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@TECHREPORT{Schtz:863763,
      author       = {Schütz, Gunter M.},
      title        = {{I}ntegrable stochastic many-body systems},
      volume       = {3555},
      number       = {Juel-3555},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich, Zentralbibliothek, Verlag},
      reportid     = {FZJ-2019-03761, Juel-3555},
      series       = {Berichte des Forschungszentrums Jülich},
      pages        = {227 p.},
      year         = {1998},
      abstract     = {This work investigates classical interacting particle
                      systems for which the stochastic time evolution is defined
                      by a master equation. We use a quantum Hamiltonian
                      representation of the master equation to employ the
                      mathematical tools of manybody quantum mechanics for the
                      derivation of exact results on the stationary and dynamical
                      properties of these stochastic processes. We consider mainly
                      integrable lattice reaction-diffusion processes of a single
                      species of particles which hop on a onedimensional lattice
                      and which may undergo simple nearest-neighbour chemical
                      reactions. Integrability in this context refers to the
                      integrability of the associated manybody quantum
                      Hamiltonian. We treat some standard models of
                      non-equilibrium mechanics, including the exclusion process,
                      Glauber dynamics and diffusion-limited pair annihilation, as
                      well as various other less well-known, but nevertheless
                      rather interesting interacting particle systems in one
                      dimension. Thus this work attempts to expose the unified
                      mathematical framework underlying the exact treatment of
                      these systems and to provide insight in the role of
                      inefficient diffusive mixing for the kinetics of
                      diffusion-limited chemical reactions, in the dynamics of
                      shocks and in other fundamental mechanisms which determine
                      the behaviour of low-dimensional systems far from thermal
                      equilibrium. Our treatment consists of three parts. Chapters
                      2 - 5 are pedagogical in nature. We introduce some of the
                      basic tools and notions used later and thus provide a
                      "dictionary" for the correspondence between quantities in
                      probabilistic and quantum spin language respectively. The
                      second part is concerned with the theoretical investigation
                      of purely diffusive systems of hard-core particles (Chapters
                      6 and 7). We use the Bethe ansatz and a related purely
                      algebraic formulation of the symmetric exclusion process to
                      find a quasi-stationary relaxational behaviour (Chapter 6).
                      Perhaps the most far-reaching result discussed here is the
                      exact derivation of stationary properties of the asymmetric
                      exclusion process with open boundaries. With the picture of
                      shocks (domain walls separating regions of low and high
                      density) propagating through the system we develop an
                      essentially complete understanding of how the interplay of
                      boundary effects and shock dynamics leads to the boundary
                      induced phase transitions obtained from the exact solution
                      of the model. These arguments allow us to predict the phase
                      diagram of quite generic one-dimensional driven lattice
                      gases (Chapter 7). In the third part we investigate
                      dynamical properties of reaction-diffusion mechanisms
                      (Chapters 8 and 9). We review various approaches for the
                      exact treatment, particularly the free-fermion approach
                      (Chapter 9) which allows for a full discussion of the
                      dynamics of such systems, even if the initial probability
                      distributions have a complicated, non-translationally
                      invariant structure. The free-fermion property becomes
                      manifest for various models by some suitably chosen
                      similarity transformation of the stochastic generator and
                      constitutes the common mathematical ground on which these
                      models stand. Our main message is that all known
                      equivalences between these models can be generated by two
                      families of similarity transformations. Our derivation and
                      the form of these transformations leads us to conjecture
                      that the models described here are all equivalent
                      single-species free-fermion processes with pair-interaction
                      between sites. We also discuss some peculiar non-equilibrium
                      phenomena associated with the presence of an external
                      driving force (Chapter 8). Chapter 10 concludes with
                      selected experimental applications of integrable stochastic
                      processes - gel electrophoresis, kinetics of
                      biopolymerization and exciton dynamics on polymer chains.},
      cin          = {PRE-2000},
      cid          = {I:(DE-Juel1)PRE2000-20140101},
      pnm          = {899 - ohne Topic (POF3-899)},
      pid          = {G:(DE-HGF)POF3-899},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)29},
      url          = {https://juser.fz-juelich.de/record/863763},
}