Electron transport through quantum wires and point contacts

We have studied quantum wires using the Green's function technique and the density-functional theory, calculating the electronic structure and the conductance. All the numerics are implemented using the finite-element method with a high-order polynomial basis. For short wires, i.e. quantum point contacts, the zero-bias conductance shows, as a function of the gate voltage and at a finite temperature, a plateau at around 0.7G_0. (G_0 = 2e^2/h is the quantum conductance). The behavior, which is caused in our mean-field model by spontaneous spin polarization in the constriction, is reminiscent of the so-called 0.7-anomaly observed in experiments. In our model the temperature and the wire length affect the conductance-gate voltage curves in the same way as in the measured data.Comment: 8 page

Scalable Similarity Search for Molecular Descriptors

Similarity search over chemical compound databases is a fundamental task in the discovery and design of novel drug-like molecules. Such databases often encode molecules as non-negative integer vectors, called molecular descriptors, which represent rich information on various molecular properties. While there exist efficient indexing structures for searching databases of binary vectors, solutions for more general integer vectors are in their infancy. In this paper we present a time- and space- efficient index for the problem that we call the succinct intervals-splitting tree algorithm for molecular descriptors (SITAd). Our approach extends efficient methods for binary-vector databases, and uses ideas from succinct data structures. Our experiments, on a large database of over 40 million compounds, show SITAd significantly outperforms alternative approaches in practice.Comment: To be appeared in the Proceedings of SISAP'1

Fractional differentiability for solutions of nonlinear elliptic equations

We study nonlinear elliptic equations in divergence form $${\operatorname{div}}{\mathcal A}(x,Du)={\operatorname{div}}G.$$ When ${\mathcal A}$ has linear growth in $Du$, and assuming that $x\mapsto{\mathcal A}(x,\xi)$ enjoys $B^\alpha_{\frac{n}\alpha, q}$ smoothness, local well-posedness is found in $B^\alpha_{p,q}$ for certain values of $p\in[2,\frac{n}{\alpha})$ and $q\in[1,\infty]$. In the particular case ${\mathcal A}(x,\xi)=A(x)\xi$, $G=0$ and $A\in B^\alpha_{\frac{n}\alpha,q}$, $1\leq q\leq\infty$, we obtain $Du\in B^\alpha_{p,q}$ for each $p<\frac{n}\alpha$. Our main tool in the proof is a more general result, that holds also if ${\mathcal A}$ has growth $s-1$ in $Du$, $2\leq s\leq n$, and asserts local well-posedness in $L^q$ for each $q>s$, provided that $x\mapsto{\mathcal A}(x,\xi)$ satisfies a locally uniform $VMO$ condition

Quantum Interaction ϕ44\phi^4_4: the Construction of Quantum Field defined as a Bilinear Form

We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation $\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can be expanded over Wick polynomials of the free $in$-field, and where $:\!\phi^3(t,{\bf x})\!:$ is defined as the normal ordered product with respect to the free $in$-field. The constructed solution is correctly defined as a bilinear form on $D_{\theta}\times D_{\theta}$, where $D_{\theta}$ is a dense linear subspace in the Fock space of the free $in$-field. On $D_{\theta}\times D_{\theta}$ the diagonal Wick symbol of this bilinear form satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe

High-pressure, low-abundance water in bipolar outflows. Results from a Herschel-WISH survey

(Abridged) We present a survey of the water emission in a sample of more than 20 outflows from low mass young stellar objects with the goal of characterizing the physical and chemical conditions of the emitting gas. We have used the HIFI and PACS instruments on board the Herschel Space Observatory to observe the two fundamental lines of ortho-water at 557 and 1670 GHz. These observations were part of the "Water In Star-forming regions with Herschel" (WISH) key program, and have been complemented with CO and H2 data. We find that the emission from water has a different spatial and velocity distribution from that of the J=1-0 and 2-1 transitions of CO, but it has a similar spatial distribution to H2, and its intensity follows the H2 intensity derived from IRAC images. This suggests that water traces the outflow gas at hundreds of kelvins responsible for the H2 emission, and not the component at tens of kelvins typical of low-J CO emission. A warm origin of the water emission is confirmed by a remarkable correlation between the intensities of the 557 and 1670 GHz lines, which also indicates the emitting gas has a narrow range of excitations. A non-LTE radiative transfer analysis shows that while there is some ambiguity on the exact combination of density and temperature values, the gas thermal pressure nT is constrained within less than a factor of 2. The typical nT over the sample is 4 10^{9} cm^{-3}K, which represents an increase of 10^4 with respect to the ambient value. The data also constrain within a factor of 2 the water column density. When this quantity is combined with H2 column densities, the typical water abundance is only 3 10^{-7}, with an uncertainty of a factor of 3. Our data challenge current C-shock models of water production due to a combination of wing-line profiles, high gas compressions, and low abundances.Comment: 21 pages, 13 figures. Accepted for publication in A&

Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

APEX-CHAMP+ high-J CO observations of low-mass young stellar objects: II. Distribution and origin of warm molecular gas

The origin and heating mechanisms of warm (50<T<200 K) molecular gas in low-mass young stellar objects (YSOs) are strongly debated. Both passive heating of the inner collapsing envelope by the protostellar luminosity as well as active heating by shocks and by UV associated with the outflows or accretion have been proposed. We aim to characterize the warm gas within protosteller objects, and disentangle contributions from the (inner) envelope, bipolar outflows and the quiescent cloud. High-J CO maps (12CO J=6--5 and 7--6) of the immediate surroundings (up to 10,000 AU) of eight low-mass YSOs are obtained with the CHAMP+ 650/850 GHz array receiver mounted on the APEX telescope. In addition, isotopologue observations of the 13CO J=6--5 transition and [C I] 3P_2-3P_1 line were taken. Strong quiescent narrow-line 12CO 6--5 and 7--6 emission is seen toward all protostars. In the case of HH~46 and Ced 110 IRS 4, the on-source emission originates in material heated by UV photons scattered in the outflow cavity and not just by passive heating in the inner envelope. Warm quiescent gas is also present along the outflows, heated by UV photons from shocks. Shock-heated warm gas is only detected for Class 0 flows and the more massive Class I sources such as HH~46. Outflow temperatures, estimated from the CO 6--5 and 3--2 line wings, are ~100 K, close to model predictions, with the exception of the L~1551 IRS 5 and IRAS 12496-7650, for which temperatures <50 K are found. APEX-CHAMP+ is uniquely suited to directly probe a protostar's feedback on its accreting envelope gas in terms of heating, photodissociation, and outflow dispersal by mapping 1'x1' regions in high-J CO and [C I] lines.Comment: 18 pages, accepted by A&A, A version with the figures in higher quality can be found on my website: http://www.cfa.harvard.edu/~tvankemp

APEX-CHAMP+ high-J CO observations of low-mass young stellar objects: III. NGC 1333 IRAS 4A/4B envelope, outflow and UV heating

NGC 1333 IRAS 4A and IRAS 4B sources are among the best studied Stage 0 low-mass protostars which are driving prominent bipolar outflows. Most studies have so far concentrated on the colder parts (T<30K) of these regions. The aim is to characterize the warmer parts of the protostellar envelope in order to quantify the feedback of the protostars on their surroundings in terms of shocks, UV heating, photodissociation and outflow dispersal. Fully sampled large scale maps of the region were obtained; APEX-CHAMP+ was used for 12CO 6-5, 13CO 6-5 and [CI] 2-1, and JCMT-HARP-B for 12CO 3-2 emissions. Complementary Herschel-HIFI and ground-based lines of CO and its isotopologs, from 1-0 upto 10-9 (Eu/k 300K), are collected at the source positions. Radiative-transfer models of the dust and lines are used to determine temperatures and masses of the outflowing and UV-heated gas and infer the CO abundance structure. Broad CO emission line profiles trace entrained shocked gas along the outflow walls, with typical temperatures of ~100K. At other positions surrounding the outflow and the protostar, the 6-5 line profiles are narrow indicating UV excitation. The narrow 13CO 6-5 data directly reveal the UV heated gas distribution for the first time. The amount of UV-heated and outflowing gas are found to be comparable from the 12CO and 13CO 6-5 maps, implying that UV photons can affect the gas as much as the outflows. Weak [CI] emission throughout the region indicates a lack of CO dissociating photons. Modeling of the C18O lines indicates the necessity of a "drop" abundance profile throughout the envelope where the CO freezes out and is reloaded back into the gas phase, thus providing quantitative evidence for the CO ice evaporation zone around the protostars. The inner abundances are less than the canonical value of CO/H_2=2.7x10^-4, indicating some processing of CO into other species on the grains.Comment: 20 pages, 22 figures, Accepted by A&

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.