Bohmian transmission and reflection dwell times without trajectory sampling

Dwell times for transmission and reflection

As was shown in quant-ph/0405028, the state of a tunneling particle can be uniquely presented as a coherent superposition of two states to describe alternative sub-processes, transmission and reflection. In this paper, on the basis of the stationary wave functions for these sub-processes, we give new definitions of the dwell times for transmission and reflection. In the case of rectangular potential barriers the dwell times are obtained explicitly. In contrast with the well-known Büttiker's dwell-time, our dwell time for transmission increases exponentially, for the under-barrier tunneling, wi…

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

A Bohmian analysis of the so-called Schrödinger-Langevin or Kostin nonlinear differential equation is provided to study how thermal fluctuations of the environment affects the dynamics of the wave packet from a quantum hydrodynamical point of view. In this way, after obtaining the Schrödinger-Langevin-Bohm equation from the Kostin equation its application to simple but physically insightful systems such as the Brownian-Bohmian motion, motion in a gravity field and transmission through a parabolic repeller is studied. % If a time-dependent Gaussian ansatz for the probability density is assumed,…

Understanding Quantum Superarrivals using the Bohmian model

We investigate the orgin of ``quantum superarrivals'' in the reflection and transmission probabilities of a Gaussian wave packet for a rectangular potential barrier while it is perturbed by either reducing or increasing its height. There exists a finite time interval during which the probability of reflection is {\it larger} (superarrivals) while the barrier is {\it lowered} compared to the unperturbed case. Similarly, during a certain interval of time, the probability of transmission while the barrier is {\it raised} {\it exceeds} that for free propagation. We compute {\it particle trajectori…

重申对玻姆力学的挑战

Reaffirming a Challenge to Bohmian Mechanics

针对玻姆力学在隧穿速度测量中的争议，本文区分了密度再现与运动状态分配两个问题，并提出了双向玻姆模型，证明标准引导方程在倏逝波区域与实验测量速度不一致。

Interference in Bohmian Mechanics with Complex Action

In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex [JCP {125}, 231103 (2006)]. In the alternative formulation there is a significant reduction in the magnitude of the quantum force as compared with the conventional Bohmian formulation, at the price of propagating complex trajectories. In this paper we show that Bohmian mechanics with complex …

Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, …

More About Tunnelling Times, the Dwell Time, and the ``Hartman Effect"

In a recent review paper [{\em Phys. Reports} {\bf 214} (1992) 339] we proposed, within conventional quantum mechanics, new definitions for the sub-barrier tunnelling and reflection times. \ Aims of the present paper are: \ (i) presenting and analysing the results of various numerical calculations (based on our equations) on the penetration and return times $<τ_{\, \rm Pen}>$, $<τ_{\, \rm Ret}>$, during tunnelling {\em inside} a rectangular potential barrier, for various penetration depths $x_{\rm f}$; \ (ii) putting forth and discussing suitable definitions, besides of the mean values, also o…

Larmor times for transmission and reflection

On the basis of quant-ph/0405028 we define the Larmor times for transmission and reflection. These times are valid both for the stationary and time-dependent scattering processes, without any restrictions on the shape of Gaussian-like wave packets. We show that in the stationary case both the Larmor times coincide with the corresponding dwell times obtained in quant-ph/0502073. The Larmor-time concept gives the way to verify the approach presented in quant-ph/0405028.

Scattering a quantum particle on the potential step: Characteristic times for transmission and reflection

We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model predicts the existence of a transitional spatial region behind the potential step where the probability to find reflected particles is nonzero and the average velocity of transmitted particles monotonously varies between asymptotic values. For both subprocesses we define the dwell and asymptotic group times.

Interaction time of a wave packet interact with a potential barrier

We study the evolution of a wave packet impinging onto a one dimensional potential barrier. The transmission and reflection times discussed in the literature for stationary states do not correspond to the times required for the emergence of a transmitted or a reflected packet. We propose new definitions for the interaction (dwell) time and the transmission and reflection times which are suitable for packets and fit better the actual time evolution of the packet.

Average clock times for scattering through asymmetric barriers

The reflection and transmission Salecker-Wigner-Peres clock times averaged over the post-selected reflected and transmitted sub-ensembles, respectively, are investigated for the one dimensional scattering of a localized wave packet through an asymmetric barrier. The dwell time averaged over the same post-selected sub-ensembles is also considered. The emergence of negative average reflection times is examined and we show that while the average over the reflected sub-ensemble eliminates the negative peaks at resonance for the clock time, it still allows negative values for transparent barriers. …

On the generalized Hartman effect and transmission time for a particle tunneling through two identical rectangular potential barriers

We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection -- at all stages of scattering. On its basis we define, for each subprocess, the dwell time as well as the local (exact) and asymptotic (extrapolated) group times. Our concept of the asymptotic transmission group time confirms the validity of the Wigner phase time in the opaque limit, as well as the existence of the usual and generalized Hartman effects pred…

Electron transmission and phase time in semiconductor superlattices

We discuss the time spent by an electron propagating through a finite periodic system such as a semiconductor superlattice. The relation between dwell-time and phase-time is outlined. The envelopes of phase-time at maximum and minimum transmission are derived, and it is shown that the peaks and valleys of phase-time can be well described by parameters fitted at the extrema. For a many-period system this covers most of the allowed band. Comparison is made to direct numerical solutions of the time-dependent Schrödinger equation by Veenstra et al. [cond-mat/0411118] who compared systems with and …