Moment formalisms applied to a solvable model with a quantum phase transition (I). Exponential moment methods

Moment Formalisms Applied to a Solvable Model with a Quantum Phase Transition. I. Exponential Moment Methods

We examine the Ising chain in a transverse field at zero temperature from the point of view of a family of moment formalisms based upon the cumulant generating function, where we find exact solutions for the generating functions and cumulants at arbitrary couplings and hence for both the ordered and disordered phases of the model. In a t-expansion analysis, the exact Horn-Weinstein function E(t...

Multivariate exponential integral approximations: a moment approach

We propose a method to approximate a class of exponential multivariate integrals using moment relaxations. Using this approach, both lower and upper bounds of the integrals are obtained and we show that these bound values asymptotically converge to the real value of the integrals when the moment degree r increases. We further demonstrate the method by calculating both hypercubic and order stati...

Moment Analysis Applied to LMC Star Clusters

Statistical moment-based ellipse fitting was performed on observations of Large Magellanic Cloud clusters, confirming that trends are evident in their position angles and ellipticities, as had been reported in the literature. Artificial cluster images with known parameters were generated, and subjected to the same analysis techniques, revealing apparent trends caused by stochastic processes. Ca...

Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation.

We study a one-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in a previous study [M. Žnidarič J. Stat. Mech. (2010) L05002] is extended to arbitrary coupling constants, driving, and a homogeneous magnetic field. All one-, two-, and three-...

Anomalous Moment Corrections to Transition Matrix Elements