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

    Teaching 2007 Semester 1 :

    MATH3104 "Mathematical Biology" material

    Some recent lectures on quantum mechanics in phase space 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 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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