Circuit theory and full counting statistics of charge transfer through mesoscopic systems: A random-matrix approach

2007 ◽  
Vol 76 (7) ◽  
Author(s):  
G. C. Duarte-Filho ◽  
A. F. Macedo-Junior ◽  
A. M. S. Macêdo
Keyword(s):  
Charge Transfer ◽  
Random Matrix ◽  
Circuit Theory ◽  
Matrix Approach ◽  
Mesoscopic Systems ◽  
Full Counting Statistics ◽  
Counting Statistics

scholarly journals Full counting statistics for interacting trapped fermions

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Naftali Smith ◽  
Pierre Le Doussal ◽  
Satya Majumdar ◽  
Gregory Schehr
Keyword(s):  
Random Matrix ◽  
One Dimension ◽  
Explicit Calculation ◽  
Liquid Theory ◽  
Full Counting Statistics ◽  
Long Range Interactions ◽  
Random Matrix Models ◽  
System Maps ◽  
Counting Statistics ◽  
Trapped Fermions

We study NN spinless fermions in their ground state confined by an external potential in one dimension with long range interactions of the general Calogero-Sutherland type. For some choices of the potential this system maps to standard random matrix ensembles for general values of the Dyson index \betaβ. In the fermion model \betaβ controls the strength of the interaction, \beta=2β=2 corresponding to the noninteracting case. We study the quantum fluctuations of the number of fermions N_DND in a domain DD of macroscopic size in the bulk of the Fermi gas. We predict that for general \betaβ the variance of N_DND grows as A_{\beta} \log N + B_{\beta}AβlogN+Bβ for N \gg 1N≫1 and we obtain a formula for A_\betaAβ and B_\betaBβ. This is based on an explicit calculation for \beta\in\left\{ 1,2,4\right\}β∈{1,2,4} and on a conjecture that we formulate for general \betaβ. This conjecture further allows us to obtain a universal formula for the higher cumulants of N_DND. Our results for the variance in the microscopic regime are found to be consistent with the predictions of the Luttinger liquid theory with parameter K = 2/\betaK=2/β, and allow to go beyond. In addition we present families of interacting fermion models in one dimension which, in their ground states, can be mapped onto random matrix models. We obtain the mean fermion density for these models for general interaction parameter \betaβ. In some cases the fermion density exhibits interesting transitions, for example we obtain a noninteracting fermion formulation of the Gross-Witten-Wadia model.

COUNTING STATISTICS OF NONEQUILIBRIUM TUNNELING PROCESS USING FUNCTIONAL RENORMALIZATION GROUP

2010 ◽  
Vol 24 (05) ◽  
pp. 575-585 ◽  
Author(s):  
QING-QIANG XU ◽  
BEN-LING GAO ◽  
SHI-JIE XIONG
Keyword(s):  
Renormalization Group ◽  
Charge Transfer ◽  
Quantum Dot ◽  
Group Method ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Nonequilibrium Transport ◽  
Cumulant Generating Function ◽  
Full Counting Statistics ◽  
Counting Statistics

We develop a scheme to investigate the flux of nonequilibrium transport based on the full counting statistics and nonequilibrium functional renormalization group method. As an illustrative example, we study the charge transfer in the system of an interacting quantum dot connected to two noninteracting reservoirs via tunneling. Within the lowest approximation in functional renormalization group, we obtain the cumulant generating function analytically.

scholarly journals Full counting statistics of spin-flip and spin-conserving charge transitions in Pauli-spin blockade

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Sadashige Matsuo ◽  
Kazuyuki Kuroyama ◽  
Shunsuke Yabunaka ◽  
Sascha R. Valentin ◽  
Arne Ludwig ◽  
...  
Keyword(s):  
Spin Flip ◽  
Full Counting Statistics ◽  
Spin Blockade ◽  
Counting Statistics
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