Related papers: Generalized Borel Transform Technique in Quantum M…
In this paper, we study supersymmetry in quantum mechanics using the generalized uncertainty principle (GUP), or in other words, generalized supersymmetry in quantum mechanics. We construct supersymmetry in the generalized form of the…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
Existing works on Binary Neural Network (BNN) mainly focus on model's weights and activations while discarding considerations on the input raw data. This article introduces Generic Learned Thermometer (GLT), an encoding technique to improve…
The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…
Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
Borel summable divergent series usually appear when studying solutions of analytic ODE near a multiple singular point. Their sum, uniquely defined in certain sectors of the complex plane, is obtained via the Borel--Laplace transformation.…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
The generalized quantum master equation provides a powerful framework for non-Markovian dynamics of open quantum systems. However, the accurate and efficient evaluation of the memory kernel remains a challenge. In this work, we introduce a…
In this paper, we consider the direct application of the relativistic extended thermodynamics theory of polyatomic gases developed in [Ann. Phys. 377 (2017) 414--445] to the relativistic BGK model proposed by Marle. We present the perturbed…
We present an exact treatment of the thermodynamics of physical systems in the framework of the generalized uncertainty principle (GUP). Our purpose is to study and compare the consequences of two GUPs that one implies a minimal length…
We determine masses of light quarks ($m_u$,$m_d$,$m_s$) using Borel-Laplace sum rules and renormalization group summed perturbation theory (RGSPT) from the divergence of the axial vector current. The RGSPT significantly reduces the scale…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
The generalized Heitler-London (GHL) theory provides a straightforward way to express the potential energy surface of H_3 in terms of Coulomb and exchange energies which can be calculated either by perturbation theory or using the surface…
A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems it has been shown that exact and approximate quantum dynamics methods can be made dramatically…
Taking into account the importance of the unified theory of quantum mechanics and gravity, and the existence of a minimal length of the order of the Planck scale, we consider a modified Schr\"odinger equation resulting from a generalized…
We present an approach to quantum gravity based on the general boundary formulation of quantum mechanics, path integral quantization, spin foam models and renormalization.
A model for the bonding of hypervalent molecules containing sulfur is presented using generalized valence bond wavefunctions. To delineate the model from more commonly used DFT and delocalized wavefunctions, we present detailed comparisons…