2,228,372 research outputs found
Effective Hamiltonian Theory and Its Applications in Quantum Information
This paper presents a useful compact formula for deriving an effective
Hamiltonian describing the time-averaged dynamics of detuned quantum systems.
The formalism also works for ensemble-averaged dynamics of stochastic systems.
To illustrate the technique we give examples involving Raman processes,
Bloch-Siegert shifts and Quantum Logic Gates.Comment: 5 pages, 3 figures, to be published in Canadian Journal of Physic
On the Mathematics of Music: From Chords to Fourier Analysis
Mathematics is a far reaching discipline and its tools appear in many
applications. In this paper we discuss its role in music and signal processing
by revisiting the use of mathematics in algorithms that can extract chord
information from recorded music. We begin with a light introduction to the
theory of music and motivate the use of Fourier analysis in audio processing.
We introduce the discrete and continuous Fourier transforms and investigate
their use in extracting important information from audio data
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