In this note we relate the Hamiltonian of the integrable non-compact spin $s$ XXZ chain to the Markov generator of a stochastic particle process. The hopping rates of the continuous-time process are identified with the ones of a q-Hahn asymmetric zero range model. The main difference with the asymmetric simple exclusion process (ASEP), which can be mapped to the ordinary XXZ spin chain, is that multiple particles can occupy one and the same site. For the non-compact spin $\\frac{1}{2}$ XXZ chain the associated stochastic process reduces to the multiparticle asymmetric diffusion model introduced by Sasamoto-Wadati.In this note we relate the Hamiltonian of the integrable non-compact spin $s$ XXZ chain to the Markov generator of a stochastic particle process. The hopping rates of the continuous-time process are identified with the ones of a q-Hahn asymmetric zero range model. The main difference with the asymmetric simple exclusion process (ASEP), which can be mapped to the ordinary XXZ spin chain, is that multiple particles can occupy one and the same site. For the non-compact spin $\\frac{1}{2}$ XXZ chain the associated stochastic process reduces to the multiparticle asymmetric diffusion model introduced by Sasamoto-Wadati.

Jan 1, 20197 citations

Comparison between different markov approximations for open spin systems

M. Celio, Daniel Loss

Physica A Statistical Mechanics and its ApplicationsJul 1, 198914 citations

The non-compact XXZ spin chain as stochastic particle process

Rouven Frassek

Abstract In this note we relate the Hamiltonian of the integrable non-compact spin s XXZ chain to the Markov generator of a stochastic particle process. The hopping rates of the continuous-time process are identified with the ones of a q-Hahn asymmetric zero range model. The main difference with the asymmetric simple exclusion process, which can be mapped to the ordinary XXZ spin chain, is that multiple particles can occupy one and the same site. For the non-compact spin XXZ chain the associated stochastic process reduces to the multiparticle asymmetric diffusion model introduced by Sasamoto–Wadati.Abstract In this note we relate the Hamiltonian of the integrable non-compact spin s XXZ chain to the Markov generator of a stochastic particle process. The hopping rates of the continuous-time process are identified with the ones of a q-Hahn asymmetric zero range model. The main difference with the asymmetric simple exclusion process, which can be mapped to the ordinary XXZ spin chain, is that multiple particles can occupy one and the same site. For the non-compact spin XXZ chain the associated stochastic process reduces to the multiparticle asymmetric diffusion model introduced by Sasamoto–Wadati.

arXiv:1904.02191Journal of Physics A Mathematical and TheoreticalJul 8, 20199 citations

Multimodal dynamics of nonhomogeneous absorbing Markov chains evolving at stochastic transition rates

Victor I. Teslenko, Oleksiy L. Kapitanchuk

The Tokuyama–Mori projection operator method for a reduced time-convolutionless description of a local temporal behavior of an open quantum system interacting with the weakly dissipative and fluctuating pervasive environment is applied to a Markov chain subject to random transition probabilities. The solution to the problem of the multimodal dynamics of a two-stage absorbing Markov chain with the fluctuating forward rate constant augmented by a symmetric dichotomous stochastic process is found exactly and compared with that of the problem for the same Markov chain with the fluctuating backward rate constant. It is shown that these two different tetramodal solutions cannot generally be reduced to but be complementary to each other. In the limit of very frequent fluctuations in forward/backward rate constants of a two-stage absorbing Markov chain, as well as in the case of a one-stage recurrent Markov chain, both solutions become bimodal and superimposed to one another. However, there is a distinction between using of those solutions for the dynamics of a two-stage absorbing Markov chain in the limit of very rare fluctuations at the critical point, in which the former solution shows the resonance effect exhibiting itself as the stochastic immobilization in an initial state, while the latter demonstrates the deterministic decay to the other state.The Tokuyama–Mori projection operator method for a reduced time-convolutionless description of a local temporal behavior of an open quantum system interacting with the weakly dissipative and fluctuating pervasive environment is applied to a Markov chain subject to random transition probabilities. The solution to the problem of the multimodal dynamics of a two-stage absorbing Markov chain with the fluctuating forward rate constant augmented by a symmetric dichotomous stochastic process is found exactly and compared with that of the problem for the same Markov chain with the fluctuating backward rate constant. It is shown that these two different tetramodal solutions cannot generally be reduced to but be complementary to each other. In the limit of very frequent fluctuations in forward/backward rate constants of a two-stage absorbing Markov chain, as well as in the case of a one-stage recurrent Markov chain, both solutions become bimodal and superimposed to one another. However, there is a distinction between using of those solutions for the dynamics of a two-stage absorbing Markov chain in the limit of very rare fluctuations at the critical point, in which the former solution shows the resonance effect exhibiting itself as the stochastic immobilization in an initial state, while the latter demonstrates the deterministic decay to the other state.

International Journal of Modern Physics BApr 30, 20201 citation

Accelerating hybrid stochastic algorithm for spin models

John B. Kogut

Nuclear Physics BSep 1, 198620 citations

In this note we relate the Hamiltonian of the integrable non-compact spin

s

XXZ chain to the Markov generator of a stochastic particle process. The hopping rates of the continuous-time process are identified with the ones of a q-Hahn asymmetric zero range model. The main difference with the asymmetric simple exclusion process (ASEP), which can be mapped to the ordinary XXZ spin chain, is that multiple particles can occupy one and the same site. For the non-compact spin

\\frac{1}{2}

XXZ chain the associated stochastic process reduces to the multiparticle asymmetric diffusion model introduced by Sasamoto-Wadati.