id string | prompt string | output_type string | domain string | evaluation_mode string | solvability int64 | numeric_value string | source_url string | source_note string | test_points list | metric_key string | optimization_direction string | baseline_value int64 | baseline_note string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
anderson_lyapunov_exponent | Consider the following open problem in mathematical physics.
**Lyapunov Exponent of the 1D Anderson Model at Band Center**
**Definition:** Consider the discrete 1D Schrödinger (Anderson) equation on \(\mathbb{Z}\):
\[
-\psi_{n+1} - \psi_{n-1} + v_n\,\psi_n = 0, \qquad n \in \mathbb{Z},
\]
where \(v_n \overset{\mathrm... | function | continuum_physics | ground_truth_computable | 2 | null | https://arxiv.org/abs/1207.0725 | Comtet, Texier, Tourigny (2013), "Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices", J. Phys. A: Math. Theor. 46, 254003 (arXiv:1207.0725). For the band-center weak-disorder anomaly, see also Tessieri and related references: \(\gamma(\sigma) \sim (\Gamma(3/4)/\Gamma(1/4))^2\sigm... | [
{
"args": [
1
],
"expected": "0.108782735725609"
},
{
"args": [
1.25
],
"expected": "0.163920031851611"
},
{
"args": [
1.5
],
"expected": "0.225431857793137"
},
{
"args": [
1.75
],
"expected": "0.290658290222303"
},
{
"args"... | null | null | null | null |
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