Jon Harrison

PREPRINTS AND PUBLICATIONS

  • J.M. Harrison, “Quantizing graphs, one way or two?” Rev. Math. Phys. doi: 10.1142/S0129055X24600018 arXiv:2302.07193
  • J.M. Harrison and T. Weyand, “Can one hear the spanning trees of a quantum graph?” Lett. Math. Phys. 113 (2023) 31 arXiv:2209.01284
  • J.M. Harrison and T. Hudgins, “Complete dynamical evaluation of the characteristic polynomial of binary quantum graphs,” J. Phys. A: Math. Theor. 55 (2022) 425202 arXiv:2011.05213
  • J.M. Harrison and T. Hudgins, “Periodic-orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit,” EPL 138 (2022) 30002 arXiv:2101.00006
  • J.M. Harrison and E. Swindle, “Spectral properties of quantum circulant graphs,” J. Phys. A: Math. Theor. 52 (2019) 285101 arXiv:1810.08664
  • R. Band, J.M. Harrison and M. Sepanski, “Lyndon word decompositions and pseudo orbits on q-nary graphs,” J. Math. Anal. Appl. 470 (2019) 135-144 arXiv:1610.03808
  • J.M. Harrison and T. Weyand, “Relating zeta functions of discrete and quantum graphs,” Lett. Math. Phys. 108 (2018) 377-390 arXiv:1612.04273
  • J.M. Harrison, T. Weyand and K. Kirsten, “Zeta functions of the Dirac operator on quantum graphs,” J. Math. Phys. 57 (2016) 102301 arXiv:1606.07834
  • J.M. Harrison, J.P. Keating, J.M. Robbins and A. Sawicki, “n-particle quantum statistics on graphs,” Commun. Math. Phys. 33 (2014) 1293-1326 arXiv:1304.5781
  • G. Berkolaiko, J.M. Harrison and M. Novaes, “On inequivalent factorizations of a cycle,” arXiv:0809.3476
  • J.M. Harrison and B. Winn, “Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph,” J. Phys. A: Math. Theor. 45 (2012) 435101 arXiv:1205.6073
  • J.M. Harrison and K. Kirsten, “Vacuum energy of Schrödinger operators on metric graphs,” in: M. Asorey, M. Bordag and E. Elizalde (ed.’s) Quantum field theory under the influence of external conditions (QFEXT11), Int. J. Mod. Phys. Conf. Ser. 14 (2012) 357-366 arXiv:1201.3754
  • R. Band, J.M. Harrison and C.H. Joyner, “Finite pseudo orbit expansions for spectral quantities of quantum graphs,” J. Phys. A: Math. Theor. 45 (2012) 325204 arXiv:1205.4214
  • J.M. Harrison, K. Kirsten and C. Texier, “Spectral determinants and zeta functions of Schrödinger operators on metric graphs,” J. Phys. A: Math. Theor. 45 (2012) 125206 arXiv:1111.0643
  • J.M. Harrison and K. Kirsten, “Zeta functions of quantum graphs,” J. Phys. A: Math. Theor. 44 (2011) 235301 arXiv:0911.2509
  • J.M. Harrison, J.P. Keating and J.M. Robbins, “Quantum statistics on graphs,”  Proc. R. Soc. A (2010) doi:10.1098/rspa.2010.0254 arXiv:1101.1535
  • J.M. Harrison and K. Kirsten, “Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions,” in: K. A. Milton and M. Bordag (ed.’s) Quantum field theory under the influence of external conditions (QFEXT09), (World Scientific 2010) 421-425 arXiv:0912.0036
  • G. Berkolaiko, J.M. Harrison and J. Wilson, “Mathematical aspects of vacuum energy on quantum graphs,” J. Phys. A: Math. Theor. 42 (2009) 025204 arXiv:0711.2707
  • J.M. Harrison, “Quantum graphs with spin Hamiltonians,” in: Analysis on graphs and its applications P. Exner, J.P. Keating, P. Kuchment, T. Sunada, A. Teplyaev (ed.’s), Proceedings of Symposia in Pure Mathematics 77 AMS (2008) 261-277 arXiv:0712.0869
  • G. Berkolaiko, J.M. Harrison and M. Novaes, “Full counting statistics of chaotic cavities from classical action correlations,” J. Phys. A: Math. Theor. 41 (2008) 365102. Included in IOP select arXiv:cond-mat/0703803
  • J.M. Harrison, U. Smilansky and B. Winn, “Quantum graphs where back-scattering is prohibited,” J. Phys. A: Math. Theor. 40 (2007) 14181-14193 arXiv:0708.0839
  • J.M. Harrison, P. Kuchment, A. Sobolev and B. Winn, “On occurrence of spectral edges for periodic operators inside the Brillouin zone,” J. Phys. A: Math. Theor. 40 (2007) 7597-7618 arXiv:math-ph/0702035
  • J. Bolte and J.M. Harrison, “The spectral form factor for quantum graphs with spin-orbit coupling,” in: G. Berkolaiko, R. Carlson, S. A. Fulling, and P. Kuchment (ed.’s) Quantum Graphs and Their Applications, Contemporary Mathematics, 415, (AMS 2006) 51-64 arXiv:nlin.CD/0511011
  • J.M. Harrison and J.M. Robbins, “Quantum indistinguishability from general representations of SU(2n),” J. Math. Phys. 45 (2004) 1332-1358 arXiv:math-ph/0302037
  • J. Bolte and J.M. Harrison, “The spin contribution to the form factor of quantum graphs,” J. Phys. A: Math. Gen. 36 (2003) L433-L440 arXiv:nlin.CD/0304046
  • J. Bolte and J.M. Harrison, “Spectral statistics for the Dirac operator on graphs,” J. Phys. A: Math. Gen. 36 (2003) 2747-2769 arXiv:nlin.CD/0210029
  • J.M. Harrison and J.M. Robbins, “A group-theoretic approach to constructions of non-relativistic spin-statistics,” in: R. C. Hilborn and G. M. Tino (ed.’s): Spin-Statistics Connection and Commutation Relations, (AIP 2000) 67-71

Dissertations

  • J.M. Harrison, Group representations and the quantum statistics of spins, PhD thesis, 2001 (pdf)
  • J.M. Harrison, The wavelet analysis of fractal wave functions, final year MSci project report, 1997