21 research outputs found
Universality of Bose-Einstein Condensation and Quenched Formation Dynamics
The emergence of macroscopic coherence in a many-body quantum system is a
ubiquitous phenomenon across different physical systems and scales. This
Chapter reviews key concepts characterizing such systems (correlation
functions, condensation, quasi-condensation) and applies them to the study of
emerging non-equilibrium features in the dynamical path towards such a
highly-coherent state: particular emphasis is placed on emerging universal
features in the dynamics of conservative and open quantum systems, their
equilibrium or non-equilibrium nature, and the extent that these can be
observed in current experiments with quantum gases. Characteristic examples
include symmetry-breaking in the Kibble-Zurek mechanism, coarsening and
phase-ordering kinetics, and universal spatiotemporal scalings around
non-thermal fixed points and in the context of the Kardar- Parisi-Zhang
equation; the Chapter concludes with a brief review of the potential relevance
of some of these concepts in modelling the large-scale distribution of dark
matter in the universe.Comment: Invited contribution to the Encyclopedia of Condensed Matter Physics
(Elsevier, 2nd Edition
Unified description of corpuscular and fuzzy bosonic dark matter
We derive from first principles equations for bosonic, non-relativistic and
self-interacting dark matter which can include both a condensed, low momentum
"fuzzy" component and one with higher momenta that may be approximated as a
collection of particles. The resulting coupled equations consist of a modified
Gross-Pitaevskii equation describing the condensate and a kinetic equation
describing the higher momentum modes, the "particles", along with the Poisson
equation for the gravitational potential sourced by the density of both
components. Our derivation utilizes the Schwinger-Keldysh path integral
formalism and applies a semi-classical approximation which can also accommodate
collisional terms amongst the particles and between the particles and the
condensate to second order in the self-coupling strength. The equations can
therefore describe both CDM and Fuzzy Dark Matter in a unified way, allowing
for the coexistence of both phases and the inclusion of quartic
self-interactions.Comment: 22 pages, 6 figures. V2: Final version, accepted in PR
Hybrid model of condensate and particle Dark Matter: linear perturbations in the hydrodynamic limit
We analyse perturbations of self-interacting, scalar field dark matter that
contains modes both in a coherent condensate state and an incoherent
particle-like state. Starting from the coupled equations for the condensate,
the particles and their mutual gravitational potential, first derived from
first principles in earlier work by the authors, we derive a hydrodynamic limit
of two coupled fluids and study their linearized density perturbations in an
expanding universe. We find that away from the condensate-only or particle-only
limits, and for certain ranges of the parameters, such self-interacting
mixtures can significantly enhance the density power spectrum above the
standard linear CDM value at localised wavenumbers, even pushing
structure formation into the non-linear regime earlier than expected in
CDM for these scales. We also note that such mixtures can lead to
degeneracies between models with different boson masses and self-coupling
strengths, in particular between self-coupled models and non-coupled Fuzzy Dark
Matter made up of heavier bosons. These findings open up the possibility of a
richer phenomenology in scalar field dark matter models and could further
inform efforts to place observational limits on their parameters.Comment: 16 pages, 7 figures. v2: references adde
Coherent and incoherent structures in fuzzy dark matter halos
We show that fuzzy dark matter halos exhibit spatial differentiation in the
degree of coherence of the field configuration, ranging from completely
coherent in the central solitonic core to incoherent outside it, with a
crossover region in between the two phases. The solitonic core is indeed a pure
condensate which overlaps almost perfectly with the Penrose-Onsager mode
corresponding to the largest eigenvalue of the one-particle density matrix. The
virialized outer halo surrounding the core exhibits no clear coherence as a
whole upon radial and temporal averaging. However, when viewed locally and for
short times, it can be described as a collection of quasi-condensate lumps
exhibiting locally suppressed fluctuations which can be identified with the
structures commonly referred to as granules. Phase coherence across the entire
halo is inhibited by a dynamically evolving tangled web of vortices separating
the localized quasi-condensate regions. Moreover, the dimensionless phase-space
density in the outer halo drops significantly below its value at the core. We
further examine the dynamics of this spatial structure and find that the
oscillations of the core can be accurately described by two time-dependent
parameters respectively characterizing the size of the core, , and the
crossover region, . For the halos produced in our merger simulations
this feature is reflected in the (anti-)correlated oscillation of the peak
value of the field configuration's power-spectrum. The turbulent vortex tangle
of the virialized halo appears to reach a quasi-equilibrium state over probed
timescales, with the incompressible component of the kinetic energy exhibiting
a characteristic tail in its spectrum, indicative of a
density profile around the quantum vortex cores. Comparison of the peak
wavenumbers in the corresponding power-spectra shows that the inter-vortex..
Reconciling the Classical-Field Method with the Beliaev Broken Symmetry Approach
We present our views on the issues raised in the chapter by Griffin and
Zaremba [A. Griffin and E. Zaremba, in Quantum Gases: Finite Temperature and
Non-Equilibrium Dynamics, N. P. Proukakis, S. A. Gardiner, M. J. Davis, and M.
H. Szymanska, eds., Imperial College Press, London (in press)]. We review some
of the strengths and limitations of the Bose symmetry-breaking assumption, and
explain how such an approach precludes the description of many important
phenomena in degenerate Bose gases. We discuss the theoretical justification
for the classical-field (c-field) methods, their relation to other
non-perturbative methods for similar systems, and their utility in the
description of beyond-mean-field physics. Although it is true that present
implementations of c-field methods cannot accurately describe certain
collective oscillations of the partially condensed Bose gas, there is no
fundamental reason why these methods cannot be extended to treat such
scenarios. By contrast, many regimes of non-equilibrium dynamics that can be
described with c-field methods are beyond the reach of generalised mean-field
kinetic approaches based on symmetry-breaking, such as the ZNG formalism.Comment: 8 pages. Unedited version of chapter to appear in Quantum Gases:
Finite Temperature and Non-Equilibrium Dynamics (Vol. 1 Cold Atoms Series).
N.P. Proukakis, S.A. Gardiner, M.J. Davis and M.H. Szymanska, eds. Imperial
College Press, London (in press). See
http://www.icpress.co.uk/physics/p817.html v2: Added arXiv cross-reference