1,809 research outputs found

### Convergence to equilibrium for time inhomogeneous jump diffusions with state dependent jump intensity

We consider a time inhomogeneous jump Markov process $X = (X_t)_t$ with state
dependent jump intensity, taking values in $R^d .$ Its infinitesimal generator
is given by \begin{multline*} L_t f (x) = \sum_{i=1}^d \frac{\partial
f}{\partial x_i } (x) b^i ( t,x) - \sum_{ i =1}^d \frac{\partial f}{\partial
x_i } (x) \int_{E_1} c_1^i ( t, z, x) \gamma_1 ( t, z, x ) \mu_1 (dz ) \\ +
\sum_{l=1}^3 \int_{E_l} [ f ( x + c_l ( t, z, x)) - f(x)] \gamma_l ( t, z, x)
\mu_l (dz ) , \end{multline*} where $(E_l , {\mathcal E}_l, \mu_l ) , 1 \le l
\le 3,$ are sigma-finite measurable spaces describing three different jump
regimes of the process (fast, intermediate, slow).
We give conditions proving that the long time behavior of $X$ can be related
to the one of a time homogeneous limit process $\bar X .$ Moreover, we
introduce a coupling method for the limit process which is entirely based on
certain of its big jumps and which relies on the regeneration method. We state
explicit conditions in terms of the coefficients of the process allowing to
control the speed of convergence to equilibrium both for $X$ and for $\bar X.

### Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition

We uncover new topology-related features of the $\pi$-flux saddle-point
solution of the $D$=2+1 Heisenberg antiferromagnet. We note that symmetries of
the spinons sustain a built-in competition between antiferromagnetic (AF) and
valence-bond-solid (VBS) orders, the two tendencies central to recent
developments on quantum criticality. An effective theory containing an analogue
of the Wess-Zumino-Witten term is derived, which generates quantum phases
related to AF monopoles with VBS cores, and reproduces Haldane's hedgehog Berry
phases. The theory readily generalizes to $\pi$-flux states for all $D$.Comment: 4 pages, revise

- â€¦