Related papers: Notes on Mayer Expansions and Matrix Models
In the limit of the lattice spacing going to zero, we consider the dimer model on isoradial graphs in the presence of singular $SL(N,\mathbb{C})$ gauge fields flat away from a set of punctures. We consider the cluster expansion of this…
Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict field configurations to those that satisfy the classical equations of motion, leads to at most one-loop radiative corrections. This approach can be used with…
In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and independent increments. For convenience we refer to them as…
This paper presents a revolutionary approach to the characterization, forecast, and control of collective systems. Collective systems are an ensemble of conservatively interacting entities. The evolution of the entities are determined by…
An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the…
We investigate the kinetics of constant-kernel aggregation which is augmented by either: (a) evaporation of monomers from finite-mass clusters, or (b) continuous cluster growth -- \ie, condensation. The rate equations for these two…
We investigate the Magnus expansion of the $N$-operator in relativistic quantum field theory, which is related to the $S$-matrix via $S = e^{iN}$. We develop direct methods to compute matrix elements of the $N$-operator, which we refer to…
We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of…
As one of the most powerful probes of cosmological structure formation, the abundance of massive galaxy clusters is a sensitive probe of modifications to gravity on cosmological scales. In this paper, we present results from N-body…
Many experimentally-accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled…
A $\theta$ term, which couples to topological charge, is added to the two-dimensional lattice CP^3 model and U(1) gauge theory. Monte Carlo simulations are performed and compared to strong-coupling character expansions. In certain…
A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum…
The extended dynamical mean field theory has played an important role in the study of quantum phase transitions in heavy fermion systems. In order to incorporate the physics of unconventional superconductivity, we develop a cluster version…
We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial value conditions. The initial value…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
The iteration dynamics of the coupled cluster equations exhibits a synergistic relationship among the cluster amplitudes. The iteration scheme may be viewed as a multivariate discrete-time propagation of nonlinearly coupled equations, which…
This is an introduction to cluster algebras and their common triangular bases. These bases are Kazhdan-Lusztig-type and serve as the canonical bases of cluster algebras from the representation-theoretic point of view. We review seeds…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of…
A microscopic $n\alpha$ cluster model was applied to $^{8}$Be, $^{12}$C, and $^{16}$O systems to investigate cluster motion in the ground state and radial excitation. In the microscopic calculation of $^{12}$C and $^{16}$O using the…