Fantasia of a Superfluid Universe — In Memory of Kerson Huang

Low, Hwee-Boon; Xiong, Chi

doi:10.1142/9789813207431_0010

Cited by 2 publications

(3 citation statements)

References 32 publications

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“…Equation (1.1) has been used to describe the creation and dynamics of the quantized vortices of a galaxy in 2D or 3D models as a "cosmic rotating superfluid". The vortices generation that obeys the relativistic Feynman relation, quantum turbulence in the form of a vortex tangle that follows mechanism for matter creation during the big bang era, and the formation and transmission of Kelvin waves correspond well to observations [28,31,39,53,54]. For generalisations of (1.1) to curved spacetime Klein-Gordon models, e.g.…”

Section: Introductionsupporting

confidence: 60%

“…Such superfluids [37] are often described by a complex-valued scalar field as Ginzburg and Landau proposed an order parameter for the phase coherence [26]. The nonlinear Klein-Gordon equation has then become a popular superfluid model, which is able to cover the entire velocity range, especially the relativistic region [28,55,31,39,53,54,15,48,23,49,21,52]. As a model for describing a rotating galaxy in Minkowski metric, the nonlinear Klein-Gordon equation in a rotating frame [28,31,39,53,54] is used.…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear Klein-Gordon equation has then become a popular superfluid model, which is able to cover the entire velocity range, especially the relativistic region [28,55,31,39,53,54,15,48,23,49,21,52]. As a model for describing a rotating galaxy in Minkowski metric, the nonlinear Klein-Gordon equation in a rotating frame [28,31,39,53,54] is used. Also, the nonlinear Klein-Gordon equation appears as a relativistic generalization of the Gross-Pitaevskii equation, a nonlinear Schrödinger equation that serves as a basic model for Bose-Einstein Condensates [2], also in the rotating case, see e.g.…”

Section: Introductionmentioning

confidence: 99%

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On the Rotating Nonlinear Klein--Gordon Equation: NonRelativistic Limit and Numerical Methods

Mauser¹,

Zhang²,

Zhao³

2020

Multiscale Model. Simul.

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We consider numerics / asymptotics for the rotating nonlinear Klein-Gordon (RKG) equation, an important PDE in relativistic quantum physics that can model a rotating galaxy in Minkowski metric and serves also as a model e.g. for a "cosmic superfluid". Firstly, we formally show that in the non-relativistic limit RKG converges to coupled rotating nonlinear Schrödinger equations (RNLS), which is used to describe the particle-antiparticle pair dynamics. Investigations of the vortex state of RNLS are carried out. Secondly, we propose three different numerical methods to solve RKG from relativistic regimes to non-relativistic regimes in polar and Cartesian coordinates. In relativistic regimes, a semi-implicit finite difference Fourier spectral method is proposed in polar coordinates where both rotation terms are diagonalized simultaneously. While in non-relativistic regimes, to overcome the fast temporal oscillations, we adopt the rotating Lagrangian coordinates and introduce two efficient multiscale methods with uniform accuracy, i.e., the multi-revolution composition method and the exponential integrator. Various numerical results confirm (uniform) accuracy of our methods. Simulations of vortices dynamics are presented.

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Section: Introductionsupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Rotating Nonlinear Klein--Gordon Equation: NonRelativistic Limit and Numerical Methods

Mauser¹,

Zhang²,

Zhao³

2020

Multiscale Model. Simul.

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Does the Penrose Suggestion as to Black Holes from a Prior Universe Showing Up in Today’s Universe Have Credibility? Examined from a Singular, and Nonsingular Beginning of Cosmological Expansion

Beckwith¹

2021

JHEPGC

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We examine if there are grounds to entertain the Penrose suggestion as to black holes from a prior cycle of creation appearing in the present cosmos. There are two cases to consider. One a singular start to the Universe or as Karen Freeze and others have modeled a non-singular start. The two cases are different and touch upon the limits of validity of the Penrose singularity theorem. We will first of all state the two cases, singular and nonsingular, and then afterwards, briefly allude to the Penrose singularity theorem. The plausibility of the singular cosmological expansion start point w case analysis of Black holes from a prior universe will be discussed first Afterwards, a synopsis of the Penrose singularity theorem. After that, the Nonsingular case of a starting point of the expansion of the Universe will be entertained and described. Since the nonsingular start to the expansion of the Universe is not so well known, a considerable amount of space will be spent upon what I view as mathematical constructions allowing for its analysis. About the only way to ascertain these cases will be by GW astronomy, hence the details of GW production from the early Universe will be covered in excruciating detail. The methodology for that section is simple. Use a construction for a minimal time-step, then from there get emergent space-time conditions for a bridge from a nonsingular start to the universe, to potential Quantum gravity conditions. Our Methodology is to construct using a "trivial" solution to massive gravitons, and a nonsingular start for expansion of the universe. Our methodology has many unintended consequences, not the least is a relationship between a small timestep, which is called t, and then the minimum scale fac-How to cite this paper: Beckwith, A.W.

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Fantasia of a Superfluid Universe — In Memory of Kerson Huang

Cited by 2 publications

References 32 publications

On the Rotating Nonlinear Klein--Gordon Equation: NonRelativistic Limit and Numerical Methods

On the Rotating Nonlinear Klein--Gordon Equation: NonRelativistic Limit and Numerical Methods

Does the Penrose Suggestion as to Black Holes from a Prior Universe Showing Up in Today’s Universe Have Credibility? Examined from a Singular, and Nonsingular Beginning of Cosmological Expansion

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