arXiv subjects

Zhi-Cheng Zhu

Publications and source records attributed to Zhi-Cheng Zhu.

4 recordsLinked to original sources

arXiv2022

A Poincaré-Birkhoff-Witt theorem for the universal enveloping algebra of a Rota-Baxter Lie algebra

Rota-Baxter associative algebras and Rota-Baxter Lie algebras are both important in mathematics and mathematical physics, with the former a basic structure in quantum field renormalization and the latter a operator form of the classical Yang-Baxter equation. An outstanding problem posed by Gubarev is to determine whether there is a Poincaré-Birkhoff-Witt theorem for the universal enveloping Rota-Baxter associative algebra of a Rota-Baxter Lie algebra. This paper resolves this problem positively, working with operated algebras and applying the method of Gröbner-Shirshov bases.

math.QA↗

arXiv2022

Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects

Groups with various types of operators, in particular the recently introduced Rota-Baxter groups, have generated renowned interest with close connections to numerical integrals, Yang-Baxter equation, integrable systems and post-Hopf algebras. This paper gives the general notion of operated groups and provides explicit constructions of free operated groups, free differential groups and free Rota-Baxter groups.

math.GR↗

arXiv2009

Effect of Quantum Point Contact Measurement on Electron Spin State in Quantum Dot

We study the time evolution of two electron spin states in a double quantum-dot system, which includes a nearby quantum point contact (QPC) as a measurement device. We obtain that the QPC measurement induced decoherence is in time scales of microsecond. We also find that the enhanced QPC measurement will trap the system in its initial spin states, which is consistent with quantum Zeno effect.

quant-ph↗

arXiv2008

Eliminating interactions between non-neighboring qubits in the preparation of cluster states in quantum molecules

We propose a scheme to eliminate the effect of non-nearest-neighbor qubits in preparing cluster state with double-dot molecules. As the interaction Hamiltonians between qubits are Ising-model and mutually commute, we can get positive and negative effective interactions between qubits to cancel the effect of non-nearest-neighbor qubits by properly changing the electron charge states of each quantum dot molecule. The total time for the present multi-step cluster state preparation scheme is only doubled for one-dimensional qubit chain and tripled for two-dimensional qubit array comparing with the time of previous protocol leaving out the non-nearest-neighbor interactions.

quant-ph↗