Concentration for one and two-species one-dimensional reaction-diffusion systems

Simon, H.

doi:10.1088/0305-4470/28/23/013

Cited by 69 publications

(76 citation statements)

References 26 publications

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“…A large fraction of analytical studies belong to low-dimensional (specially one-dimensional) systems, as solving lowdimensional systems should in principle be easier. [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Exactly solvable reaction diffusion models on a Cayley tree

2007

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The most general reaction-diffusion model on a Cayley tree with nearestneighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.

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Section: Introductionmentioning

confidence: 99%

Exactly solvable reaction diffusion models on a Cayley tree

2007

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“…Here some standard material [2,3,5] is introduced, just to fix notation. The master equation for P (σ, t) is…”

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confidence: 99%

Similarity transformation in one-dimensional reaction-diffusion systems: the voting model as an example

Aghamohammadi¹,

Khorrami²

2000

J. Phys. A: Math. Gen.

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The exact solution for a system with two-particle annihilation and decoagulation has been studied.The spectrum of the Hamiltonian of the system is found. It is shown that the steady state is two-fold degenerate. The average number density in each cite ni(t) and the equal time two-point functions ni(t)nj(t) are calculated. Any equal time correlation functions at large times, ni(∞)nj (∞) · · · , is also calculated. The relaxation behaviour of the system toward its final state is investigated and it is shown that generally it is exponential, as it is expected. For the special symmetric case, the relaxation behaviour of the system is a power law. For the asymmetric case, it is shown that the profile of deviation from the final values is an exponential function of the position.

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“…Approximation methods are generally different in different dimensions, as for example the mean filed techniques, working good for high dimensions, generally do not give correct results for low-dimensional systems. A large fraction of analytical studies belong to low-dimensional (especially one-dimensional) systems, as solving low-dimensional systems should in principle be easier [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%