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Transport in Single Quantum Dots: A Review from Linear Response to Nonlinear Regimes

Quantum dots are versatile systems for exploring quantum transport, electron correlations, and many-body phenomena such as the Kondo effect. While equilibrium properties are well understood through methods like the numerical renormalization group and density matrix renormalization group, nonequilibrium transport remains a major theoretical challenge. From the experimental point of view, recent advances in nanofabrication and measurement techniques have enabled the investigation of far-from-equilibrium regimes. These conditions give rise to new transport phenomena, where strong correlations and nonequilibrium dynamics interplay in complex ways; beyond the reach of conventional linear response theory. To meet these challenges, new approaches such as nonequilibrium Green's functions, real-time NRG, and time-dependent DMRG have emerged. This work reviews the established results for quantum dot transport in and beyond the linear regime, highlights recent theoretical and experimental advances, and discusses open problems and future prospects.