Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left-and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.

A uniform phase representation for the harmonic model in speech synthesis applications

Feature-based vocoders, e.g., STRAIGHT, offer a way to manipulate the perceived characteristics of the speech signal in speech transformation and synthesis. For the harmonic model, which provide excellent perceived quality, features for the amplitude parameters already exist (e.g., Line Spectral Frequencies (LSF), Mel-Frequency Cepstral Coefficients (MFCC)). However, because of the wrapping of the phase parameters, phase features are more difficult to design. To randomize the phase of the harmonic model during synthesis, a voicing feature is commonly used, which distinguishes voiced and unvoiced segments. However, voice production allows smooth transitions between voiced/unvoiced states which makes voicing segmentation sometimes tricky to estimate. In this article, two-phase features are suggested to represent the phase of the harmonic model in a uniform way, without voicing decision. The synthesis quality of the resulting vocoder has been evaluated, using subjective listening tests, in the context of resynthesis, pitch scaling, and Hidden Markov Model (HMM)-based synthesis. The experiments show that the suggested signal model is comparable to STRAIGHT or even better in some scenarios. They also reveal some limitations of the harmonic framework itself in the case of high fundamental frequencies.