Bistability in a nonequilibrium quantum system with electron-phonon interactions

Abstract

The existence of more than one steady-state in a many-body quantum system driven out-ofequilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this paper, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows us to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot, consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the nonequilibrium dynamics and on the emergence of bistability is discussed.

Beyond mean-field bistability in driven-dissipative lattices: Bunching-antibunching transition and quantum simulation

“…It is important to mention that in a realistic scenario the qubits experience relaxation and dephasing with typical coherence times of about T 1 ∼ 1µs and T 2 ∼ 0.6µs [77]. In the latter experiment, the qubits have frequencies ω (1) c /2π = 6 GHz ±2 MHz, ω (2) c /2π = 7 GHz ±2 MHz, and ω (3) c /2π = 8 GHz ±2 MHz. The coherence time T 1 gives a relaxation rate γ 1 ∼ 1 MHz, so Ω ranges from 0.1 MHz to 2 MHz, ∆ c from −2 MHz to 10 MHz, and J from 0 to 10 MHz.…”

Extension of the Nakajima-Zwanzig approach to multitime correlation functions of open systems

“…This property, also valid forK(t 2 , t 1 ), can be seen directly from Eqs. (26) and (29) and formally reads…”

“…In [25,26] the NakajimaZwanzig generalised quantum master equation is used to extract the specific memory kernels from the early time evolution of the system, which was initially obtained by the use of one of the exact approaches mentioned above. The memory kernels are then used for the calculation of the system dynamics for arbitrary long times.…”

A quasi-classical mapping approach to vibrationally coupled electron transport in molecular junctions

“…44,[55][56][57][58][59][60][61][62][63] In addition, a variety of numerically exact schemes have employed, including numerical pathintegral approaches, [64][65][66] the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method, 67, 68 the scattering state numerical renormalization group approach, 69 and a combination of reduced density matrix techniques and impurity solvers. 32,70 All these methods employ a quantum mechanical treatment of both the electronic and nuclear DoF. An alternative strategy is to use classical concepts, which typically scale much more favorably with the dimensionality of the problem, i.e., the number of nuclear DoF, than fully quantum mechanical methods, and also allow a straightforward application to systems with anharmonic potential energy surfaces, which is a challenge, e.g., for NEGF theory and path-integral methods.…”