Mathematical physics

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  Subject Areas on Research

  • (2, 2)-Superconformal field theories near orbifold points 
  • A Generalization of Schur–Weyl Duality with Applications in Quantum Estimation 
  • A Gårding domain for quantum fields 
  • A Simple Derivation of Mean Field Limits for Quantum Systems 
  • A characterization of subsystems in physics 
  • A mathematical condition for a sublattice of a propositional system to represent a physical subsystem, with a physical interpretation 
  • A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps 
  • A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula 
  • A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities 
  • A novel method for designing S-boxes based on chaotic maps 
  • A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays 
  • A study of the regularized lid-driven cavity's progression to chaos 
  • A universal magnification theorem for higher-order caustic singularities 
  • A universal magnification theorem. II. Generic caustics up to codimension five 
  • A universal magnification theorem. III. Caustics beyond codimension 5 
  • A variational perspective on cloaking by anomalous localized resonance 
  • Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials 
  • Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion 
  • Adventures of the coupled Yang-Mills oscillators: II. YM-Higgs quantum mechanics 
  • An application of hyperdifferential operators to holomorphic quantization 
  • An experimental impact oscillator 
  • An experimental impact oscillator 
  • An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps 
  • An integral transform related to quantization 
  • An integral transform related to quantization. II. Some mathematical properties 
  • An intensity-expansion method to treat non-stationary time series: An application to the distance between prime numbers 
  • An uncertainty principle for fermions with generalized kinetic energy 
  • Analytical error analysis of Clifford gates by the fault-path tracer method 
  • Applications of singularity theory to gravitational lensing. I. Multiple lens planes 
  • Approximate criterion for capsize based on deterministic dynamics 
  • Arnold's singularity theory and gravitational lensing 
  • Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case 
  • Blow-up, Zero α Limit and the Liouville Type Theorem for the Euler-Poincaré Equations 
  • Bogoliubov corrections and trace norm convergence for the Hartree dynamics 
  • Bounds on number of cusps due to point mass gravitational lenses 
  • Computation of superpotentials for D-branes 
  • Constructing measures for path integrals 
  • Continuity statements and counterintuitive examples in connection with Weyl quantization 
  • D-brane bound states redux 
  • Derivation of the time dependent Gross-Pitaevskii equation with external fields 
  • Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0 
  • Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas 
  • Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity 
  • Escape over a fluctuating barrier: The white noise limit 
  • Explicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order 
  • Explicit exact solutions for new general two-dimensional KdV-type and two-dimensional KdV-Burgers-type equations with nonlinear terms of any order 
  • Finite Time Blow Up for a 1D Model of 2D Boussinesq System 
  • Fixed points due to gravitational lenses 
  • Flux-across-surfaces theorem for a Dirac particle 
  • Forbidden Regions for Shock Formation in Diffusive Systems 
  • Fractal Behavior of an Asymmetric Rigid Block Overturning Due to Harmonic Motion of a Tilted Foundation 
  • Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit 
  • General projective Riccati equation method and exact solutions for generalized KdV-type and KdV-Burgers-type equations with nonlinear terms of any order 
  • Generalized eigenfunctions for Dirac operators near criticality 
  • Generalized inverse mean curvature flows in spacetime 
  • Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation 
  • Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance 
  • Improved kinetic renormalisation group approach to diffusion-limited aggregation 
  • Inaccessible states in time-dependent reaction diffusion 
  • Information capacity of a perceptron 
  • Inhomogeneous percolation problems and incipient infinite clusters 
  • Integrable systems and modular forms of level 2 
  • Integrated optical approach to trapped ion quantum computation 
  • Integrated optical approach to trapped ion quantum computation 
  • Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation 
  • Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: Creation and propagation 
  • Landau-Ginzburg to Calabi-Yau dictionary for D-branes 
  • Large-time behavior of discrete velocity boltzmann equations 
  • Large-time behavior of the Broadwell model of a discrete velocity gas 
  • Lensing by Kerr black holes. I. General lens equation and magnification formula 
  • Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables 
  • Lindblad equation and its semiclassical limit of the Anderson-Holstein model 
  • Localized bound states of fermions interacting via massive vector bosons 
  • Long-time asymptotics for integrable systems. Higher order theory 
  • Lorentz deformation in the O(4) and light-cone coordinate systems 
  • Massless D-branes on Calabi-Yau threefolds and monodromy 
  • Mean-Field dynamics: Singular potentials and rate of convergence 
  • Measures for more quadratic path integrals 
  • Mirror manifolds in higher dimension 
  • Modified prüfer and EFGP transforms and the spectral analysis of one dimensional schrödinger operators 
  • Monopoles on the Bryant-Salamon G2-manifolds 
  • Morse theory and gravitational microlensing 
  • Multidimensional random walks in random environments with subclassical limiting behavior 
  • Multiplane gravitational lensing. I. Morse theory and image counting 
  • Multiplane gravitational lensing. II. Global geometry of caustics 
  • Multiplane gravitational lensing. III. Upper bound on number of images 
  • New Weierstrass elliptic function solutions of the N-coupled nonlinear Klein-Gordon equations 
  • Nonlinear steepest descent asymptotics for semiclassical limit of Integrable systems: Continuation in the parameter space 
  • Numerical experiments in a modified Beeler-Reuter cable model: Initiating fast (Na) and slow (Ca) waves 
  • Observation and investigation of a non-monotonic period function for an impact oscillator 
  • On Finsler surfaces of constant flag curvature with a Killing field 
  • On Randers spaces of constant flag curvature 
  • On adiabatic pair creation 
  • On gravitation theories with limiting curvature 
  • On the algebro-geometric integration of the Schlesinger equations 
  • On the distributions corresponding to bounded operators in the Weyl quantization 
  • On the sign problem in the Hirsch-Fye algorithm for impurity problems 
  • On the solvability of Painlevé II and IV 
  • One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum 
  • One-electron relativistic molecules with Coulomb interaction 
  • Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing 
  • Painless nonorthogonal expansions 
  • Particles in a stationary spherically symmetric gravitational field 
  • Quantum chaos in Ga/AlxGa1-xAs microstructures 
  • Quantum chaos in Ga/Al_x Ga_1-x As microstructures 
  • Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II 
  • Quivers from Matrix Factorizations 
  • Random walk in random environment: A counterexample? 
  • Rational curves and (0, 2)-deformations 
  • Remarks on the breakdown of smooth solutions for the 3-D Euler equations 
  • Representations of the Poincaré group for relativistic extended hadrons 
  • S-duality in Abelian gauge theory revisited 
  • SU(N) Transitions in M-Theory on Calabi–Yau Fourfolds and Background Fluxes 
  • Scalable digital hardware for a trapped ion quantum computer 
  • Self-similar asymptotics for linear and nonlinear diffusion equations 
  • Simple systems with anomalous dissipation and energy cascade 
  • Simulation of a toy model with constrained dynamics 
  • Singularities of the one- and two-point mass gravitational lens 
  • Some navigation rules for D-brane monodromy 
  • Space-time topology change and stringy geometry a 
  • Special issue on experimental aspects of quantum computing 
  • Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model 
  • Stable singularities in string theory 
  • Stationary self-organized fractal structures in an open, dissipative electrical system 
  • Storage capacity of neural networks: Effect of the fluctuations of the number of active neurons per memory 
  • Studies of perturbed three vortex dynamics 
  • Support properties of the free measure for Boson fields 
  • Surface Hall effect in magneto-electric media 
  • Symbolic computation and construction of soliton-like solutions for a breaking soliton equation 
  • Symplectic discretization for spectral element solution of Maxwell's equations 
  • System design for large-scale ion trap quantum information processor 
  • The Berry Connection of the Ginzburg–Landau Vortices 
  • The Influence of a Nonzero Angle of Attack and Gust Loads on the Nonlinear Response of a Typical Airfoil Section with a Control Surface Freeplay 
  • The TF limit for rapidly rotating bose gases in anharmonic traps 
  • The damped self-interaction 
  • The flux-across-surfaces theorem under conditions on the scattering state 
  • The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps 
  • The invariant measure for scattering matrices with block symmetries 
  • The partition function in the Wigner-Kirkwood expansion 
  • The replica method and solvable spin glass model 
  • The structure of internal layers for unstable nonlinear diffusion equations 
  • The thermodynamic limit and the replica method for short-range random systems 
  • Thermodynamic inequalities for percolation 
  • Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass 
  • Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II 
  • Topological field theory and rational curves 
  • Two examples illustrating the differences between classical and quantum mechanics 
  • Using information to generate derivative coordinates from noisy time series 
  • Variational Principle of KPP Front Speeds in Temporally Random Shear Flows with Applications 
  • Volume thresholds for quantum fault tolerance 
  • WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials 
  • Wavefronts, caustic sheets, and caustic surfing in gravitational lensing 
  • Wavepackets in Inhomogeneous Periodic Media: Propagation Through a One-Dimensional Band Crossing 
  • Wavepackets in inhomogeneous periodic media: Effective particle-field dynamics and Berry curvature 
  • Weak matching rules for quasicrystals 
  • Wiener measures for path integrals with affine kinematic variables 
  • Witten Spinors on Nonspin Manifolds 
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  Keywords of People

  • Bray, Hubert, Professor of Mathematics, Mathematics
  • Pickl, Peter, Visiting Professor of Mathematics at Duke Kunshan University, DKU Faculty