Non-Markovian decay beyond the Fermi Golden Rule: Survival Collapse of the polarization in spin chains

The decay of a local spin excitation in an inhomogeneous spin chain is evaluated exactly: I) It starts quadratically up to a spreading time t_{S}. II) It follows an exponential behavior governed by a self-consistent Fermi Golden Rule. III) At longer times, the exponential is overrun by an inverse power law describing return processes governed by quantum diffusion. At this last transition time t_{R} a survival collapse becomes possible, bringing the polarization down by several orders of magnitude. We identify this strongly destructive interference as an antiresonance in the time domain. These general phenomena are suitable for observation through an NMR experiment.Comment: corrected versio

Survival probability of surface excitations in a 2d lattice: non-Markovian effects and Survival Collapse

The evolution of a surface excitation in a two dimentional model is analyzed. I) It starts quadratically up to a spreading time t_{S}. II) It follows an exponential behavior governed by a self-consistent Fermi Golden Rule. III) At longer times, the exponential is overrun by an inverse power law describing return processes governed by quantum diffusion. At this last transition time t_{R} a survival collapse becomes possible, bringing the survival probability down by several orders of magnitude. We identify this strongly destructive interference as an antiresonance in the time domain.Comment: 4 pages, 3 figures. Braz. Journ. of Phys., in press. Braz. Journ. of Phys., in press. Braz. Journ. of Phys., in press. Braz. Journ. of Phys., in press. Braz. Journ. of Phys., in press. Braz. Journ. of Phys., in press. Braz. Journ. of Phys., in pres

Majority Rule Dynamics in Finite Dimensions

We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group of spins with a fixed (odd) size is specified and all members of the group adopt the local majority state. Repeated application of this update step leads to a coarsening mosaic of spin domains and ultimate consensus in a finite system. The approach to consensus is governed by two disparate time scales, with the longer time scale arising from realizations in which spins organize into coherent single-opinion bands. The consequences of this geometrical organization on the long-time kinetics are explored.Comment: 8 pages, 2-column revtex format, 11 figures. Version 2: minor changes in response to referee comments and typos corrected; final version for PR

Modeling of ductile damage using numerical analyses on the micro-scale

The presentation deals with a continuum damage model which has been generalized to take into account the effect of stress state on damage criteria as well as on evolution equations of damage strains. It is based on the introduction of damaged and corresponding undamaged configurations. Plastic behavior is modeled by a yield criterion and a flow rule formulated in the effective stress space (undamaged configurations). In a similar way, damage behavior is governed by a damage criterion and a damage rule considering the damaged configurations. Different branches of the damage criterion are considered corresponding to various damage mechanisms depending on stress intensity, stress triaxiality and the Lode parameter. Experiments with carefully designed specimens are performed and the test results are used to identify basic material parameters. However, it is not possible to determine all parameters based on these tension and shear tests. To be able to get more insight in the complex damage behavior under different loading conditions, additional series of micro-mechanical numerical analyses of void containing unit cells have been performed. These finite element calculations on the micro-level cover a wide range of stress triaxialities and Lode parameters in the tension, shear and compression domain. The numerical results are used to show general trends, to develop equations for the stress-statedependent damage criteria, to propose evolution equations of damage strains, and to identify parameters of the continuum model

- A BAYESIAN APPROACH TO UNCERTAINTY AVERSION

The Ellsberg paradox demonstrates that peoples belief over uncertainevents might not be representable by subjective probability. We relate this paradox to other commonly observed anomalies, suchas a rejection of the backward induction prediction in the one-shot Ultimatum Game. We argue that the pattern common to theseobservations is that the behavior is governed by rational rules. These rules have evolved and are optimal within the repeated andconcurrent environments that people usually encounter. When an individual relies on these rules to analyzeone-shot or single circumstances, paradoxes emerge. We show that when a risk averse individualhas a Bayesian prior and uses a rule which is optimal for simultaneous and positively correlatedambiguous risks to evaluate a single vague circumstance, his behavior will exhibit uncertaintyaversion. Thus, the behavior predicted by Ellsberg may be explained within the Bayesian expectedutility paradigm.Ellsberg paradox, rule rationality, ambiguity aversion, risk aversion,

Rational Samaritans, Strategic Moves, and Rule-Governed Behavior: Some Remarks on James Buchanan's "Samaritan's Dilemma"

Using James Buchanan's "Samaritan's Dilemma" as a basic example, this paper analyses the problems that have to be solved if strategic behavior is necessary to escape from dilemma situations by changing the opponents' incentives. These problems are addressed within one-shot games as well as repeated games. Furthermore, the implications resulting from the assumption of common knowledge of rationality are analyzed. By using the concept of finite automata to model strategies for supergames, the possible relations with evolutionary game theory are spelled out. -- Dieser Beitrag untersucht am Beispiel von James Buchanans "Samariter-Dilemma" die Probleme, die es zu lösen gilt, wenn "strategisches Verhalten" im Sinne der Veränderung von Handlungsanreizen durch glaubhafte Drohungen und Versprechen notwendig ist, um Dilemmasituationen zu vermeiden. Dabei werden neben den grundelgenden Strukturen "Einmalspiel" und "Superspiel" auch die Besonderheiten der Annahme von "common knowledge" analysiert, und mit dem Konzept der als finite Automaten abbildbaren Superspielstrategien Brücken zur evolutorischen Spieltheorie geschlagen.rationality,altruism,evolutionary stability,strategic moves

Imperfect Decision-Making and the Tax Payer Puzzle

Even if the expected punishment on tax evasion is negligible, empirical studies show that actual tax evasion is smaller than rational choice models predict. In addition to this, tax payer do not respond on parameter changes as predicted. Some authors tried to explain this puzzle by assuming "tax morale". Our paper models tax payers as imperfect decision-makers and explains deviations from the optimal solution by making use of a weaker assumption: The imperfect tax payer's decision to deviate from a given rule depends on their competence and on the complexity of their situation. --tax compliance,bounded rationality,imperfect decision-making,detection skill,rule-governed behavior

Exploring the potential impact of relational coherence on persistent rule-following : the first study

Rule-governed behavior and derived relational responding have both been identified as important variables in human learning. Recent developments in the relational frame theory (RFT) have outlined a number of key variables of potential importance when analyzing the dynamics involved in derived relational responding. Recent research has explored the impact of one of these variables, level of derivation, on persistent rule-following and implicated another, coherence, as possibly important. However, no research to date has examined the impact of coherence on persistent rule-following directly. Across two experiments, coherence was manipulated through the systematic use of performance feedback, and its impact was examined on persistent rule-following. A training procedure based on the implicit relational assessment procedure (IRAP) was used to establish novel combinatorially entailed relations that manipulated the feedback provided on the trained relations (A-B and B-C) in Experiment 1, and on the untrained, derived relations (A-C) in Experiment 2. One of these relations was then inserted into the rule for responding on a subsequent contingency-switching match-to-sample (MTS) task to assess rule persistence. While no significant differences were found in Experiment 1, the provision or non-provision of feedback had a significant differential impact on rule-persistence in Experiment 2. Specifically, participants in the Feedback group resurged back to the original rule for significantly more responses after demonstrating contingency-sensitive responding than did the No-Feedback group, after the contingency reversal. The results highlight the subtle complexities that appear to be involved in persistent rule-following in the face of reversed reinforcement contingencies

Survival Probability of a Local Excitation in a Non-Markovian Environment: Survival Collapse, Zeno and Anti-Zeno effects

The decay dynamics of a local excitation interacting with a non-Markovian environment, modeled by a semi-infinite tight-binding chain, is exactly evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i) early quadratic decay of the initial-state survival probability, up to a spreading time $t_{S}$, (ii) exponential decay described by a self-consistent Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion through the return processes and leading to an inverse power law decay. At this last cross-over time $t_{R}$ a survival collapse becomes possible. This could reduce the survival probability by several orders of magnitude. The cross-overs times $t_{S}$ and $t_{R}$ allow to assess the range of applicability of the Fermi Golden Rule and give the conditions for the observation of the Zeno and Anti-Zeno effect