Diffusion of a polymer in a gel is studied within the framework of de Gennes' model for reptation. Our results for the scaling of the diffusion coefficient D and the longest relaxation time τ are markedly different from the most recently reported results, and are in agreement with de Gennes' reptation arguments: D ∼ N −2 and τ ∼ N 3 . The leading exponent of the finite-size corrections to the diffusion coefficient is consistent with the value of -2/3 that was reported for the Rubinstein model. This agreement suggests that its origin might be physical rather than an artifact of these models.
The Larmor clock which was proposed to determine tunneling times of particles with spin through barriers is studied. Tunneling of wave packets is numerically derived from the time-dependent Schrödinger-Pauli equation. The Larmor clock often does not proceed unidirectionally in time. The asymptotic readings are well defined. For wide wave packets the asymptotic Larmor times agree with the stationary-state predictions; deviations are seen for narrow wave packets. Büttiker's dwell time is investigated and its connection with the Larmor times is confirmed in the case of wave packets.
The tunneling of Gaussian wave packets has been investigated by n umerically solving the one-dimensional Schr odinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier width, height and initial width of the wave packet. Compared to the case of free propagation, the maximum of a tunneled wavepacket exhibits a shift, which can be interpreted as an enhanced velocity during tunneling.
The tunneling of Gaussian wave packets has been investigated by numerically solving the one‐dimensional Schrödinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier width, height and initial width of the wave packet. Compared to the case of free propagation, the maximum of a tunneled wavepacket exhibits a shift, which can be interpreted as an enhanced velocity during tunneling.
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