| We numerically study the dynamics of a system consisting of a quantum dot coupled to a lead, with the quantum dot modeled by the Anderson impurity Hamiltonian. We focus on the transport regime where the dot is occupied by a single electron, leading to Kondo correlations. First, by using the numerical renormalization group method we generate an approximate eigenbasis of the full system. Then, to study the dynamics of the system's density matrix, we use the Liouville equation in the Lindblad form, where the Lindblad quantum jump operators model the dissipative coupling to the environment. The Liouville equation is solved by adapting the quantum trajectory method, in which one averages over an ensemble of trajectories generated for different states of the system. Each trajectory is generated stochastically according to a probability distribution of quantum jump operators, combined with a coherent evolution due to a non-hermitian yet symmetric effective Hamiltonian. We show that by combining the quantum trajectory method with numerical renormalization group we are able to study nonequilibrium steady state situations of the Anderson impurity model. |
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