In this paper, we introduce a new definition of fractional derivative which contains a fractional factor, and its physical meanings are given. When studying the fractional Schrdinger equation(FSE) with this form of fr...In this paper, we introduce a new definition of fractional derivative which contains a fractional factor, and its physical meanings are given. When studying the fractional Schrdinger equation(FSE) with this form of fractional derivative, the result shows that under the description of time FSE with fractional factor, the probability of finding a particle in the whole space is still conserved. By using this new definition to construct space FSE, we achieve a continuous transition from standard Schrdinger equation to the fractional one. When applying this form of Schrdinger equation to a particle in an infinite symmetrical square potential well, we find that the probability density distribution loses spatial symmetry and shows a kind of attenuation property. For the situation of a one-dimensional infinite δ potential well,the first derivative of time-independent wave function Φ to space coordinate x can be continuous everywhere when the particle is at some special discrete energy levels, which is much different from the standard Schrdinger equation.展开更多
In this study,Au+Au collisions with an impact parameter of 0≤b≤12.5 fm at√(s_(NN))=200 GeV are simulated using the AMPT model to provide preliminary final-state information.After transforming this information into ...In this study,Au+Au collisions with an impact parameter of 0≤b≤12.5 fm at√(s_(NN))=200 GeV are simulated using the AMPT model to provide preliminary final-state information.After transforming this information into appropriate input data(the energy spectra of final-state charged hadrons),we construct a multi-layer perceptron(MLP)and convolutional neural network(CNN)to connect final-state observables with the impact parameters.The results show that both the MLP and CNN can reconstruct the impact parameters with a mean absolute error approximately 0.4 fm,although the CNN behaves slightly better.Subsequently,we test the neural networks at different beam energies and pseudorapidity ranges in this task.These two models work well at both low and high energies.However,when conducting a test for a larger pseudorapidity window,the CNN exhibits a higher prediction accuracy than the MLP.Using the Grad-CAM method,we shed light on the'attention'mechanism of the CNN model.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11472247 and 11872335
文摘In this paper, we introduce a new definition of fractional derivative which contains a fractional factor, and its physical meanings are given. When studying the fractional Schrdinger equation(FSE) with this form of fractional derivative, the result shows that under the description of time FSE with fractional factor, the probability of finding a particle in the whole space is still conserved. By using this new definition to construct space FSE, we achieve a continuous transition from standard Schrdinger equation to the fractional one. When applying this form of Schrdinger equation to a particle in an infinite symmetrical square potential well, we find that the probability density distribution loses spatial symmetry and shows a kind of attenuation property. For the situation of a one-dimensional infinite δ potential well,the first derivative of time-independent wave function Φ to space coordinate x can be continuous everywhere when the particle is at some special discrete energy levels, which is much different from the standard Schrdinger equation.
基金Supported by the National Natural Science Foundation of China(12075061)Shanghai NSF(20ZR1404100)。
文摘In this study,Au+Au collisions with an impact parameter of 0≤b≤12.5 fm at√(s_(NN))=200 GeV are simulated using the AMPT model to provide preliminary final-state information.After transforming this information into appropriate input data(the energy spectra of final-state charged hadrons),we construct a multi-layer perceptron(MLP)and convolutional neural network(CNN)to connect final-state observables with the impact parameters.The results show that both the MLP and CNN can reconstruct the impact parameters with a mean absolute error approximately 0.4 fm,although the CNN behaves slightly better.Subsequently,we test the neural networks at different beam energies and pseudorapidity ranges in this task.These two models work well at both low and high energies.However,when conducting a test for a larger pseudorapidity window,the CNN exhibits a higher prediction accuracy than the MLP.Using the Grad-CAM method,we shed light on the'attention'mechanism of the CNN model.
