Exact Solution of the Master Equation for the Asymmetric Exclusion Process
نویسنده
چکیده
Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P (x1, . . . , xN ; t|y1, . . . , yN ; 0) of finding N particles on lattice sites x1, . . . , xN at time t with initial occupation y1, . . . , yN at time t = 0.
منابع مشابه
Exact solution of a one-parameter family of asymmetric exclusion processes
We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter λ ∈ [0, 1], interpolating between the completely asymmetric processes [1] (for λ = 1 ) and the n = 1 drop-push models [2] (for λ = 0 ). For arbitrary λ, the model describes an exclusion process, in which a particle pushes its right neighbouring particles to the right, with ...
متن کاملSolvable reaction-diffusion processes without exclusion
For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master equation of the asymmetric diffusion process. The annihilation process is also added. The Bethe ansatz solution and the exact N-particle conditional probabilitie...
متن کاملBethe ansatz and current distribution for the TASEP with particle-dependent hopping rates
Using the Bethe ansatz we obtain in a determinant form the exact solution of the master equation for the conditional probabilities of the totally asymmetric exclusion process with particle-dependent hopping rates on Z. From this we derive a determinant expression for the timeintegrated current for a step-function initial state.
متن کاملA two–parametric family of asymmetric exclusion processes and its exact solution
A two–parameter family of asymmetric exclusion processes for particles on a onedimensional lattice is defined. The two parameters of the model control the driftand the diffusion-rate of the particles. Using the Bethe ansatz, the exact solution of the master equation, and from that the driftand the diffusion-rate in the two–particle sector, is obtained. It is shown that for long times, each of t...
متن کاملThe Exact Solution of the Asymmetric Exclusion Problem With Particles of Arbitrary Size: Matrix Product Ansatz
The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product ansatz. Due to the similarity of the master equation and the Schrödinger equation at imaginary times the solution of these problems reduces to the diagonalization of a one dimensional quantum Hamiltonian. We present initially the solution of the problem when an arbitrary mix...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997