Structural phase transitions:
Influence of defects; dynamics; central peak
(Landau-Ginzburg theory of disordered systems; renormalization group).
Dynamic critical behavior near equilibrium phase transitions:
Universality classes; anomalies in the ordered phase of isotropic systems;
crossover behavior; stability against non-equilibrium perturbations
(Langevin equations; dynamic field theory; renormalization group).
Phase transitions and scaling in systems far from equilibrium:
Directed percolation; Burgers/Kardar-Parisi-Zhang equation;
branching and annihilating random walks; diffusion-limited reactions;
driven diffusive systems; driven-dissipative Bose-Einstein condensation
(master and Langevin equations; field theory; renormalization group;
Monte Carlo simulations).
NSF "nugget" (powerpoint): Reaction-controlled diffusion
DOE "highlight" (powerpoint): Non-equilibrium Relaxation and Critical Aging for Driven Ising Lattice Gases
Statistical mechanics of flux lines in superconductors:
Mapping to boson quantum mechanics; influence of correlated disorder;
properties of the Bose glass phase; vortex transport and flux pinning;
critical properties of the normal- to superconducting transition with disorder;
voltage and flux density noise; non-equilibrium relaxation and aging features
(path integral description; Monte Carlo and Langevin dynamics simulations).
DOE "highlight" (powerpoint): Magnetic Field Quench Effects on Vortex Relaxation Dynamics in Disordered Type-II Superconductors
Applications of statistical physics to biological problems:
Glassy properties of prokaryotic bacteria; receptor-ligand binding kinetics
on cell membranes; predator-prey population dynamics -> movies;
cyclic competition models in ecology; evolutionary population dynamics
(mean-field and Smoluchowski theory; field theory; Monte Carlo simulations).
NSF "nuggets" (powerpoint): Correlations in chemical reaction kinetics
Complex patterns and fluctuations in stochastic lattice models for predator-prey competition and coexistence
Stochastic lattice models for predator-prey coexistence and host-pathogen competition
My research has in the past been funded by the Deutsche
the European Commission TMR program, the U.S. National Science Foundation,
the U.S. Army Research Office, and the Jeffress Memorial Trust.
Current funding through the U.S. Department of Energy, Office of Basic Energy
Sciences under grant no. DE-FG02-09ER46613 is gratefully acknowledged.
Obituary Prof. Dr. Franz Schwabl (1938 - 2009)
Isaac Newton Institute School
Non-equilibrium dynamics of interacting particle systems, Cambridge, U.K., March 27 - April 7, 2006:
Lecture notes Field-theoretic approaches to interacting particle systems.
Mechanics Conference, Rutgers University, May 6-8, 2007:
Invited talk Current distribution in driven diffusive systems.
Second annual French complex systems summer school,
Lyon and Paris, France, July 15 - August 10, 2008
Fluctuations and correlations in complex systems: An introduction to stochastic nonlinear dynamics.
school for condensed matter and materials physics:
Nonequilibrium statistical mechanics - fundamental problems and applications,
Boulder, Colorado, USA, July 6 - 24, 2009.
EPSRC symposium workshop on non-equilibrium dynamics of spatially
extended interacting particle systems (NEQ),
Warwick, U.K., January 11 - 13, 2010: Invited talk
Stochastic predator-prey models: population oscillations, spatial correlations, and the effect of randomized rates.
Model and data hierarchies
for simulating and understanding climate: simulation hierarchies for climate
Institute for Pure and Applied Mathematics (IPAM), UCLA, Los Angeles, California, USA, May 3 - 7, 2010:
Invited talk (powerpoint) Stochastic fluctuations and emerging correlations in simple reaction-diffusion systems.
Continuum Models and Discrete
Systems Symposium 12,
Centre for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics,
Kolkata, India, February 21 - 25, 2011: Invited talk (powerpoint)
Stochastic population oscillations in spatial predator-prey models.
Universitätswochen für Theoretische Physik,
Schladming, Austria, February 26 - March 5, 2011: Four lectures
Renormalization Group: Applications in Statistical Physics; lectures 1 & 2; lectures 3 & 4; lecture notes.
Arnold Sommerfeld Center
for Theoretical Physics, Ludwig-Maximilians University Munich,
Sommerfeld Theory Colloquium, December 12, 2012: slides; Nonequilibrium Relaxation and Aging Kinetics (Video).
STATPHYS 25, XXV IUPAP Conference
on Statistical Physics, Seoul, South Korea, July 22 - 26, 2013:
Invited talk (powerpoint) Environmental vs. demographic variability in stochastic lattice predator-prey models;
see also invited talk at 2014 APS March Meeting, Denver, CO, March 3 - 7, 2014.
Workshop on Statistical Physics, Bogota, Columbia, September 22 - 26, 2014:
Conference Renormalization Methods in Statistical Physics and Lattice Field
Montpellier, France, August 24 - 28, 2015:
Invited talk Critical dynamics in driven-dissipative Bose-Einstein condensation.
STATPHYS 26 Satellite Meeting, Non-Equilibrium Dynamics in
Classical and Quantum Systems: From Quenches to Slow Relaxations,
Pont-\`a-Mousson, France, July 13, 2016: Invited talk Aging scaling in driven systems.
Physics Department Colloquium (powerpoint):
The 2016 Nobel prize in physics: Topological phase transitions and topological phases of matter
Introducing a unified framework for describing and understanding complex
interacting systems common in physics, chemistry, biology, ecology, and the
social sciences, this comprehensive overview of dynamic critical phenomena
covers the description of systems at thermal equilibrium, quantum systems,
and non-equilibrium systems.
Powerful mathematical techniques for dealing with complex dynamic systems are carefully introduced, including field-theoretic tools and the perturbative dynamical renormalization group approach, rapidly building up a mathematical toolbox of relevant skills. Heuristic and qualitative arguments outlining the essential theory behind each type of system are introduced at the start of each chapter, alongside real-world numerical and experimental data, firmly linking new mathematical techniques to their practical applications. Each chapter is supported by carefully tailored problems for solution, and comprehensive suggestions for further reading, making this an excellent introduction to critical dynamics for graduate students and researchers across many disciplines within physical and life sciences.
List of contents:
Chap. 1: Equilibrium critical phenomena
Chap. 2: Stochastic dynamics
Chap. 3: Dynamic scaling
Chap. 4: Dynamic perturbation theory
Chap. 5: Dynamic renormalization group
Chap. 6: Hydrodynamic modes and reversible mode couplings
Chap. 7: Phase transitions in quantum systems
Chap. 8: Non-equilibrium critical dynamics
Chap. 9: Reaction-diffusion systems
Chap. 10: Active to absorbing state transitions
Chap. 11: Driven diffusive systems and growing interfaces
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