The stationary tunneling current and differential conductance of the coupled quantum dots system with split-gates are calculated by generalizing the Beenaker's linear response theory for the description of the Coulomb-blockade oscillations of the conductance in the single quantum dot. The calculation of the charging diagram in parallel through the double dot as function of the two side-gate voltages shows a remarkable agreement with the recent experimental results by Hatano et al. (Science, 2005, 309: 268-271) quantum transport, quantum dots, Coulomb blockade, differential conductivityOver the past decades great attention has been paid to artificially fabricated nanostructures, among which semiconductor quantum dot (QD) has been proven to be a useful system in both theoretical and experimental facet. QD has become the indispensable member in the electro-optical devices such as semiconductor lasers [1] , and single-electron transistors [2,3] . Single quantum dot can function as a microelectronic unit such as a transistor to form the basis of nanoelectronics [4] . Quantum dots and coupled quantum dots (CQDs) have also been proposed as the candidate for the quantum information processing and quantum computation [5][6][7][8] by using the electron-electron and electron-hole interactions and spin dynamics [9] . QD and coated-QD nanoparticles have been applied in biodetection by using the fluorescence resonance transfer [10][11][12] . Many peculiar quantum transport properties have been found in the QDs, for example, Coulomb blockade effect [13] , due to Hubbard interaction among the charged carriers [3,14] , photon-assisted transport properties [15][16][17][18] , Kondo effect in the quantum dots due to the coupling of local degenerate state to the mobile electron reservoirs [19][20][21] . The optical absorption [22] and electric capacitance spectra [23] have been studied in QD within the multiple-electron configuration, the luminescence in porous silicon can be interpreted by the QD model taking into account of the interfacial-confined polarons [24] .There are many approaches to attack the quantum transport problems in QD, among which we have master equation method [25] , Keldysh non-equilibrium Green's function [26,27] , and ensemble method [14,28,29] . In the early theoretical study on transport properties in QD, Korotkov et al. [14] , Meir et al. [28] , and Beenakker [29] proposed a linear theory of transport through the single quantum dot which had incorporated both single electron charging and energy level quantization. The linear transport theory for the electron by Beenakker's also took account of the thermal broadening and the deviation of the electron distribution in the dot level from the standard FermiDirac law. In a recent experiment [30][31][32] , using the hybrid vertically coupled quantum dots, Hatano and coworkers
