Jon Harrison

Associate Professor of Mathematics

Education

Ph.D. in Mathematics, University of Bristol, 2001

Biography

Dr. Harrison joined the Baylor faculty in 2007. Prior to coming to Baylor served as a post-doctoral researcher at the Universität Ulm in Germany (2001-2004) and Visiting Assistant Professor at Texas A&M University (2004-2007). He is a graduate of Bristol University in the United Kingdom and is originally from Cranleigh, UK, the birth place of the famous Cambridge mathematician G.H. Hardy.  To date Dr. Harrison has supervised two Ph.D. students

Research

Dr. Harrison's research is in mathematical physics. He is particularly interested in quantum mechanics on graphs and quantum chaos.  Topics of particular interest include anyons on graphs, zeta functions of graphs, the Dirac operator and dynamical calculations of spectral statistics.  

Selected Publications

Complete dynamical evaluation of the characteristic polynomial of binary quantum graphs, J.M. Harrison and T. Hudgins, J. Phys. A (2022) https://doi.org/10.1088/1751-8121/ac95e1 arXiv:2101.00006

Periodic-orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit, J.M. Harrison and T. Hudgins, EPL 138 (2022) 30002 arXiv:2101.00006

Lyndon word decompositions and pseudo orbits on q-nary graphs, R. Band, J.M. Harrison and M. Sepanski, J. Math. Anal. Appl. 470 (2019) 135-144 arXiv:1610.03808

n-particle quantum statistics on graphs, J.M. Harrison, J.P. Keating, J.M. Robbins and A. Sawicki, Commun. Math. Phys. 33 (2014) 1293-1326 arXiv:1304.5781

Finite pseudo orbit expansions for spectral quantities of quantum graphs, R. Band, J.M. Harrison and C.H. Joyner, J. Phys. A: Math. Theor. 45 (2012) 325204 arXiv:1205.4214

Quantum statistics on graphs, J.M. Harrison, J.P. Keating and J.M. Robbins, Proc. R. Soc. A (2010) doi:10.1098/rspa.2010.0254 arXiv:1101.1535

Full counting statistics of chaotic cavities from classical action correlations, G. Berkolaiko, J.M. Harrison and M. Novaes, J. Phys. A: Math. Theor. 41 (2008) 365102 arXiv:cond-mat/0703803

On occurrence of spectral edges for periodic operators inside the Brillouin zone, J.M. Harrison, P. Kuchment, A. Sobolev and B. Winn, J. Phys. A 40 (2007) 7597-7618, arXiv:math-ph/0702035

Quantum graphs where back-scattering is prohibited, J.M. Harrison, U. Smilansky and B. Winn, J. Phys. A: Math. Theor. 40 (2007) 14181-14193 arXiv:0708.0839

Quantum Indistinguishability from General Representations of SU(2n), J.M. Harrison and J.M. Robbins, J. Math. Phys. 45 (2004), 1332-1358, arXiv:math-ph/0302037

The Spin Contribution to the Form Factor of Quantum Graphs, J. Bolte and J.M. Harrison, J. Phys. A: Math. Gen. 36 (2003), L433-L440, arXiv:nlin.CD/0304046

Spectral Statistics for the Dirac Operator on Graphs, J. Bolte and J.M. Harrison, J. Phys. A: Math. Gen. 36 (2003), arXiv:nlin.CD/0210029

Awards

Simons Foundation Collaboration Grant 354583, “Quantum Statistics of Networks Collaboration,” PI, 2015-2022.

NSF Conference Grant DMS-1838054, “Texas Analysis and Mathematical Physics Symposia,” PI (with B. Simanek), 2018-2019.

NSF Grant DMS 0604859 ``Spectral Properties of Quantum Graphs and Related Systems,'' CoPI (with G. Berkolaiko and B. Winn), 2006-2010.

Former Ph.D. Students

Victoria Hudgins (Now at the Univeristy of Kansas)

Erica Oldaker  (Now at Gordon College)

Teaching Interests

Dr. Harrison has taught a variety of courses including the calculus and advanced calculus sequences, foundations of mathematics, partial differential equations, linear algebra, and graduate real and complex analysis, graph theory, and nonlinear dynamics and chaos.