Polya's theorem and migration + capture of a quantum particle

1Zagorodny, AG, 1Christophorov, LN
1Bogolyubov Institute for Theoretical Physics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 11:44-51
Section: Physics
Language: Ukrainian

Due to Polya's theorem, the quantum yield of capture of a particle, walking randomly on a low-dimensional lattice, by a trap located on one of its nodes is always 100 %, irrespective of the capture intensity. Under quantum migration, however, it is practically always less than 100 % and, contrary to intuition, only diminishes down to zero with the capture intensity growing.

Keywords: low-dimensional lattices, migration and capture, particle transport, Polya's theorem, quantum yield
  1. Kempe J. Contemporary Physics, 2003, 44, No 4: 307—327.
  2. Shenvi N., Kempe J., Whaley K.B. Phys. Rev. A, 2003, 67, No 5: 052307. doi: https://doi.org/10.1103/PhysRevA.67.052307
  3. Aharonov D., Gottesman D., Irani S., Kempe J. Comm. Math. Phys., 2009, 287, No 1: 41—65. doi: https://doi.org/10.1007/s00220-008-0710-3
  4. Polya G. Math. Ann., 1921, 84, No 1: 149—160. doi: https://doi.org/10.1007/BF01458701
  5. Montroll E.W. Lattice statistics. In: Appl. Combinatorial Math. Ed. by E.F. Beckenbach, N.-Y.: Wiley, 1964: 96—143.
  6. Yahnke E., Emde F., Lösch F. Tables of higher functions, N.-Y.: McGraw-Hill, 1960.
  7. Christophorov L.N., Kharkyanen V.N. Phys. Stat. Sol. (b), 1983, 116, No 2: 415—425. doi: https://doi.org/10.1002/pssb.2221160203
  8. Bateman H. Tables of integral transforms, Vol. 1, N.-Y.: McGraw-Hill, 1954.