A new family of exactly solvable disordered reaction–diffusion systems

Ghadermazi, Mohammad; Jafarpour, Farhad H.

doi:10.1088/1742-5468/2013/09/p09023

Cited by 3 publications

(6 citation statements)

References 20 publications

(67 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, µ) at the nearest neighbors. Thus, the microscopic dynamics considered here is different from previously studied models like TASEP with internal degrees of freedom [64] and multi-species reaction-diffusion processes [65,66]. Notably, the distinction in the microscopic dynamics also makes µ-ASEP-IAF non-ergodic in nature in contrast to the ergodic models [64][65][66].…”

Section: Introductionmentioning

confidence: 72%

Multi species asymmetric simple exclusion process with impurity activated flips

Chatterjee

Hayakawa

2023

SciPost Phys.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 72%

Multi species asymmetric simple exclusion process with impurity activated flips

Chatterjee

Hayakawa

2023

SciPost Phys.

View full text Add to dashboard Cite

show abstract

“…, µ) at the nearest neighbors. Thus, the microscopic dynamics considered here is different from previously studied models like TASEP with internal degrees of freedom [61] and multi-species reaction-diffusion processes [62,63]. Notably, the distinction in the microscopic dynamics also makes µ-ASEP-IAF non-ergodic in nature in contrast to the ergodic models [61][62][63].…”

mentioning

confidence: 72%

“…Thus, the microscopic dynamics considered here is different from previously studied models like TASEP with internal degrees of freedom [61] and multi-species reaction-diffusion processes [62,63]. Notably, the distinction in the microscopic dynamics also makes µ-ASEP-IAF non-ergodic in nature in contrast to the ergodic models [61][62][63]. We should mention that the non-ergodicity of exactly solvable models is related to undecidability of thermalization in integrable models [64].…”

mentioning

confidence: 72%

Multi species asymmetric simple exclusion process with impurity activated flips

Chatterjee¹,

Hayakawa²

2022

Preprint

View full text Add to dashboard Cite

We obtain an exact matrix product steady state for a class of multi species asymmetric simple exclusion process with impurities, under periodic boundary condition. Alongside the usual hopping dynamics, an additional flip dynamics is activated only in the presence of impurities. Although the microscopic dynamics renders the system to be non-ergodic, exact analytical results for observables are obtained in steady states for a specific class of initial configurations. Interesting physical features including negative differential mobility and transition of correlations from negative to positive with changing vacancy density, have been observed. We discuss plausible connections of this exactly solvable model with multi lane asymmetric simple exclusion processes as well as enzymatic chemical reactions. Two-point correlations 17 4.4 Flip current 18 4.5 Non-ergodicity: dependence on initial configuration 19 5 Partially asymmetric generalization: µ-ASEP-IAF 21 5.1 Matrix algebra, auxiliaries and matrix representations 21 5.2 Partition function for special initial configuration 23 5.3 Species densities, drift current and flip current 23 5.4 Negative differential mobility 24 6 Summary and future directions 26 A Connection between µ-TASEP-IAF and multi lane TASEP 28 B A variation of µ-TASEP-IAF, connection to multi-lane traffic flow 30 C Connection between µ-TASEP-IAF and enzymatic chemical reactions 31 References 33

show abstract

“…In [17] the authors have shown that the quadratic algebra (10) has a finitedimensional representation which depends on the number of types of particles. The dimension of the matrix is M if the number of types of the particles is equal to M. Hence for our model with two species of particles the quadratic algebra (10) has a 2-dimensional matrix representation given by…”

Section: The Spatial Correlationsmentioning

confidence: 99%

“…To find the critical exponent defined by q / ðz À z c Þ b , we only need to consider the behavior of the density of the first-class particles as a function of fugacity z at the critical point z c ¼ 1þqÀp p in the thermodynamic limit. According to (17), it can be seen that the density of the first-class particles in the vicinity of z c can be With the correlation function given asymptotically by…”

Section: The Spatial Correlationsmentioning

confidence: 99%

Non-equilibrium phase transition in a two-species driven-diffusive model of classical particles

Ghadermazi

Jafarpour

2016

J Theor Appl Phys

Self Cite

View full text Add to dashboard Cite

A two-species driven-diffusive model of classical particles is introduced on a lattice with periodic boundary condition. The model consists of a finite number of first class particles in the presence of a second class particle. While the first class particles can only hop forward, the second class particle is able to hop both forward and backward with specific rates. We have shown that the partition function of this model can be calculated exactly. The model undergoes a non-equilibrium phase transition when a condensation of the first class particles occurs behind the second class particle. The phase transition point and the spatial correlations between the first class particles are calculated exactly. On the other hand, we have shown that this model can be mapped onto a two-dimensional walk model. The random walker can only move on the first quarter of a two-dimensional plane and that it takes the paths which can start at any height and end at any height upper than the height of the starting point. The initial vertex (starting point) and the final vertex (end point) of each lattice path are weighted. The weight of the outset point depends on the height of that point while the weight of the end point depends on the height of both the outset point and the end point of each path. The partition function of this walk model is calculated using a transfer matrix method.

show abstract

A new family of exactly solvable disordered reaction–diffusion systems

Cited by 3 publications

References 20 publications

Multi species asymmetric simple exclusion process with impurity activated flips

Multi species asymmetric simple exclusion process with impurity activated flips

Multi species asymmetric simple exclusion process with impurity activated flips

Non-equilibrium phase transition in a two-species driven-diffusive model of classical particles

Contact Info

Product

Resources

About