相关论文: Weakly bound states in 2+\epsilon dimensions
We show that critical Anderson electron in 3 dimensions is present in its spatial effective support, which was recently determined to be a region of fractal dimension $\approx \! 8/3$, with probability 1 in infinite volume. Hence, its…
We have extended a previous calculation of the energy of a weakly heterogeneous waveguide to fourth order in the density perturbation, deriving its general expression. For particular configurations where the second and third orders both…
The effect of the uniform magnetic field on the electron in the spherically symmetric square-well potential is studied. A transcendental equation that determines the electron energy spectrum is derived. The approximate value of the lowest…
Recently, the issue of whether the Kondo problem in quantum dots at large bias is a weak-coupling problem or not has been raised. In this paper, we revisit this problem by carefully analyzing a corresponding model in the solvable limit --…
We study the properties of a quantum critical point which develops in a BCS superconductor when pair-breaking suppresses the transition temperature to zero. The pair fluctuations are characterized by a dynamical critical exponent z=2.…
We study non-interacting systems with a power-law quasiparticle dispersion $\xi_{\bf k}\propto k^\alpha$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2\alpha$ there exists a…
The Weak Gravity Conjecture (WGC) is usually formulated in terms of the stability of extremal black-holes or in terms of long distance Coulomb/Newton potentials. However one can think of other physical processes to compare the relative…
The elementary quadratic plus inverse sextic interaction containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate $x = s-{\rm i}\varepsilon$. The shift $\varepsilon>0$ is fixed while the…
We consider the 3-state Potts model in $d\geq2$ dimensions. For $d$ less than the upper critical dimension $d_\text{crit}$, the model has a critical and a tricritical fixed point. In $d=2$, these fixed points are described by minimal…
Let $\Omega$ be a smooth bounded simply connected domain in $\mathbb{R}^2$. We investigate the existence of critical points of the energy $E_\varepsilon (u)=1/2\int_\Omega |\nabla u|^2+1/(4\varepsilon^2)\int_\Omega (1-|u|^2)^2$, where the…
We study and compare the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with magnetic filling factors f=1/3 and f=2/5. In addition to the spin waves, the low energy excitations of the system consist…
The composite nature of a shallow bound state is studied by using the weak-binding relation, which connects the compositeness of the bound state with observables. We first show that the previous weak-binding relation cannot be applied to…
We consider the $n$-component $|\varphi|^4$ lattice spin model ($n \ge 1$) and the weakly self-avoiding walk ($n=0$) on $\mathbb{Z}^d$, in dimensions $d=1,2,3$. We study long-range models based on the fractional Laplacian, with spin-spin…
In the standard model, for the t --> W b decay mode, the relative phase is 0-degrees between the dominant A(0,-1/2) and A(-1, -1/2) helicity amplitudes. However, in the case of an additional large t_R --> b_L chiral weak-transition moment,…
Common wisdom asserts that bound excitons cannot form in high-dimensional (d>1) metallic structures because of their overwhelming screening and unavoidable resonance with nearby continuous bands. Strikingly, here we illustrate that this…
We theoretically study spin-$1/2$ fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting - a prototypical system for developing…
We present the first results of numerical simulations of a 2+1 dimensional fermion field theory based on a recent proposal for a model of graphene, consisting of N_f four-component Dirac fermions moving in the plane and interacting via an…
We present exact diagonalization and density matrix renormalization group results for the entanglement entropy of critical spin-1/2 XXZ chains. We find that open boundary conditions induce an alternating term in both the energy density and…
We study the transmission through different small systems as a function of the coupling strength $v$ to the two attached leads. The leads are identical with only one propagating mode $\xi^E_C$ in each of them. Besides the conductance $G$,…
The depinning of a contact line is studied as a dynamical critical phenomenon by a functional renormalization group technique. In $D=2-\epsilon$ interface dimensions, the roughness exponent is $\zeta=\epsilon/3$ to all orders in…