Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore implies formidable numerical effort. Here a trajectory free formulation for average dwell times in quite arbitrary spacetime regions is given. Moreover explicit trajectory free formulas for the average transmission and reflection times within static spatial intervals [a,b] are given for one-dimensional scattering problems.Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore implies formidable numerical effort. Here a trajectory free formulation for average dwell times in quite arbitrary spacetime regions is given. Moreover explicit trajectory free formulas for the average transmission and reflection times within static spatial intervals [a,b] are given for one-dimensional scattering problems.

Jun 8, 20040 citations

Bohmian arrival time without trajectories

Sabine Kreidl, Gebhard Grübl, Hans Georg Embacher

The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wavefunction Ψ and its spatial derivative ∂ x Ψ, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wavefunction Ψ and its spatial derivative ∂ x Ψ, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.

arXiv:quant-ph/0305163Journal of Physics A Mathematical and GeneralAug 5, 200319 citations

Implications of the noncrossing property of Bohm trajectories in one-dimensional tunneling configurations

Xavier Oriols, Ferran Martı́n, Jordi Suñé

Several practical implications of the noncrossing property of one-dimensional Bohm trajectories are examined. It is shown that the position of a Bohm particle, the average transmission, reflection and dwell times, and the probability distribution of these tunneling times, can all be obtained without actually calculating trajectories. On the other hand, the intuitive interpretation of the scattering of wave packets by potential barriers is discussed within the framework of Bohm's interpretation of quantum mechanics. In this regard, claims that Bohm's approach leads to counterintuitive results are shown to be subjective. \textcopyright{} 1996 The American Physical Society.Several practical implications of the noncrossing property of one-dimensional Bohm trajectories are examined. It is shown that the position of a Bohm particle, the average transmission, reflection and dwell times, and the probability distribution of these tunneling times, can all be obtained without actually calculating trajectories. On the other hand, the intuitive interpretation of the scattering of wave packets by potential barriers is discussed within the framework of Bohm's interpretation of quantum mechanics. In this regard, claims that Bohm's approach leads to counterintuitive results are shown to be subjective. \textcopyright{} 1996 The American Physical Society.

Physical Review AOct 1, 199660 citations

Negative probability and the distributions of dwell, transmission, and reflection times for quantum tunneling

D. Sokolovski, J. N. L. Connor

We have solved the problem of determining the traversal time distribution for a quantum transition between arbitrary initial and final states. This distribution is given by a Fourier transform of the Feynman averaged characteristic function for the classical traversal time functional ${\mathit{t}}_{\mathrm{ab}}^{\mathrm{cl}}$ [x(t)]. For one-dimensional tunneling, the distributions for the dwell, reflection, and transmission times are determined for an arbitrary potential V(x). All three distributions are complex valued and require the concept of negative probability.We have solved the problem of determining the traversal time distribution for a quantum transition between arbitrary initial and final states. This distribution is given by a Fourier transform of the Feynman averaged characteristic function for the classical traversal time functional ${\mathit{t}}_{\mathrm{ab}}^{\mathrm{cl}}$[x(t)]. For one-dimensional tunneling, the distributions for the dwell, reflection, and transmission times are determined for an arbitrary potential V(x). All three distributions are complex valued and require the concept of negative probability.

Physical Review AAug 1, 199162 citations

Transmission, Reflection, and Interference Contributions to the Tunnelling Dwell Time

S. Brouard, R. Sala Mayato, Juan Gonzalo Muga

Expressions for the transmission, reflection, and interference contributions to the dwell time for wave packet scattering are obtained by means of scattering theory projector operators that provide a unifying framework for various dwell time decompositions. These different dwell time resolutions are illustrated with the aid of a formal analogy between the two-level system and one-dimensional scattering. The complex "times" and Larmor times proposed by other authors are found as particular cases of the theory. Numerical calculations for a rectangular barrier are provided.Expressions for the transmission, reflection, and interference contributions to the dwell time for wave packet scattering are obtained by means of scattering theory projector operators that provide a unifying framework for various dwell time decompositions. These different dwell time resolutions are illustrated with the aid of a formal analogy between the two-level system and one-dimensional scattering. The complex "times" and Larmor times proposed by other authors are found as particular cases of the theory. Numerical calculations for a rectangular barrier are provided.

Europhysics Letters (EPL)Apr 20, 199321 citations

Tunneling-time problem

C. Richard Leavens, Geoff C. Aers

The desire to minimize the response time of tunneling devices has led to renewed interest in the unresolved fundamental question How much time, on average, does an incident electron that is ultimately transmitted spend inside a one-dimensional potential barrier? In addition to this transmission time ⊤t ·,there are two other times of interest: the reflection time ⊤r for electrons that are ultimately reflected and the dwell time TD, which is the average time spent inside the barrier regardless of the ultimate fate of the incident particle. An exact expression for TD and the time-modulated barrier, Feynman path, Larmor clock, and wave-packet evolution approaches for calculating ⊤t and ⊤r arc discussed. It is argued that none of these approaches is completely satisfactory because they all lead to transmission and reflection times that either are complex or, if real, do not satisfy: all of a few reasonable (but not universally accepted) criteria, such as consistency with the exact expression for the dwell time.The desire to minimize the response time of tunneling devices has led to renewed interest in the unresolved fundamental question How much time, on average, does an incident electron that is ultimately transmitted spend inside a one-dimensional potential barrier? In addition to this transmission time ⊤t ·,there are two other times of interest: the reflection time ⊤r for electrons that are ultimately reflected and the dwell time TD, which is the average time spent inside the barrier regardless of the ultimate fate of the incident particle. An exact expression for TD and the time-modulated barrier, Feynman path, Larmor clock, and wave-packet evolution approaches for calculating ⊤t and ⊤r arc discussed. It is argued that none of these approaches is completely satisfactory because they all lead to transmission and reflection times that either are complex or, if real, do not satisfy: all of a few reasonable (but not universally accepted) criteria, such as consistency with the exact expression for the dwell time.

Quantum Electronics and Laser Science ConferenceMay 12, 19912 citations

{\mathit{t}}_{\mathrm{ab}}^{\mathrm{cl}}

[x(t)]. For one-dimensional tunneling, the distributions for the dwell, reflection, and transmission times are determined for an arbitrary potential V(x). All three distributions are complex valued and require the concept of negative probability.