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We consider a generalized coagulation-decoagulation system on a one-dimensional discrete lattice with reflecting boundaries. It is known that a Bernoulli shock measure with two shock fronts might have a simple random-walk dynamics, provided that some constraints on the microscopic reaction rates of this system are fulfilled. Under these constraints the steady-state of the system can be written as a linear superposition of such shock measures. We show that the coefficients of this expansion can be calculated using the finite-dimensional representation of the quadratic algebra of the system obtained from a matrix-product approach.
The power of matrix product states to describe infinite-size translational-invariant critical spin chains is investigated. At criticality, the accuracy with which they describe ground state properties of a system is limited by the size $chi$ of the m
We revisit the question of describing critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theorie
Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics of dynamic
We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of 1D quantum systems, to simulate the time-evolution of non-equilibrium stochastic systems. We describe this method in detail; a systems probab
The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute the relevant leading eigenvalues and eige