Related papers: How Do Transformers "Do" Physics? Investigating th…
The quantum description of a particle moving in a deformed potential is investigated. A pseudostate (PS) basis is used to represent the states of the composite system. This PS basis is obtained by diagonalizing the system Hamiltonian in a…
This paper explains a unified approach for teaching the electrical model of power transformers to undergraduate students using magnetic circuits. The commonly used approach for explaining the electrical model of power transformers is a…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
When the Standard Model is interpreted as the renormalizable sector of a low-energy effective theory, the effects of new physics are encoded into a set of higher dimensional operators. These operators potentially deform the shapes of…
Sustained oscillations (SOs) are commonly observed in systems dominated by converters. Under specific conditions, even though the origin of SOs can be identified through negative damping modes using conventional linear analysis, utilizing…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Despite their nearly universal adoption for large language models, the internal workings of transformers are not well understood. We aim to better understand the impact of removing or reorganizing information throughout the layers of a…
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
Understanding the transformer architecture and its workings is essential for machine learning (ML) engineers. However, truly understanding the transformer architecture can be demanding, even if you have a solid background in machine…
World modelling, i.e. building a representation of the rules that govern the world so as to predict its evolution, is an essential ability for any agent interacting with the physical world. Recent applications of the Transformer…
The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system…
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
In this work, we study theoretical models of \emph{programmable matter} systems. The systems under consideration consist of spherical modules, kept together by magnetic forces and able to perform two minimal mechanical operations (or…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory, for the case when the…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
This paper presents a mathematical framework for causal nonlinear prediction in settings where observations are generated from an underlying hidden Markov model (HMM). Both the problem formulation and the proposed solution are motivated by…