References

References#

[AM05]

Karim M. Abadir and Jan R. Magnus. Matrix Algebra. Econometric Exercises. Cambridge University Press (CUP), 2005. ISBN 978-0-521-53746-9.

[AC91]

M. A. Ablowitz and P. A. Clarkson. Solitons, Nonlinear Evolution Equations and Inverse Scattering. Volume 149 of London Mathematical Society Lecture Note Series. Cambridge University Press, December 1991. ISBN 9780511623998. URL: http://dx.doi.org/10.1017/CBO9780511623998, doi:10.1017/cbo9780511623998.

[AAPkecakFWlazlowski26]

J. E. Alba-Arroyo, Daniel Pęcak, Michael McNeil Forbes, and Gabriel Wlazłowski. Local quantum friction with pairing: unitary dissipation in large Fermi systems. 2026. URL: https://arxiv.org/abs/2512.12866, arXiv:2512.12866, doi:10.48550/ARXIV.2512.12866.

[AT25]

Samuel Alperin and Eddy Timmermans. Counterflow leads to roton spectra in locally interacting superfluids. 2025. URL: https://arxiv.org/abs/2507.08985, arXiv:2507.08985, doi:10.48550/ARXIV.2507.08985.

[BDP+26]

Manon Ballu, Romain Dubessy, Aurélien Perrin, Hélène Perrin, and Anna Minguzzi. Soliton turbulence of a strongly driven one-dimensional Bose gas. 2026. URL: https://arxiv.org/abs/2603.24832, arXiv:2603.24832, doi:10.48550/ARXIV.2603.24832.

[BH86]

Daniel Baye and P-H Heenen. Generalised meshes for quantum mechanical problems. J. Phys. A, 19(11):2041–2059, 1986. doi:10.1088/0305-4470/19/11/013.

[Boy89]

John P. Boyd. Chebyshev and Fourier Spectral Methods. Volume 49 of Lecture Notes in Engineering. Dover, Berlin Heidelberg, 2 edition, 1989. ISBN 978-0486411835. URL: http://www-personal.umich.edu/~jpboyd/BOOK_Spectral2000.html.

[Bul07]

Aurel Bulgac. Local density functional theory for superfluid fermionic systems: the unitary gas. Phys. Rev. A, 76:040502, 2007. arXiv:cond-mat/0703526, doi:10.1103/PhysRevA.76.040502.

[BFK+14]

Aurel Bulgac, Michael McNeil Forbes, Michelle M. Kelley, Kenneth J. Roche, and Gabriel Wlazłowski. Quantized superfluid vortex rings in the unitary Fermi gas. Phys. Rev. Lett., 112(2):025301, January 2014. URL: http://arxiv.org/abs/1306.4266, arXiv:1306.4266, doi:10.1103/PhysRevLett.112.025301.

[BFRWlazlowski13]

Aurel Bulgac, Michael McNeil Forbes, Kenneth J. Roche, and Gabriel Wlazłowski. Quantum friction: cooling quantum systems with unitary time evolution. 2013. URL: http://arxiv.org/abs/1305.6891, arXiv:1305.6891.

[CD96]

Y. Castin and R. Dum. Bose-Einstein condensates in time dependent traps. Phys. Rev. Lett., 77:5315–5319, December 1996. URL: http://link.aps.org/doi/10.1103/PhysRevLett.77.5315, doi:10.1103/PhysRevLett.77.5315.

[DHM25]

Yu Deng, Zaher Hani, and Xiao Ma. Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory. 2025. arXiv:2503.01800, doi:10.48550/ARXIV.2503.01800.

[FT87]

Ludwig D. Faddeev and Leon A. Takhtajan. Hamiltonian Methods in the Theory of Solitons. Classics in Mathematics. Springer Berlin Heidelberg, 1987. ISBN 9783540699699. URL: http://dx.doi.org/10.1007/978-3-540-69969-9, doi:10.1007/978-3-540-69969-9.

[Fet09]

Alexander L. Fetter. Rotating trapped Bose-Einstein condensates. Rev. Mod. Phys., 81(2):647–691, May 2009. doi:10.1103/RevModPhys.81.647.

[Fey98]

Richard P. Feynman. Statistical Mechanics: A Set of Lectures. Advanced Book Classics. Perseus Books, Reading, Massachusetts, 2 edition, 1998. ISBN 978-0201360769.

[FGG12]

Michael McNeil Forbes, Stafano Gandolfi, and Alexandros Gezerlis. Effective-range dependence of resonantly interacting fermions. Phys. Rev. A, 86:053603, November 2012. arXiv:1205.4815, doi:10.1103/PhysRevA.86.053603.

[Gau00]

Walter Gautschi. Gauss–Radau formulae for Jacobi and Laguerre weight functions. Mathematics and Computers in Simulation, 54(4–5):403–412, December 2000. URL: http://dx.doi.org/10.1016/S0378-4754(00)00179-8, doi:10.1016/s0378-4754(00)00179-8.

[HHebertLarreA23]

J. Huynh, F. Hébert, P.-É. Larré, and M. Albert. Stationary transport above the critical velocity in a one-dimensional superflow past an obstacle. Europhys. Lett., 143(4):46005, August 2023. URL: http://dx.doi.org/10.1209/0295-5075/acf15a, doi:10.1209/0295-5075/acf15a.

[ITT10]

S. Ishino, H. Takeuchi, and M. Tsubota. Counterflow quantum turbulence and the instability in two-component bose-einstein condensates. J. Low Temp. Phys., 162(3-4):361–366, December 2010. URL: http://dx.doi.org/10.1007/s10909-010-0324-y, doi:10.1007/s10909-010-0324-y.

[JTKA11]

J. A. Joseph, John E. Thomas, M. Kulkarni, and A. G. Abanov. Observation of shock waves in a strongly interacting Fermi gas. Phys. Rev. Lett., 106(15):150401, April 2011. doi:10.1103/PhysRevLett.106.150401.

[KJM+14]

Mark J. H. Ku, Wenjie Ji, Biswaroop Mukherjee, Elmer Guardado-Sanchez, Lawrence W. Cheuk, Tarik Yefsah, and Martin W. Zwierlein. Motion of a Solitonic Vortex in the BEC-BCS Crossover. Phys. Rev. Lett., 113(6):065301, August 2014. arXiv:1402.7052, doi:10.1103/PhysRevLett.113.065301.

[KMYZ15]

Mark J. H. Ku, Biswaroop Mukherjee, Tarik Yefsah, and Martin W. Zwierlein. From planar solitons to vortex rings and lines: cascade of solitonic excitations in a superfluid Fermi gas. Phys. Rev. Lett., 116:045304, 2015. URL: http://arxiv.org/abs/1507.01047, arXiv:1507.01047, doi:10.1103/PhysRevLett.116.045304.

[LP01]

P. Leboeuf and N. Pavloff. Bose-Einstein beams: coherent propagation through a guide. Phys. Rev. A, 64(3):033602, August 2001. URL: http://link.aps.org/doi/10.1103/PhysRevA.64.033602, arXiv:cond-mat/0103294, doi:10.1103/PhysRevA.64.033602.

[LGL10]

Ruxu Lian, Zhenhua Guo, and Hai-Liang Li. Dynamical behaviors for 1d compressible navier–stokes equations with density-dependent viscosity. Journal of Differential Equations, 248(8):1926–1954, April 2010. URL: http://dx.doi.org/10.1016/j.jde.2009.11.029, doi:10.1016/j.jde.2009.11.029.

[LC02]

Robert G. Littlejohn and Matthew Cargo. Bessel discrete variable representation bases. J. Chem. Phys., 117(1):27–36, July 2002. doi:10.1063/1.1481388.

[LCC+02]

Robert G. Littlejohn, Matthew Cargo, Tucker Carrington, Jr., Kevin A. Mitchell, and Bill Poirier. A general framework for discrete variable representation basis sets. J. Chem. Phys., 116(20):8691–8703, 2002. doi:10.1063/1.1473811.

[MM03]

Pietro Massignan and Michele Modugno. One-dimensional model for the dynamics and expansion of elongated Bose-Einstein condensates. Phys. Rev. A, 67:023614, February 2003. URL: https://link.aps.org/doi/10.1103/PhysRevA.67.023614, doi:10.1103/PhysRevA.67.023614.

[MD09]

A. Muñoz Mateo and V. Delgado. Effective one-dimensional dynamics of elongated bose–einstein condensates. Annals of Physics, 324(3):709 – 724, 2009. URL: http://www.sciencedirect.com/science/article/pii/S0003491608001516, doi:https://doi.org/10.1016/j.aop.2008.10.002.

[Osb10]

Alfred R. Osborne. Nonlinear Ocean Waves and the Inverse Scattering Transform. Volume 97 of International Geophysics. Academic Press, 2010. ISBN 978-0-12-528629-9. URL: https://www.sciencedirect.com/science/article/pii/S0074614210970393, doi:https://doi.org/10.1016/S0074-6142(10)97039.

[PB99]

T. Papenbrock and George F. Bertsch. Pairing in low-density Fermi gases. Phys. Rev. C, 59:2052–2055, 1999. arXiv:nucl-th/9811077, doi:10.1103/PhysRevC.59.2052.

[PMSM+17]

A. Paris-Mandoki, J. Shearring, F. Mancarella, T. M. Fromhold, A. Trombettoni, and P Krüger. Superfluid flow above the critical velocity. Sci. Rep., 7:9070, August 2017. doi:10.1038/s41598-017-08941-8.

[PS02]

C.J. Pethick and H. Smith. Bose-Einstein Condensation in Dilute Gases. Cambridge University Press, 2002. ISBN 9780521665803. URL: https://www.cambridge.org/core/books/boseeinstein-condensation-in-dilute-gases/CC439EAD70D78E47E9AF536DA7B203EC\.

[PS03]

Lev. P. Pitaevskii and Sandro Stringari. Bose-Einstein Condensation. Volume 116 of International Series of Monographs on Physics. Oxford University Press, Oxford, 2003. ISBN 9780198507192. doi:10.1093/acprof:oso/9780198758884.001.0001.

[PTVF07]

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, third edition, 2007.

[SN04]

Barry I. Schneider and Nicolai Nygaard. Discrete variable representation for singular Hamiltonians. Phys. Rev. E, 70:056706, November 2004. URL: https://link.aps.org/doi/10.1103/PhysRevE.70.056706, arXiv:physics/0407076, doi:10.1103/PhysRevE.70.056706.

[Sch19]

Nicolas Schunck, editor. Energy Density Functional Methods for Atomic Nuclei. IOP Publishing, 2019. ISBN 978-0-7503-1422-0. doi:10.1088/2053-2563/aae0ed.

[Sil00]

John R. Silvester. Determinants of block matrices. The Mathematical Gazette, 84(501):460–467, November 2000. URL: http://dx.doi.org/10.2307/3620776, doi:10.2307/3620776.

[Str22]

Marta Strani. Stability properties of the steady state for the isentropic compressible Navier-Stokes equations with density dependent viscosity in bounded intervals. Commun. Math. Sci., 20(1):231–264, 2022. URL: https://arxiv.org/abs/1905.00770, doi:10.4310/cms.2022.v20.n1.a7.

[Tre00]

Lloyd N. Trefethen. Spectral Methods in MATLAB. SIAM, January 2000. ISBN 978-0-89871-959-8. doi:10.1137/1.9780898719598.

[Wan99]

Sanwu Wang. Generalization of the Thomas-Reiche-Kuhn and the Bethe sum rules. Phys. Rev. A, 60(1):262–266, July 1999. URL: http://dx.doi.org/10.1103/PhysRevA.60.262, doi:10.1103/physreva.60.262.

[WlazlowskiSMM18]

Gabriel Wlazłowski, Kazuyuki Sekizawa, Maciej Marchwiany, and Piotr Magierski. Suppressed solitonic cascade in spin-imbalanced superfluid Fermi gas. Phys. Rev. Lett., 120:253002, June 2018. doi:10.1103/PhysRevLett.120.253002.

[WlazlowskiBFR15]

Gabriel Wlazłowski, Aurel Bulgac, Michael McNeil Forbes, and Kenneth J. Roche. Life cycle of superfluid vortices and quantum turbulence in the unitary Fermi gas. Phys. Rev. A, 91:031602(R), 2015. arXiv:1404.1038, doi:10.1103/PhysRevA.91.031602.

[WN03]

Biao Wu and Qian Niu. Superfluidity of bose–einstein condensate in an optical lattice: landau–zener tunnelling and dynamical instability. New J. Phys., 5:104–104, July 2003. URL: http://dx.doi.org/10.1088/1367-2630/5/1/104, doi:10.1088/1367-2630/5/1/104.

[WZ14]

Zhigang Wu and Eugene Zaremba. Dynamics of harmonically-confined systems: some rigorous results. Ann. Phys. (NY), 342:214–238, March 2014. URL: http://dx.doi.org/10.1016/j.aop.2014.01.006, doi:10.1016/j.aop.2014.01.006.

[YSK+13]

Tarik Yefsah, Ariel T. Sommer, Mark J. H. Ku, Lawrence W. Cheuk, Wenjie Ji, Waseem S. Bakr, and Martin W. Zwierlein. Heavy solitons in a fermionic superfluid. Nature, 499:426–430, July 2013. arXiv:1302.4736, doi:10.1038/nature12338.

[ZTS25]

M. Zhao, J. Tao, and I. B. Spielman. Kolmogorov scaling in turbulent 2d bose-einstein condensates. Phys. Rev. Lett., February 2025. URL: http://dx.doi.org/10.1103/PhysRevLett.134.083402, doi:10.1103/physrevlett.134.083402.

[ZakharovShabat72]

V. E. Zakharov and A. B. Shabat. Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media. Sov. Phys.–JETP, 34:62, January 1972. [Zh. Èksp. Teor. Fiz. \textbf 61, 118-134 (1971)]. URL: http://www.jetp.ras.ru/cgi-bin/dn/e_034_01_0062.pdf.