Incorporating Dissipation in Quantum Dynamics

A. O. Caldeira

Yu-Wei Huang, Pei-Yun Yang, Wei-Min Zhang

We develop a quantum theory for topological systems incorporating dissipations, noises, and thermal effects with strong non-Markovian dynamics, while other approaches in the literature may not be applicable. We derive the exact master equation and transient quantum transport for the study of dissipative topological systems, mainly focusing on noninteracting topological insulators and topological superconductors. The resulting exact master equation is also applicable to systems initially entangled with environments. In this theory, dissipations and topological states can be related to each other through spectral densities which tie up the reservoir spectra and topological-state wave functions in the system-reservoir couplings when either the system or environment is a topological system. We also apply the theory to study quantized Majorana conductance in superconductor-semiconductor hybrid systems incorporating different dissipations, noises, and thermal effects.

Kazuki Nishino, Kentaro Ohki, Koji Tsumura

This paper proposes an improved quantum coding method based on Markovian dissipative dynamics that is robust against thermal noise. A method for correcting information errors is indispensable for the practical use of quantum information devices, and stabilizer codes for quantum systems have been devised. One of the quantum coding methods, namely, quantum coding based on Markovian dissipative dynamics, has a favorable feature that it does not require strict time control, however it is known that these methods are susceptible to thermal noise. In this paper, we propose a quantum coding method that incorporates a new mechanism to correct the disturbance of the quantum state caused by thermal noise into the quantum coding method using dissipative dynamics. We also analyze the stability of the proposed quantum dynamics in the quantum state corresponding to the target code word. Numerical experiments confirm the effectiveness of the proposed method.

Michael Genkin, F. Ferro, Eva Lindroth

Using a simple model potential, we study the effects of weak Markovian dissipation on the quantum arrival time. The interaction with the environment is incorporated into the dynamics through a Markovian master equation of Lindblad type, which allows us to compare time-of-arrival distributions and approximate crossing probabilities for different dissipation strengths and temperatures. We also establish a connection to an earlier study where quantum tunneling with dissipation was investigated, which leads us to some conclusions concerning the formulation of the continuity equation in the Lindblad theory.