We consider N strongly interacting electrons in a one-dimensional circular loop that is pierced by a time-periodic magnetic flux ${a(t)=a}_{0}{+a}_{1}(t)$ with the angular frequency $\ensuremath{\omega}.$ Similar to our previous work, where we have considered a static magnetic flux ${a}_{0},$ the electron positions are expressed in terms of collective and relative coordinates. Strong $e\ensuremath{-}e$ interaction can then be treated in a harmonic approximation for the relative motion. The presently searched solutions of the time-dependent Schr\"odinger equation for a time-periodic flux are given by the Floquet states. The Floquet states for a spatially constant one-particle potential form a complete set of Floquet-basis states, which is used to study the influence of the one-particle potential on the electronic states. While for a spatially constant one-particle potential the time-averaged observables, such as the electronic energy and the electronic current or angular momentum, depend solely on the time-averaged magnetic flux ${a}_{0},$ a spatially varying one-particle potential leads to pronounced resonances. In the case of moderate electronic relaxation, the stationary properties are determined by the Floquet state with lowest time-averaged energy. For the associated persistent angular momentum we predict jumps with heights proportional to the number of electrons N. We further show that, already by measuring the locations of these jumps in the ${(a}_{0},\ensuremath{\omega})$ plane, one could determine the number of electrons N as well as the effective $e\ensuremath{-}e$ interaction.We consider N strongly interacting electrons in a one-dimensional circular loop that is pierced by a time-periodic magnetic flux ${a(t)=a}_{0}{+a}_{1}(t)$ with the angular frequency $\ensuremath{\omega}.$ Similar to our previous work, where we have considered a static magnetic flux ${a}_{0},$ the electron positions are expressed in terms of collective and relative coordinates. Strong $e\ensuremath{-}e$ interaction can then be treated in a harmonic approximation for the relative motion. The presently searched solutions of the time-dependent Schr\"odinger equation for a time-periodic flux are given by the Floquet states. The Floquet states for a spatially constant one-particle potential form a complete set of Floquet-basis states, which is used to study the influence of the one-particle potential on the electronic states. While for a spatially constant one-particle potential the time-averaged observables, such as the electronic energy and the electronic current or angular momentum, depend solely on the time-averaged magnetic flux ${a}_{0},$ a spatially varying one-particle potential leads to pronounced resonances. In the case of moderate electronic relaxation, the stationary properties are determined by the Floquet state with lowest time-averaged energy. For the associated persistent angular momentum we predict jumps with heights proportional to the number of electrons N. We further show that, already by measuring the locations of these jumps in the ${(a}_{0},\ensuremath{\omega})$ plane, one could determine the number of electrons N as well as the effective $e\ensuremath{-}e$ interaction.

Physical review. B, Condensed matterApr 3, 20032 citations

One atom at a time

아이작 아시모프

과학동아Jul 1, 19900 citations

The Tunneling Time of an Electron

K.K. Thornber, T. C. McGill, Carver Mead

There is a widely spread misconception regarding the physical significance of the various tunneling times currently used to describe metal-insulator-metal tunneling phenomena. Using quantum mechanics, the transition time of an electron tunneling from a state on one side of the barrier to a state on the other side can be determined. This time is the period of interaction between the \nelectron and the barrier, since before and after the transition, the electron is in a quantum state of one of the metals. Furthermore, the RC time constant of the sandwich-like device and the electron transition or interaction time are equivalent representations \nof the same physical parameter. But none of these times is the quasiclassical "transmission time" analyzed by Hartman, which has become widely accepted as the electron-barrier interaction time, although this was clearly not his intention. In this communication we wish to point out that it is the (quantum mechanical) transition time which is the characteristic time of tunneling phenomena.There is a widely spread misconception regarding the physical significance of the various tunneling times currently used to describe metal-insulator-metal tunneling phenomena. Using quantum mechanics, the transition time of an electron tunneling from a state on one side of the barrier to a state on the other side can be determined. This time is the period of interaction between the \nelectron and the barrier, since before and after the transition, the electron is in a quantum state of one of the metals. Furthermore, the RC time constant of the sandwich-like device and the electron transition or interaction time are equivalent representations \nof the same physical parameter. But none of these times is the quasiclassical "transmission time" analyzed by Hartman, which has become widely accepted as the electron-barrier interaction time, although this was clearly not his intention. In this communication we wish to point out that it is the (quantum mechanical) transition time which is the characteristic time of tunneling phenomena.

Journal of Applied PhysicsApr 1, 196773 citations

One Atom at a Time

Mariette DiChristina

Scientific AmericanNov 19, 20130 citations

The Amazing Electron

Victor Francis Hess

ThoughtJan 1, 19470 citations

Novel Electron Correlation in the Scattering Continuum for a Stability Analysis of the Electron Pair in the “Atomic” Level

Akitomo Tachibana

Abstract Wannier phenomenon is examined for a stability analysis of a time-reversal electron pair scattering. Imagine a pair of electrons interacting one another. It is found that the nature of the interelectron interaction is to stabilize the time-reversal scattering state. This nature survives even under the influence of a scattering center. To conclude, we shall prove the following results: 1) inside the reaction zone of the scattering center, one of the electrons is trapped, pressing the other electron to the barrier of the reaction zone, or letting the other electron go away over the barrier of the reaction zone, namely, a time-reversal scattering state of the electron pair is unstable, while 2) outside the reaction zone, if the critical radius rc is reached, then the time-reversal scattering state of the electron pair is stabilized. The critical radius rc has an intrinsic importance as a measure of the coherence length ξ of the Cooper pair that exhibits the time-reversal symmetry.Abstract Wannier phenomenon is examined for a stability analysis of a time-reversal electron pair scattering. Imagine a pair of electrons interacting one another. It is found that the nature of the interelectron interaction is to stabilize the time-reversal scattering state. This nature survives even under the influence of a scattering center. To conclude, we shall prove the following results: 1) inside the reaction zone of the scattering center, one of the electrons is trapped, pressing the other electron to the barrier of the reaction zone, or letting the other electron go away over the barrier of the reaction zone, namely, a time-reversal scattering state of the electron pair is unstable, while 2) outside the reaction zone, if the critical radius rc is reached, then the time-reversal scattering state of the electron pair is stabilized. The critical radius rc has an intrinsic importance as a measure of the coherence length ξ of the Cooper pair that exhibits the time-reversal symmetry.

Bulletin of the Chemical Society of JapanNov 1, 19934 citations

We consider N strongly interacting electrons in a one-dimensional circular loop that is pierced by a time-periodic magnetic flux

{a(t)=a}_{0}{+a}_{1}(t)

with the angular frequency $\ensuremath{\omega}.$ Similar to our previous work, where we have considered a static magnetic flux

{a}_{0},

the electron positions are expressed in terms of collective and relative coordinates. Strong $e\ensuremath{-}e$ interaction can then be treated in a harmonic approximation for the relative motion. The presently searched solutions of the time-dependent Schr\"odinger equation for a time-periodic flux are given by the Floquet states. The Floquet states for a spatially constant one-particle potential form a complete set of Floquet-basis states, which is used to study the influence of the one-particle potential on the electronic states. While for a spatially constant one-particle potential the time-averaged observables, such as the electronic energy and the electronic current or angular momentum, depend solely on the time-averaged magnetic flux

{a}_{0},

a spatially varying one-particle potential leads to pronounced resonances. In the case of moderate electronic relaxation, the stationary properties are determined by the Floquet state with lowest time-averaged energy. For the associated persistent angular momentum we predict jumps with heights proportional to the number of electrons N. We further show that, already by measuring the locations of these jumps in the ${(a}_{0},\ensuremath{\omega})$ plane, one could determine the number of electrons N as well as the effective $e\ensuremath{-}e$ interaction.