Dr Nicholas Witte staff profile picture

Contact details +64 (06) 356 9099  ext. 84655

Dr Nicholas Witte PhD

Senior Lecturer in Physics

Institute of Fundamental Sciences

Professional

Contact details

  • Ph: 64 6 951 7655 or ext. 84655
    Location: B.3.23, Tower B, Institute of Fundamental Sciences
    Campus: Turitea

Qualifications

  • Doctor of Philosophy - Melbourne University (1990)

Research Expertise

Research Interests

• Analysis
- 42C05 orthogonal functions and polynomial, general theory
- 33C45 orthogonal polynomials and functions of hypergeometric type,
- 30E05, 44A60 moment problems,
- 30B70 Continued fractions,
- 65R10, 65R20 integral transforms and integral equations,
- 35Q15 Riemann-Hilbert problems,
- 34E05, 35C20 asymptotic expansions,
- 34A34 nonlinear differential equations and systems, general
- 34A05 explicit solutions of differential equations and reductions,
• Integrable Systems
- 34M55 Painlevé and other special equations, classification, hierarchies and isomonodromic deformation,
- 33E17 Painlevé-type functions,
- 58F07 completely integrable systems,
• Combinatorics
- 05A15 exact enumeration problems, generating functions,
- 05E10 Tableaux, representation of the symmetric group,
- 05E15 symmetric functions
• Probability Theory
- 60E05 distributions, general theory
- 60E10 characteristic functions
- 60F05 central limit and other weak theorems
- 82C22 interacting particle systems,
- 60K35 Interacting random processes; statistical mechanics type models,
1- 15A52 random matrices,
• Mathematical Physics
- 81T25 quantum field theory on lattices,
- 82B10 quantum equilibrium statistical mechanics,
- 82B26, 82B27 phase transitions and critical phenomena,
- 82B23 exactly solvable models,
• Spectral Theory
- 47A75, 58F19 eigenvalue and spectral problems,
- 47A10 spectrum, resolvent,
- 81U40 inverse scattering problems,
• Representation Theory
- 20F55 Reflection and Coxeter groups

Area of Expertise

Field of research codes
Applied Mathematics (010200): Approximation Theory and Asymptotic Methods (010201): Integrable Systems (Classical and Quantum) (010502): Lie Groups, Harmonic and Fourier Analysis (010106): Mathematical Physics (010500): Mathematical Sciences (010000): Operator Algebras and Functional Analysis (010108): Ordinary Differential Equations, Difference Equations and Dynamical Systems (010109): Probability Theory (010404): Pure Mathematics (010100): Real and Complex Functions (incl. Several Variables) (010111): Statistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matter (010506): Statistics (010400)

Research Outputs

Journal

Witte, NS. (2017). http://dx.doi.org10.1063/1.4997778. Journal of Mathematical Physics.
[Journal article]Authored by: Witte, N.
Forrester, PJ., Rahman, AA., & Witte, NS. (2017). Large N expansions for the Laguerre and Jacobi β-ensembles from the loop equations.
[Internet publication]Authored by: Witte, N.
Witte, NS., & Forrester, PJ. (2017). Singular Values of Products of Ginibre Random Matrices. Studies in Applied Mathematics. 138(2), 135-184
[Journal article]Authored by: Witte, N.
Ito, M., & Witte, NS. (2015). On a family of integrals that extend the Askey-Wilson integral. Journal of Mathematical Analysis and Applications. 421(2), 1101-1130
[Journal article]Authored by: Witte, N.
Witte, NS., & Forrester, PJ. (2015). Loop equation analysis of the circular β ensembles. Journal of High Energy Physics. 2015(2)
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2015). Painlevé II in Random Matrix Theory and Related Fields. Constructive Approximation. 41(3), 589-613
[Journal article]Authored by: Witte, N.
Witte, NS. (2015). Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy. Nagoya Mathematical Journal. 219(1), 127-234
[Journal article]Authored by: Witte, N.
Witte, NS. (2015). The diagonal two-point correlations of the Ising model on the anisotropic triangular lattice and Garnier systems. Nonlinearity. 29(1), 131-160
[Journal article]Authored by: Witte, N.
Witte, NS., & Forrester, PJ. (2014). Moments of the Gaussian β ensembles and the large-N expansion of the densities. Journal of Mathematical Physics. 55(8)
[Journal article]Authored by: Witte, N.
Witte, NS., Bornemann, F., & Forrester, PJ. (2013). Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles. Nonlinearity. 26(6), 1799-1822
[Journal article]Authored by: Witte, N.
Witte, NS., & Forrester, PJ. (2012). ON THE VARIANCE OF THE INDEX FOR THE GAUSSIAN UNITARY ENSEMBLE. RANDOM MATRICES-THEORY AND APPLICATIONS. 1(4)
[Journal article]Authored by: Witte, N.
Witte, NS., & Forrester, PJ. (2012). Fredholm Determinant Evaluations of the Ising Model Diagonal Correlations and their λ Generalization. Studies in Applied Mathematics. 128(2), 183-223
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2012). Asymptotic forms for hard and soft edge general β conditional gap probabilities. Nuclear Physics B. 859(3), 321-340
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2012). Erratum to "Asymptotic forms for hard and soft edge general β conditional gap probabilities" [Nucl. Phys. B 859 (3) (2012) 321-340]. Nuclear Physics B. 860(3), 516
[Journal article]Authored by: Witte, N.
Witte, NS., & Ormerod, CM. (2012). Construction of a lax pair for the E<sup>(1)</sup><inf>6</inf> q-Painlevé system. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 8
[Journal article]Authored by: Witte, N.
Ormerod, CM., Witte, NS., & Forrester, PJ. (2011). Connection preserving deformations and q-semi-classical orthogonal polynomials. Nonlinearity. 24(9), 2405-2434
[Journal article]Authored by: Witte, N.
Feverati, G., Pearce, PA., & Witte, NS. (2009). Physical combinatorics and quasiparticles. Journal of Statistical Mechanics: Theory and Experiment. 2009(10)
[Journal article]Authored by: Witte, N.
Witte, NS. (2009). Bi-orthogonal systems on the unit circle, regular semi-classical weights and integrable systems - II. Journal of Approximation Theory. 161(2), 565-616
[Journal article]Authored by: Witte, N.
Witte, NS. (2009). Biorthogonal systems on the unit circle, regular semiclassical weights, and the discrete Garnier equations. International Mathematics Research Notices. 2009(6), 988-1025
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2007). The distribution of the first eigenvalue spacing at the hard edge of the laguerre unitary ensemble. Kyushu Journal of Mathematics. 61(2), 457-526
[Journal article]Authored by: Witte, N.
Kitaev, AV., & Witte, NS. (2007). Boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Journal of Physics A: Mathematical and Theoretical. 40(42), 12725-12740
[Journal article]Authored by: Witte, N.
Witte, NS. (2007). Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model. Journal of Physics A: Mathematical and Theoretical. 40(24)
[Journal article]Authored by: Witte, N.
Hamamoto, T., Kajiwara, K., & Witte, NS. (2006). Hypergeometric solutions to the q-Painlevé equation of type (A <inf>1</inf> +A<inf>1</inf>́)<sup>(1)</sup>. International Mathematics Research Notices. 2006
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2006). Bi-orthogonal polynomials on the unit circle, regular semi-classical weights and integrable systems. Constructive Approximation. 24(2), 201-237
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2006). Boundary conditions associated with the Painlevé III′ and v evaluations of some random matrix averages. Journal of Physics A: Mathematical and General. 39(28), 8983-8995
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2006). Random matrix theory and the sixth Painlevé equation. Journal of Physics A: Mathematical and General. 39(39), 12211-12233
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2005). Discrete Painlevé equations for a class of P<inf>VI</inf> τ-functions given as U(N) averages. Nonlinearity. 18(5), 2061-2088
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2004). Discrete Painlevé Equations, Orthogonal Polynomials on the Unit Circle, and N-Recurrences for Averages over u(N) - PIII′ and PV τ-Functions. International Mathematics Research Notices. (4), 159-183
[Journal article]Authored by: Witte, N.
Witte, NS. (2004). Gap probabilities for double intervals in hermitian random matrix ensembles as τ-functions - Spectrum singularity case. Letters in Mathematical Physics. 68(3), 139-149
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2004). Application of the τ-function theory of Painlevé equations to random matrices: P<inf>VI</inf>, the JUE, CyUE, cJUE and scaled limits. Nagoya Mathematical Journal. 174, 29-114
[Journal article]Authored by: Witte, N.
Witte, NS. (2004). New transformations for Painlevé's third transcendent. Proceedings of the American Mathematical Society. 132(6), 1649-1658
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2003). Discrete Painlevé equations and random matrix averages. Nonlinearity. 16(6), 1919-1944
[Journal article]Authored by: Witte, N.
Forrester, PJ., Frankel, NE., Garoni, TM., & Witte, NS. (2003). Finite one-dimensional impenetrable Bose systems: Occupation numbers. Physical Review A - Atomic, Molecular, and Optical Physics. 67(4), 436071-4360717
[Journal article]Authored by: Witte, N.
Forrester, PJ., Frankel, NE., Garoni, TM., & Witte, NS. (2003). Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable bosons. Communications in Mathematical Physics. 238(1-2), 257-285
[Journal article]Authored by: Witte, N.
Witte, NS., Forrester, PJ., & Cosgrove, CM. (2002). Integrability, random matrices and Painlevé transcendents. ANZIAM Journal. 44(1), 41-50
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2002). τ-function evaluation of gap probabilities in orthogonal and symplectic matrix ensembles. Nonlinearity. 15(3), 937-954
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2002). Application of the τ-Function Theory of Painlevé Equations to Random Matrices: P<inf>v</inf>, P<inf>III</inf>, the LUE, JUE, and CUE. Communications on Pure and Applied Mathematics. 55(6), 679-727
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2001). Application of the τ-function theory of Painlevé equations to Random Matrices: PIV, PII and the GUE. Communications in Mathematical Physics. 219(2), 357-398
[Journal article]Authored by: Witte, N.
Ismail, MEH., & Witte, NS. (2001). Discriminants and functional equations for polynomials orthogonal on the unit circle. Journal of Approximation Theory. 110(2), 200-228
[Journal article]Authored by: Witte, N.
Cockayne, DJH., Gjonnes, J., Humphreys, CJ., Lehmpfuhl, G., Murphy, J., Shmueli, U., . . . Witte, NS. (2000). Peter Goodman. JOURNAL OF APPLIED CRYSTALLOGRAPHY. 33, 1302-1302
[Journal article]Authored by: Witte, N.
Witte, NS., & Forrester, PJ. (2000). Gap probabilities in the finite and scaled cauchy random matrix ensembles. Nonlinearity. 13(6), 1965-1986
[Journal article]Authored by: Witte, N.
Witte, NS., Forrester, PJ., & Cosgrove, CM. (2000). Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles. Nonlinearity. 13(5), 1439-1464
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS. (2000). Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles. Letters in Mathematical Physics. 53(3), 195-200
[Journal article]Authored by: Witte, N.
Wellard, CJ., Witte, NS., & Hollenberg, LCL. (1999). Some results on the phase diagram of the 2D Hubbard model using an analytic Lanczos method. Physica B: Condensed Matter. 259-261, 766-768
[Journal article]Authored by: Witte, N.
Witte, NS., & Shankar, R. (1999). Moment formalisms applied to a solvable model with a quantum phase transition (I). Exponential moment methods. Nuclear Physics B. 556(3), 445-462
[Journal article]Authored by: Witte, N.
Witte, NS. (1999). The exact realisation of the Lanczos method for a quantum many-body system. Physics Letters, Section A: General, Atomic and Solid State Physics. 254(1-2), 18-23
[Journal article]Authored by: Witte, N.
Witte, NS., & Bessis, D. (1999). The Lanczos algorithm for extensive many-body systems in the thermodynamic limit. Journal of Mathematical Physics. 40(10), 4975-4994
[Journal article]Authored by: Witte, N.
Witte, NS. (1998). Exact solution for the reflection and diffraction of atomic de Broglie waves by a travelling evanescent laser wave. Journal of Physics A: Mathematical and General. 31(2), 807-832
[Journal article]Authored by: Witte, N.
Witte, NS., Goodman, P., Lincoln, FJ., March, RH., & Kennedy, SJ. (1998). Electrical and magnetic phases of the layered perovskite Ca4-xLaxMn3O10. Applied Physics Letters. 72(7), 853-855
[Journal article]Authored by: Witte, N.
Witte, NS., & Hollenberg, LCL. (1997). Accurate calculation of ground-state energies in an analytic Lanczos expansion. Journal of Physics Condensed Matter. 9(9), 2031-2042
[Journal article]Authored by: Witte, N.
Witte, NS., Hollenberg, LCL., & Weihong, Z. (1997). Two-dimensional XXZ model ground-state properties using an analytic Lanczos expansion. Physical Review B - Condensed Matter and Materials Physics. 55(16), 10412-10419
[Journal article]Authored by: Witte, N.
Witte, NS. (1997). Exact solution to the moment problem for the XY chain. International Journal of Modern Physics B. 11(12), 1503-1517
[Journal article]Authored by: Witte, N.
Hollenberg, LCL., Bardos, DC., & Witte, NS. (1996). Lanczos cluster expansion for non-extensive systems. Zeitschrift fur Physik D-Atoms Molecules and Clusters. 38(3), 249-252
[Journal article]Authored by: Witte, N.
Hollenberg, LCL., & Witte, NS. (1996). Analytic solution for the ground-state energy of the extensive many-body problem. Physical Review B - Condensed Matter and Materials Physics. 54(23), 16309-16312
[Journal article]Authored by: Witte, N.
Feng, XP., Witte, NS., Hollenberg, LCL., & Opat, GI. (1996). Reflection and diffraction of atomic de broglie waves by evanescent laser waves - Bare-state method. Australian Journal of Physics. 49(4), 765-775
[Journal article]Authored by: Witte, N.
SMITH, BJK., WITTE, NS., & HINES, KC. (1995). SYSTEMATICS OF THE ELECTROWEAK PLASMA AT FINITE-TEMPERATURE .2.. AUSTRALIAN JOURNAL OF PHYSICS. 48(5), 775-811
[Journal article]Authored by: Witte, N.
SMITH, BJK., WITTE, NS., & HINES, KC. (1995). SYSTEMATICS OF THE ELECTROWEAK PLASMA AT FINITE-TEMPERATURE .1.. AUSTRALIAN JOURNAL OF PHYSICS. 48(5), 739-774
[Journal article]Authored by: Witte, N.
Hollenberg, LCL., Wilson, MP., & Witte, NS. (1995). General non-perturbative mass gap to first order in 1 V. Physics Letters B. 361(1-4), 81-86
[Journal article]Authored by: Witte, N.
Witte, NS., & Hollenberg, LCL. (1995). First order in the plaquette expansion. Zeitschrift für Physik B Condensed Matter. 99(1), 101-110
[Journal article]Authored by: Witte, N.
Witte, NS., & Hollenberg, LCL. (1994). Plaquette expansion proof and interpretation. Zeitschrift für Physik B Condensed Matter. 95(4), 531-539
[Journal article]Authored by: Witte, N.
Hollenberg, LCL., & Witte, NS. (1994). General nonperturbative estimate of the energy density of lattice Hamiltonians. Physical Review D. 50(5), 3382-3386
[Journal article]Authored by: Witte, N.
Witte, NS. (1993). Van der Waals energies of cylindrical and spherical single layer systems. The Journal of Chemical Physics. 99(10), 8168-8182
[Journal article]Authored by: Witte, N.
Witte, NS. (1990). Polarization of the magnetized scalar and spinor vacua. Journal of Physics A: Mathematical and General. 23(22), 5257-5283
[Journal article]Authored by: Witte, N.
Witte, NS., Kowalenko, V., & Hines, KC. (1989). Erratum: Relativistic charged-boson plasma in a magnetic field. II. Phys Rev D Part Fields. 40(4), 1370
[Journal article]Authored by: Witte, N.
Witte, NS., Kowalenko, V., & Hines, KC. (1989). Erratum: Relativistic charged-boson plasma in a magnetic field. II (Physical Review D (1989) 40, 4 (1370)). Physical Review D. 40(4), 1370-1371
[Journal article]Authored by: Witte, N.
Witte, NS., Kowalenko, V., & Hines, KC. (1988). Relativistic charged-boson plasma in a magnetic field. II. Physical Review D. 38(12), 3667-3709
[Journal article]Authored by: Witte, N.
Witte, NS., Dawe, RL., & Hines, KC. (1987). Relativistic charged bosons in a magnetic field. I. Wave functions and matrix elements. Journal of Mathematical Physics. 28(8), 1864-1874
[Journal article]Authored by: Witte, N.
Witte, NS., Hollenberg, LCL., & Weihong, Z.2D XXZ Model ground state Properties using an analytic Lanczos Expansion. Retrieved from http://dx.doi.org/10.1103/PhysRevB.55.10412
[Journal article]Authored by: Witte, N.
Witte, NS.The Analytic Lanczos Method.
[Journal article]Authored by: Witte, N.
Forrester, PJ., & Witte, NS.Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and $N$-recurrences for averages over U(N) -- \PVI $τ$-functions.
[Journal article]Authored by: Witte, N.

Conference

Lincoln, FJ., Goodman, P., Witte, NS., & March, RH.GIANT MAGNETORESISTANCE EFFECT IN THE LAYERED PEROVSKITES (Ca,La)(4)Mn3O10. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES. (pp. C388 - C388). 2053-2733.
[Conference]Authored by: Witte, N.

Supervision and Teaching

Summary of Doctoral Supervision

Position Current Completed
Co-supervisor 1 0

Current Doctoral Supervision

Co-supervisor of:

  • William Marks - Doctor of Philosophy
    An Investigation into the connection between neutrinos and dark matter.

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