Related papers: New Quantitative Deformation Lemma and New Mountai…
We show that a closed quantum system driven through a quantum critical point with two rates $\omega_1$ (which controls its proximity to the quantum critical point) and $\omega_2$ (which controls the dispersion of the low-energy…
We investigate the threshold of gravitational collapse with angular momentum, under the assumption that the critical solution is spherical and self-similar and has two growing modes, namely one spherical mode and one axial dipole mode…
This paper focuses on the critical Kirchhoff equation with concave perturbation \begin{align*} \begin{cases} \displaystyle -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=|u|^4u+\lambda|u|^{q-2}u\ \ &\mbox{in}\ \Omega, \displaystyle u=0\ \…
Topological phase transitions in condensed matters accompany emerging singularities of the electronic wave function, often manifested by gap-closing points in the momentum space. In conventional topological insulators in three dimensions…
Transport measurements on the cuprates suggest the presence of a quantum critical point hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster…
We propose in this paper New Q-Newton's method. The update rule is very simple conceptually, for example $x_{n+1}=x_n-w_n$ where $w_n=pr_{A_n,+}(v_n)-pr_{A_n,-}(v_n)$, with $A_n=\nabla ^2f(x_n)+\delta _n||\nabla f(x_n)||^2.Id$ and…
A new class of change point test statistics is proposed that utilizes a weighting and trimming scheme for the cumulative sum (CUSUM) process inspired by R\'enyi (1953). A thorough asymptotic analysis and simulations both demonstrate that…
We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power-law in time. The optimal power is proportional to the…
The classic Schneider-Lang theorem in transcendence theory asserts that there are only finitely many points at which algebraically independent complex meromorphic functions of finite order of growth can simultaneously take values in a…
We investigate convergence of point processes associated with critical faces for a \v{C}ech filtration built over a homogeneous Poisson point process in the $d$-dimensional flat torus. The convergence of our point process is established in…
We investigate the universality of an Ising symmetry breaking phase transition of tilted two-dimensional Dirac fermions, in the type-I phase as well as at the Lifshitz transition between a type-I and a type-II semimetal, where the Fermi…
In this paper we obtain generalized Calabi-type compactness criteria for complete Riemannian manifolds that allow the presence of negative amounts of Ricci curvature. These, in turn, can be rephrased as new conditions for the positivity,…
We present a functional renormalization group analysis of a quantum critical point in two-dimensional metals involving Fermi surface reconstruction due to the onset of spin-density wave order. Its critical theory is controlled by a fixed…
We introduce a new approach to obtaining pointwise estimates for solutions of elliptic boundary value problems when the operator being considered satisfies a certain type of weighted integral inequalities. The method is illustrated on…
In this paper we prove the existence of at least one positive solution for the nonlocal semipositone problem \[ \displaystyle \left\{\begin{array}{rcll} (-\Delta)_p^s(u) &=& \lambda f(u) \qquad & \text{in} \ \ \Omega \\u &=& 0 & \text{in} \…
Quantum criticality provides a means to understand the apparent non-Fermi liquid phenomena in correlated electron systems. How to properly describe quantum critical points in electronic systems has however been poorly understood. The issues…
We provide a general argument for the possible existence of a new critical point associated with a deconfinement phase transition in QCD at finite temperature $T$ and in a magnetic field $B$ with zero chemical potential. This is the first…
Multi-critical point principle (MPP) is one of the interesting theoretical possibilities that can explain the fine-tuning problems of the Universe. It simply claims that "the coupling constants of a theory are tuned to one of the…
Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…
We show that when there is a sudden transition from a small to a large Fermi surface at a field-induced quantum critical point, similar to what may have been observed in some heavy-fermion compounds, an additional term has to be taken into…