7 problems

The paper considers the prescription for constructing the effective lightcone Hamiltonian $H_{\rm eff}$, including its application to $\lambda\phi^4$ theory in two dimensions. All-…

Let $m$ denote the number of Fourier modes in the periodic potentials, let $n$ be the ambient dimension, and let $V_1,V_2$ be smooth periodic functions. The rigidity result referre…

Let $n\geq 2$, let $H(p)=\frac{1}{2}|p|^2$ for $p\in\mathbb{R}^n$, and let $V_1,V_2\in C(\mathbb{R}^n)$ be $\mathbb{Z}^n$-periodic potential energy functions. Let $\overline{H}_1$…

Let $(\Omega,\mathcal{F},\mathbb{P})$ be the probability space underlying the stationary random potential $V(x,\omega)$, and let $\varphi:[0,\infty)\to\mathbb{R}$ be continuous and…

Assume that $H(p)=\varphi(|p|)$, where $\varphi:[0,\infty)\to\mathbb{R}$ satisfies (H7), and let … be the associated sequence, with $M_i=\varphi(s_{2i-1})$ and…

Tracer-particle reduction conjecture. All the physics boils down to the motion of the tracer particles, with the tracer wave function governed by the effective Hamiltonian…

Let $V$ be a nonzero periodic flow in two-dimensional space, and let $dalpha_A$ denote the effective burning velocity associated with the flow velocity $A V$. For…