Related papers: Finite volume analysis of scattering theory in the…
We apply the massive analogue of the truncated conformal space approach to study the two dimensional $\phi^{4}$ theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We…
We consider the two-dimensional dilute q-state Potts model on its first order phase transition surface for 0<q\leq 4. After determining the exact scattering theory which describes the scaling limit, we compute the two-kink form factors of…
We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e. only neglecting contributions that decay exponentially with volume). Using the scaling Lee-Yang model and the Ising…
We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
This manuscript, presented to receive habilitated doctor degree, contains an overview of my recent works in developing complex scaling method and its applications in the few-body physics.
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
The study of Finite Size Effects in Quantum Field Theory allows the extraction of precious perturbative and non-perturbative information. The use of scaling functions can connect the particle content (scattering theory formulation) of a QFT…
The dispersion relations and S-matrix of the one-dimensional Hubbard model at half filling are considered in a certain scaling limit. (In the process we derive a useful small-coupling expansion of the exact lattice dispersion relations.)…
A simple finite-size scaling theory is proposed here for anisotropic percolation models considering the cluster size distribution function as generalized homogeneous function of the system size and two connectivity lengths. The proposed…
We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
This work thoroughly examines several analytical tools, each possessing a different level of mathematical intricacy, for the purpose of characterizing the orientation distribution function of elongated objects under flow. Our investigation…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved…
The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional $Q$-state Potts model. Four-point functions of the Potts conformal field theory are…
We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a…
We prove small data energy estimates of all orders of differentiability between past null infinity and future null infinity of de Sitter space for the conformally invariant Maxwell-scalar field system. This allows us to construct bounded…
Some general properties of perturbed (rational) CFT in the background metric of symmetric 2D sphere of radius $R$ are discussed, including conformal perturbation theory for the partition function and the large $R$ asymptotic. The truncated…
The charge on a conducting cylinder becomes uniformly distributed at large aspect ratios, albeit very slowly and with nonuniformity persisting near the ends. We show that the charge density and field magnitude are enhanced near the ends by…