Hysteresis in one-dimensional reaction-diffusion systems

We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics which exhibits ergodicity breaking and hysteresis in one dimension. These phenomena can be understood through a description of the dominant stochastic many-body dynamics in terms of an equilibrium single-particle problem, viz. the random motion of a shock in an effective potential. This picture also leads to the exact phase diagram of the system and suggests a new generic mechanism for "freezing by heating".Comment: 4 Pages, 5 figure

Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model

The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled. The dynamics of a product shock measure with two shock fronts, generated by the Hamiltonian of this model, is also studied. It turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied.Comment: Minor revision

Management of Febrile Neutropenia - a German Prospective Hospital Cost Analysis in Lymphoproliferative Disorders, Non-Small Cell Lung Cancer, and Primary Breast Cancer

Background: Febrile neutropenia/leukopenia (FN/FL) is the most frequent dose-limiting toxicity of myelosuppressive chemotherapy, but German data on economic consequences are limited. Patients and Methods: A prospective, multicentre, longitudinal, observational study was carried out to evaluate the occurrence of FN/FL and its impact on health resource utilization and costs in non-small cell lung cancer (NSCLC), lymphoproliferative disorder (LPD), and primary breast cancer (PBC) patients. Costs are presented from a hospital perspective. Results: A total of 325 consecutive patients (47% LPD, 37% NSCLC, 16% PBC; 46% women; 38% age >= 65 years) with 68 FN/FL episodes were evaluated. FN/FL occurred in 22% of the LPD patients, 8% of the NSCLC patients, and 27% of the PBC patients. 55 FN/FL episodes were associated with at least 1 hospital stay (LPD n = 34, NSCLC n = 10, PBC n = 11). Mean (median) cost per FN/FL episode requiring hospital care amounted to (sic) 3,950 ((sic) 2,355) and varied between (sic) 4,808 ((sic) 3,056) for LPD, (sic) 3,627 ((sic) 2,255) for NSCLC, and (sic) 1,827 ((sic) 1,969) for PBC patients. 12 FN/FL episodes (LPD n = 9, NSCLC n = 3) accounted for 60% of the total expenses. Main cost drivers were hospitalization and drugs (60 and 19% of the total costs). Conclusions: FN/FL treatment has economic relevance for hospitals. Costs vary between tumour types, being significantly higher for LPD compared to PBC patients. The impact of clinical characteristics on asymmetrically distributed costs needs further evaluation

Ergodicity breaking in one-dimensional reaction-diffusion systems

We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems can exhibit ergodicity breaking in the thermodynamic limit. The triggering mechanism is the random motion of a shock in an effective potential. Based on this physical picture we provide a simple condition for the existence of a non-ergodic phase in the phase diagram of such systems. In the thermodynamic limit this phase exhibits two or more stationary states. However, for finite systems transitions between these states are possible. It is shown that the mean lifetime of such a metastable state is exponentially large in system-size. As an example the ASEP with the A0A--AAA reaction kinetics is analyzed in detail. We present a detailed discussion of the phase diagram of this particular model which indeed exhibits a phase with broken ergodicity. We measure the lifetime of the metastable states with a Monte Carlo simulation in order to confirm our analytical findings.Comment: 25 pages, 14 figures; minor alterations, typos correcte

Scaling of the magnetic linear response in phase-ordering kinetics

The scaling of the thermoremanent magnetization and of the dissipative part of the non-equilibrium magnetic susceptibility is analysed as a function of the waiting-time $s$ for a simple ferromagnet undergoing phase-ordering kinetics after a quench into the ferromagnetically ordered phase. Their scaling forms describe the cross-over between two power-law regimes governed by the non-equilibrium exponents $a$ and $\lambda_R/z$, respectively. A relation between $a$, the dynamical exponent $z$ and the equilibrium exponent $\eta$ is derived from scaling arguments. Explicit tests in the Glauber-Ising model and the kinetic spherical model are presented.Comment: 7 pages, 2 figures included, needs epl.cls, version to appear in Europhys. Let

Multi shocks in Reaction-diffusion models

It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbor interaction, there are only four independent models possessing double-shocks. Evolution of the width of the double-shocks in different models is investigated. Double-shocks may vanish, and the final state is a state with no shock. There is a model for which at large times the average width of double-shocks will become smaller. Although there may exist stationary single-shocks in nearest neighbor reaction diffusion models, it is seen that in none of these models, there exist any stationary double-shocks. Models admitting multi-shocks are classified, and the large time behavior of multi-shock solutions is also investigated.Comment: 17 pages, LaTeX2e, minor revisio

Relaxation time in a non-conserving driven-diffusive system with parallel dynamics

We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit.Comment: 10 page

Ageing in bosonic particle-reaction models with long-range transport

Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is found and analysed. Exact results for non-equilibrium exponents and scaling functions are derived. The behaviour of the fluctuation-dissipation ratio is analysed. A passage time from the quasi-stationary regime to the ageing regime is defined, in qualitative agreement with kinetic spherical models and p-spin spherical glasses.Comment: Latex2e, 24 pages, with 9 figures include

Reaction fronts in stochastic exclusion models with three-site interactions

The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different densities connected by a sharp wall without correlations. In all cases fluctuating domains grow at the expense of ordered domains, the absence of growth is possible between ordered domains. It is shown that these models give rise to aspects not seen in nearest neighbor models, viz. double shocks and additional symmetries. A classification of the systems by their symmetries is given and the link of domain wall motion and a free fermion description is discussed.Comment: 29 pages, 5 figure

Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method

The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles meet. The exact two-time correlation and response function in the one-dimensional coagulation-diffusion process are derived from the empty-interval-particle method. The main quantity is the conditional probability of finding an empty interval of n consecutive sites, if at distance d a site is occupied by a particle. Closed equations of motion are derived such that the probabilities needed for the calculation of correlators and responses, respectively, are distinguished by different initial and boundary conditions. In this way, the dynamical scaling of these two-time observables is analysed in the longtime ageing regime. A new generalised fluctuation-dissipation ratio with an universal and finite limit is proposed.Comment: 31 pages, submitted to J.Stat.Mec