Sound Synthesis of a Gaussian Quantum Particle in an Infinite Square Well

Abstract

This article describes a synthesis technique based on the sonification of the dynamic behavior of a quantum particle enclosed in an infinite square well. More specifically, we sonify the momentum distribution of a one-dimensional Gaussian bouncing wave packet model. We have chosen this particular case because of its relative simplicity and interesting dynamic behavior, which makes it suitable for a novel sonification mapping that can be applied to standard synthesis techniques, resulting in the generation of appealing sounds. In addition, this sonification might provide useful insight into the behavior of the quantum particle. In particular, this model exhibits quantum revivals, minimizes uncertainty, and exhibits similarities to the case of a classical bouncing ball. The proposed model has been implemented in real time in both the Max/MSP and the Pure Data environments. The algorithm is based on concepts of additive synthesis where each oscillator describes the eigenfunctions that characterize the state evolution of the wave packet. We also provide an analysis of the sounds produced by the model from both a physical and a perceptual point of view.

Characterisation of the Degree of Musical Non-Markovianity

“…Noticeably, quantum computing has been applied to music (Miranda, 2021). There have been other proposals of sonifications based on quantum mechanics ideas and techniques (Kontogeorgakopoulos & Bugarth, 2014), including sonification of dynamic behaviours (Cádiz & Ramos, 2014). Time series appear to be relevant in the framework of generative music (Dean, 2017), and they might be related to the idea of memory (Toop, 2004).…”

“…Some of the applications mentioned concern mathematical techniques for quantum systems that demonstrate effectiveness in analysing music (Dalla Chiara et al, 2015;Mannone et al, 2020;Kontogeorgakopoulos & Bugarth, 2014;Dean, 2017). Some other studies involve the direct application of the basics of quantum systems (Gabor, 1947;Rocchesso & Mannone, 2020) and quantum computing in sound and music (Miranda, 2021;Cádiz & Ramos, 2014;beim Graben & Blutner, 2020;beim Graben & Mannone, 2020;Kulpa et al, 2020). While there is a flourishing of studies on quantum computing applied to music, here we focus in particular on methods and concepts from open quantum systems.…”

Gaussian Process Synthesis of Artificial Sounds

“…Analytic and synthetic approaches can be combined elegantly in the Bayesian framework. Turner [26] Cádiz and Ramos [27] used quantum physical equations to generate sound. In their work, they explored an implementation based on multiple wavetables but settled to use an approach based on additive synthesis because of its better performance.…”

Experiments in Sound and Music Quantum Computing

“…Another paper defines what it calls Quantum Music (Putz and Svozil 2015), though once again this is by analogy to the equations of quantum mechanics, rather than directly concerned with quantum physics. Certain equations of quantum mechanics have also been used to synthesize new sounds (Cadiz and Ramos 2014). The orchestral piece "Music of the Quantum" (Coleman 2003) was written as an outreach tool for a physics research group, and has been performed on various occasions.…”