Related papers: The axiom system of classical harmony
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
Many people enjoy classical symphonic music. Its diverse instrumentation makes for a rich listening experience. This diversity adds to the conductor's expressive freedom to shape the sound according to their imagination. As a result, the…
The decay of the overlap between a wave packet evolved with a Hamiltonian H and the same state evolved with H}+$\Sigma $ serves as a measure of the decoherence time $\tau_{\phi}$. Recent experimental and analytical evidence on classically…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
We demonstrate a conditional autoregressive pipeline for efficient music recomposition, based on methods presented in van den Oord et al.(2017). Recomposition (Casal & Casey, 2010) focuses on reworking existing musical pieces, adhering to…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
Duhamel's principle reduces the Cauchy problem for an inhomogeneous partial differential equation to the corresponding homogeneous problem. In the fractional-order setting, the classical principle does not apply directly because fractional…
We present a new approach to harmonic analysis that is trained to segment music into a sequence of chord spans tagged with chord labels. Formulated as a semi-Markov Conditional Random Field (semi-CRF), this joint segmentation and labeling…
Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index of the main products of graphs. Here, we obtain several…
This paper presents the proof of the coherence theorem for Ann-categories whose set of axioms and original basic properties were given in [9]. Let $$\A=(\A,{\Ah},c,(0,g,d),a,(1,l,r),{\Lh},{\Rh})$$ be an Ann-category. The coherence theorem…
Quantum algorithms with a proven theoretical speedup over classical computation are rare. Among the most prominent is the Harrow-Hassidim-Lloyd (HHL) algorithm for solving sparse linear systems. Here, HHL is applied to encode melodic…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical…
Music creation involves not only composing the different parts (e.g., melody, chords) of a musical work but also arranging/selecting the instruments to play the different parts. While the former has received increasing attention, the latter…
Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic…
We study how decoherence rules the quantum-classical transition of the Kicked Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system presents a classical dynamics that range from regular to a strong chaotic…
We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter…
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to…
For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a…