Theoretical Physics with Focus on Complex Fluids

Postdoc (CRC 910)


Johannes Schmidt

Postdoc (CRC 910)

+49 30 314 24474

Organization name Institute for Theoretical Physics
Office EW 7-1
Building EW
Room EW 279

Research interests

Research topics of interest are universal properties of dynamical Systems far from Equilibrium.
The precise description of numerous complex systems appearing in nature involves so many degrees of freedom that it is impossible to consider all of them. Universality, which was established by the study of specific systems and simple models, asserts that the system’s properties do not depend on its details such as the precise form of interactions. Therefore, universality permits the identification of appropriate variables and simpler underlying mechanisms that are considered to be essential for the understanding of observations in real systems.
As nonequilibrium steady states are easier to handle and still cover anomalous transport properties, one promising inroad for the identification of underlying mechanisms characterizing nonequilibrium phenomena in general is the study of universal behavior in nonequilibrium steady states.

In my doctorate thesis, I worked on the identification of dynamical universality classes in 1D driven diffusive systems far from equilibrium with multiple locally conserved densities. Using mode-coupling theory for nonlinear fluctuating hydrodynamics we discovered that all feasible dynamical exponents (z) are ratios of neighboring Fibonacci numbers (1,1,2,3,5,8,...), including the diffusive (z=2/1) and super-diffusive Kardar-Parisi-Zhang (z=3/2) class as a special case. In addition to the analytical approach, I performed large scale Monte Carlo simulations to confirm these findings. Note that, super-diffusive spread of density fluctuations is not only an one dimensional effect. Solving the 2D nonlinear fluctuating hydrodynamic equation using mode coupling theory the solution predicts: The diffusive constant, in the direction of the drive, diverges with time as ln(t)^{2/3}. Using the advanced various reduction techniques, we were able to design an optimal model in order to provide the first numerical verification of this super-diffusive spread.

Large Deviation, Microscopic Fluctuation Theory, Nonlinear Fluctuation Hydrodynamics, Mode Coupling Theory, Advanced Monte Carlo Methods, Bayesian Statistics, Scaling approaches


  • Exact Anomalous current fluctuations in a deterministic interacting model
    Ziga Krajinik, Johannes Schmidt, Enej Ilievski, Tomaz Prosen
    Accepted for publication in Physical Review Letters
    ArXiv: 2201.05126

  • A lattice Gas Model for Generic One-Dimensional Hamiltonian
    Johannes Schmidt, Gunter M. Schütz, Henk van Beijeren
    DOI: 10.1007/s10955-021-02709-1
    ArXiv: 2011.02940
  • Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model 
    Jan de Gier, Andreas Schadschneider, Johannes Schmidt, Gunter M. Schütz
    DOI: 10.1103/PhysRevE.100.052111
    ArXiv: 1907.00636
  • Height distribution tails in the Kardar-Parisi-Zhang equation with Brownian initial conditions 
    Baruch Meerson, Johannes Schmidt 
    DOI: 10.1088/1742-5468/aa8c12 
    ArXiv: 1707.00662
  • Logarithmic superdiffusion in two dimensional driven lattice gases
    Joachim Krug, Robert A. Neiss, Andreas Schadschneider, Johannes Schmidt
    DOI: 10.1007/s10955-018-1995-z
    ArXiv: 1711.03728
  • Spin-helix states in the XXZ-spin chain with strong dissipation 
    Vladislav Popkov, Johannes Schmidt, Carlo Presilla 
    DOI: 10.1088/1751-8121/aa86cb 
    ArXiv: 1703.08233
  • Targeting pure quantum states by strong noncommutative dissipation 
    Vladislav Popkov, Carlo Presilla, Johannes Schmidt 
    DOI: 10.1103/PhysRevA.95.052131 
    ArXiv: 1702.00287
  • Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension 
    Vladislav Popkov, Andreas Schadschneider, Johannes Schmidt, Gunter M. Schütz 
    DOI: 10.1088/1742-5468/2016/09/093211 
    ArXiv: 1608.03267
  • Fibonacci family of dynamical universality classes 
    Vladislav Popkov, Andreas Schadschneider, Johannes Schmidt, Gunter M. Schütz 
    DOI: 10.1073/pnas.1512261112 
    ArXiv: 1505.04461
  • Universality classes in two-component driven diffusive systems
    Vladislav Popkov, Johannes Schmidt, Gunter M. Schütz 
    DOI: 10.1007/s10955-015-1241-x
    ArXiv: 1410.8026
  • When is a bottleneck a bottleneck?
    Andreas Schadschneider, Johannes Schmidt, Vladislav Popkov
    ISBN: 978-3-319-33482-0
    ArXiv: 1512.02626
  • Defect-induced phase transition in the asymmetric simple exclusion process 
    Johannes Schmidt, Vladislav Popkov, Andreas Schadschneider 
    DOI: 10.1209/0295-5075/110/20008 
    ArXiv: 1504.04652
  • Non-KPZ modes in two-species driven diffusive systems
    Vladislav Popkov, Johannes Schmidt, Gunter Schütz
    DOI: 10.1103/PhysRevLett.112.200602
    ArXiv: 1312.5920


Doctorate Thesis:
Universal Behavior of Driven Diffusive Lattice Gases