The Time In Quantum Tunneling

Tunneling is a purely quantum phenomenon in which a microscopic particle penetrates a barrier with a height greater than the total energy of the particle,and it is purely quantum mechanical without any classical analogy.Whether quantum tunneling is an instantaneous process or not is a long debated issue since the beginning of quantum mechanics.In order to clarify the above problems,firstly,we briefly review the development of quantum tunneling time,and give a short introduction to the definitions of phase time,dwell time,Buttiker-Landauer time and Larmor time.Besides,we also shortly review the interesting Hartman effect and the possible superluminal issue,and we also discuss the relevant measurement in tunneling times=Secondly,as a toy model,we discuss the scattering of ultracold neutral particles(such as neutron)in the linear gravitational potential.By calculating the tunneling time delay,we find that:with the increase of the neutron wave number k,the time delay of phase time,dwell time and Larmor time all decrease.However,compared with other time delays,the amplitude of Larmor time delay decreases slightly with the increase of k.By analyzing phase time and dwell time,we have obtained the relation between reflective phase time and dwell time,and we also find that time delay clearly demonstrate oscillation behaviors,which are due to the self-interference of incident and reflected partial waves.According to the traditional definition,the coincidence between the Larmor time and the phase time is very well.With the new definition of Larmor time,as the weak magnetic field decreases toward zero,the Larmor time approaches the classical returning time ?CE=2v/g.and the Larmor time may provide alternative configuration for realization in experiments compared with traditional Larmor time definition.Finally,we calculate the phase times and dwell time of a neutron particle tunneling through triangular potential barriers with mirror configurations:one with a vertical edge on the left side and the other with a vertical edge on the right side.From our results,we find that:for two kinds of triangle barriers with mirror symmetry,the transmission phase times are the same,while the reflection phase times and dwell times show distinctions for the two mirror configurations:the larger the barrier width,the more transparent the distinctions.Both phase times and dwell times show peak for the wave number spectrum and the apparently oscillatingc behaviors of phase times and dwell times are caused by the self-interference of incoming and reflected partial waves.