Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases
Abstract
1. Introduction
2. Model and Methods
3. Modulation Instability Versus QDs
3.1. The Single-Component GP Model
3.1.1. The Droplet Solution
3.1.2. The Plane-Wave Solution
3.1.3. Modulational Instability of the Plane Waves
3.2. The Two-Component Gross–Pitaevskii Model
3.2.1. Asymmetric QDs with Unequal Populations () for ()
3.2.2. Asymmetric QDs in the System with ()
3.2.3. The MI of the Asymmetric PW States
3.2.4. The MI for
3.2.5. The MI for
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Other Exact Solutions for the Single-Component GP Equation
Appendix A.1. δg/g>0
Appendix A.2. δg/g<0
Appendix B. Analytical Solutions for Strongly Asymmetric Fundamental and Dipole States
Appendix C. Other Exact Solutions in the Case of N1 ≪ N2
Appendix C.1. Solution of Equation (A7)
Appendix C.2. Solutions of Equation (A6)
Appendix C.2.1. Solution I
Appendix C.2.2. Solution II
Appendix C.2.3. Solution III
Appendix C.2.4. Solution IV
Appendix C.2.5. Solution V
Appendix C.2.6. Solution VI
Appendix C.2.7. Solution VII
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Mithun, T.; Maluckov, A.; Kasamatsu, K.; Malomed, B.A.; Khare, A. Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases. Symmetry 2020, 12, 174. https://doi.org/10.3390/sym12010174
Mithun T, Maluckov A, Kasamatsu K, Malomed BA, Khare A. Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases. Symmetry. 2020; 12(1):174. https://doi.org/10.3390/sym12010174
Chicago/Turabian StyleMithun, Thudiyangal, Aleksandra Maluckov, Kenichi Kasamatsu, Boris A. Malomed, and Avinash Khare. 2020. "Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases" Symmetry 12, no. 1: 174. https://doi.org/10.3390/sym12010174
APA StyleMithun, T., Maluckov, A., Kasamatsu, K., Malomed, B. A., & Khare, A. (2020). Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases. Symmetry, 12(1), 174. https://doi.org/10.3390/sym12010174