In three-dimensional O(N) models, we investigate the low-momentum be-havior of the two-point Green’s function G(x) in the critical region of thesymmetric phase. We consider physical systems whose criticality is charac-terized by a rotational-invariant fixed point. Several approaches are exploited,such as strong-coupling expansion of lattice non-linear O(N) σ models, 1/N -exp...

Quantum trajectories are Markov processes that describe the time evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they defined as solutions so-called Stochastic Schrödinger Equations, which nonlinear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to study invariant measures trajectories. Particularly, we p...

We exhibit a change of variables that maintains the Mahler measure given polynomial. This method leads to construction highly non-trivial polynomials with and settles some conjectural numerical formulas due Boyd Brunault.