Quantum Phase Transition in a Resonant Level Coupled to Interacting Leads

An interacting one-dimensional electron system, the Luttinger liquid, is distinct from the "conventional" Fermi liquids formed by interacting electrons in two and three dimensions. Some of its most spectacular properties are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Here, we create a system which emulates tunneling in a Luttinger liquid, by controlling the interaction of the tunneling electron with its environment. We further replace a single tunneling barrier with a double-barrier resonant level structure and investigate resonant tunneling between Luttinger liquids. For the first time, we observe perfect transparency of the resonant level embedded in the interacting environment, while the width of the resonance tends to zero. We argue that this unique behavior results from many-body physics of interacting electrons and signals the presence of a quantum phase transition (QPT). In our samples many parameters, including the interaction strength, can be precisely controlled; thus, we have created an attractive model system for studying quantum critical phenomena in general. Our work therefore has broadly reaching implications for understanding QPTs in more complex systems, such as cold atoms and strongly correlated bulk materials.Comment: 11 pages total (main text + supplementary

Time ordering and counting statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a quantum point contact.Comment: 19 pages, 1 figure; inconsequential mistake and typos correcte

Measurement of finite-frequency current statistics in a single-electron transistor

Electron transport in nano-scale structures is strongly influenced by the Coulomb interaction which gives rise to correlations in the stream of charges and leaves clear fingerprints in the fluctuations of the electrical current. A complete understanding of the underlying physical processes requires measurements of the electrical fluctuations on all time and frequency scales, but experiments have so far been restricted to fixed frequency ranges as broadband detection of current fluctuations is an inherently difficult experimental procedure. Here we demonstrate that the electrical fluctuations in a single electron transistor (SET) can be accurately measured on all relevant frequencies using a nearby quantum point contact for on-chip real-time detection of the current pulses in the SET. We have directly measured the frequency-dependent current statistics and hereby fully characterized the fundamental tunneling processes in the SET. Our experiment paves the way for future investigations of interaction and coherence induced correlation effects in quantum transport.Comment: 7 pages, 3 figures, published in Nature Communications (open access

Evolutionary Games with Affine Fitness Functions: Applications to Cancer

We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified payoffs. The affine terms also influence the stochastic dynamics of a two-strategy Moran model of a finite population. We then apply the affine fitness function in a model for tumor-normal cell interactions to determine which are the most successful tumor strategies. In order to analyze the dynamics of concurrent strategies within a tumor population, we extend the model to a three-strategy game involving distinct tumor cell types as well as normal cells. In this model, interaction with normal cells, in combination with an increased constant fitness, is the most effective way of establishing a population of tumor cells in normal tissue.Comment: The final publication is available at http://www.springerlink.com, http://dx.doi.org/10.1007/s13235-011-0029-

Conserved Alternative Splicing and Expression Patterns of Arthropod N-Cadherin

Metazoan development requires complex mechanisms to generate cells with diverse function. Alternative splicing of pre-mRNA not only expands proteomic diversity but also provides a means to regulate tissue-specific molecular expression. The N-Cadherin gene in Drosophila contains three pairs of mutually-exclusive alternatively-spliced exons (MEs). However, no significant differences among the resulting protein isoforms have been successfully demonstrated in vivo. Furthermore, while the N-Cadherin gene products exhibit a complex spatiotemporal expression pattern within embryos, its underlying mechanisms and significance remain unknown. Here, we present results that suggest a critical role for alternative splicing in producing a crucial and reproducible complexity in the expression pattern of arthropod N-Cadherin. We demonstrate that the arthropod N-Cadherin gene has maintained the three sets of MEs for over 400 million years using in silico and in vivo approaches. Expression of isoforms derived from these MEs receives precise spatiotemporal control critical during development. Both Drosophila and Tribolium use ME-13a and ME-13b in “neural” and “mesodermal” splice variants, respectively. As proteins, either ME-13a- or ME-13b-containing isoform can cell-autonomously rescue the embryonic lethality caused by genetic loss of N-Cadherin. Ectopic muscle expression of either isoform beyond the time it normally ceases leads to paralysis and lethality. Together, our results offer an example of well-conserved alternative splicing increasing cellular diversity in metazoans