Professor Tony Bracken's Homepage

Research Profile

Research Interests

Mathematical Physics

  • Symmetries in relativistic and nonrelativistic quantum mechanics
  • Relativistic wave equations
  • Localization of relativistic particles
  • Semiquantum mechanics
  • Quantum random walks
  • Subspace entanglement

    Biomathematics

  • Modelling liver pharmacokinetics
  • Flux-ratio theorems in membrane transport
  • Deterministic modelling of urban growth.
  • Modelling drug-delivery through the skin

    Chapters from Michelle Hackett's 2001 Honours Thesis "Classical Randomness in a Quantum Walk on a Line" can be found here.

    Chapters from James Wood's 1997 Honours Thesis "Asymptotic Localisation of Neutrinos in Relativistic Quantum Mechanics" can be found here.

    Some lectures on quantum mechanics in phase space given at SMFT07, Melbourne, 2007, can be found here: Lecture 1, Lecture 2, Lecture 3.

    Some recent lectures on diffusion in biological systems can be found here: Lecture 1, Lectures 2-3, Lecture 4-5, Lecture 6.

    A PowerPoint presentation (5.2Mb) given to a general audience while a Fellow of the Hungarian Institute for Advanced Studies "Collegium Budapest" in 2007-8, can be found here: From Guido d'Arezzo to Wigner of Budapest: The Uncertainty Principle and Musical Notation.

    A list of some recent publications can be found here.

    Some papers on the quantum paradox of probability backflow:--

    A.J. Bracken and G.F. Melloy, 1994. "Probability backflow and a new dimensionless quantum number."

    G.F. Melloy and A.J. Bracken, 1998. "Probability backflow for a Dirac particle."

    Some older publications:--

    A.J. Bracken and H.A. Cohen, 1969. "On Canonical SO(4,1)transformations of the Dirac equation."

    A.J. Bracken and H.S. Green, 1971. "Vector operators and a polynomial identity for SO(n)."

    A.J. Bracken and H.S. Green, 1973. "Parastatistics and the quark model."

    L. Bass and A.J. Bracken, 1977. "Time-dependent elimination of substrates flowing through the liver or kidney."

    A.J. Bracken, 1978. "Point form of quantum dynamics and a four-vector coordinate operator for a spinless particle."

    L. Bass, P.J. Robinson and A.J. Bracken, 1978. "Hepatic elimination of flowing substrates: the distributed model."

    A.J. Bracken and H.I. Leemon, 1980. "The isotropic harmonic oscillator in an angular momentum basis: an algebraic formulation."

    A.J. Bracken and H.I. Leemon, 1981. "A new set of coherent states for the isotropic harmonic oscillator: coherent angular momentum states."

    A.O. Barut and A.J. Bracken, 1981. "Zitterbewegung and the internal geometry of the electron."

    A.J. Bracken and Barry Jessup, 1982. "Local conformal-invariance of the wave equation for finite-component fields I."

    A.J. Bracken and Barry Jessup, 1982. "Local conformal-invariance of the wave equation for finite-component fields II."

    L. Bass, J. Aisbett and A.J. Bracken, 1984. "Asymptotic forms of tracer clearance curves."

    A.O. Barut and A.J. Bracken, 1985. "Compact quantum systems: internal geometry of relativistic systems."

    A.O. Barut and A.J. Bracken, 1985. "Neutral Dirac particle coupled to a fixed monopole."

    L.Bass, A.J. Bracken and J. Hilden, 1986. "Flux ratio theorems for membrane transport with temporary capture of tracer."

    Y.G. Anissimov, A.J. Bracken and M.S. Roberts, 1997. "Interconnected-tubes model of hepatic elimination."

    Y.G. Anissimov, A.J. Bracken and M.S. Roberts, 1999. "Interconnected-tubes model of hepatic elimination: steady state considerations."

    Y.G. Anissimov, A.J. Bracken and M.S. Roberts, 2002. "Catheter effects in organ perfusion experiments."

    International Congress of Mathematical Physics, 1997

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