6
votes
1answer
133 views
+50

Are there any explicit probability conserving solvers for Pauli equation?

I know that there exist probability conserving explicit solvers for time-dependent Schrödinger's equation, for example, Visscher's one. But when I tried to add spin into account in this scheme, it ...
8
votes
0answers
420 views
+150

Distributivity of group topologies on $\Bbb Z$

Let $\mathcal L$ be the set of all group topologies on $\Bbb Z$. It is known that $(\mathcal L,\subseteq)$ is a modular complete lattice [1]. Is $(\mathcal L,\subseteq)$ distributive? $$~$$ ...
7
votes
1answer
389 views
+50

Ways to show a system of polynomial equations has no solution

I came across the following system of polynomial equations on $X_1,\dots,X_{m-2}$: $$ \begin{cases} 2X_{2s}+\sum\limits_{t=1}^{2s-1}(-1)^tX_tX_{2s-t}=0,\quad s=1,\dots,\frac{m}{2}-1,\\ ...