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 $\Lambda$CDM value at localised wavenumbers, even pushing structure formation into the non-linear regime earlier than expected in $\Lambda$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, $r_c(t)$, and the crossover region, $r_t(t)$. 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 $k^{-3}$ tail in its spectrum, indicative of a $\rho\sim r^2$ 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