Related papers: Free Variable Loop Equations for the 3-State Potts…
We evaluate the partition function of three dimensional theories of gravity in the quantum regime, where the AdS radius is Planck scale and the central charge is of order one. The contribution from the AdS vacuum sector can - with certain…
This short note shows that the recently proposed generating function for loop hafnians -- originally derived using quantum-optical methods for a restricted class of matrices -- is in fact valid for arbitrary symmetric matrices. The proof…
Monte Carlo simulations and series expansion data for the energy, specific heat, magnetization and susceptibility of the 3-state Potts model on the square lattice are analyzed in the vicinity of the critical point in order to estimate…
In discrete-time linear dynamical systems (LDSs), a linear map is repeatedly applied to an initial vector yielding a sequence of vectors called the orbit of the system. A weight function assigning weights to the points in the orbit can be…
Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient…
We argue that one does not need to know the explicit solutions of the scattering equations in order to evaluate a given amplitude. We consider the most general quantity consistent with SL(2,C) invariance that can appear in an amplitude that…
We give further evidence that the matrix-tensor model studied in \cite{belin2023} is dual to AdS$_{3}$ gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random…
A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…
Ising and Potts models are an important class of discrete probability distributions which originated from statistical physics and since then have found applications in several disciplines. Simulation from these models is a well known…
Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…
By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero--dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be…
The operator expansion of free Green function of Helmholtz equation for arbitrary N- dimension space leads to asymptotic extension of 3- dimension Grimus-Stockinger formula closely related to multipole expansion. Analytical examples…
It is shown that the vacuum value of the $2d$ gravity stress tensor in the free field theory is singular in the fundamental region on the complex plane where the genus-$n>1$ Riemann surface are mapped. Because of the above singularity, one…
We propose a mechanism that couples matter fields to three-dimensional quantum gravity, which can be used for theories with a positive or negative cosmological constant. Our proposal is rooted in the Chern-Simons formulation of…
Most of deterministic solvers for rarefied gas dynamics use discrete velocity (or discrete ordinate) approximations of the distribution function on a Cartesian grid. This grid must be sufficiently large and fine to describe the distribution…
We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We…
We investigate the evolution of the phase-space distribution function around slightly perturbed stationary states and the process of violent relaxation in the context of the dissipationless collapse of an isolated spherical self-gravitating…
The increase of discrepancy in the standard procedure to choose the arbitrary functional form of the Lagrangian $f(Q)$ motivates us to solve this issue in modified theories of gravity. In this regard, we investigate the Gaussian process…
Following recent developments in discrete gravity, we study geometrical variables (angles and forms) of simplices in the discrete geometry point of view. Some of our relatively new results include: new ways of writing a set of simplices…
Analytic gravitational collapse and expansion solutions with anisotropic pressure are generated. Metric functions are found by requiring zero heat flow scalar. It emerges that a single function generates the anisotropic solutions. Each…