Related papers: When to carry out analytic continuation?
In this paper, we explore propagation of energy flux in the future Poincar\'e patch of de Sitter spacetime. We present two results. First, we compute the flux integral of energy using the symplectic current density of the covariant phase…
A protocol for explicitly constructing the exact time-evolution operators generated by $2 \times 2$ time-dependent $PT$-symmetry Hamiltonians is reported. Its mathematical applicability is illustrated with the help of appropriate examples.…
We introduce the scalar and tensor modes of the gravitational perturbation in the presence of a scalar field which describes inflation. We investigate the back-reaction of the perturbations to the background by studying the effective…
Long-time asymptotic of field-field correlator for radiation propagated through a medium composed of random point-like scatterers is studied using Bete-Salpeter equation. It is shown that for plane source the fluctuation intensity (zero…
Numerical analytical heat transfer models play a critical role in geothermal design and feasibility studies. Classical solutions, such as those proposed by Gringarten et al. 1975, rely on simplified assumptions and systematically…
We study inflation in a model with constant second slow-roll parameter $\eta$. In this case, the Hubble expansion rate equation has analytical solutions describing four possible, nontrivial inflation scenarios. The evolution of the inflaton…
In this paper we will analyse quantum field theory on de Sitter spacetime. We will analyse a general scalar and vector field theory on de Sitter spacetime. This is done by first calculating these propagators on four-Sphere and then…
To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…
We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help…
This article discusses the analyticity and the long-time asymptotic behavior of solutions to space-time fractional diffusion equations in $\mathbb{R}^d$. By a Laplace transform argument, we prove that the decay rate of the solution as…
The aim of this paper is to develop the theory of distributions, not necessarily of compact support, in a topos model of Synthetic Differential Geometry, the so-called "Cahiers Topos". As an application, we study the evolution through time…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
We consider an explicit example of a process, where the entropy carried by radiation through an accelerating two-plane is proportional to the decrease in the area of that two-plane even when the two-plane is not a part of any horizon of…
Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the…
This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order $\alpha\in(0,1)$. Firstly, the uniqueness of solutions to a lateral Cauchy problem for the…
We present a new method for extracting the persistence exponent theta for the diffusion equation, based on the distribution P of `sign-times'. With the aid of a numerically verified Ansatz for P we derive an exact formula for theta in…
A well-known difficulty of perturbative approaches to quantum field theory at finite temperature is the necessity to address theoretical constraints that are not present in the vacuum theory. In this work, we use lattice simulations of…
Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…
This work is aimed at the study and analysis of the heat transport on a metal bar of length $L$ with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials.…
We consider a thermodynamically consistent model for the evolution of thermally conducting two-phase incompressible fluids. Complementing previous results, we prove additional regularity properties of solutions in the case when the…