Calculating the relative entropy of entanglement

We extend Vedral and Plenio's theorem (theorem 3 in Phys. Rev. A 57, 1619) to a more general case, and obtain the relative entropy of entanglement for a class of mixed states, this result can also follow from Rains' theorem 9 in Phys. Rev. A 60, 179.Comment: 2 pages, RevTex, an important reference adde

Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material

Two-dimensional (2D) transition metal dichalcogenide (TMD) nanosheets exhibit remarkable electronic and optical properties. The 2D features, sizable bandgaps, and recent advances in the synthesis, characterization, and device fabrication of the representative MoS$_2$, WS$_2$, WSe$_2$, and MoSe$_2$ TMDs make TMDs very attractive in nanoelectronics and optoelectronics. Similar to graphite and graphene, the atoms within each layer in 2D TMDs are joined together by covalent bonds, while van der Waals interactions keep the layers together. This makes the physical and chemical properties of 2D TMDs layer dependent. In this review, we discuss the basic lattice vibrations of monolayer, multilayer, and bulk TMDs, including high-frequency optical phonons, interlayer shear and layer breathing phonons, the Raman selection rule, layer-number evolution of phonons, multiple phonon replica, and phonons at the edge of the Brillouin zone. The extensive capabilities of Raman spectroscopy in investigating the properties of TMDs are discussed, such as interlayer coupling, spin--orbit splitting, and external perturbations. The interlayer vibrational modes are used in rapid and substrate-free characterization of the layer number of multilayer TMDs and in probing interface coupling in TMD heterostructures. The success of Raman spectroscopy in investigating TMD nanosheets paves the way for experiments on other 2D crystals and related van der Waals heterostructures.Comment: 30 pages, 23 figure

Digital Quantum Simulation of Yang-Mills Theory and Hadronization

A quantum algorithm with polynomial complexity to non-perturbatively calculate the Dyson series of SU(N) Yang-Mills theory is formulated in terms of quantum circuits. Applying it to the quantum simulation of quantum chromodynamics (QCD), the quark and gluon's wave functions evolved from the initial states by the interactions can be observed and the information from wave functions can be extracted at any discrete time. This may help us understand the natures of the hadronization which has been an outstanding question of significant implication on high energy phenomenological studies.Comment: 8 pages, 1 figur

Low Intensity of Running Favors for Anabolic Response after Resistance Exercise

Purpose: Whether active or passive recovery after resistance exercise may affect anabolic and catabolic response is not clear. The aim of this study was to examine the effect of active (moderate or low intensity running) and passive (rest) recovery after resistance exercise on testosterone, cortisol and testosterone/cortisol ratio (T/C) responses. Methods: By counter-balanced design, nine recreationally active males (age: 23.89 ± 0.86 yrs of age; height: 172.89 ± 1.30 cm; weight: 68.37 ± 2.72 kg; VO2max: 56.56 ± 1.70 ml/kg/min) completed three tests including: 65% VO2max running (moderate intensity, RM), 40% VO2max running (low intensity, RL) and passive rest (RR) following 3sets of four resistance exercises (bench press, leg extension, front lat pulldown and leg curl, 12 repetitions at 60%1RM with 2min rest among all sets and exercises). In order to evaluate the systemic anabolic status, we measured plasma testosterone, cortisol and T/C ratio before resistance exercise (baseline), immediately after either active or passive recovery (post), and 30min after recovery (rest). Results: In RM group, T/C was significantly lower (decrease 18.5%, p\u3c.05) than baseline at rest. In RL group, T/C was significantly higher (increase 79.1% at post and increase 123.2% at rest, p\u3c.05) than baseline at post and rest, respectively. At rest, the T/C of RL was higher than RM (RM: 0.49 ± 0.12, RL: 1.08 ± 0.19, p\u3c.05). Conclusions: Resistance exercise and low intensity aerobic exercise is more favorable to enhance anabolic response during post-exercise recovery