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

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

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