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566 results on '"Li, Wen Long"'

2. Quantum Optimal Control Theory for the Shaping of Flying Qubits

Author

Dong, Xue, Cao, Xi, Li, Wen-Long, Zhang, Guofeng, Peng, Zhihui, and Wu, Re-Bing

Subjects
Quantum Physics
Abstract

The control of flying qubits carried by itinerant photons is ubiquitous in quantum networks. Beside their logical states, the shape of flying qubits must also be tailored for high-efficiency information transmission. In this paper, we introduce quantum optimal control theory to the shaping of flying qubits. Building on the flying-qubit control model established in our previous work, we design objective functionals for the generation of shaped flying qubits under practical constraints on the emitters and couplers. Numerical simulations employing gradient-descent algorithms demonstrate that the optimized control can effectively mitigate unwanted level and photon leakage caused by these non-idealities. Notably, while coherent control offers limited shaping capacity with a fixed coupler, it can significantly enhance the shaping performance when combined with a tunable coupler that has restricted tunability. The proposed optimal control framework provides a systematic approach to achieving high-quality control of flying qubits using realistic quantum devices., Comment: 12 pages, 8 figures

Published
2024

3. Infinite transition solutions for an Allen-Cahn equation

Author

Li, Wen-Long

Subjects
Mathematics - Analysis of PDEs, Mathematics - Dynamical Systems
Abstract

We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining infinite transition solutions for an Allen--Cahn equation. Rabinowitz and Stredulinsky have constructed infinite transition solutions as locally minimal solutions, but it is still an interesting question to establish these solutions by other method. Our result may attract the interest of constructing solutions with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for problems defined on descrete group.

Published
2024

4. Variational construction of basic heteroclinic solutions for an Allen-Cahn equation

Author

Li, Wen-Long

Subjects
Mathematics - Analysis of PDEs, Mathematics - Dynamical Systems
Abstract

We establish a variational construction of minimal and without self-intersection solutions for an Allen-Cahn equation, especially for those corresponding to irrational rotation vectors. These consequences generalize the results of rational cases of Rabinowitz and Stredulinsky to irrational cases.

Published
2023

19. Mountain pass type solutions for a generalized Frenkel-Kontorova model

Author

Li, Wen-Long

Subjects
Mathematics - Dynamical Systems, Mathematics - Analysis of PDEs
Abstract

We study a generalized Frenkel-Kontorova model and obtain periodic and heteroclinic mountain pass solutions. Heteroclinic mountain pass solution in the second laminations is new to the generalized Frenkel-Kontorova model. Our proof follows that of Bolotin and Rabinowitz for an Allen-Cahn equation, which is different with heat flow method for finding critical point of Frenkel-Kontorova model in the literature. The proofs depend on suitable choices of functionals and working spaces. We also study the multiplicity of these mountain pass solutions.

Published
2020

20. Multitransition solutions for a generalized Frenkel-Kontorova model

Author

Li, Wen-Long and Cui, Xiaojun

Subjects
Mathematics - Dynamical Systems, 35A15, 37K60, 74G25, 74G35
Abstract

We study a generalized Frenkel-Kontorova model. Using minimal and Birkhoff solutions as building blocks, we construct a lot of homoclinic solutions and heteroclinic solutions for this generalized Frenkel-Kontorova model under gap conditions. These new solutions are not minimal and Birkhoff any more. We use constrained minimization method to prove our results., Comment: 22 pages

Published
2020

24. Heteroclinic solutions for a generalized Frenkel-Kontorova model by minimization methods of Rabinowitz and Stredulinsky

Author

Li, Wen-Long and Cui, Xiaojun

Subjects
Mathematics - Dynamical Systems, 37J50, 37K60, 74G65
Abstract

We study heteroclinic solutions of a generalized Frenkel-Kontorova model. Using the methods of Rabinowitz and Stredulinsky, we prove that if the rotation vector of the configuration is rational and if there is an adjacent pair of periodic configurations, then there is a solution that is heteroclinic in one fixed direction and periodic in other directions. Furthermore, if the above heteroclinic solutions have an adjacent pair, then there is a solution that is heteroclinic in two directions and periodic in other directions. The procedure can be repeated to produce more complex solutions. Thus we obtain a variational construction for these minimal and Birkhoff solutions., Comment: 40 pages, 4 figures

Published
2019

25. Busemann functions on the Wasserstein space

Author

Zhu, Guomin, Li, Wen-Long, and Cui, Xiaojun

Subjects
Mathematics - Dynamical Systems, Mathematics - Differential Geometry, Mathematics - Metric Geometry
Abstract

We study rays and co-rays in the Wasserstein space $P_p(\mathcal{X})$ ($p > 1$) whose ambient space $\mathcal{X}$ is a complete, separable, non-compact, locally compact length space. We show that rays in the Wasserstein space can be represented as probability measures concentrated on the set of rays in the ambient space. We show the existence of co-rays for any prescribed initial probability measure. We introduce Busemann functions on the Wasserstein space and show that co-rays are negative gradient lines in some sense.

Published
2019

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