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| 001 | 863763 | ||
| 005 | 20210130002318.0 | ||
| 024 | 7 | _ | |a 2128/22428 |2 Handle |
| 037 | _ | _ | |a FZJ-2019-03761 |
| 041 | _ | _ | |a English |
| 088 | 1 | _ | |a Juel-3555 |
| 088 | _ | _ | |a Juel-3555 |2 JUEL |
| 100 | 1 | _ | |a Schütz, Gunter M. |0 P:(DE-Juel1)130966 |b 0 |e Corresponding author |u fzj |
| 245 | _ | _ | |a Integrable stochastic many-body systems |
| 260 | _ | _ | |a Jülich |c 1998 |b Forschungszentrum Jülich, Zentralbibliothek, Verlag |
| 300 | _ | _ | |a 227 p. |
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| 336 | 7 | _ | |a Report |b report |m report |0 PUB:(DE-HGF)29 |s 1562827070_491 |2 PUB:(DE-HGF) |
| 336 | 7 | _ | |a TECHREPORT |2 BibTeX |
| 490 | 0 | _ | |a Berichte des Forschungszentrums Jülich |v 3555 |
| 520 | _ | _ | |a 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. |
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