Editing Superfluid helium-4 (section)

=== Gaussian cluster approach ===
This is a two-scale approach which describes the superfluid component of liquid helium-4. It
consists of two [[Critical phenomena|nested models linked via parametric space]]. The short-wavelength part describes the interior structure of the [[fluid element]] using a non-perturbative approach based on the [[logarithmic Schrödinger equation]]; it suggests the [[Gaussian]]-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions.<ref>{{cite journal | url=https://link.aps.org/doi/10.1103/PhysRevLett.90.250403 | doi=10.1103/PhysRevLett.90.250403 | title=Roton-Maxon Spectrum and Stability of Trapped Dipolar Bose-Einstein Condensates | year=2003 | last1=Santos | first1=L. | last2=Shlyapnikov | first2=G. V. | last3=Lewenstein | first3=M. | journal=Physical Review Letters | volume=90 | issue=25 | page=250403 | pmid=12857119 | arxiv=cond-mat/0301474 | bibcode=2003PhRvL..90y0403S | s2cid=25309672 }}</ref> The approach provides a unified description of the [[phonon]], [[maxon excitation|maxon]] and [[roton]] excitations, and has noteworthy agreement with experiment: with one essential parameter to fit one reproduces at high accuracy the Landau roton spectrum, [[sound velocity]] and [[structure factor]] of superfluid helium-4.<ref>{{cite journal|author=K. G. Zloshchastiev|journal= Eur. Phys. J. B |volume= 85|page= 273 |year=2012|doi=10.1140/epjb/e2012-30344-3|title=Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation|issue=8|bibcode = 2012EPJB...85..273Z|arxiv = 1204.4652 |s2cid= 118545094 }}</ref> This model utilizes the general theory of quantum Bose liquids with logarithmic nonlinearities<ref>{{cite journal|author=A. V. Avdeenkov|author2=K. G. Zloshchastiev|name-list-style=amp|journal= J. Phys. B: At. Mol. Opt. Phys. |volume= 44|page= 195303|year=2011|doi=10.1088/0953-4075/44/19/195303|title=Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent|issue=19|bibcode = 2011JPhB...44s5303A|arxiv = 1108.0847 |s2cid=119248001}}</ref> which is based on introducing a [[Open quantum system|dissipative]]-type contribution to energy related to the quantum [[Entropic uncertainty|Everett–Hirschman entropy function]].<ref>[[Hugh Everett]], III. The Many-Worlds Interpretation of Quantum Mechanics: the theory of the universal wave function. [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Everett's Dissertation]</ref><ref name="Hirschman">[[Isidore Isaac Hirschman, Jr.|I.I. Hirschman, Jr.]], ''A note on entropy''. American Journal of Mathematics (1957) pp. 152–156</ref>