Dynamical properties of a nonequilibrium quantum dot close to localized-delocalized quantum phase transitions

We calculate the dynamical decoherence rate and susceptibility of a nonequilibrium quantum dot close to the delocalized-to-localized quantum phase transitions. The setup concerns a resonance-level coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an anisotropic Kondo model. As the dissipation strength increases, the system at zero temperature and zero bias show quantum phase transition between a conducting delocalized phase to an insulating localized phase. Within the nonequilibrium functional Renormalization Group (FRG) approach, we address the finite bias crossover in dynamical decoherence rate and charge susceptibility close to the phase transition. We find the dynamical decoherence rate increases with increasing frequency. In the delocalized phase, it shows a singularity at frequencies equal to positive or negative bias voltage. As the system crossovers to the localized phase, the decoherence rate at low frequencies get progressively smaller and this sharp feature is gradually smeared out, leading to a single linear frequency dependence. The dynamical charge susceptibility shows a dip-to-peak crossover across the delocalized-to-localized transition. Relevance of our results to the experiments is discussed.Comment: 7 pages, 7 figure

Promissory Estoppel and the Protection of Interpersonal Trust

This paper examines the role of trust in promissory estoppel and the extent to which the law should protect trust when a promise is made. Part II of this Article summarizes some of the scholarship discussing the nature and role of trust. In particular, it discusses the role of trust in a market economy, and the related role of trust in Contracts law. Part III examines whether there is a difference between trust and reliance, and whether it matters. Part III further asserts that a separate discussion of trust is beneficial because it has the potential to guide and inform internal decision-making in a way that is not possible by simply focusing on outward reliance. Part IV of this Article discusses the role of trust in the doctrine of promissory estoppel. Part V sets forth why the law should promote an optimal level of trust, as opposed to a maximum protection of trust no matter what. It discusses the need for promisees to exercise self-reliance and self-protection in order to avoid overreliance. Part VI identifies the types of cases where trust should be protected. Such cases include ones where the promisee is engaged in a transaction that she cannot avoid, where she has no control over the structure of the transaction, and where she has no choice but to trust the promisor (or more accurately, trust the legal system to enforce the promise). Part VII presents the polar end of the spectrum where trust should not be protected. Part VIII concludes the Article