We present a comprehensive Fermi liquid description for thermoelectric transport and current noise, applicable to multilevel quantum dots (QD) and magnetic alloys (MA) without electron-hole or time-reversal symmetry. Our formulation for the low-energy transport is based on an Anderson model with
N discrete impurity levels, and is asymptotically exact at low energies, up to the next-leading order terms in power expansions with respect to temperature
T and bias voltage
eV. The expansion coefficients can be expressed in terms of the Fermi liquid parameters, which include the three-body correlation functions defined with respect to the equilibrium ground state in addition to the linear susceptibilities and the occupation number
Nd of impurity electrons. We apply this formulation to the
SU(N) symmetric QD and MA, and calculate the correlation functions for
N=4 and 6, using numerical renormalization group approach. The three-body correlations are shown to be determined by a single parameter over a wide range of electron fillings $1\ensuremath{\lesssim}{N}_{d}^{}\ensuremath{\lesssim}N\ensuremath{-}1$ for strong Coulomb interactions
U, and they also exhibit the plateau structures due to the
SU(N) Kondo effects at integer values of
Nd. We find that the Lorenz number $L=\ensuremath{\kappa}/(T\ensuremath{\sigma})$ for QD and MA, defined as the ratio of the thermal conductivity $\ensuremath{\kappa}$ to the electrical conductivity $\ensuremath{\sigma}$, deviates from the universal Wiedemann-Franz value ${\ensuremath{\pi}}^{2}/(3{e}^{2})$ as the temperature increases from
T=0, showing the
T2 dependence, the coefficient for which depends on the three-body correlations away from half filling. Furthermore, we find that the current noise for the SU(4) quantum dots and that for SU(6) show a pronounced difference at the quarter
Nd/N=1/4 and
3/4 fillings. In particular, the linear noise for
N=4 exhibits a flat peak while the peak for
N=6 shows a round shape, reflecting the fact that, at these filling points, the
SU(N) Kondo effects occur for $N\ensuremath{\equiv}0$ (mod 4), whereas the intermediate-valence fluctuations occur for $N\ensuremath{\equiv}2$ (mod 4). We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.
We study the three-body Fermi liquid effects in the SU(
N) Anderson impurity model within the strong interaction limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$, where the occupation number
Nd of the impurity levels varies over the range of
0<Nd<1. The three-body correlations arise among the impurity electrons when the electron-hole symmetry, the time-reversal symmetry, or both are broken by external fields or potentials. They play a key role in low-energy transport, particularly in the next-to-leading-order terms of power expansion with respect to temperature
T and bias voltage
eV. Using the numerical renormalization group approach, we calculate the differential conductance and nonlinear current noise through quantum dots, as well as the thermal conductivity of both quantum dots and magnetic alloys. Specifically, we focus on the SU(2) and SU(4) cases, demonstrating how the three-body correlations evolve in the strong interaction limit across the
1/N-filling Kondo regime at ${N}_{d}^{}\ensuremath{\simeq}1.0$ and the valence fluctuation regime where the occupation number
Nd varies rapidly with the position ${\ensuremath{\epsilon}}_{d}^{}$ of the impurity levels. We also show that the three-body correlations strongly couple with asymmetries in the tunnel couplings between quantum dots and reservoirs. For
N=4, this coupling significantly affects the order
(eV)3 nonlinear current through the quarter-filling Kondo state, where the electron-hole symmetry is broken. In particular, in the $U\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, the expansion coefficients exhibit clear plateau structures associated with the Kondo effect at ${N}_{d}^{}\ensuremath{\simeq}1.0$. Our formulation and analysis pave the way for deducing the three-body correlations from the low-energy experiments on the next-to-leading-order transport.