A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploratio...A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.展开更多
We study the phase,Larmor and dwell times of a particle scattered off triangular barriers(TBs).It is interesting that the dependences of dwell,reflective phase and Larmor times on the wave number,barrier width and hei...We study the phase,Larmor and dwell times of a particle scattered off triangular barriers(TBs).It is interesting that the dependences of dwell,reflective phase and Larmor times on the wave number,barrier width and height for a pair of mirror-symmetric(MS)exact triangular barriers(ETBs)are quite different,as the two ETBs have quite distinct scattering surfaces.In comparison,the dependence of the transmitted phase or Larmor times is exactly the same,since the transmitted amplitudes are the same for a pair of MS TBs.We further study the Hartman effect by defining the phase and Larmor velocities associated with the phase and Larmor times.We find no barrier width saturation effect for the transmitted and reflected times.This is indicated by the fact that all the velocities approach finite constants that are much smaller than the speed of light in vacuum for TBs with positive-slope impact faces.As for ETBs with vertical left edges,the naive velocities seem to also indicate the absence of the Hartman effect.These are quite distinct from rectangular barriers and may shed new light on the clarification of the tunneling time issues.展开更多
基金Project supported by the National Natural Science Foun dation of China(Grant No.11274398).
文摘A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974108,11875127,and 12211530044)the Fundamental Research Funds for the Central Universities(Grant No.2020MS052).
文摘We study the phase,Larmor and dwell times of a particle scattered off triangular barriers(TBs).It is interesting that the dependences of dwell,reflective phase and Larmor times on the wave number,barrier width and height for a pair of mirror-symmetric(MS)exact triangular barriers(ETBs)are quite different,as the two ETBs have quite distinct scattering surfaces.In comparison,the dependence of the transmitted phase or Larmor times is exactly the same,since the transmitted amplitudes are the same for a pair of MS TBs.We further study the Hartman effect by defining the phase and Larmor velocities associated with the phase and Larmor times.We find no barrier width saturation effect for the transmitted and reflected times.This is indicated by the fact that all the velocities approach finite constants that are much smaller than the speed of light in vacuum for TBs with positive-slope impact faces.As for ETBs with vertical left edges,the naive velocities seem to also indicate the absence of the Hartman effect.These are quite distinct from rectangular barriers and may shed new light on the clarification of the tunneling time issues.
