Intermediate coherent-incoherent charge transport: DNA as a case study

We study an intermediate quantum coherent-incoherent charge transport mechanism in metal-molecule-metal junctions using B\"uttiker's probe technique. This tool allows us to include incoherent effects in a controlled manner, and thus to study situations in which partial decoherence affects charge transfer dynamics. Motivated by recent experiments on intermediate coherent-incoherent charge conduction in DNA molecules [L. Xiang {\it et al.}, Nature Chem. 7, 221-226 (2015)], we focus on two representative structures: alternating (GC)$_n$ and stacked G$_n$C$_n$ sequences; the latter structure is argued to support charge delocalization within G segments, and thus an intermediate coherent-incoherent conduction. We begin our analysis with a highly simplified 1-dimensional tight-binding model, while introducing environmental effects through B\"uttiker's probes. This minimal model allows us to gain fundamental understanding of transport mechanisms and derive analytic results for molecular resistance in different limits. We then use a more detailed ladder-model Hamiltonian to represent double-stranded DNA structures---with environmental effects captured by B\"uttiker's probes. We find that hopping conduction dominates in alternating sequences, while in stacked sequences charge delocalization (visualized directly through the electronic density matrix) supports significant resonant-ballistic charge dynamics reflected by an even-odd effect and a weak distance dependence for resistance. Our analysis illustrates that lessons learned from minimal models are helpful for interpreting charge dynamics in DNA.Comment: 16 pages, 14 figure

Sequences of globally regular and black hole solutions in SU(4) Einstein-Yang-Mills theory

SU(4) Einstein-Yang-Mills theory possesses sequences of static spherically symmetric globally regular and black hole solutions. Considering solutions with a purely magnetic gauge field, based on the 4-dimensional embedding of $su(2)$ in $su(4)$, these solutions are labelled by the node numbers $(n_1,n_2,n_3)$ of the three gauge field functions $u_1$, $u_2$ and $u_3$. We classify the various types of solutions in sequences and determine their limiting solutions. The limiting solutions of the sequences of neutral solutions carry charge, and the limiting solutions of the sequences of charged solutions carry higher charge. For sequences of black hole solutions with node structure $(n,j,n)$ and $(n,n,n)$, several distinct branches of solutions exist up to critical values of the horizon radius. We determine the critical behaviour for these sequences of solutions. We also consider SU(4) Einstein-Yang-Mills-dilaton theory and show that these sequences of solutions are analogous in most respects to the corresponding SU(4) Einstein-Yang-Mills sequences of solutions.Comment: 40 pages, 5 tables, 19 Postscript figures, use revtex.st

Long range correlations in DNA : scaling properties and charge transfer efficiency

We address the relation between long range correlations and charge transfer efficiency in aperiodic artificial or genomic DNA sequences. Coherent charge transfer through the HOMO states of the guanine nucleotide is studied using the transmission approach, and focus is made on how the sequence-dependent backscattering profile can be inferred from correlations between base pairs.Comment: Submitted to Phys. Rev. Let

An Electrostatics Problem on the Sphere Arising from a Nearby Point Charge

For a positively charged insulated d-dimensional sphere we investigate how the distribution of this charge is affected by proximity to a nearby positive or negative point charge when the system is governed by a Riesz s-potential 1/r^s, s>0, where r denotes Euclidean distance between point charges. Of particular interest are those distances from the point charge to the sphere for which the equilibrium charge distribution is no longer supported on the whole of the sphere (i.e. spherical caps of negative charge appear). Arising from this problem attributed to A. A. Gonchar are sequences of polynomials of a complex variable that have some fascinating properties regarding their zeros.Comment: 44 pages, 9 figure

Topological charge on the lattice: a field theoretical view of the geometrical approach

We construct sequences of ``field theoretical'' (analytical) lattice topological charge density operators which formally approach geometrical definitions in 2-d $CP^{N-1}$ models and 4-d $SU(N)$ Yang Mills theories. The analysis of these sequences of operators suggests a new way of looking at the geometrical method, showing that geometrical charges can be interpreted as limits of sequences of field theoretical (analytical) operators. In perturbation theory renormalization effects formally tend to vanish along such sequences. But, since the perturbative expansion is asymptotic, this does not necessarily lead to well behaved geometrical limits. It indeed leaves open the possibility that non-perturbative renormalizations survive.Comment: 14 pages, revte

Charge Pattern Matching as a "Fuzzy" Mode of Molecular Recognition for the Functional Phase Separations of Intrinsically Disordered Proteins

Biologically functional liquid-liquid phase separation of intrinsically disordered proteins (IDPs) is driven by interactions encoded by their amino acid sequences. Little is currently known about the molecular recognition mechanisms for distributing different IDP sequences into various cellular membraneless compartments. Pertinent physics was addressed recently by applying random-phase-approximation (RPA) polymer theory to electrostatics, which is a major energetic component governing IDP phase properties. RPA accounts for charge patterns and thus has advantages over Flory-Huggins and Overbeek-Voorn mean-field theories. To make progress toward deciphering the phase behaviors of multiple IDP sequences, the RPA formulation for one IDP species plus solvent is hereby extended to treat polyampholyte solutions containing two IDP species. The new formulation generally allows for binary coexistence of two phases, each containing a different set of volume fractions $(\phi_1,\phi_2)$ for the two different IDP sequences. The asymmetry between the two predicted coexisting phases with regard to their $\phi_1/\phi_2$ ratios for the two sequences increases with increasing mismatch between their charge patterns. This finding points to a multivalent, stochastic, "fuzzy" mode of molecular recognition that helps populate various IDP sequences differentially into separate phase compartments. An intuitive illustration of this trend is provided by Flory-Huggins models, whereby a hypothetical case of ternary coexistence is also explored. Augmentations of the present RPA theory with a relative permittivity $\epsilon_{\rm r}(\phi)$ that depends on IDP volume fraction $\phi=\phi_1+\phi_2$ lead to higher propensities to phase separate, in line with the case with one IDP species we studied previously. ...Comment: Accepted for publication in New Journal of Physics (IOP) for the "Focus On Phase Transitions in Cells" Special Issue; 37 pages, 11 figure

Latched Detection of Excited States in an Isolated Double Quantum Dot

Pulsed electrostatic gating combined with capacitive charge sensing is used to perform excited state spectroscopy of an electrically isolated double-quantum-dot system. The tunneling rate of a single charge moving between the two dots is affected by the alignment of quantized energy levels; measured tunneling probabilities thereby reveal spectral features. Two pulse sequences are investigated, one of which, termed latched detection, allows measurement of a single tunneling event without repetition. Both provide excited-state spectroscopy without electrical contact to the double-dot system.Comment: related papers available at http://marcuslab.harvard.ed