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Yisong Yang

Publications and source records attributed to Yisong Yang.

At least 37 records · Page 2Linked to original sources
arXiv2019

Domain Wall Solitons Arising in Classical Gauge Field Theories

Domain wall solitons are basic constructs realizing phase transitions in various field-theoretical models and are solutions to some nonlinear ordinary differential equations descending from the corresponding full sets of governing equations in higher dimensions. In this paper, we present a series of domain wall solitons arising in several classical gauge field theory models. In the context of the Abelian gauge field theory, we unveil the surprising result that the solutions may explicitly be constructed, which enriches our knowledge on integrability of the planar Liouville type equations in their one-dimensional limits. In the context of the non-Abelian gauge field theory, we obtain some existence theorems for domain wall solutions arising in the electroweak type theories by developing some methods of calculus of variations formulated as direct and constrained minimization problems over a weighted Sobolev space.

math-ph↗
arXiv2019

Determination of AdS Monopole Wall via Minimization

In this note we solve a minimization problem arising in a recent work of Bolognesi and Tong on the determination of an AdS monopole wall. We show that the problem has a unique solution. Although the solution cannot be obtained explicitly, we show that it may practically be constructed via a shooting method for which the correct shooting slope is unique. We also obtain some energy estimates which allow an asymptotic explicit determination of the monopole wall in a large coupling parameter limit.

hep-th↗
arXiv2019

Coexisting Vortices and Antivortices Generated by Dually Gauged Harmonic Maps

In this paper we first formulate a dually gauged harmonic map model, suggested from a product Abelian Higgs field theory arising in impurity-inspired field theories, and obtain a new BPS system of equations governing coexisting vortices and antivortices, which are topologically characterized by the first Chern class of the underlying Hermitian bundle and the Thom class of the associated dual bundle. We then establish existence and uniqueness theorems for such vortices. For the equations over a compact surface, we obtain necessary and sufficient conditions for the existence of solutions. For the equations over the full plane, we obtain all finite-energy solutions. Besides, we also present precise expressions giving the values of various physical quantities of the solutions, including magnetic charges and energies, in terms of the total numbers of vortices and antivortices, of two species, and the coupling parameters involved.

math-ph↗
arXiv2018

Topological Bounds of Bending Energy for Lipid Vesicles

The Helfrich bending energy plays an important role in providing a mechanism for the conformation of a lipid vesicle in theoretical biophysics, which is governed by the principle of energy minimization over configurations of appropriate topological characteristics. We will show that the presence of a quantity called the spontaneous curvature obstructs the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. Besides, despite the well-realized knowledge that lipid vesicles may present themselves in a variety of shapes of complicated topology, there is a lack of topological bounds for the Helfrich energy. To overcome these difficulties, we consider a general scale-invariant anisotropic curvature energy that extends the Canham elastic bending energy developed in modeling a biconcave-shaped red blood cell. We will show that, up to a rescaling of the generating radii, there is a unique minimizer of the energy over the set of embedded ring tori, in the entire parameter regime, which recovers the Willmore minimizer in its Canham isotropic limit. We also show how elevated anisotropy favors energetically a clear transition from spherical-, to ellipsoidal-, and then to biconcave-shaped surfaces, for a lipid vesicle. We then establish some genus-dependent topological lower and upper bounds for the anisotropic energy. Finally, we derive the shape equation of the generalized bending energy, which extends the well-known Helfrich shape equation.

cond-mat.soft↗
arXiv2017

Boundary charges and integral identities for solitons in $(d+1)$-dimensional field theories

We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in $d$ spatial dimensions. The construction provides five boundary charges that are related to certain integrals of the profile functions of the solitons in question. The framework is quite generic and we give examples of both topological defects (like vortices and monopoles) and topological textures (like Skyrmions) in 2 and 3 dimensions. The class of theories considered here is based on a kinetic term and three functionals often encountered in reduced Lagrangians for solitons. One particularly interesting case provides a generalization of the well-known Pohozaev identity. Our construction, however, is fundamentally different from scaling arguments behind Derrick's theorem and virial relations. For BPS vortices, we find interestingly an infinity of integrals simply related to the topological winding number.

hep-th↗
arXiv2017

Determination of Angle of Light Deflection in Higher-Derivative Gravity Theories

Gravitational light deflection is known as one of three classical tests of general relativity and the angle of deflection may be computed explicitly using approximate or exact solutions describing the gravitational force generated from a point mass. In various generalized gravity theories, however, such explicit determination is often impossible due to the difficulty with obtaining an exact expression for the deflection angle. In this work, we present some highly effective globally convergent iterative methods to determine the angle of semiclassical gravitational deflection in higher- and infinite-derivative formalisms of quantum gravity theories. We also establish the universal properties that the deflection angle always stays below the classical Einstein angle and is a strictly decreasing function of the incident photon energy, in these formalisms.

gr-qc↗
arXiv2016

Non-Abelian clouds around Reissner-Nordström black holes: the existence line

A known feature of electrically charged Reissner-Nordström-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein--Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisite for the existence of the nA clouds is $i)$ a large enough gauge group and $ii)$ the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four and the other in five dimensional asymptotically flat spacetime. In the first case, we augment the usual $SU(3)$ Yang-Mills Lagrangian with higher order (quartic) curvature term, while for the second one we add the Chern-Simons density to the $SO(6)$ Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.

gr-qc↗
arXiv2015

Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds

An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite.

hep-th↗
arXiv2015

Determination of Gap Solution and Critical Temperature in Doped Graphene Superconductivity

It is shown that the gap solution and critical transition temperature are significantly enhanced by doping in a recently developed BCS formalism for graphene superconductivity in such a way that positive gap and transition temperature both occur in arbitrary pairing coupling as far as doping is present. The analytic construction of the BCS gap and transition temperature offers highly effective globally convergent iterative methods for the computation of these quantities. A series of numerical examples are presented as illustrations consolidating the analytic understanding achieved.

cond-mat.supr-con↗
arXiv2015

Friedmann-Lemaitre Cosmologies via Roulettes and Other Analytic Methods

In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.

gr-qc↗
arXiv2015

Topologically Stratified Energy Minimizers in a Product Abelian Field Theory

We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from $N_s$ vortices and $P_s$ anti-vortices ($s=1,2$) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface $S$ which states that a solution with prescribed $N_1, N_2$ vortices and $P_1,P_2$ anti-vortices of two designated species exists if and only if the inequalities \[ \left|N_1+N_2-(P_1+P_2)\right|<\frac{|S|}π,\quad \left|N_1+2N_2-(P_1+2P_2)\right|<\frac{|S|}π, \] hold simultaneously, which give bounds for the `differences' of the vortex and anti-vortex numbers in terms of the total surface area of $S$. The minimum energy of these solutions is shown to assume the explicit value \[ E= 4π(N_1+N_2+P_1+P_2), \] given in terms of several topological invariants, measuring the total tension of the vortex-lines.

math-ph↗
arXiv2015

Relativistic Chern--Simons--Higgs Vortex Equations

An existence theorem is established for the solutions to the non-Abelian relativistic Chern--Simons--Higgs vortex equations over a doubly periodic domain when the gauge group $G$ assumes the most general and important prototype form, $G=SU(N)$

math.AP↗
arXiv2015

Resolution of Chern--Simons--Higgs Vortex Equations

It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix $K$ of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.

math-ph↗
arXiv2015

Explicit Integration of Friedmann's Equation with Nonlinear Equations of State

This paper is a continuation of our earlier study on the integrability of the Friedmann equations in the light of the Chebyshev theorem. Our main focus will be on a series of important, yet not previously touched, problems when the equation of state for the perfect-fluid universe is nonlinear. These include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born--Infeld, and two-fluid models. We show that some of these may be integrated using Chebyshev's result while other are out of reach by the theorem but may be integrated explicitly by other methods. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution. For example, in the Chaplygin gas universe, it is seen that, as far as there is a tiny presence of nonlinear matter, linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied.

gr-qc↗
arXiv2015

Existence of Hyperbolic Calorons

Recent work of Harland shows that the $SO(3)$-symmetric, dimensionally-reduced, charge-$N$ self-dual Yang--Mills calorons on the hyperbolic space $ H^3\times S^1$ may be obtained through constructing $N$-vortex solutions of an Abelian Higgs model as in the study of Witten on multiple instantons. In this paper we establish the existence of such minimal action charge-$N$ calorons by constructing arbitrarily prescribed $N$-vortex solutions of the Witten type equations.

math-ph↗
arXiv2014

Friedmann's Equations in All Dimensions and Chebyshev's Theorem

This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time $t$ and conformal time $η$ of the Friedmann equations in all dimensions and with an arbitrary cosmological constant $Λ$. More precisely, it is shown that for spatially flat universes an explicit integration in $t$ may always be carried out, and that, in the non-flat situation and when $Λ$ is zero and the ratio $w$ of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension $n$ of space and $w$ obey some specific relations among an infinite family. The situation for explicit integration in $η$ is complementary to that in $t$. More precisely, it is shown in the flat-universe case with $Λ\neq0$ that an explicit integration in $η$ can be carried out if and only if $w$ and $n$ obey similar relations among a well-defined family which we specify, and that, when $Λ=0$, an explicit integration can always be carried out whether the space is flat, closed, or open. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear.

astro-ph.CO↗