Numerical ansatz for solving integro-differential equations with increasingly smooth memory kernels: spin-boson model and beyond

We present an efficient and stable numerical ansatz for solving a class of integro-differential equations. We define the class as integro-differential equations with increasingly smooth memory kernels. The resulting algorithm reduces the computational cost from the usual T^2 to T*C(T), where T is the total simulation time and C(T) is some function. For instance, C(T) is equal to lnT for polynomially decaying memory kernels. Due to the common occurrence of increasingly smooth memory kernels in physical, chemical, and biological systems, the algorithm can be applied in quite a wide variety of situations. We demonstrate the performance of the algorithm by examining two cases. First, we compare the algorithm to a typical numerical procedure for a simple integro-differential equation. Second, we solve the NIBA equations for the spin-boson model in real time.Comment: 19 pages, 6 figure

Educational commitment and social networking: The power of informal networks

The lack of an engaging pedagogy and the highly competitive atmosphere in introductory science courses tend to discourage students from pursuing science, technology, engineering, and mathematics (STEM) majors. Once in a STEM field, academic and social integration has been long thought to be important for students' persistence. Yet, it is rarely investigated. In particular, the relative impact of in-class and out-of-class interactions remains an open issue. Here, we demonstrate that, surprisingly, for students whose grades fall in the "middle of the pack," the out-of-class network is the most significant predictor of persistence. To do so, we use logistic regression combined with Akaike's information criterion to assess in- and out-of-class networks, grades, and other factors. For students with grades at the very top (and bottom), final grade, unsurprisingly, is the best predictor of persistence---these students are likely already committed (or simply restricted from continuing) so they persist (or drop out). For intermediate grades, though, only out-of-class closeness---a measure of one's immersion in the network---helps predict persistence. This does not negate the need for in-class ties. However, it suggests that, in this cohort, only students that get past the convenient in-class interactions and start forming strong bonds outside of class are or become committed to their studies. Since many students are lost through attrition, our results suggest practical routes for increasing students' persistence in STEM majors.Comment: 12 pages, 2 figures, 8 tables, 6 pages of Supplementary Material

Colloquium: Physical approaches to DNA sequencing and detection

With the continued improvement of sequencing technologies, the prospect of genome-based medicine is now at the forefront of scientific research. To realize this potential, however, a revolutionary sequencing method is needed for the cost-effective and rapid interrogation of individual genomes. This capability is likely to be provided by a physical approach to probing DNA at the single-nucleotide level. This is in sharp contrast to current techniques and instruments that probe (through chemical elongation, electrophoresis, and optical detection) length differences and terminating bases of strands of DNA. Several physical approaches to DNA detection have the potential to deliver fast and low-cost sequencing. Central to these approaches is the concept of nanochannels or nanopores, which allow for the spatial confinement of DNA molecules. In addition to their possible impact in medicine and biology, the methods offer ideal test beds to study open scientific issues and challenges in the relatively unexplored area at the interface between solids, liquids, and biomolecules at the nanometer length scale. This Colloquium emphasizes the physics behind these methods and ideas, critically describes their advantages and drawbacks, and discusses future research opportunities in the field

Breaking the entanglement barrier: Tensor network simulation of quantum transport

The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global dynamics elevates many particles into excited states, and can lead to macroscopic entanglement and the failure of tensor networks. Here, we show that for quantum transport -- one of the most important cases of this failure -- the fundamental issue is the canonical basis in which the scenario is cast: When particles flow through an interface, they scatter, generating a "bit" of entanglement between spatial regions with each event. The frequency basis naturally captures that -- in the long-time limit and in the absence of inelastic scattering -- particles tend to flow from a state with one frequency to a state of identical frequency. Recognizing this natural structure yields a striking -- potentially exponential in some cases -- increase in simulation efficiency, greatly extending the attainable spatial- and time-scales, and broadening the scope of tensor network simulation to hitherto inaccessible classes of non-equilibrium many-body problems.Comment: Published version; 6+9 pages; 4+4 figures; Added: an example of interacting reservoirs, further evidence on performance scaling, and extended discussion of the numerical detail

Electronic signature of DNA nucleotides via transverse transport

We report theoretical studies of charge transport in single-stranded DNA in the direction perpendicular to the backbone axis. We find that, if the electrodes which sandwich the DNA have the appropriate spatial width, each nucleotide carries a unique signature due to the different electronic and chemical structure of the four bases. This signature is independent of the nearest-neighbor nucleotides. Furthermore, except for the nucleotides with Guanine and Cytosine bases, we find that the difference in conductance of the nucleotides is large for most orientations of the bases with respect to the electrodes. By exploiting these differences it may be possible to sequence single-stranded DNA by scanning its length with conducting probes.Comment: 4 pages, 5 figure