The B�ttiker-Landauer model generalized

Jurgen Michael Honig, Józef Spałek

Michael Ridley, Eliahu Cohen, Christian Flindt +1 more

The clock speed of topological quantum computers based on Majorana zero mode (MZM)-supporting nanoscale devices is limited by the time taken for electrons to traverse the device. We employ the time-dependent Landauer-B{ü}ttiker transport theory for current cross-lead correlations in a superconducting nanowire junction hosting MZMs. From the time-dependent quantum noise, we are able to extract traversal times for electrons crossing the system. After demonstrating a linear scaling of traversal times with nanowire length, we present a heuristic formula for the traversal times which accurately captures their behaviour. We then connect our framework to a proposed experimental verification of this discriminant between spurious and genuine MZMs utilizing time-resolved transport measurements.

Qi Zhang, Zhong‐Xiao Man, Yun‐Jie Xia

We study non-Markovianity and the Landauer principle in a composite thermal environment consisting of a memory dissipated to a Markovian reservoir. We consider non-Markovianity with respect to four different combinations of two parts of the environment regarding their bosonic and fermionic natures represented by a quantum harmonic oscillator and a qubit, respectively. It is found that non-Markovianity can be suppressed, kept invariant, or enhanced by increasing environmental temperature conditioned on different combinations. Focusing on our model, we establish a modified Landauer principle which holds in the non-Markovian process. We then generalize the model to the case with multiple environments to explore scaling effects of the environments on non-Markovianity. We find that non-Markovianity can be increased by enlarging the size of the environments. We also derive a Landauer bound in these multiple non-Markovian thermal environments. Our results provide strategies for acquiring and enhancing non-Markoviaity in the thermal environments and show the possibility to generalize the conventional Landauer principle to the non-Markovian process.

Shigeji Fujita, Kei Ito, Salvador Godoy

Zhong‐Xiao Man, Yun‐Jie Xia, Rosario Lo Franco

We study the validity of the Landauer principle in the non-Markovian regime by means of collisional models where the intracollisions inside the reservoir cause memory effects generating system-environment correlations. We adopt the system-environment correlations created during the dynamical process to assess the effect of non-Markovianity on the Landauer principle. Exploiting an exact equality for the entropy change of the system, we find the condition for the violation of the Landauer principle, which occurs when the established system-environment correlations become larger than a threshold. We then generalize the study to the nonequilibrium situation where the system is surrounded by many reservoirs at different temperatures. Our results, verified through collisional models with Heisenberg-type interactions, suggest that the complexity of the environment does not play a significant role in the qualitative mechanisms underlying the violation of the Landauer principle under non-Markovian processes.

Paul Bracken