### Professor Tony Bracken's Homepage

- Email: a.bracken@uq.edu.au
- Phone: (07) 3365 3278
- Fax: (07) 3365 1477

### 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.

### 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."