Note on the anisotropy of the correlation function for impurity angular momentum and the conduction electrons spins in alloys with cerium impurities

1970 ◽  
Vol 48 (24) ◽  
pp. 2912-2916
Author(s):  
A. D. Singh Nagi
Keyword(s):  
Correlation Function ◽  
Angular Momentum ◽  
Exchange Interaction ◽  
Second Order ◽  
Anisotropic Behavior ◽  
Conduction Electrons ◽  
Diagrammatic Method

Using a diagrammatic method and employing the exchange interaction Hamiltonian given by Coqblin and Schrieffer, the correlation function for the impurity angular momentum and the conduction electrons spins for alloys with cerium impurities is computed up to second order in J. The correlation function shows a strong anisotropic behavior.

scholarly journals Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

2021 ◽  
Author(s):  
Tilo Schwalger
Keyword(s):  
Correlation Function ◽  
Hazard Rate ◽  
Second Order ◽  
Level Crossing ◽  
Input Noise ◽  
Integrate And Fire ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
Decoupling Approximation ◽  
Crossing Theory

AbstractNoise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Second-order correlation function of fluorescence from a few atoms near plasmonic surface

2020 ◽  
Vol 95 (3) ◽  
pp. 034011
Author(s):  
Mojtaba Moazzezi ◽  
Augustine M Urbas ◽  
Vladimir P Drachev ◽  
Yuri Rostovtsev
Keyword(s):  
Correlation Function ◽  
Second Order

CONTINUOUS-VARIABLE ENTANGLEMENT OF THE CAVITY AND EXCITON MODE

2009 ◽  
Vol 07 (01) ◽  
pp. 357-363
Author(s):  
E. WU ◽  
XIAO-AN ZHANG ◽  
XI-MING WANG ◽  
LI-XIA ZENG
Keyword(s):  
Correlation Function ◽  
Sudden Death ◽  
Quantum Well ◽  
Continuous Variable ◽  
Second Order ◽  
Intensity Correlation ◽  
Exciton Mode ◽  
Semiconductor Quantum Well ◽  
Intensity Correlation Function ◽  
Antibunching Effect

We consider a semiconductor quantum well in the excitation system. Applying the pertinent Hamiltonian, we investigate the second-order intensity correlation function and the entanglement properties between the cavity and exciton mode. It is found that nonclassical (antibunching) effect and sudden death effect occur in our system.

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