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We study a system-bath description in the strong coupling regime where it is not possible to derive a master equation for the reduced density matrix by a direct expansion in the system-bath coupling. A particular example is a bath with significant spectral weight at low frequencies. Through a unitary transformation it can be possible to find a more suitable small expansion parameter. Within such approach we construct a formally exact expansion of the master equation on the Keldysh contour. We consider a system diagonally coupled to a bosonic bath and expansion in terms of a non-diagonal hopping term. The lowest-order expansion is equivalent to the so-called $P(E)$-theory or non-interacting blip approximation (NIBA). The analysis of the higher-order contributions shows that there are two different classes of higher-order diagrams. We study how the convergence of this expansion depends on the form of the spectral function with significant weight at zero frequency.
We consider the coupling of a single mode microwave resonator to a tunnel junction whose contacts are at thermal equilibrium. We derive the quantum master equation describing the evolution of the resonator field in the strong coupling regime, where t
By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state and a variational approach `a la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagneticall
The interplay of optical driving and hyperfine interaction between an electron confined in a quantum dot and its surrounding nuclear spin environment produces a range of interesting physics such as mode-locking. In this work, we go beyond the ubiquit
We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system
We investigate three kinds of heat produced in a system and a bath strongly coupled via an interaction Hamiltonian. By studying the energy flows between the system, the bath, and their interaction, we provide rigorous definitions of two types of heat