相关论文: Champagne subdomains with unavoidable bubbles

We investigate the possibility of hidden non-Abelian Local Phase symmetries in large-U doped planar Hubbard antiferromagnets, believed to simulate the physics of two-dimensional (magnetic) superconductors. We present a spin-charge…

An extension is given for the standard two component model of adiabatic, Born-Oppenheimer (BO) electronic states in a polyatonic molecule, by use of Mathieu functions of arbitrary order. The curl or compatibility conditions for the…

For any closed Riemannian manifold $X$ we prove that large isoperimetric regions in $X\times{\mathbb R}^n$ are of the form $X\times$(Euclidean ball). We prove that if $X$ has non-negative Ricci curvature then the only soap bubbles enclosing…

We study the possibility of obtaining metastable supersymmetry breaking vacua in a perturbative gauge theory without singlet fields, thus allowing for scenarios where a grand unified symmetry and supersymmetry are broken by the same sector.…

We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying continuous, possibly gauged, flavor symmetry SU(2) or SU(3) through spontaneous symmetry breaking. We consider all possible cases, where the…

If supersymmetry is dynamically broken in a hidden sector, the gauginos typically have unacceptably small masses. This situation can be corrected if a non-Abelian gauge interaction becomes strong at a scale of order 1 TeV and induces…

We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group $SU(N)$. Pair creation of partons (fermion quanta) is not suppressed in the large-$N$ limit, where the glueball-like bound states…

A family of sets $\mathcal{A}$ is union-closed if it is finite and nonempty with member sets that are all finite and distinct (at least one of which is nonempty) and it satisfies the property $X, Y \in \mathcal{A} \implies X \cup Y \in…

We give examples of string compactifications to 4d Minkowski space with different amounts of supersymmetry that can be connected by spherical domain walls. The tension of these domain walls is tunably lower than the 4d Planck scale. The…

We investigate the possibility that supersymmetry is not a fundamental symmetry of nature, but emerges as an accidental approximate global symmetry at low energies. This can occur if the visible sector is non-supersymmetric at high scales,…

We study the existence of long-lived meta-stable supersymmetry breaking vacua in gauge theories with massless quarks, upon the addition of extra massive flavors. A simple realization is provided by a modified version of SQCD with N_{f,0} <…

We present a supersymmetric model of flavor. A single U(1) gauge group is responsible for both generating the flavor spectrum and communicating supersymmetry breaking to the visible sector. The problem of Flavor Changing Neutral Currents is…

The union-closed sets conjecture states that in any nonempty union-closed family $\mathcal{F}$ of subsets of a finite set, there exists an element contained in at least a proportion $1/2$ of the sets of $\mathcal{F}$. Using the…

The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both non-local and gauge dependent. For that reason they are also ambiguous as a guide to phase structure. We point out that a global…

We prove that the tagged particles of infinitely many Brownian particles in $ \Rtwo $ interacting via a logarithmic (two-dimensional Coulomb) potential with inverse temperature $ \beta = 2 $ are sub-diffusive. The associated delabeled…

Let $B_1$ be a ball of radius $r_1$ in $S^n(\Hy^n)$, and let $B_0$ be a smaller ball of radius $r_0$ such that $\bar{B_0}\subset B_1$. For $S^n$ we consider $r_1< \pi$. Let $u$ be a solution of the problem $-\La u =1$ in $\Om :=…

Given a connected Lipschitz domain U we let L(U) be the subset of functions in 2nd order Sobolev space whose gradient (in the sense of trace) is equal to the inward pointing unit normal to U. The the Aviles Giga functional over L(U) serves…

We construct a nonseparable Banach space $\mathcal X$ (actually, of density continuum) such that any uncountable subset $\mathcal Y$ of the unit sphere of $\mathcal X$ contains uncountably many points distant by less than $1$ (in fact, by…

Let $(\xi(s))_{s\geq 0}$ be a standard Brownian motion in $d\geq 1$ dimensions and let $(D_s)_{s \geq 0}$ be a collection of open sets in $\R^d$. For each $s$, let $B_s$ be a ball centered at 0 with $\vol(B_s) = \vol(D_s)$. We show that…

Spontaneous symmetry breaking (SSB) is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the…