Photo by Amanda Loman, December 13, 2013 ©Virginia Tech
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
and epidemic spreading;
(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
Forschungsgemeinschaft,
the European Commission TMR program,
the U.S. National Science Foundation,
the U.S. Department of Energy,
the U.S. Army Research Office, and the Jeffress Memorial Trust.
Current funding through the U.S. National Science Foundation, Division of
Mathematical Sciences,
under grant NSF-DMS-2128587 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.
97th Statistical Mechanics Conference, Rutgers University, May 6-8, 2007:
Invited talk
Current distribution in driven diffusive systems.
2009 Boulder
school for condensed matter and materials physics:
Nonequilibrium statistical mechanics - fundamental problems and applications,
Boulder, Colorado, USA, July 6 - 24, 2009.
Model and data hierarchies
for simulating and understanding climate: simulation hierarchies for climate
modeling,
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.
49. Internationale Universitätswochen für Theoretische Physik,
Schladming, Austria, February 26 - March 5, 2011:
Renormalization Group: Applications in Statistical Physics;
lectures 1 & 2;
lectures 3 & 4;
lecture notes (published
in Nuclear Physics B).
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.
2nd Workshop on Statistical Physics, Bogota, Columbia, September 22 - 26, 2014:
Field theory approach to
equilibrium critical phenomena.
Conference Renormalization Methods in Statistical Physics and Lattice Field
Theories,
Montpellier, France, August 24 - 28, 2015:
Invited talk
Critical dynamics in driven-dissipative Bose-Einstein condensation.
Physics Department Colloquium (powerpoint):
The 2016 Nobel
prize in physics: Topological phase transitions and topological phases of
matter.
Bangalore School on
Statistical Physics VIII, ICTS Bangalore, India, July 11, 2017:
Invited research talk
Non-equilibrium relaxation and aging scaling in driven Systems.
Workshop The Many Facets of Non-equilibrium Physics: From Many-Body Theory to
Quantum Thermodynamics,
Mazara del Vallo, Sicily, Italy, July 12, 2019: Invited talk (powerpoint)
Temperature interfaces
in the Katz-Lebowitz-Spohn driven lattice gas.
LPMMC Seminar, CNRS< Grenoble, France, August 28, 2019: Seminar talk
(powerpoint)
Nucleation and aging
transient dynamics in the two-dimensional complex Ginzburg-Landau equation.
ICSM 2020/21 Conference Bodrum, Turkey, October 26, 2021: Invited talk
(presented online)
Non-equilibrium relaxation
and critical aging of flux lines following current quenches.
Ising Lectures,
Lviv, Ukraine, May 11, 2023: Invited talk (presented online, powerpoint)
Stochastic spatial
Lotka-Volterra predator-prey models.
Dynamics Days
Europe, Naples, Italy, September 5, 2023:
Invited talk
Spatially inhomogeneous
stochastic cyclic competition models:
Stabilizing vulnerable ecologies through immigration waves.
15th Conference on
Dynamical Systems Applied to Biology and Natural Sciences (DSABNS15),
Caparica, Portugal, February 7, 2024: Invited mini-symposium talk
Fluctuations
and spatial correlations in chemical reaction kinetics, population dynamics,
and epidemic spreading.
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
Corrections
Office: Virginia Tech, Department of Physics, MC 0435
Address: 850 West Campus Drive, Robeson Hall, Room 109
Office hours: Monday, 1.25 - 2.15 pm;
Thursday 11.00 am - 12.15 pm (Hahn North 300); or by appointment
E-mail: tauber@vt.edu