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Figueroa, D. G., Florio, A., Torrenti, F., & Valkenburg, W. (2021). The art of simulating the early universe. Part I. Integration techniques and canonical cases. J. Cosmol. Astropart. Phys., 04(4), 035–108pp.
Abstract: We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of O(delta t(2)) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to O(delta t(4)) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to O(delta t(10)) We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of 'self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian U(1) gauge theories, and iii) Non-Abelian SU(2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from O(delta t(2)) up to O(delta t(10)) For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when 'self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under SU(2) x U(1). We note that the present manuscript is meant to be part of the theoretical basis for the code CosmoLattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosrnolattice.net.
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Park, B. Y., Paeng, W. G., & Vento, V. (2019). The inhomogeneous phase of dense skyrmion matter. Nucl. Phys. A, 989, 231–245.
Abstract: It was predicted qualitatively in ref. [I] that skyrmion matter at low density is stable in an inhomogeneous phase where skyrmions condensate into lumps while the remaining space is mostly empty. The aim of this paper is to proof quantitatively this prediction. In order to construct an inhomogeneous medium we distort the original FCC crystal to produce a phase of planar structures made of skyrmions. We implement mathematically these planar structures by means of the 't Hooft instanton solution using the Atiyah-Manton ansatz. The results of our calculation of the average density and energy confirm the prediction suggesting that the phase diagram of the dense skyrmion matter is a lot more complex than a simple phase transition from the skyrmion FCC crystal lattice to the half-skyrmion CC one. Our results show that skyrmion matter shares common properties with standard nuclear matter developing a skin and leading to a binding energy equation which resembles the Weiszacker mass formula.
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Navarro, J., & Guardiola, R. (2011). Thermal Effects on Small Para-Hydrogen Clusters. Int. J. Quantum Chem., 111(2), 463–471.
Abstract: A brief review of different quantum Monte Carlo simulations of small (p-H-2)(N) clusters is presented. The clusters are viewed as a set of N structureless p-H-2 molecules, interacting via an isotropic pairwise potential. Properties as superfluidity, magic numbers, radial structure, excitation spectra, and abundance production of (p-H-2)(N) clusters are discussed and, whenever possible, a comparison with He-4(N) droplets is presented. All together, the simulations indicate that temperature has a paradoxical effect of the properties of (p-H-2)(N) clusters, as they are solid-like at high T and liquid-like at low T, due to quantum delocalization at the lowest temperature.
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Horvat, S., Magas, V. K., Strottman, D. D., & Csernai, L. P. (2010). Entropy development in ideal relativistic fluid dynamics with the Bag Model equation of state. Phys. Lett. B, 692(4), 277–280.
Abstract: We consider an idealized situation where the Quark-Gluon Plasma (QGP) is described by a perfect, (3 + 1)-dimensional fluid dynamic model starting from an initial state and expanding until a final state where freeze-out and/or hadronization takes place. We study the entropy production with attention to effects of (i) numerical viscosity, (ii) late stages of flow where the Bag Constant and the partonic pressure are becoming similar, (iii) and the consequences of final freeze-out and constituent quark matter formation.
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