A note on edge degree and spanning trail containing given edges

Let $G$ be a simple graph with $n\geq4$ vertices and $d(x)+d(y)\geq n+k$ for each edge $xy\in E(G)$. In this work we prove that $G$ either contains a spanning closed trail containing any given edge set $X$ if $|X|\leq k$, or $G$ is a well characterized graph. As a corollary, we show that line graphs of such graphs are $k$-hamiltonian.Comment: 7 page

Realizing degree sequences as Z3Z_3-connected graphs

An integer-valued sequence $\pi=(d_1, \ldots, d_n)$ is {\em graphic} if there is a simple graph $G$ with degree sequence of $\pi$. We say the $\pi$ has a realization $G$. Let $Z_3$ be a cyclic group of order three. A graph $G$ is {\em $Z_3$-connected} if for every mapping $b:V(G)\to Z_3$ such that $\sum_{v\in V(G)}b(v)=0$, there is an orientation of $G$ and a mapping $f: E(G)\to Z_3-\{0\}$ such that for each vertex $v\in V(G)$, the sum of the values of $f$ on all the edges leaving from $v$ minus the sum of the values of $f$ on the all edges coming to $v$ is equal to $b(v)$. If an integer-valued sequence $\pi$ has a realization $G$ which is $Z_3$-connected, then $\pi$ has a {\em $Z_3$-connected realization} $G$. Let $\pi=(d_1, \ldots, d_n)$ be a graphic sequence with $d_1\ge \ldots \ge d_n\ge 3$. We prove in this paper that if $d_1\ge n-3$, then either $\pi$ has a $Z_3$-connected realization unless the sequence is $(n-3, 3^{n-1})$ or is $(k, 3^k)$ or $(k^2, 3^{k-1})$ where $k=n-1$ and $n$ is even; if $d_{n-5}\ge 4$, then either $\pi$ has a $Z_3$-connected realization unless the sequence is $(5^2, 3^4)$ or $(5, 3^5)$

Continuously tunable electronic structure of transition metal dichalcogenides superlattices

Two dimensional transition metal dichalcogenides (TMDC) have very interesting properties for optoelectronic devices. In this work we theoretically investigate and predict that superlattices comprised of MoS$_{2}$ and WSe$_{2}$ multilayers possess continuously tunable electronic structure having direct band gap. The tunability is controlled by the thickness ratio of MoS$_{2}$ versus WSe$_{2}$ of the superlattice. When this ratio goes from 1:2 to 5:1, the dominant K-K direct band gap is continuously tuned from 0.14 eV to 0.5 eV. The gap stays direct against -0.6% to 2% in-layer strain and up to -4.3% normal-layer compressive strain. The valance and conduction bands are spatially separated. These robust properties suggest that MoS$_{2}$ and WSe$_{2}$ multilayer superlattice should be an exciting emerging material for infrared optoelectronics.Comment: 5 pages, 4 figures and 1 tabl

Time-convolutionless non-Markovian master equation in strong-coupling regime

The time-convolutionless (TCL) non-Markovian master equation was generally thought to break down at finite time due to its singularity and fail to produce the asymptotic behavior in strong coupling regime. However, in this paper, we show that the singularity is not an obstacle for validity of the TCL master equation. Further, we propose a multiscale perturbative method valid for solving the TCL master equation in strong coupling regime, though the ordinary perturbative method invalidates therein.Comment: 4 pages, 2 figure

Explicit non-canonical symplectic algorithms for charged particle dynamics

We study the non-canonical symplectic structure, or K-symplectic structure inherited by the charged particle dynamics. Based on the splitting technique, we construct non-canonical symplectic methods which is explicit and stable for the long-term simulation. The key point of splitting is to decompose the Hamiltonian as four parts, so that the resulting four subsystems have the same structure and can be solved exactly. This guarantees the K-symplectic preservation of the numerical methods constructed by composing the exact solutions of the subsystems. The error convergency of numerical solutions is analyzed by means of the Darboux transformation. The numerical experiment display the long-term stability and efficiency for these methods.Comment: 9 pages,6 figure

Coupled Cluster Treatment of the Alternating Bond Diamond Chain

By the analytical coupled cluster method (CCM), we study both the ground state and lowest-lying excited-state properties of the alternating bond diamond chain. The numerical exact diagonalization (ED) method is also applied to the chain to verify the accuracy of CCM results. The ED results show that the ground-state phase diagram contains two exact spin cluster solid ground states, namely, the tetramer-dimer (TD) state and dimer state, and the ferrimagnetic long-range-ordered state. We prove that the two exact spin cluster solid ground states can both be formed by CCM. Moreover, the exact spin gap in the TD state can be obtained by CCM. In the ferrimagnetic region, we find that the CCM results for some physical quantities, such as the ground-state energy, the sublattice magnetizations, and the antiferromagnetic gap, are comparable to the results obtained by numerical methods. The critical line dividing the TD state from the ferrimagnetic state is also given by CCM and is in perfect agreement with that determined by the ED method.Comment: arXiv admin note: text overlap with arXiv:1502.0680

A bias-free quantum random number generation using photon arrival time selectively

We present a high-quality, bias-free quantum random number generator (QRNG) using photon arrival time selectively in accordance with the number of photon detection events within a sampling time interval in attenuated light. It is well showed in both theoretical analysis and experiments verification that this random number production method eliminates both bias and correlation perfectly without more post processing and the random number can clearly pass the standard randomness tests. We fulfill theoretical analysis and experimental verification of the method whose rate can reach up to 45Mbps

Primordial non-Gaussianity in noncanonical warm inflation: three- and four-point correlations

Non-Gaussianity generated in inflation can be contributed by two parts. The first part, denoted by $f_{NL}^{\delta N}$, is the contribution from four-point correlation of inflaton field which can be calculated using $\delta N$ formalism, and the second part, denoted by $f_{NL}^{int}$, is the contribution from the three-point correlation function of the inflaton field. We consider the two contributions to the non-Gaussianity in noncanonical warm inflation throughout (noncanonical warm inflation is a new inflationary model which is proposed in \cite{Zhang2014}). We find the two contributions are complementary to each other. The four-point correlation contribution to the non-Gaussianity is overwhelmed by the three-point one in strong noncanonical limit, while the conclusion is opposite in the canonical case. We also discuss the influence of the field redefinition, thermal dissipative effect and noncanonical effect to the non-Gaussianity in noncanonical warm inflation.Comment: 7 pages. Accepted for publication in Physical Review

Hamiltonian integration methods for Vlasov-Maxwell equations

Hamiltonian integration methods for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, i.e., the electrical energy, the magnetic energy, and the kinetic energy in three Cartesian components. Each of the subsystems is a Hamiltonian system with respect to the Morrison-Marsden-Weinstein Poisson bracket and can be solved exactly. Compositions of the exact solutions yield Poisson structure preserving, or Hamiltonian, integration methods for the Vlasov-Maxwell equations, which have superior long-term fidelity and accuracy

Comment on "Hamiltonian splitting for the Vlasov-Maxwell equations"

The paper [1] by Crouseilles, Einkemmer, and Faou used an incorrect Poisson bracket for the Vlasov-Maxwell equations. If the correct Poisson bracket is used, the solution of one of the subsystems cannot be computed exactly in general. As a result, one cannot construct a symplectic scheme for the Vlasov-Maxwell equations using the splitting Hamiltonian method proposed in Ref [1].Comment: 6 page