Related papers: The Turing machine of a harmonic oscillator: from …
This study investigates the dynamics of quantum information and computational resources using a tractable model of coupled harmonic oscillators. We precisely characterize the interplay between mutual information, synchronization, and…
Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by…
In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of…
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
Harmonic theory provides a mathematical framework to describe the structure, behavior, evolution and emergence of harmonic systems. A harmonic system is context aware, contains elements that manifest characteristics either collaboratively…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the…
It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model…
What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent…
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is…
For the model of a linearly driven quantum anharmonic oscillator, the role of damping is investigated. We compare the position of the stable points in phase space obtained from a classical analysis to the result of a quantum mechanical…
The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space…
The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…
We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear…