Categories of holomorphic line bundles on higher dimensional noncommutative complex tori

We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them introduced by A. Schwarz. We obtain differential graded (DG) categories as full subcategories of curved DG categories of Heisenberg modules over the complex noncommutative tori. Also, we present the explicit composition formula of morphisms, which in fact depends on the noncommutativity.Comment: 28 page

Energy dissipation in DC-field driven electron lattice coupled to fermion baths

Electron transport in electric-field-driven tight-binding lattice coupled to fermion baths is comprehensively studied. We reformulate the problem by using the scattering state method within the Coulomb gauge. Calculations show that the formulation justifies direct access to the steady-state bypassing the time-transient calculations, which then makes the steady-state methods developed for quantum dot theories applicable to lattice models. We show that the effective temperature of the hot-electron induced by a DC electric field behaves as $T_{\rm eff}=C\gamma(\Omega/\Gamma)$ with a numerical constant $C$, tight-binding parameter $\gamma$, the Bloch oscillation frequency $\Omega$ and the damping parameter $\Gamma$. In the small damping limit $\Gamma/\Omega\to 0$, the steady-state has a singular property with the electron becoming extremely hot in an analogy to the short-circuit effect. This leads to the conclusion that the dissipation mechanism cannot be considered as an implicit process, as treated in equilibrium theories. Finally, using the energy flux relation, we derive a steady-state current for interacting models where only on-site Green's functions are necessary.Comment: 11 pages, 5 figure

A complete classification of which (n,k)(n,k)-star graphs are Cayley graphs

The $(n,k)$-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al.~(Graphs and Combinatorics 2017) and complete the classification of all the $(n,k)$-star graphs that are Cayley.Comment: We have proved the conjecture in the first version, thus completed the classification of which $(n,k)$-star graphs are Cayle

On the framing of patent citations and academic paper citations in refl ecting knowledge linkage: A discussion of the discrepancy of their divergent value-orientations

It has been widely recognized that academic paper citations will reflect scientific knowledge linkage. Patent citations are similar to academic paper citations in many aspects: Citation frequency distribution is often skewed; citation frequency varies from one subject field to another and authors&rsquo;/inventors&rsquo;preference for citing relevant literature is usually confined to their own native language. However, regardless of these seemingly similarities, the patent citation is unique and special. It is constructed by incorporating information providers from multiple sources, such as from examiners, inventors, attorneys and/or the public. It is driven by a value-orientation for the monopolization of market production under regulations of Patent Laws. It is also practiced under the sway of an industrial culture embedded with a notion of &ldquo;creative destruction&rdquo;. In view of the contextual complexities of patent citations, simply applying the data criteria and citation behavior analysis of academic paper citations to that of patentbibliometrics for the purpose of reflecting knowledge linkage is both conceptually and technically illogical and unreasonable. This paper attempts to delve into the issue of the currently misconceived assertions and practice about &quot;transplanting&rdquo; the methodology of academic paper citations en masse indiscriminately into the practice of patent citations. It is hoped that such a study would yield improved result stemming from the practice of patent citations for reflecting knowledge linkage in the future.</p

Theory of 2D transport in graphene for correlated disorder

We theoretically revisit graphene transport properties as a function of carrier density, taking into account possible correlations in the spatial distribution of the Coulomb impurity disorder in the environment. We find that the charged impurity correlations give rise to a density dependent graphene conductivity, which agrees well qualitatively with the existing experimental data. We also find, quite unexpectedly, that the conductivity could increase with increasing impurity density if there is sufficient inter-impurity correlation present in the system. In particular, the linearity (sublinearity) of graphene conductivity at lower (higher) gate voltage is naturally explained as arising solely from impurity correlation effects in the Coulomb disorder.Comment: 5 pages, 3 figure