Emeritus Professor Tony Bracken
Emeritus Professor
School of Mathematics and Physics
Personal page
Book Chapter
Bracken, Anthony J., Gould, Mark D., Zhang, Yao-Zhong and Delius, Gustav W. (1995). Infinite families of gauge-equivalent R-matrices and gradations of quantized affine algebras. Perspectives on Solvable Models. (pp. 231-243) Singapore, Singapore: World Scientific. doi: 10.1142/9789812831279_0015
Journal Articles
Bracken, A. J. and Melloy, G. F. (2023). Comment on ‘Backflow in relativistic wave equations’. Journal of Physics A: Mathematical and Theoretical, 56 (13) 138002, 1-4. doi: 10.1088/1751-8121/acbd70
Bracken, Anthony J (2021). Probability flow for a free particle: new quantum effects. Physica Scripta, 96 (4) 045201, 1-11. doi: 10.1088/1402-4896/abdd54
Bracken, Anthony J. (2019). Solutions of Painlevé II on real intervals: novel approximating sequences. Experimental Mathematics, 30 (2), 147-156. doi: 10.1080/10586458.2018.1507852
Bracken, A. J. (2018). Mathematics underfoot: the formulas that came to Würzburg from New Haven. Mathematical Intelligencer, 40 (2), 67-75. doi: 10.1007/s00283-018-9790-x
Bracken, A. J. and Bass, L. (2017). Series solution of Painlevé II in electrodiffusion: conjectured convergence. Journal of Physics A: Mathematical and Theoretical, 51 (3) 035202, 035202. doi: 10.1088/1751-8121/aa9bb0
Bracken, A. J. and Bass, L. (2017). Differential equations of electrodiffusion: constant field solutions, uniqueness, and new formulas of Goldman-Hodgkin-Katz type. Siam Journal On Applied Mathematics, 76 (6), 2286-2305. doi: 10.1137/15M1042292
Bracken, Tony (2016). The mystery of the strange formulae. Physics World, 29 (10), 22-22. doi: 10.1088/2058-7058/29/10/36
Bracken, A. J. and Melloy, G. F. (2014). Waiting for the quantum bus: the flow of negative probability. Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics, 48 (PA), 13-19. doi: 10.1016/j.shpsb.2014.09.001
Watson, P. and Bracken, A. J. (2014). Quantum Phase Space from Schwinger's Measurement Algebra. Foundations of Physics, 44 (7), 762-780. doi: 10.1007/s10701-014-9813-1
Bass, L. and Bracken, A. J. (2014). Emergent behaviour in electrodiffusion: Planck's other quanta. Reports On Mathematical Physics, 73 (1), 65-75. doi: 10.1016/S0034-4877(14)60032-X
Ellinas, D., Bracken, A. J. and Smyrnakis, I. (2012). Discrete randomness in discrete time quantum walk: study via stochastic averaging. Reports On Mathematical Physics, 70 (2), 221-227. doi: 10.1016/S0034-4877(12)60041-X
Bracken, A. J., Bass, L. and Rogers, C. (2012). Backlund flux quantization in a model of electrodiffusion based on Painlevé II. Journal of Physics A: Mathematical and Theoretical, 45 (10) 105204, 105204. doi: 10.1088/1751-8113/45/10/105204
Watson, P. and Bracken, A. J. (2011). Phase-space spinor amplitudes for spin-1/2 systems. Physical Review A, 83 (4) 042102, 042102.1-042102.8. doi: 10.1103/PhysRevA.83.042102
Bracken, A. J. and Watson, P. (2010). The quantum state vector in phase space and Gabor's windowed Fourier transform. Journal of Physics A: Mathematical and Theoretical, 43 (39) 395304, 395304-1-395304-19. doi: 10.1088/1751-8113/43/39/395304
Ellinas, Demosthenes and Bracken, Anthony J. (2008). Phase-space-region operators and the Wigner function: Geometric constructions and tomography. Physical Review A, 78 (5) 052106, 052106-1-052106-9. doi: 10.1103/PhysRevA.78.052106
Bracken, A. J., Ellinas, D. and Smyrnakis, I. (2007). Free-Dirac-particle evolution as a quantum random walk. Physical Review A: Atomic, Molecular, and Optical Physics, 75 (2) 022322, 022322-1-022322-7. doi: 10.1103/PhysRevA.75.022322
Mollee, T. R. and Bracken, A. J. (2007). A model of solute transport through stratum corneum using solute capture and release. Bulletin of Mathematical Biology, 69 (6), 1887-1907. doi: 10.1007/s11538-007-9197-x
Bracken, A.J. (2006). Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions. Reports On Mathematical Physics, 57 (1), 17-26. doi: 10.1016/S0034-4877(06)80005-4
Bracken, A. J. and Wood, J. G. (2006). Semiquantum versus semiclassical mechanics for simple nonlinear systems. Physical Review A, 73 (1) 012104, 012104-1-012104-10. doi: 10.1103/PhysRevA.73.012104
Bracken, A.J., Flohr, J.A. and Melloy, G.F. (2005). Time-evolution of highly localized positive-energy states of the free Dirac electron. Proceedings of The Royal Society A-mathematical Physical And Engineering Sciences, 461 (2063), 3633-3645. doi: 10.1098/rspa.2005.1538
Wood, J. G and Bracken, A. J. (2005). Bounds on integrals of the Wigner function: The hyperbolic case. Journal of Mathematical Physics, 46 (4) 042103, 1-14. doi: 10.1063/1.1851971
Bracken, A. J., Ellinas, D. and Tsohantjis, I. (2004). Pseudo memory effects, majorization and entropy in quantum random walks. Journal of Physics A-mathematical And General, 37 (8), L91-L97. doi: 10.1088/0305-4470/37/8/L02
Bracken, A. J. and Wood, J. G. (2004). Non-positivity of Groenewold operators. Europhysics Letters, 68 (1), 1-7. doi: 10.1209/epl/i2004-10175-8
Bracken, A. J. (2004). Entangled subspaces and quantum symmetries. Physical Review A, 69 (5) 052331, 052331-1-052331-7. doi: 10.1103/PhysRevA.69.052331
Bracken, A. J. (2003). Quantum mechanics as an approximation to classical mechanics in Hilbert space. Journal of Physics A: Mathematical and General, 36 (23), L329-L335. doi: 10.1088/0305-4470/36/23/101
Bracken, Anthony J., Ellinas, Demosthenes and Wood, James G. (2003). Group theory and quasiprobability integrals of Wigner functions. Journal of Physics A-mathematical And General, 36 (20), L297-L305. doi: 10.1088/0305-4470/36/20/102
Bracken, A. J., Cassinelli, G. and Wood, J. G. (2003). Quantum symmetries and the Weyl–Wigner product of group representations. Journal of Physics A: Mathematical and General, 36 (4), 1033-1056. doi: 10.1088/0305-4470/36/4/313
Shapira, D., Biham, O., Bracken, A. J. and Hackett, M. (2003). One-dimensional quantum walk with unitary noise. Physical Review A, 68 (6) 062315, 062315. doi: 10.1103/PhysRevA.68.062315
Anissimov, Yuri G., Bracken, Anthony J. and Roberts, Michael S. (2002). Catheter effects in organ perfusion experiments. Journal of Theoretical Biology, 214 (2), 263-273. doi: 10.1006/jtbi.2001.2450
Bracken, Anthony J., Ge, Xiang-Yu, Gould, Mark D., Links, Jon and Zhou, Huan-Qiang (2001). Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions. Journal of Physics A-mathematical And General, 34 (21), 4459-4474. doi: 10.1088/0305-4470/34/21/304
Bracken, A. J., Ge, X. Y., Gould, M. D. and Zhou, H. Q. (2001). Integrable extended hubbard models with boundary Kondo impurities. Bulletin of The Australian Mathematical Society, 64 (3), 445-467. doi: 10.1017/S0004972700019912
McNabb, A, Suzuki, M and Bracken, AJ (2001). A flux ratio theorem for multicomponent linear diffusion equations. Applied Mathematics Letters, 14 (1), 123-129. doi: 10.1016/S0893-9659(00)00123-3
Bracken, A. J., Doebner, H. and Wood, J. G. (1999). Bounds on integrals of the Wigner function. Physical Review Letters, 83 (19), 3758-3761. doi: 10.1103/PhysRevLett.83.3758
Anissimov, YG, Bracken, AJ and Roberts, MS (1999). Interconnected-Tubes model of hepatic elimination: Steady-state considerations. Journal of Theoretical Biology, 199 (4), 435-447. doi: 10.1006/jtbi.1999.0970
Bracken, A. J., Ge, X. Y., Zhang, Y. Z. and Zhou, H. Q. (1999). Boundary two-parameter eight-state supersymmetric Fermion model and Bethe Ansatz solution. Bulletin of the Australian Mathematical Society, 59 (3), 375-390. doi: 10.1017/S0004972700033050
Bracken, A. J. and Melloy, G. F. (1999). Localizing the relativistic electron. Journal of Physics A: Mathematical and General, 32 (34), 6127-6139. doi: 10.1088/0305-4470/32/34/302
Melloy, GF and Bracken, AJ (1998). Probability backflow for a Dirac particle. Foundations of Physics, 28 (3), 505-514. doi: 10.1023/A:1018724313788
Bracken, AJ, Ge, XY, Zhang, YZ and Zhou, HQ (1998). Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons. Nuclear Physics B, 516 (3), 588-602. doi: 10.1016/S0550-3213(98)00067-4
Melloy, GF and Bracken, AJ (1998). The velocity of probability transport in quantum mechanics. Annalen Der Physik, 7 (7-8), 726-731. doi: 10.1002/(SICI)1521-3889(199812)7:7/8<726::AID-ANDP726>3.0.CO;2-P
Bracken, AJ, Ge, XY, Zhang, YZ and Zhou, HQ (1998). An open-boundary integrable model of three coupled XY spin chains. Nuclear Physics B, 516 (3), 603-622. doi: 10.1016/S0550-3213(98)00066-2
Mellick, GD, Anissimov, YG, Bracken, AJ and Roberts, MS (1997). Metabolite mean transit times in the liver as predicted by various models of hepatic elimination. Journal of Pharmacokinetics And Biopharmaceutics, 25 (4), 477-505. doi: 10.1023/A:1025797126763
Anissimov, YG, Bracken, AJ and Roberts, MS (1997). Interconnected-tubes model of hepatic elimination. Journal of Theoretical Biology, 188 (1), 89-101. doi: 10.1006/jtbi.1997.0455
Clark, I. J. and Bracken, A. J. (1996). Bound states in tubular quantum waveguides with torsion. Journal of Physics A: Mathematical and General, 29 (15), 4527-4535. doi: 10.1088/0305-4470/29/15/022
Suzuki, M., McNabb, A. and Bracken, A. J. (1996). Membrane diffusion and flux response. Applied Mathematics Letters, 9 (4), 35-40. doi: 10.1016/0893-9659(96)00048-1
Clark I.J. and Bracken A.J. (1996). Effective potentials of quantum strip waveguides and their dependence upon torsion. Journal of Physics A: Mathematical and General, 29 (2), 339-348. doi: 10.1088/0305-4470/29/2/014
Bracken, AJ, Gould, MD and Zhang, YZ (1995). Quantized Affine Algebras and Parameter-Dependent R-Matrices. Bulletin of the Australian Mathematical Society, 51 (2), 177-194. doi: 10.1017/S0004972700014040
Bracken, AJ, Gould, MD, Links, JR and Zhang, YZ (1995). New Supersymmetric and Exactly Solvable Model of Correlated Electrons. Physical Review Letters, 74 (14), 2768-2771. doi: 10.1103/PhysRevLett.74.2768
Bracken, AJ, Gould, MD, Zhang, YZ and Delius, GW (1994). Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras. International Journal of Modern Physics B, 8 (25-26), 3679-3691. doi: 10.1142/S0217979294001585
Bracken, AJ, Gould, MD, Zhang, YZ and Delius, GW (1994). Solutions of the Quantum Yang-Baxter Equation with Extra Nonadditive Parameters. Journal of Physics A-Mathematical and General, 27 (19) 025, 6551-6561. doi: 10.1088/0305-4470/27/19/025
Bracken A.J. and Melloy G.F. (1994). Probability backflow and a new dimensionless quantum number. Journal of Physics A: Mathematical and General, 27 (6) 040, 2197-2211. doi: 10.1088/0305-4470/27/6/040
Gould, MD, Tsohantjis, I and Bracken, AJ (1993). Quantum Supergroups and Link Polynomials. Reviews in Mathematical Physics, 5 (3), 533-549. doi: 10.1142/S0129055X93000152
Gould, MD, Zhang, RB and Bracken, AJ (1993). Quantum Double Construction for Graded Hopf-Algebras. Bulletin of the Australian Mathematical Society, 47 (3), 353-375. doi: 10.1017/S0004972700015197
Bracken, AJ, Gould, MD and Tsohantjis, I (1993). Boson-Fermion Models for Osp(1,2) and Uq[Osp(1,2)]. Journal of Mathematical Physics, 34 (5), 1654-1664. doi: 10.1063/1.530182
Gould, M. D., Links, J. and Bracken, A. J. (1992). Matrix elements and Wigner coefficients for Uq[gl(n)]. Journal of Mathematical Physics, 33 (3), 1008-1022. doi: 10.1063/1.529986
Bracken, A. J. and Tuckwell, H. C. (1992). Simple mathematical models for urban growth. Proceedings - Royal Society of London, A, 438 (1902), 171-181. doi: 10.1098/rspa.1992.0100
Gould, MD, Zhang, RB and Bracken, AJ (1991). Generalized Gelfand Invariants and Characteristic Identities for Quantum Groups. Journal of Mathematical Physics, 32 (9), 2298-2303. doi: 10.1063/1.529152
Zhang, RB, Gould, MD and Bracken, AJ (1991). From Representations of the Braid Group to Solutions of the Yang-Baxter Equation. Nuclear Physics B, 354 (2-3), 625-652. doi: 10.1016/0550-3213(91)90369-9
Bracken, AJ, McAnally, DS, Zhang, RB and Gould, MD (1991). A Q-Analog of Bargmann Space and its Scalar Product. Journal of Physics A-Mathematical and General, 24 (7) 015, 1379-1391. doi: 10.1088/0305-4470/24/7/015
Zhang, RB, Gould, MD and Bracken, AJ (1991). Solutions of the Graded Classical Yang-Baxter Equation and Integrable Models. Journal of Physics A-Mathematical and General, 24 (6), 1185-1197. doi: 10.1088/0305-4470/24/6/012
Zhang, RB, Gould, MD and Bracken, AJ (1991). Generalized Gelfand Invariants of Quantum Groups. Journal of Physics A-Mathematical and General, 24 (5) 009, 937-943. doi: 10.1088/0305-4470/24/5/009
Zhang, RB, Bracken, AJ and Gould, MD (1991). Solution of the Graded Yang-Baxter Equation Associated with the Vector Representation of Uq(Osp(M/2N)). Physics Letters B, 257 (1-2), 133-139. doi: 10.1016/0370-2693(91)90870-V
Zhang, RB, Gould, MD and Bracken, AJ (1991). Quantum Group Invariants and Link Polynomials. Communications in Mathematical Physics, 137 (1), 13-27. doi: 10.1007/BF02099115
Green H.S., Bracken A.J. and Bass L. (1991). Harmonic functions satisfying a radiation boundary condition. Computers and Mathematics with Applications, 22 (2), 23-38. doi: 10.1016/0898-1221(91)90039-7
Gould, MD, Jarvis, PD and Bracken, AJ (1990). Branching-Rules for a Class of Typical and Atypical Representations of Gl(M/n). Journal of Mathematical Physics, 31 (12), 2803-2810. doi: 10.1063/1.528983
Bracken, AJ, Gould, MD and Zhang, RB (1990). Quantum Supergroups and Solutions of the Yang-Baxter Equation. Modern Physics Letters a, 5 (11), 831-840. doi: 10.1142/S0217732390000925
McAnally D.S. and Bracken A.J. (1990). Quasiclassical states of the Coulomb system and so(4, 2). Journal of Physics A: General Physics, 23 (11) 026, 2027-2047. doi: 10.1088/0305-4470/23/11/026
Gould, MD, Bracken, AJ and Hughes, Jwb (1989). Branching-Rules for Typical and Atypical Representations of Gl(N/1). Journal of Physics A-Mathematical and General, 22 (15), 2879-2896. doi: 10.1088/0305-4470/22/15/008
Bracken A.J. and Zhang R.B. (1989). Equivalence of two character formulae for typical and singly atypical irreducible modules of sl(m/n). Journal of Physics A: Mathematical and General, 22 (22) 001, L1049-L1053. doi: 10.1088/0305-4470/22/22/001
Bracken A.J. and Cant A. (1989). Singular indecomposable representations of sl(2,ℂ) and relativistic wave equations. Journal of Mathematical Physics, 30 (12), 2963-2972. doi: 10.1063/1.528484
Bass L., Bracken A.J. and Green H.S. (1988). Boundary layers and images in dispersed flow reactors: A green's function approach. Chemical Engineering Science, 43 (7), 1583-1590. doi: 10.1016/0009-2509(88)85149-2
McAnally D.S. and Bracken A.J. (1988). Time dependence of variables in the quantum-mechanical and classical Coulomb problems, and the dynamical algebra so(4,2). Physical Review A, 37 (7), 2304-2308. doi: 10.1103/PhysRevA.37.2304
Bass L., Bracken A.J. and Hilden J. (1986). Flux ratio theorems for nonstationary membrane transport with temporary capture of tracer. Journal of Theoretical Biology, 118 (3), 327-338. doi: 10.1016/S0022-5193(86)80063-7
Bass L., Aisbett J. and Bracken A.J. (1984). Asymptotic forms of tracer clearance curves: Theory and applications of improved extrapolations. Journal of Theoretical Biology, 111 (4), 755-785. doi: 10.1016/S0022-5193(84)80266-0
Bracken, A. J. and MacGibbon, J. H. (1984). Creation and annihilation operators for SU(3) in an SO(6,2) model. Journal of Physics A: Mathematical and General, 17 (13) 011, 2581-2597. doi: 10.1088/0305-4470/17/13/011
Barut, A. O. and Bracken, A. J. (1983). A duality between massless particles and a charge-monopole system. Letters in Mathematical Physics, 7 (5), 407-414. doi: 10.1007/BF00398762
Bass L. and Bracken A.J. (1983). The flux-ratio equation under nonstationary boundary conditions. Mathematical Biosciences, 66 (1), 87-92. doi: 10.1016/0025-5564(83)90078-0
Bracken, A. J. and Jessup, Barry (1982). Local conformal invariance of the wave equation for finite‐component fields. II. Classification of relevant indecomposable fields. Journal of Mathematical Physics, 23 (10), 1947-1952. doi: 10.1063/1.525245
Bracken, A. J. and Jessup, Barry (1982). Local conformal‐invariance of the wave equation for finite‐component fields. I. The conditions for invariance, and fully‐reducible fields. Journal of Mathematical Physics, 23 (10), 1925-1946. doi: 10.1063/1.525222
Barut, A. O. and Bracken, A. J. (1981). Magnetic-moment operator of the relativistic electron. Physical Review D, 24 (12), 3333-3334. doi: 10.1103/PhysRevD.24.3333
Holt J.N. and Bracken A.J. (1980). First-kind Fredholm integral equation of liver kinetics: numerical solutions by constrained least squares. Mathematical Biosciences, 51 (1-2), 11-24. doi: 10.1016/0025-5564(80)90088-7
Bracken A.J. and Leemon H.I. (1980). A new set of coherent states for the isotropic harmonic oscillator: Coherent angular momentum states. Journal of Mathematical Physics, 22 (4), 719-732. doi: 10.1063/1.524964
Bass L. and Bracken A.J. (1979). The problem of thrown string (reply). Nature, 277 (5692), 154-154. doi: 10.1038/277154a0
Bracken A.J. and Leemon H.I. (1979). The isotropic harmonic oscillator in an angular momentum basis: An algebraic formulation. Journal of Mathematical Physics, 21 (8), 2170-2181. doi: 10.1063/1.524699
Bracken A.J. and Bass L. (1979). Statistical mechanics of hepatic elimination. Mathematical Biosciences, 44 (1-2), 97-120. doi: 10.1016/0025-5564(79)90031-2
Bass, L. and Bracken, A. J. (1978). The problem of the thrown string [9]. Nature, 275 (5677), 205-206. doi: 10.1038/275205a0
Bass L., Robinson P. and Bracken A.J. (1978). Hepatic elimination of flowing substrates: The distributed model. Journal of Theoretical Biology, 72 (1), 161-184. doi: 10.1016/0022-5193(78)90023-1
Bass, L. and Bracken, A. J. (1977). Time-dependent elimination of substrates flowing through the liver or kidney. Journal of Theoretical Biology, 67 (4), 637-652. doi: 10.1016/0022-5193(77)90251-X
Bracken, A. J. (1977). The point form of quantum dynamics and a 4-vector coordinate operator for a spinless particle. Journal of Mathematical Physics, 19 (12), 2520-2527. doi: 10.1063/1.523635
Bracken, A. J. (1975). Commutation and anti-commutation relations for a class of Gel'fand-Yaglom matrices. Journal of Physics A: Mathematical and General, 8 (5), 800-807. doi: 10.1088/0305-4470/8/5/015
Bracken, A. J. (1975). O(4,2): An exact invariance algebra for the electron. Journal of Physics A: Mathematical and General, 8 (5) 016, 808-815. doi: 10.1088/0305-4470/8/5/016
Bracken, A. J. (1974). Wave functions for free, massless particles and nonintegrable representations of sl(2,c). Physical Review D, 10 (4), 1168-1181. doi: 10.1103/PhysRevD.10.1168
Conference Papers
Ellinas, Demosthenes and Bracken, Anthony J. (2019). Phase space regions operators and ISp(2) maps. 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018, Prague, Czech Republic, 9-13 July 2018. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/1194/1/012033
Worsley, Susan, Bracken, Anthony, Hibberd, Katrina and Isaac, Phillip (2009). Introducing a group research project into a second-level mathematics course. UniServe Science Conference 2009, Sydney, NSW, Australia, 30 September - 2 October 2009. Sydney, NSW, Australia: UniServe Science.
Bracken, A. J., Ellinas, D. and Wood, J. G. (2004). Non-positivity of the wigner function and bounds on associated integrals. doi: 10.1556/APH.20.2004.1-2.24