Related papers: Counting the exponents of single transfer matrices
Threshold amplitudes are considered for $n$-particle production in arbitrary scalar theory. It is found that, like in $\phi ^4$, leading-$n$ corrections to the tree level amplitudes, being summed over all loops, exponentiate. This result…
This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are…
We introduce a class of self-interacting scalar theories in which the various coupling contants obey a recursive relation. These imply a particularly simple form for the generating function of the Feynman amplitudes with vanishing external…
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…
In the article integer divisibility properties and related prime factors natural number representation concepts have been defined over the whole infinite hyperoperation hierarchy. The definitions have been made across and above of unique…
Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial…
We suggest a new approach for the automatic and fully numerical evaluation of one-loop scattering amplitudes in perturbative quantum field theory. We use suitably formulated dispersion relations to perform the calculation as a convolution…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous…
The manifold under consideration consists of the faithful normal states on a sigma-finite von Neumann algebra in standard form. Tangent planes and approximate tangent planes are discussed. A relative entropy/divergence function is assumed…
Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given…
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…
A mono-component is a real-valued signal of finite energy that has non-negative instantaneous frequencies, which may be defined as the derivative of the phase function of the given real-valued signal through the approach of canonical…
In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is…
I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped,…
Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. It derives the ground state properties of a multi-atomic ensemble directly from the computation of its one-particle density \nr…
We investigate the probability of observing a given pattern of $n$ rises and falls in a random stationary data series. The data are modelled as a sequence of $n+1$ independent and identically distributed random numbers. This probabilistic…
The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently…
Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $\Lambda_n\subset \mathbb{R}$, and we show that it converges to…