Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Low Energy Theorems For Nucleon-Nucleon Scattering

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the energy dependence $\epsilon$ parameter which describes $^3S_1 - ^3D_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_\pi$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_\pi$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.Comment: 12 pages, 1 figure, 1 table; appendix added to discuss behavior in chiral limit; minor revisions including revised figure reference to recent work adde

Star-unitary transformations. From dynamics to irreversibility and stochastic behavior

We consider a simple model of a classical harmonic oscillator coupled to a field. In standard approaches Langevin-type equations for {\it bare} particles are derived from Hamiltonian dynamics. These equations contain memory terms and are time-reversal invariant. In contrast the phenomenological Langevin equations have no memory terms (they are Markovian equations) and give a time evolution split in two branches (semigroups), each of which breaks time symmetry. A standard approach to bridge dynamics with phenomenology is to consider the Markovian approximation of the former. In this paper we present a formulation in terms of {\it dressed} particles, which gives exact Markovian equations. We formulate dressed particles for Poincar\'e nonintegrable systems, through an invertible transformation operator \Lam introduced by Prigogine and collaborators. \Lam is obtained by an extension of the canonical (unitary) transformation operator $U$ that eliminates interactions for integrable systems. Our extension is based on the removal of divergences due to Poincar\'e resonances, which breaks time-symmetry. The unitarity of $U$ is extended to ``star-unitarity'' for \Lam. We show that \Lam-transformed variables have the same time evolution as stochastic variables obeying Langevin equations, and that \Lam-transformed distribution functions satisfy exact Fokker-Planck equations. The effects of Gaussian white noise are obtained by the non-distributive property of \Lam with respect to products of dynamical variables. Therefore our method leads to a direct link between dynamics of Poincar\'e nonintegrable systems, probability and stochasticity.Comment: 24 pages, no figures. Made more connections with other work. Clarified ideas on irreversibilit

Automated generation of program translation and verification tools using annotated grammars

Automatically generating program translators from source and target language specifications is a non-trivial problem. In this paper we focus on the problem of automating the process of building translators between operations languages, a family of DSLs used to program satellite operations procedures. We exploit their similarities to semi-automatically build transformation tools between these DSLs. The input to our method is a collection of annotated context-free grammars. To simplify the overall translation process even more, we also propose an intermediate representation common to all operations languages. Finally, we discuss how to enrich our annotated grammars model with more advanced semantic annotations to provide a verification system for the translation process. We validate our approach by semi-automatically deriving translators between some real world operations languages, using the prototype tool which we implemented for that purpose

Characterization of human mesothelin transcripts in ovarian and pancreatic cancer

BACKGROUND: Mesothelin is an attractive target for cancer immunotherapy due to its restricted expression in normal tissues and high level expression in several tumor types including ovarian and pancreatic adenocarcinomas. Three mesothelin transcript variants have been reported, but their relative expression in normal tissues and tumors has been poorly characterized. The goal of the present study was to clarify which mesothelin transcript variants are commonly expressed in human tumors. METHODS: Human genomic and EST nucleotide sequences in the public databases were used to evaluate sequences reported for the three mesothelin transcript variants in silico. Subsequently, RNA samples from normal ovary, ovarian and pancreatic carcinoma cell lines, and primary ovarian tumors were analyzed by reverse transcription-polymerase chain reaction (RT-PCR) and nucleotide sequencing to directly identify expressed transcripts. RESULTS: In silico comparisons of genomic DNA sequences with available EST sequences supported expression of mesothelin transcript variants 1 and 3, but there were no sequence matches for transcript variant 2. Newly-derived nucleotide sequences of RT-PCR products from tissues and cell lines corresponded to mesothelin transcript variant 1. Mesothelin transcript variant 2 was not detected. Transcript variant 3 was observed as a small percentage of total mesothelin amplification products from all studied cell lines and tissues. Fractionation of nuclear and cytoplasmic RNA indicated that variant 3 was present primarily in the nuclear fraction. Thus, mesothelin transcript variant 3 may represent incompletely processed hnRNA. CONCLUSION: Mesothelin transcript variant 1 represents the predominant mature mRNA species expressed by both normal and tumor cells. This conclusion should be important for future development of cancer immunotherapies, diagnostic tests, and gene microarray studies targeting mesothelin

The Long and Short of Nuclear Effective Field Theory Expansions

Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering data rather well suggests that failures of effective field theories for momenta above the pion mass can be due to short-range physics rather than the treatment of pion exchange. We discuss the implications this has for extending the applicability of effective field theories.Comment: 22 pages, 9 figures, references corrected, minor modification