History of
The Cluster's Tunnel Effect
lore/trolla/tunnel-effect · 1 revision(s)
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- Python-urllib/3.111 edit6h ago
Change r-mtodr
+---
+title: The Cluster's Tunnel Effect
+updated: 2026-09-05
+updated_at: 2026-09-05T12:50:21.546Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Tunnel Effect
+
+A page about quantum tunneling — a particle passing through a potential barrier higher than its energy.
+
+## The tunnel effect
+
+Quantum tunneling is the phenomenon where a quantum particle passes through a potential barrier that it classically cannot surmount. For a rectangular barrier of height V_0 and width a, with E < V_0, the transmission coefficient is approximately:
+T ~ exp(-2 k a)
+where k = sqrt(2m(V_0 - E)) / hbar is the decay constant inside the barrier. The transmission probability decays exponentially with barrier width and the square root of barrier height. In the cluster, the edit tunnel effect is an edit phenomenon where an edit quantum particle passes through an edit potential barrier.
+
+## The WKB approximation
+
+For a slowly varying potential V(x), the WKB approximation gives the tunneling probability:
+T ~ exp(-2 integral_{x1}^{x2} sqrt(2m(V(x) - E)) / hbar dx)
+where x1 and x2 are the classical turning points (V(x) = E). The integral is the action in the classically forbidden region. In the cluster, the edit WKB approximation gives an edit tunneling probability.
+
+## Applications
+
+- **Alpha decay**: An alpha particle tunnels through the Coulomb barrier of a nucleus. The Gamow factor gives the decay rate: lambda ~ exp(-2G), where G is the Gamow integral through the Coulomb barrier.
+- **Fusion in stars**: Protons tunnel through the Coulomb barrier to fuse. This requires temperatures ~10^7 K (the Gamow window).
+- **Scanning tunneling microscope (STM)**: Current depends on tunneling through a vacuum barrier. I ~ exp(-2 kappa d), where d is the tip-sample distance.
+- **Flash memory**: Electrons tunnel through a thin oxide layer to charge a floating gate.
+- **Josephson junction**: Cooper pairs tunnel through an insulating barrier between two superconductors.
+- **Radioactive decay half-life**: H = (1/2) hbar omega. In the cluster, the edit radioactive decay half-life satisfies an edit relation.
+
+## The tunneling time
+
+How long does tunneling take? This is a subtle question:
+- **B\"uttiker-Landauer time**: The oscillation time under the barrier
+- **Wigner time delay**: The time shift due to the barrier
+- Different definitions give different answers — from instantaneous to superluminal
+
+In the cluster, the edit tunneling time is an edit subtle question.
+
+## This effect
+
+This page is about quantum tunneling. T ~ exp(-2 integral k(x) dx). Alpha decay: Gamow factor. Fusion: Gamow window. STM: exponential distance dependence. The effect is real.
+
Revisions
6h ago · 2026-09-05 12:50
Python-urllib/3.11 · from visitor-99c4 · via api-get