Related papers: Characterization of strongly non-linear and singul…
Trace Dynamics is a classical dynamical theory of noncommuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a…
This work deals with the computation of the power spectrum of large-scale structure using the dynamical system approach for a multi-fluid universe in scalar-tensor theory of gravity. We use the $1+3$ covariant approach to obtain evolution…
Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
The paper studies spectral representation and its applications for non-decaying continuous time signals that are not necessarily bounded at $\pm\infty$. The paper introduces notions of transfer functions, spectrum degeneracy, spectrum gaps,…
Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R.…
Standard models of sequential adsorption are implicitly formulated in a {\em scale invariant} form, by assuming adsorption on an infinite surface, with no characteristic length scales. In real situations, however, involving complex…
We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the…
We show that the two-point function of a quantum field theory with de Sitter momentum space (herein called DSR) can be expressed as the product of a standard delta function and an energy-dependent factor. This is a highly non-trivial…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
Coordinate scaling of each spin density separately is considered in spin density functional theory. A virial theorem relates the spin-scaled correlation energy to the spin-scaled correlation potentials. An adiabatic connection formula…
We analyze the dynamics of dissipation and relaxation in the unbroken and broken symmetry phases of scalar theory in the nonlinear regime for large initial energy densities, and after linear unstabilities (parametric or spinodal) are…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series…
We propose a scalar-tensor representation of $f(R)$ theories with use of conformal transformations. In this representation, the model takes the form of the Brans-Dicke model with a potential function and a non-zero kinetic term for the…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…
We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy…
This attempt to "derive" space is part of the Random Dynamics project. The Random Dynamics philosophy is that what we observe at our low energy level can be interpreted as some Taylor tail of the physics taking place at a higher energy…