Mean phase coherence8/25/2023 axis int, optionalĪxis along which the coherence is computed for both inputs theĭefault is over the last axis (i.e. If detrend is False, no detrending isĭone. If it is a function, it takes a segment and returns aĭetrended segment. String, it is passed as the type argument to the detrendįunction. detrend str or function or False, optional Length of the FFT used, if a zero padded FFT is desired. Number of points to overlap between segments. Phase coherence is measured using interference visibility, which shows how well the two waves cancel when combined. In physics, two waves (or a wave and a copy of itself) are said to be coherent if they have constant relative phase. Tuple, is set to 256, and if window is array_like, is set to the Share By Sweetwater on Jul 26, 2013, 4:16 PM The phase alignment of two waves, such as sound waves. Defaults to None, but if window is str or If window is array_like it will be usedĭirectly as the window and its length must be nperseg. Passed to get_window to generate the window values, which areĭFT-even by default. window str or tuple or array_like, optionalĭesired window to use. Sampling frequency of the x and y time series. Time series of measurement values fs float, optional Time series of measurement values y array_like Spectral density estimates of X and Y, and Pxy is the cross coherence ( x, y, fs = 1.0, window = 'hann', nperseg = None, noverlap = None, nfft = None, detrend = 'constant', axis = -1 ) #Įstimate the magnitude squared coherence estimate, Cxy, ofĭiscrete-time signals X and Y using Welch’s method.Ĭxy = abs(Pxy)**2/(Pxx*Pyy), where Pxx and Pyy are power About diffusive systems, please open the book by Akkermans and Montambaux, Mesoscopic Physics of Electrons and Photons, Cambridge University Press (translated from the french original edition). # scipy.signal. In such systems, an important effect if the universal conductance flutuations. Nevertheless, phase coherence plays important role in diffusive systems, both electronic or photonic ones. One may at first think that the electron phase coherence is easier to maintain in ballistic structures, when the electrons mean-free-path (basically, the distance between two scattering events of an electron between two impurities) is larger than the size of the device. The reason why is now understood as the effects of temperature and size of the device: taking a reservoir of Landauer resistors finally restaures the Ohm's law. This clearly disagrees with the Ohm's law of classical resistors. When the phase coherence length becomes smaller than the size of the electronic device, the quantum effects wash out and only classical effect survive.Īn important example of phase coherence of electron is the Landauer quantisation formula of the conductance: when one sees an electron as a pure wave, the conductance of a resistive element should follow the concept of tunneling in quantum structures. For instance, the phase coherence length associated to the electrons becomes smaller at high temperature, since the phonon bath allows more incoherent scatterings between electrons, finally changing the phase of the electrons wave-function by a significant amount, say $2\pi$. decoherence, though this word is sometimes use in the more restrictive meaning of destructing the entanglement). Coherence and Phase synchrony are the building blocks for understanding brain connectivity, how the populations of neurons communicate around a network. This is also the topic where one studies the effects destroying quantum phenomena (i.e. The branch of physics studying the interference effects of electrons in metallic, superconducting and semi-conducting structures is called the mesoscopic physics. The interference effects are one of the many signatures of the quantum regime, hence the importance of the concept of phase coherence. Among those effects, interference effects are certainly the immediate ones we can think of. The notion of phase coherence is important for modern electronics of small size devices (especially at low temperatures), since it means that for devices smaller than the phase coherence length, quantum effects associated to the phase of the wave functions are no more negligible. The length associated to the phase coherence is the length after which the phase has changed significantly, say by $2\pi$ to quantify the concept. So, what is a phase coherence length? To each electron, one associates a wave-function $\Psi=\Psi_$. This definition is the one adopted in mesoscopic physics. Strictly speaking, a phase coherent electron device is an electronic device whose dimensions is smaller than the phase coherence length of the electrons.
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