Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with an Index-two saddle

Reactivity boundaries that divide the destination and the origin of trajectories are of crucial importance to reveal the mechanism of reactions. We investigate whether such reactivity boundaries can be extracted for higher index saddles in terms of a nonlinear canonical transformation successful for index-one saddles by using a model system with an index-two saddle. It is found that the true reactivity boundaries do not coincide with those extracted by the transformation taking into account a nonlinearity in the region of the saddle even for small perturbations, and the discrepancy is more pronounced for the less repulsive direction of the index-two saddle system. The present result indicates an importance of the global properties of the phase space to identify the reactivity boundaries, relevant to the question of what reactant and product are in phase space, for saddles with index more than one

Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with Multiple Saddles

Reactivity boundaries that divide the origin and destination of trajectories are crucial of importance to reveal the mechanism of reactions, which was recently found to exist robustly even at high energies for index-one saddles [Phys. Rev. Lett. 105, 048304 (2010)]. Here we revisit the concept of the reactivity boundary and propose a more general definition that can involve a single reaction associated with a bottleneck made up of higher index saddles and/or several saddle points with different indices, where the normal form theory, based on expansion around a single stationary point, does not work. We numerically demonstrate the reactivity boundary by using a reduced model system of the $H^+_5$ cation where the proton exchange reaction takes place through a bottleneck made up of two index-two saddle points and two index-one saddle points. The cross section of the reactivity boundary in the reactant region of the phase space reveals which initial conditions are effective in making the reaction happen, and thus sheds light on the reaction mechanism.Comment: 12 pages, 7 figure

The Role of Entanglement in Quantum-Relaxation Based Optimization Algorithms

Quantum Random Access Optimizer (QRAO) is a quantum-relaxation based optimization algorithm proposed by Fuller et al. that utilizes Quantum Random Access Code (QRAC) to encode multiple variables of binary optimization in a single qubit. Differing from standard quantum optimizers such as QAOA, it utilizes the eigenstates of local quantum Hamiltonians that are not diagonal in the computational basis. There are indications that quantum entanglement may not be needed to solve binary optimization problems with standard quantum optimizers because their maximal eigenstates of diagonal Hamiltonians include classical states. In this study, while quantumness does not always improve the performance of quantum relaxations, we observed that there exist some instances in which quantum relaxation succeeds to find optimal solutions with the help of quantumness. Our results suggest that QRAO not only can scale the instances of binary optimization problems solvable with limited quantum computers but also can benefit from quantum entanglement.Comment: 14 pages, 8 figure

A case of complete atrioventricular block due to malignant lymphoma.

A case of malignant lymphoma associated with complete heart block in a 30-year-old woman is reported. The patient progressively deteriorated despite temporary pacing and died 24 days after being admitted. Microscopic examination of the heart revealed marked infiltration by lymphoma cells in the atrioventricular node and the bundle of His. A diffuse lymphoma (large cell type, B cell) was diagnosed. This case is considered to be rare, since complete heart block was the first and only manifestation of the malignant lymphoma.</p

Rotational symmetry adapted semi-classical theory and it's application to molecules(4) Quantum chaos and semiclassical theory in molecular science and nuclear theory, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

この論文は国立情報学研究所の電子図書館事業により電子化されました。回転対称性を持つ分子に関して、各々の回転固有状態ごとに自己相関関数を計算する方法論を半古典理論の枠組みの中で構築した。エネルギー固有値は半古典自己相関関数をFourier変換することにより得られる。この方法論は既存の周期軌道が必要なトレース公式によるものと比べ、多自由度系にも適用可能である。回転対称性を考慮することは必要な半古典自己相関関数の長さが短くてすむという点と、回転定数などを通して分子の形の情報を抽出できる点という二つの点で重要である。We construct a methodology to calculate auto-correlation function in each rotational symmetry eigenstate, semi-classically. Eigenvalues of Hamiltonian are given by Fourier transform of this auto-correlation function. This methodology, compared to trace formula presented by Creagh and Littlejohn[1-2], can be applied to systems that have many degrees of freedom. Symmetry-adaptation is important for the following two reasons. The one is that the shorter length of the auto-correlation function is needed in order to get same resolution of energy spectrum. The other is we can got some information of molecular morphology such as rotational constants

A Case of Mediastinal Cystic Lymphangioma

A 35-year-old Japanese manʼs routine chest radiography revealed an abnormal opacity. Chest computed tomography and magnetic resonance imaging showed a 5.5cm in dia. cystic tumor located at the left anterior mediastinum. The tumor was suspected to be an asymptomatic thymic cyst, and we chose observation for the tumor. At the 3-year follow up, the cystic tumor had gradually enlarged to 7.5cm in dia. and we thus performed a surgical resection via left video-assisted thoracic surgery. An immunohistochemical analysis showed that the cystic tumor was not a thymic cyst but rather a mediastinal cystic lymphangioma. Mediastinal cystic lymphangiomas are very rare, and they are difficult to diagnose preoperatively. Complete surgical resection is proposed for the treatment of such tumors