17,844 research outputs found
Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach
We report the investigation of full-counting statistics (FCS) of transferred
charge and spin in the transient regime where the connection between central
scattering region (quantum dot) and leads are turned on at . A general
theoretical formulation for the generating function (GF) is presented using a
nonequilibrium Green's function approach for the quantum dot system. In
particular, we give a detailed derivation on how to use the method of path
integral together with nonequilibrium Green's function technique to obtain the
GF of FCS in electron transport systems based on the two-time quantum
measurement scheme. The correct long-time limit of the formalism, the
Levitov-Lesovik's formula, is obtained. This formalism can be generalized to
account for spin transport for the system with noncollinear spin as well as
spin-orbit interaction. As an example, we have calculated the GF of
spin-polarized transferred charge, transferred spin, as well as the spin
transferred torque for a magnetic tunneling junction in the transient regime.
The GF is compactly expressed by a functional determinant represented by
Green's function and self-energy in the time domain. With this formalism, FCS
in spintronics in the transient regime can be studied. We also extend this
formalism to the quantum point contact system. For numerical results, we
calculate the GF and various cumulants of a double quantum dot system connected
by two leads in transient regime. The signature of universal oscillation of FCS
is identified. On top of the global oscillation, local oscillations are found
in various cumulants as a result of the Rabi oscillation. Finally, the
influence of the temperature is also examined
Spherical Tiling by 12 Congruent Pentagons
The tilings of the 2-dimensional sphere by congruent triangles have been
extensively studied, and the edge-to-edge tilings have been completely
classified. However, not much is known about the tilings by other congruent
polygons. In this paper, we classify the simplest case, which is the
edge-to-edge tilings of the 2-dimensional sphere by 12 congruent pentagons. We
find one major class allowing two independent continuous parameters and four
classes of isolated examples. The classification is done by first separately
classifying the combinatorial, edge length, and angle aspects, and then
combining the respective classifications together.Comment: 53 pages, 40 figures, spherical geometr
Properties of Noncommutative Renyi and Augustin Information
The scaled R\'enyi information plays a significant role in evaluating the
performance of information processing tasks by virtue of its connection to the
error exponent analysis. In quantum information theory, there are three
generalizations of the classical R\'enyi divergence---the Petz's, sandwiched,
and log-Euclidean versions, that possess meaningful operational interpretation.
However, these scaled noncommutative R\'enyi informations are much less
explored compared with their classical counterpart, and lacking crucial
properties hinders applications of these quantities to refined performance
analysis. The goal of this paper is thus to analyze fundamental properties of
scaled R\'enyi information from a noncommutative measure-theoretic perspective.
Firstly, we prove the uniform equicontinuity for all three quantum versions of
R\'enyi information, hence it yields the joint continuity of these quantities
in the orders and priors. Secondly, we establish the concavity in the region of
for both Petz's and the sandwiched versions. This completes the
open questions raised by Holevo
[\href{https://ieeexplore.ieee.org/document/868501/}{\textit{IEEE
Trans.~Inf.~Theory}, \textbf{46}(6):2256--2261, 2000}], Mosonyi and Ogawa
[\href{https://doi.org/10.1007/s00220-017-2928-4/}{\textit{Commun.~Math.~Phys},
\textbf{355}(1):373--426, 2017}]. For the applications, we show that the strong
converse exponent in classical-quantum channel coding satisfies a minimax
identity. The established concavity is further employed to prove an entropic
duality between classical data compression with quantum side information and
classical-quantum channel coding, and a Fenchel duality in joint source-channel
coding with quantum side information in the forthcoming papers
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