo method with an engineering example, and the service life of the tunnel under different criteria was predicted based on the target reliability. The results show that the predicted service life of the tunnel is 77.5 years under the durability criterion and 95 years under the bearing capacity criterion, assuming that the tunnel structure is in an erosive environment at the beginning of construction and that no protective measures are taken under the most unfavourable conditions. The durability meets the structural applicability, and the bearing capacity meets the structural safety, which is in line with the actual needs of the project. The study results can provide a basis and reference for the future durability design, life prediction, and maintenance management of similar service tunnels

The Milky Way's rotation curve out to 100 kpc and its constraint on the Galactic mass distribution

The rotation curve (RC) of the Milky Way out to $\sim$ 100 kpc has been constructed using $\sim$ 16,000 primary red clump giants (PRCGs) in the outer disk selected from the LSS-GAC and the SDSS-III/APOGEE survey, combined with $\sim$ 5700 halo K giants (HKGs) selected from the SDSS/SEGUE survey. To derive the RC, the PRCG sample of the warm disc population and the HKG sample of halo stellar population are respectively analyzed using a kinematical model allowing for the asymmetric drift corrections and re-analyzed using the spherical Jeans equation along with measurements of the anisotropic parameter $\beta$ currently available. The typical uncertainties of RC derived from the PRCG and HKG samples are respectively 5-7 km/s and several tens km/s. We determine a circular velocity at the solar position, $V_c (R_0)$ = 240 $\pm$ 6 km/s and an azimuthal peculiar speed of the Sun, $V_{\odot}$ = 12.1 $\pm$ 7.6 km/s, both in good agreement with the previous determinations. The newly constructed RC has a generally flat value of 240 km/s within a Galactocentric distance $r$ of 25 kpc and then decreases steadily to 150 km/s at $r$ $\sim$ 100 kpc. On top of this overall trend, the RC exhibits two prominent localized dips, one at $r$ $\sim$ 11 kpc and another at $r$ $\sim$ 19 kpc. From the newly constructed RC, combined with other constraints, we have built a parametrized mass model for the Galaxy, yielding a virial mass of the Milky Way's dark matter halo of $0.90^{+0.07}_{-0.08} \times 10^{12}$ ${\rm M}_{\odot}$ and a local dark matter density, $\rho_{\rm \odot, dm} = 0.32^{+0.02}_{-0.02}$ GeV cm$^{-3}$.Comment: MNRAS accepted, 18 pages, 15 figures, 4 table

Local geometry and quantum geometric tensor of mixed states

The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum states via the density matrix and its purification. The gauge-invariant QGT of mixed states is derived, whose real and imaginary parts are the Bures metric and the Uhlmann form, respectively. In contrast to the imaginary part of the pure-state QGT that is proportional to the Berry curvature, the Uhlmann form vanishes identically for ordinary physical processes. Moreover, there exists a Pythagorean-like equation that links different local distances and reflect the underlying fibration. The Bures metric reduces to the Fubini-Study metric as temperature approaches zero if the eigenvalues of the density matrix do not change during the process, establishing a correspondence between pure and mixed states. We also present two examples with contrasting local geometries and discuss experimental implications.Comment: 22 pages, 3 figure

Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases

Two geometric phases of mixed quantum states, known as the interferometric phase and Uhlmann phase, are generalizations of the Berry phase of pure states. After reviewing the two geometric phases and examining their parallel-transport conditions, we specify a class of cyclic processes that are compatible with both conditions and therefore accumulate both phases through their definitions, respectively. Those processes then facilitate a fair comparison between the two phases. We present exact solutions of two-level and three-level systems to contrast the two phases. While the interferometric phase exhibits finite-temperature transitions only in the three-level system but not the two-level system, the Uhlmann phase shows finite-temperature transitions in both cases. Thus, using the two geometric phases as finite-temperature topological indicators demonstrates the rich physics of topology of mixed states.Comment: 12 pages, 2 figures, submitte

THE BALANCE EFFECT OF REARFOOT WEDGES WITH DIFFERENT HEIGHT FOR COLLEGIATE STUDENTS WITH CHRONIC ANKLE INSTABILITY: PILOT STUDY

Chronic ankle instability (CAI) is caused by recurrent lateral ankle sprain. Foot orthotic is one option of treatment. The purpose of this study was to determinate the balance effect of rearfoot wedges with different height in collegiate students with chronic ankle instability. Eight collegiate students with CAI subjects were voluntarily particapated in this study. The area of center of pressure was used as balance variable of outcome measurement. Seven height of rearfoot wedge was used to test, included 0°, 2°, 4°, 6° of medial wedge and 2°, 4°, 6° of lateral wedge. One-way ANOVA was used to analyze the difference among sevent height of wedge intervention in CAI group. The results were showed no significantly difference among seven height of wedge intervention. However, we found a trend of balance improvement with the wedge intervention, especially in 4 degrees of medial wedge intervention