Quantum / CONCEPT
Infinitely many non-star trees admit Laplacian peak state transfer
There are arbitrarily large non-star trees with Laplacian peak state transfer. For each positive odd s, join a root to s(s+1)+1 hubs and each hub to s(s+1) leaves. Transfer from the root to every hub attains the spectral entry bound at time pi.
Closed
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES2
PROOF DEPTH5
DOCUMENT LINKS0
The answer is affirmative
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A genuine four-state superposition from level-one QAOAstructural-affinity · Closed
- Adjacency transfer through uniform clone matchingsstructural-affinity · Closed
- Divided differences over even and odd integer nodes are 2-adic unitsstructural-affinity · Closed
- Early state exclusion in seven-site transfer chains with symmetric spectrumstructural-affinity · Closed
- Energy eigenstates have no changing density recordstructural-affinity · Closed
- Interior perfect state transfer without endpoint transferstructural-affinity · Closed
- Middle-edge spectral weights, integer moments and Gram identity of even paths with end transfer at time pistructural-affinity · Closed
- Middle-vertex spectral weights and integer moments of odd paths with end transfer at time pistructural-affinity · Closed
- No perfect state transfer at time pi on rational paths with 2^k + 1 verticesstructural-affinity · Closed
- No perfect state transfer at time pi on rational paths with 2m vertices, m = 2 mod 4 or m = 3, 5 mod 8structural-affinity · Closed
- No perfect state transfer at time pi on rational paths with an odd number of verticesstructural-affinity · Closed
- Non-attained Pell phase supremum and unit asymptotic tail decay for two-level treesstructural-affinity · Closed
- Normalized-Laplacian perfect state transfer on a treestructural-affinity · Closed
- Pretty good state transfer at vertex 4 of the double blow-up of P_11structural-affinity · Closed
- Projection Probability Flowstructural-affinity · Closed
- Sharp global spectral bound for root-to-leaf Laplacian transfer on two-level treesstructural-affinity · Closed
- Spectrum and first-site amplitude of seven-site transfer chains with symmetric spectrumstructural-affinity · Closed
- The complete graph maximizes the trace of the average mixing matrixstructural-affinity · Closed
- The star bound for the least-energy uniform overlap failsstructural-affinity · Closed
- The twin end vertex of P'_9 is not sharply 1/9-sedentarystructural-affinity · Closed
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