Non-equilibrium stationary state of a two-temperature spin chain

Schmüser, F.; Schmittmann, Beate

doi:10.1088/0305-4470/35/11/304

Cited by 16 publications

(27 citation statements)

References 38 publications

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“…Hence, particle pairs are more likely to reside on (e, o) than on (o, e) sites. This also implies that (e, o) sites act as net particle sources, while (o, e) sites function as sinks [10] . Not surprisingly, therefore, we find C eo 1 (∞) > C oe 1 (∞).…”

Section: A Density Of Particles In the Rdsmentioning

confidence: 99%

Exact dynamics of a reaction-diffusion model with spatially alternating rates

2005

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We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reactiondiffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative "temperatures" have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time dependence are found: if both temperatures are positive, the magnetization, density, and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.

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Section: A Density Of Particles In the Rdsmentioning

confidence: 99%

Exact dynamics of a reaction-diffusion model with spatially alternating rates

2005

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“…We now turn to the non-equilibrium model, characterized by different temperatures, T e = T o . The associated stationary state violates detailed balance [15] and differs from the Boltzmann distribution, Eqn (5). The degree to which detailed balance is violated can be measured by the parameter d ≡ (γ o − γ e )/2.…”

Section: The Modelmentioning

confidence: 99%

“…Motivated by these considerations, we recently [15] investigated a very simple non-equilibrium Ising-like model, namely, a one-dimensional interacting spin chain with spin-flip dynamics coupled to two temperature baths. The rates are a simple but nontrivial generalization of the familiar Glauber [16] rates: spins at odd (even) sites are coupled to a temperature T o (T e ).…”

Section: Introductionmentioning

confidence: 99%

Stationary correlations for a far-from-equilibrium spin chain

Schmittmann¹,

Schmüser²

2002

Phys. Rev. E

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A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even ͑odd͒ lattice sites experience a temperature T e (T o ). Detailed balance is violated so that the spin chain settles into a nonequilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long-chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the longtime, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.

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“…A good example of a simple model driven far from equilibrium is the kinetic Ising model, coupled to two thermal reservoirs set at different temperatures [4][5][6][7][8]. In previous studies, translational invariance is kept as much as possible, e.g., every other spin being updated according to the same reservoir [5,6].…”

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confidence: 99%

Energy flux near the junction of two Ising chains at different temperatures

Lavrentovich

Zia

2010

EPL

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We consider a system in a non-equilibrium steady state by joining two semi-infinite Ising chains coupled to thermal reservoirs with different temperatures, T and T ′ . To compute the energy flux from the hot bath through our system into the cold bath, we exploit Glauber heat-bath dynamics to derive an exact equation for the two-spin correlations, which we solve for T ′ = ∞ and arbitrary T . We find that, in the T ′ = ∞ sector, the in-flux occurs only at the first spin. In the T < ∞ sector (sites x = 1, 2, ...), the out-flux shows a non-trivial profile: F (x). Far from the junction of the two chains, F (x) decays as e −x/ξ , where ξ is twice the correlation length of the equilibrium Ising chain. As T → 0, this decay crosses over to a power law (x −3 ) and resembles a "critical" system. Simulations affirm our analytic results. Recently, a simpler version of this model has been investigated [9]. On a ring of 2N + 1 spins (i.e., periodic chain), all but one is coupled to a standard bath at zero p-1

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Non-equilibrium stationary state of a two-temperature spin chain

Cited by 16 publications

References 38 publications

Exact dynamics of a reaction-diffusion model with spatially alternating rates

Exact dynamics of a reaction-diffusion model with spatially alternating rates

Stationary correlations for a far-from-equilibrium spin chain

Energy flux near the junction of two Ising chains at different temperatures

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