392,121 research outputs found
Momentum relaxation due to polar optical phonons in AlGaN/GaN heterostructures
Using the dielectric continuum (DC) model, momentum relaxation rates are calculated for electrons confined in quasi-two-dimensional (quasi-2D) channels of AlGaN/GaN heterostructures. Particular attention is paid to the effects of half-space and interface modes on the momentum relaxation. The total momentum relaxation rates are compared with those evaluated by the three-dimensional phonon (3DP) model, and also with the Callen results for bulk GaN. In heterostructures with a wide channel (effective channel width >100 Å), the DC and 3DP models yield very close momentum relaxation rates. Only for narrow-channel heterostructures do interface phonons become important in momentum relaxation processes, and an abrupt threshold occurs for emission of interface as well as half-space phonons. For a 30-Å GaN channel, for instance, the 3DP model is found to underestimate rates just below the bulk phonon energy by 70% and overestimate rates just above the bulk phonon energy by 40% compared to the DC model. Owing to the rapid decrease in the electron-phonon interaction with the phonon wave vector, negative momentum relaxation rates are predicted for interface phonon absorption in usual GaN channels. The total rates remain positive due to the dominant half-space phonon scattering. The quasi-2D rates can have substantially higher peak values than the three-dimensional rates near the phonon emission threshold. Analytical expressions for momentum relaxation rates are obtained in the extreme quantum limits (i.e., the threshold emission and the near subband-bottom absorption). All the results are well explained in terms of electron and phonon densities of states
Unimodular graded Poisson Hopf algebras
Let be a Poisson Hopf algebra over an algebraically closed field of
characteristic zero. If is finitely generated and connected graded as an
algebra and its Poisson bracket is homogeneous of degree , then
is unimodular; that is, the modular derivation of is zero. This is a
Poisson analogue of a recent result concerning Hopf algebras which are
connected graded as algebras.Comment: 14 pages; preliminary version, comments welcom
The microscopic structure of 2D CDT coupled to matter
We show that for 1+1 dimensional Causal Dynamical Triangulations (CDT)
coupled to 4 massive scalar fields one can construct an effective transfer
matrix if the masses squared is larger than or equal to 0.05. The properties of
this transfer matrix can explain why CDT coupled to matter can behave
completely different from "pure" CDT. We identify the important critical
exponent in the effective action, which may determine the universality class of
the model.Comment: 14 pages,lot of figure
A note on the Lee-Yang singularity coupled to 2d quantum gravity
We show how to obtain the critical exponent of magnetization in the Lee-Yang
edge singularity model coupled to two-dimensional quantum gravity
- …