umu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Hydrodynamics of Binary Bose-Einstein Condensates and Hydro-elasticity of the Inner Crust of Neutron Stars
Umeå University, Faculty of Science and Technology, Department of Physics.ORCID iD: 0000-0003-0827-2193
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In the present thesis, “Hydrodynamics of Binary Bose-Einstein Condensates and Hydro-elasticity of the Inner Crust of Neutron Stars”, the hydrodynamic effects, instabilities and superfluid turbulence in binary immiscible ultracold gases, and hydro-elastic macroscopic coupled modes and microscopic structure of the inner layers of the crust of neutron stars, are studied. The ultracold gas dynamics can be realized in the laboratory. The excitation modes of the inner crust determine a number of observable properties such as elasticity, thermal properties and mass transport properties. Here we focus on expanding the details, rather than repeating the results presented in the published articles.

In the part of the thesis related to atomic ultracold gases, we utilize the physical parameters in the experimentally realizable parameter region. We numerically simulate the coupled non-linear Schrödinger equations, and calculate observable quantities, such as phase and modulus of the order parameter, conditions needed for observation of the Rayleigh-Taylor instability and for turbulence generation. The numerical calculations are accompanied by analytical description of the processes. The dispersion relation for capillary-gravitational waves at the interface between two ultracold gases, is derived straightforwardly from the superfluid Lagrangian. The equations of motion for centre-of-mass of the superfluids are derived, and then used in our model of the quantum swapping of immiscible superfluids pressed by a strong external force. By numerical simulation, we find that the Kelvin-Helmholtz instability which occurs at the non-linear stage of the Rayleigh-Taylor instability, can generate quantum turbulence with peculiar properties. We find that two-dimensional superfluid systems with weak inter-component repulsion are different from previously studied strongly repulsive binary superfluids, because the quantum Kelvin-Helmholtz instability in weakly repulsive superfluids rolls up the whole interface forming a vortex bundle, similarly to dynamics of the shear fluid layers in the classical hydrodynamics. Production of vortex bundles favours the Kolmogorov spectrum of turbulence, and we find that the Kolmogorov scaling indeed is present in a freely decaying turbulence.

In the part of the thesis related to neutron stars, we study the inner crust of neutron stars, where the fully ionized atomic nuclei coexist with a superfluid of neutrons. The interaction between superfluid neutrons and the crystallized Coulomb plasma is due to the interaction between density perturbations (interaction of the scalar type), and between the current - the non-dissipative entrainment effect (interaction of the vector type). We calculate velocities of the collective modes of the crystal coupled to superfluid neutrons. As an input we use the results of microscopic nuclear calculations in the framework of the compressible liquid drop model (the Lattimer and Swesty equation of state), and more recent effective Thomas-Fermi calculations with shell corrections (N. Chamel, and the Brussels theoretical nuclear physics group). Knowledge of velocities as functions of the matter density in the inner crust is important for calculation of a number of dynamic and transport properties. The heat transport properties of the inner crust are directly observable in accreting binary systems (low-mass x-ray binaries). The mass transport properties of the inner crust are directly linked to the rotational evolution, being a key physical ingredient of the pulsar glitch phenomenon. The elastic properties are related to the vibrational modes of the star, and to the breaking stress of the crust.

In the second part of our work on neutron stars we investigate the microscopic structure of the inner crust treating the structure as an anisotropic crystal coupled to s-wave superfluid neutron liquid. As we analyse dynamics of the elementary excitations at higher wavenumbers (smaller scales), we reach the edge of the first Brillouin zone. The Lattimer-Swesty data is applicable for wavenumbers much smaller than the edge of the first Brillouin zone. We extrapolate the data through the whole first Brillouin zone to calculate the fastest growth rate of the unstable modes. The crucial step is to calculate the mode velocities in anisotropic crystal incorporating both the induced neutron-proton interactions, and the electron screening properties. We find that the combined influence of these two effects leads to softening of the longitudinal phonon of the lattice above about the Thomas-Fermi screening wavenumber of the electrons. The critical wavenumber when the frequency becomes purely imaginary is about  1/5 - 2/3  of the reciprocal lattice vector, thus validating our assumption. The imaginary mode frequency implies instability at finite wavenumbers. Our calculations suggest that the mode at the first Brillouin zone edge is the most unstable, and thus the structure experiences a displacive phase transition when the central ion of a unit cell of the body-cubic-centred lattice, is displaced to the cube face. Thus, the electronic structure of matter at densities above the neutron drip [1], is richer than previously appreciated, and new microscopic calculations of nuclear structure are necessary which take into account the high-wavenumber physics. Such calculations will provide crucial input to models interpreting the quasi-periodic oscillations in Soft Gamma Repeaters as magnetar x-ray flares, and to the theory of glitches of neutron stars.

[1] The neutron drip density is ~3×1011 g cm-3.

Place, publisher, year, edition, pages
Umeå: Umeå Universitet , 2014. , 77 p.
Keyword [en]
Binary Bose-Einstein condensates in ultracold gases, hydrodynamics, quantum turbulence, neutron stars, the inner crust, nuclear astrophysics
National Category
Astronomy, Astrophysics and Cosmology Atom and Molecular Physics and Optics Condensed Matter Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:umu:diva-86892ISBN: 978-91-7601-036-5 (print)OAI: oai:DiVA.org:umu-86892DiVA: diva2:704495
Public defence
2014-04-03, Naturvetarhuset, N420, Umeå universitet, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2014-03-13 Created: 2014-03-12 Last updated: 2014-03-14Bibliographically approved
List of papers
1. Interface dynamics of a two-component Bose-Einstein condensate driven by an external force
Open this publication in new window or tab >>Interface dynamics of a two-component Bose-Einstein condensate driven by an external force
Show others...
2011 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 83, no 4, 043623- p.Article in journal (Refereed) Published
Abstract [en]

The dynamics of an interface in a two-component Bose-Einstein condensate driven by a spatially uniform time-dependent force is studied. Starting from the Gross-Pitaevskii Lagrangian, the dispersion relation for linear waves and instabilities at the interface is derived by means of a variational approach. A number of diverse dynamical effects for different types of driving force is demonstrated, which includes the Rayleigh-Taylor instability for a constant force, the Richtmyer-Meshkov instability for a pulse force, dynamic stabilization of the Rayleigh-Taylor instability and onset of the parametric instability for an oscillating force. Gaussian Markovian and non-Markovian stochastic forces are also considered. It is found that the Markovian stochastic force does not produce any average effect on the dynamics of the interface, while the non-Markovian force leads to exponential perturbation growth.

Place, publisher, year, edition, pages
American Physical Society, 2011
Keyword
two-component bose-einstein condensate
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:umu:diva-43430 (URN)10.1103/PhysRevA.83.043623 (DOI)
Available from: 2012-03-29 Created: 2011-04-29 Last updated: 2017-12-11Bibliographically approved
2. Quantum swapping of immiscible Bose-Einstein condensates as an alternative to the Rayleigh-Taylor instability
Open this publication in new window or tab >>Quantum swapping of immiscible Bose-Einstein condensates as an alternative to the Rayleigh-Taylor instability
Show others...
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 1, 013630- p.Article, review/survey (Refereed) Published
Abstract [en]

We consider a two-component Bose-Einstein condensate in a quasi-one-dimensional harmonic trap, where the immiscible components are pressed against each other by an external magnetic force. The zero-temperature nonstationary Gross-Pitaevskii equations are solved numerically; analytical models are developed for the key steps in the process. We demonstrate that if the magnetic force is strong enough, then the condensates may swap their places in the trap due to dynamic quantum interpenetration of the nonlinear matter waves. The swapping is accompanied by development of a modulational instability leading to quasiturbulent excitations. Unlike the multidimensional Rayleigh-Taylor instability in a similar geometry of two-component quantum fluid systems, quantum interpenetration has no classical analog. In a two-dimensional geometry a crossover between the Rayleigh-Taylor instability and the dynamic quantum interpenetration is investigated.

Place, publisher, year, edition, pages
American Physical Society, 2012
Keyword
two-component bose-einstein consensate
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:umu:diva-53204 (URN)10.1103/PhysRevA.85.013630 (DOI)
Available from: 2012-03-30 Created: 2012-03-15 Last updated: 2017-12-07Bibliographically approved
3. Parametric resonance of capillary waves at the interface between two immiscible Bose-Einstein condensates
Open this publication in new window or tab >>Parametric resonance of capillary waves at the interface between two immiscible Bose-Einstein condensates
Show others...
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 86, no 2, 023614- p.Article in journal (Refereed) Published
Abstract [en]

We study the parametric resonance of capillary waves on the interface between two immiscible Bose-Einstein condensates pushed towards each other by an oscillating force. Guided by analytical models, we solve numerically the coupled Gross-Pitaevskii equations for a two-component Bose-Einstein condensate at zero temperature. We show that, at moderate amplitudes of the driving force, the instability is stabilized due to nonlinear modifications of the oscillation frequency. When the amplitude of the driving force is large enough, we observe a detachment of droplets from the Bose-Einstein condensates, resulting in the generation of quantum vortices (skyrmions). We analytically investigate the vortex dynamics, and conditions of quantized vortex generation.

National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-59524 (URN)10.1103/PhysRevA.86.023614 (DOI)000307440900007 ()
Available from: 2012-09-17 Created: 2012-09-17 Last updated: 2017-12-07Bibliographically approved
4. Turbulence in binary Bose-Einstein condensates generated by highly nonlinear Rayleigh-Taylor and Kelvin-Helmholtz instabilities
Open this publication in new window or tab >>Turbulence in binary Bose-Einstein condensates generated by highly nonlinear Rayleigh-Taylor and Kelvin-Helmholtz instabilities
Show others...
2014 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 89, 013631- p.Article in journal (Refereed) Published
Abstract [en]

Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold 87Rb atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible kinetic energy. We demonstrate that the phenomenon may be observed in the laboratory.

Place, publisher, year, edition, pages
American Physical Society, 2014
Keyword
turbulence, Bose-Einstein condensation, ultracold gases, superfluids
National Category
Atom and Molecular Physics and Optics Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-85400 (URN)10.1103/PhysRevA.89.013631 (DOI)000335225700010 ()
Available from: 2014-02-03 Created: 2014-02-03 Last updated: 2017-12-06Bibliographically approved
5. Dynamics of the inner crust of neutron stars: Hydrodynamics, elasticity, and collective modes
Open this publication in new window or tab >>Dynamics of the inner crust of neutron stars: Hydrodynamics, elasticity, and collective modes
2013 (English)In: Physical Review C. Nuclear Physics, ISSN 0556-2813, E-ISSN 1089-490X, no 87, 055803- p.Article in journal (Refereed) Published
Abstract [en]

We present calculations of the hydrodynamics of the inner crust of neutron stars, where a superfluid neutron liquid coexists with a lattice of neutron-rich nuclei. The long-wavelength collective oscillations are combinations of phonons in the lattice and phonons in the superfluid neutrons. Velocities of collective modes are calculated from information about effective nucleon-nucleon interactions derived from Lattimer and Swesty's microscopic calculations based on a compressible liquid drop picture of the atomic nuclei and the surrounding neutrons.

Place, publisher, year, edition, pages
American Physical Scoiety, 2013
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-86896 (URN)10.1103/PhysRevC.87.055803 (DOI)
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2017-12-05Bibliographically approved
6. Towards a metallurgy of neutron star crusts
Open this publication in new window or tab >>Towards a metallurgy of neutron star crusts
2014 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 112, no 11, 112504- p.Article in journal (Refereed) Published
Abstract [en]

In the standard picture of the crust of a neutron star, matter there is simple: a body-centered-cubic (bcc) lattice of nuclei immersed in an essentially uniform electron gas. We show that at densities above that for neutron drip (~4×1011 g cm-3 or roughly one thousandth of nuclear matter density), the interstitial neutrons give rise to an attractive interaction between nuclei that renders the lattice unstable. We argue that the likely equilibrium structure is similar to that in displacive ferroelectric materials such as BaTiO3. As a consequence, properties of matter in the inner crust are expected to be much richer than previously appreciated and we mention possible consequences for observable neutron star properties.

Keyword
Neutron stars, the inner crust, nuclear astrophysics, crystal structure
National Category
Astronomy, Astrophysics and Cosmology Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-86899 (URN)10.1103/PhysRevLett.112.112504 (DOI)000333163200005 ()
Projects
JC Kempe Scholarship for the project: Theoretical Study of Interior of Neutron Stars II: Plasma Properties of the Inner Crust
Note

Selected as Editor's Suggestion in Phys. Rev. Lett.

Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2017-12-05Bibliographically approved

Open Access in DiVA

Hydrodynamics of Binary Bose-Einstein Condensates and Hydro-elasticity of the Inner Crust of Neutron Stars(2035 kB)895 downloads
File information
File name FULLTEXT01.pdfFile size 2035 kBChecksum SHA-512
d634908b125ff76c0dc84df2f3bd1ad3bae4299d54c8ddca87349a771829f3e8b62e682d0b2a9629ee5fb71fe0d9b75d2e526c53c6f42af11a8312bbc417f3e0
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Kobyakov, Dmitry
By organisation
Department of Physics
Astronomy, Astrophysics and CosmologyAtom and Molecular Physics and OpticsCondensed Matter Physics

Search outside of DiVA

GoogleGoogle Scholar
Total: 895 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 507 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf