Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries

Abstract

We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using the modified algebraic Bethe ansatz, method introduced recently to study the spin chain with non-diagonal boundaries. We provide in this case a proof of this method.

References in corpus (28)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Partially Asymmetric Exclusion Process with Open Boundaries
• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Exact Current Statistics of the ASEP with Open Boundaries
• Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• The half-infinite XXZ chain in Onsager's approach
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Separation of Variables in the open XXX chain
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• Current large deviation function for the open asymmetric simple exclusion process
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
• Bethe Ansatz and Q-operator for the open ASEP
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Generalized coordinate Bethe ansatz for non diagonal boundaries
• Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices

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• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
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• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Scalar product for the XXZ spin chain with general integrable boundaries
• KPZ fluctuations in finite volume
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Bethe ansatz diagonalization of the Heun-Racah operator
• Multi species asymmetric simple exclusion process with impurity activated flips
• Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
• Time and band limiting operator and Bethe ansatz