@inproceedings{2332, abstract = {We present a rigorous proof of the appearance of quantized vortices in dilute trapped Bose gases with repulsive two-body interactions subject to rotation, which was obtained recently in joint work with Elliott Lieb.14 Starting from the many-body Schrödinger equation, we show that the ground state of such gases is, in a suitable limit, well described by the nonlinear Gross-Pitaevskii equation. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.}, author = {Robert Seiringer}, pages = {241 -- 254}, publisher = {World Scientific Publishing}, title = {{Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases}}, doi = {10.1142/9789812832382_0017}, year = {2008}, } @article{2374, abstract = {A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.}, author = {Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {595 -- 636}, publisher = {Springer}, title = {{Free energy of a dilute Bose gas: Lower bound}}, doi = {10.1007/s00220-008-0428-2}, volume = {279}, year = {2008}, } @article{2376, abstract = {We derive upper and lower bounds on the critical temperature Tc and the energy gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions interacting via a local two-body interaction potential λV(x). At weak coupling λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ) and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a universal constant, independent of both V(x) and μ. Our analysis is valid for any μ; for small μ, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x).}, author = {Hainzl, Christian and Robert Seiringer}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {18}, publisher = {American Physical Society}, title = {{Critical temperature and energy gap for the BCS equation}}, doi = {10.1103/PhysRevB.77.184517}, volume = {77}, year = {2008}, } @article{2377, abstract = {We prove that the critical temperature for the BCS gap equation is given by T c = μ ( 8\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting Euler's constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.}, author = {Hainzl, Christian and Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {2-3}, pages = {99 -- 107}, publisher = {Springer}, title = {{The BCS critical temperature for potentials with negative scattering length}}, doi = {10.1007/s11005-008-0242-y}, volume = {84}, year = {2008}, } @article{2378, abstract = {We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.}, author = {Robert Seiringer and Yin, Jun}, journal = {Journal of Statistical Physics}, number = {6}, pages = {1139 -- 1154}, publisher = {Springer}, title = {{Ground state energy of the low density hubbard model}}, doi = {10.1007/s10955-008-9527-x}, volume = {131}, year = {2008}, } @article{2379, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Journal of the American Mathematical Society}, number = {4}, pages = {925 -- 950}, publisher = {American Mathematical Society}, title = {{Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators}}, doi = {10.1090/S0894-0347-07-00582-6}, volume = {21}, year = {2008}, } @article{2380, abstract = {The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.}, author = {Hainzl, Christian and Hamza, Eman and Robert Seiringer and Solovej, Jan P}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {349 -- 367}, publisher = {Springer}, title = {{The BCS functional for general pair interactions}}, doi = {10.1007/s00220-008-0489-2}, volume = {281}, year = {2008}, } @article{2381, abstract = {We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.}, author = {Frank, Rupert L and Robert Seiringer}, journal = {Journal of Functional Analysis}, number = {12}, pages = {3407 -- 3430}, publisher = {Academic Press}, title = {{Non-linear ground state representations and sharp Hardy inequalities}}, doi = {10.1016/j.jfa.2008.05.015}, volume = {255}, year = {2008}, } @article{2382, abstract = {We show that the Lieb-Liniger model for one-dimensional bosons with repulsive δ-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived. Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼ r -2 above the ground state energy.}, author = {Robert Seiringer and Yin, Jun}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {459 -- 479}, publisher = {Springer}, title = {{The Lieb-Liniger model as a limit of dilute bosons in three dimensions}}, doi = {10.1007/s00220-008-0521-6}, volume = {284}, year = {2008}, } @article{2383, abstract = {We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.}, author = {Hainzl, Christian and Lewin, Mathieu and Robert Seiringer}, journal = {Reviews in Mathematical Physics}, number = {10}, pages = {1283 -- 1307}, publisher = {World Scientific Publishing}, title = {{A nonlinear model for relativistic electrons at positive temperature}}, doi = {10.1142/S0129055X08003547}, volume = {20}, year = {2008}, } @inbook{2415, author = {Uli Wagner}, booktitle = {Surveys on Discrete and Computational Geometry: Twenty Years Later}, editor = {Goodman, Jacob E and Pach, János and Pollack, Richard}, pages = {443 -- 514}, publisher = {American Mathematical Society}, title = {{k-Sets and k-facets}}, doi = {10.1090/conm/453}, volume = {453}, year = {2008}, } @inproceedings{2432, abstract = {We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.}, author = {Smorodinsky, Shakhar and Sulovský, Marek and Uli Wagner}, pages = {363 -- 373}, publisher = {Springer}, title = {{On center regions and balls containing many points}}, doi = {10.1007/978-3-540-69733-6_36}, volume = {5092}, year = {2008}, } @article{2497, abstract = {Cyclic nucleotide phosphodiesterase 10A (PDE10A) is a member of phosphodiesterase families that degrade cAMP and/or cGMP in distinct intracellular sites. PDE10A has a dual activity on hydrolysis of both cAMP and cGMP, and is prominently expressed in the striatum and the testis. Previous studies suggested that PDE10A is involved in regulation of locomotor activity and potentially related to psychosis, but concrete physiological roles of PDE10A remains elusive yet. In this study, we genetically inactivated PDE10A2, a prominent isoform of PDE10A in the brain, in mice, and demonstrate that PDE10A2 deficiency results in increased social interaction without any major influence on different other behaviors, along with increased levels of striatal cAMP. We also demonstrate that PDE10A2 is selectively distributed in medium spiny neurons, but not interneurons, of the striatal complex. Thus, our results establish a physiological role for PDE10A2 in regulating cAMP pathway and social interaction, and suggest that cAMP signaling cascade in striatal medium spiny neurons might be involved in regulating social interaction behavior in mice.}, author = {Sano, Hiromi and Nagai, Yumiko and Miyakawa, Tsuyoshi and Ryuichi Shigemoto and Yokoi, Mineto}, journal = {Journal of Neurochemistry}, number = {2}, pages = {546 -- 556}, publisher = {Wiley-Blackwell}, title = {{Increased social interaction in mice deficient of the striatal medium spiny neuron-specific phosphodiesterase 10A2}}, doi = {10.1111/j.1471-4159.2007.05152.x}, volume = {105}, year = {2008}, } @article{1717, abstract = {Two key processes are in the basis of morphogenesis: the spatial allocation of cell types in fields of naïve cells and the regulation of growth. Both are controlled by morphogens, which activate target genes in the growing tissue in a concentration-dependent manner. Thus the morphogen model is an intrinsically quantitative concept. However, quantitative studies were performed only in recent years on two morphogens: Bicoid and Decapentaplegic. This review covers quantitative aspects of the formation and precision of the Decapentaplegic morphogen gradient. The morphogen gradient concept is transitioning from a soft definition to a precise idea of what the gradient could really do.}, author = {Anna Kicheva and González-Gaitán, Marcos A}, journal = {Current Opinion in Cell Biology}, number = {2}, pages = {137 -- 143}, publisher = {Elsevier}, title = {{The Decapentaplegic morphogen gradient a precise definition}}, doi = {10.1016/j.ceb.2008.01.008}, volume = {20}, year = {2008}, } @article{1719, abstract = {We study the mechanics of tissue growth via cell division and cell death (apoptosis). The rearrangements of cells can on large scales and times be captured by a continuum theory which describes the tissue as an effective viscous material with active stresses generated by cell division. We study the effects of anisotropies of cell division on cell rearrangements and show that average cellular trajectories exhibit anisotropic scaling behaviors. If cell division and apoptosis balance, there is no net growth, but for anisotropic cell division the tissue undergoes spontaneous shear deformations. Our description is relevant for the study of developing tissues such as the imaginal disks of the fruit fly Drosophila melanogaster, which grow anisotropically.}, author = {Bittig, Thomas and Wartlick, Ortrud and Anna Kicheva and González-Gaitárr, Marcos and Julicher, Frank}, journal = {New Journal of Physics}, publisher = {IOP Publishing Ltd.}, title = {{Dynamics of anisotropic tissue growth}}, doi = {10.1088/1367-2630/10/6/063001}, volume = {10}, year = {2008}, } @article{1749, abstract = {Scanning probe microscopy; Semiconductor quantum dots; Composition gradients; Composition profiles; Nanotomography; Single quantum dots; Strained sige/si; Three-dimensional (3D); Wet-chemical etchings; X-ray scattering measurements; quantum dot; methodology; nanotechnology; optical tomography; scanning probe microscopy; three dimensional imaging; Imaging, Three-Dimensional; Materials Testing; Microscopy, Scanning Probe; Nanotechnology; Quantum Dots; Tomography,}, author = {Rastelli, Armando and Stoffel, Mathieu and Malachias, Ângelo S and Merdzhanova, Tsvetelina and Georgios Katsaros and Kern, Klaus and Metzger, Till H and Schmidt, Oliver G}, journal = {Nano Letters}, number = {5}, pages = {1404 -- 1409}, publisher = {American Chemical Society}, title = {{Three-dimensional composition profiles of single quantum dots determined by scanning-probe-microscopy-based nanotomography}}, doi = {10.1021/nl080290y}, volume = {8}, year = {2008}, } @article{1751, abstract = {When strained Stranski-Krastanow islands are used as "self-assembled quantum dots," a key goal is to control the island position. Here we show that nanoscale grooves can control the nucleation of epitaxial Ge islands on Si(001), and can drive lateral motion of existing islands onto the grooves, even when the grooves are very narrow and shallow compared to the islands. A position centered on the groove minimizes energy. We use as prototype grooves the trenches which form naturally around islands. During coarsening, the shrinking islands move laterally to sit directly astride that trench. In subsequent growth, we demonstrate that islands nucleate on the "empty trenches" which remain on the surface after complete dissolution of the original islands.}, author = {Georgios Katsaros and Tersoff, Jerry and Stoffel, Mathieu and Rastelli, Armando and Acosta-Diaz, P and Kar, Gouranga S and Costantini, Giovanni and Schmidt, Oliver G and Kern, Klaus}, journal = {Physical Review Letters}, number = {9}, publisher = {American Physical Society}, title = {{Positioning of strained islands by interaction with surface nanogrooves}}, doi = {10.1103/PhysRevLett.101.096103}, volume = {101}, year = {2008}, } @article{1763, abstract = {The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting and superconducting systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter-light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication.}, author = {Johannes Fink and Göppl, M and Baur, Matthias P and Bianchetti, R and Leek, Peter J and Blais, Alexandre and Wallraff, Andreas}, journal = {Nature}, number = {7202}, pages = {315 -- 318}, publisher = {Nature Publishing Group}, title = {{Climbing the Jaynes-Cummings ladder and observing its √n nonlinearity in a cavity QED system}}, doi = {10.1038/nature07112}, volume = {454}, year = {2008}, } @article{1764, abstract = {Quantum theory predicts that empty space is not truly empty. Even in the absence of any particles or radiation, in pure vacuum, virtual particles are constantly created and annihilated. In an electromagnetic field, the presence of virtual photons manifests itself as a small renormalization of the energy of a quantum system, known as the Lamb shift. We present an experimental observation of the Lamb shift in a solid-state system. The strong dispersive coupling of a superconducting electronic circuit acting as a quantum bit (qubit) to the vacuum field in a transmission-line resonator leads to measurable Lamb shifts of up to 1.4% of the qubit transition frequency. The qubit is also observed to couple more strongly to the vacuum field than to a single photon inside the cavity, an effect that is explained by taking into account the limited anharmonicity of the higher excited qubit states.}, author = {Fragner, A and Göppl, M and Johannes Fink and Baur, Matthias P and Bianchetti, R and Leek, Peter J and Blais, Alexandre and Wallraff, Andreas}, journal = {Science}, number = {5906}, pages = {1357 -- 1360}, publisher = {American Association for the Advancement of Science}, title = {{Resolving vacuum fluctuations in an electrical circuit by measuring the lamb shift}}, doi = {10.1126/science.1164482}, volume = {322}, year = {2008}, } @article{1765, abstract = {High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.}, author = {Göppl, M and Fragner, A and Baur, Matthias P and Bianchetti, R and Filipp, Stefan and Johannes Fink and Leek, Peter J and Puebla, G and Steffen, L. Kraig and Wallraff, Andreas}, journal = {Journal of Applied Physics}, number = {11}, publisher = {American Institute of Physics}, title = {{Coplanar waveguide resonators for circuit quantum electrodynamics}}, doi = {10.1063/1.3010859}, volume = {104}, year = {2008}, }