Nonadiabatically Driven Quantum Interference Effects in the Ultracold K + KRb → Rb + K 2 Chemical Reaction
- Award ID(s):
- 2110227
- PAR ID:
- 10615977
- Publisher / Repository:
- American Chemical Society
- Date Published:
- Journal Name:
- The Journal of Physical Chemistry Letters
- Volume:
- 16
- Issue:
- 24
- ISSN:
- 1948-7185
- Page Range / eLocation ID:
- 6171 to 6177
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract For a subgraph$$G$$of the blow-up of a graph$$F$$, we let$$\delta ^*(G)$$be the smallest minimum degree over all of the bipartite subgraphs of$$G$$induced by pairs of parts that correspond to edges of$$F$$. Johansson proved that if$$G$$is a spanning subgraph of the blow-up of$$C_3$$with parts of size$$n$$and$$\delta ^*(G) \ge \frac{2}{3}n + \sqrt{n}$$, then$$G$$contains$$n$$vertex disjoint triangles, and presented the following conjecture of Häggkvist. If$$G$$is a spanning subgraph of the blow-up of$$C_k$$with parts of size$$n$$and$$\delta ^*(G) \ge \left(1 + \frac 1k\right)\frac n2 + 1$$, then$$G$$contains$$n$$vertex disjoint copies of$$C_k$$such that each$$C_k$$intersects each of the$$k$$parts exactly once. A similar conjecture was also made by Fischer and the case$$k=3$$was proved for large$$n$$by Magyar and Martin. In this paper, we prove the conjecture of Häggkvist asymptotically. We also pose a conjecture which generalises this result by allowing the minimum degree conditions in each bipartite subgraph induced by pairs of parts of$$G$$to vary. We support this new conjecture by proving the triangle case. This result generalises Johannson’s result asymptotically.more » « less
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