@inproceedings{2331,
abstract = {We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of Ref. 9 as well our recent joint work with Hamza and Solovej and with Frank and Naboko, respectively. In addition, we mention some related new results.},
author = {Hainzl, Christian and Robert Seiringer},
pages = {117 -- 136},
publisher = {World Scientific Publishing},
title = {{ Spectral properties of the BCS gap equation of superfluidity}},
doi = {10.1142/9789812832382_0009},
year = {2008},
}
@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},
}
@inproceedings{2702,
abstract = {We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the role of Feynman graph expansions and of renormalization.
},
author = {László Erdös and Salmhofer, Manfred and Yau, Horng-Tzer},
pages = {167 -- 182},
publisher = {World Scientific Publishing},
title = {{Feynman graphs and renormalization in quantum diffusion}},
doi = {10.1142/9789812833556_0011},
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{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},
}
@article{2120,
abstract = {We consider the linear stochastic Cauchy problem dX (t) =AX (t) dt +B dWH (t), t≥ 0, where A generates a C0-semigroup on a Banach space E, WH is a cylindrical Brownian motion over a Hilbert space H, and B: H → E is a bounded operator. Assuming the existence of a unique minimal invariant measure μ∞, let Lp denote the realization of the Ornstein-Uhlenbeck operator associated with this problem in Lp (E, μ∞). Under suitable assumptions concerning the invariance of the range of B under the semigroup generated by A, we prove the following domain inclusions, valid for 1 < p ≤ 2: Image omitted. Here WHk, p (E, μinfin; denotes the kth order Sobolev space of functions with Fréchet derivatives up to order k in the direction of H. No symmetry assumptions are made on L p.},
author = {Jan Maas and van Neerven, Jan M},
journal = {Infinite Dimensional Analysis, Quantum Probability and Related Topics},
number = {4},
pages = {603 -- 626},
publisher = {World Scientific Publishing},
title = {{On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces}},
doi = {10.1142/S0219025708003245},
volume = {11},
year = {2008},
}
@article{2121,
abstract = {Let H be a separable real Hubert space and let double struck F sign = (ℱt)t∈[0,T] be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T] on a probability space (Ω, ℱ ℙ). We prove that if E is a UMD Banach space, 1 ≤ p < ∞, and F ∈ double struck D sign1,p(Ω E) is ℱT-measurable, then F = double struck E sign(F) + ∫0T Pdouble struck F sign(DF) dW H, where D is the Malliavin derivative of F and P double struck F sign is the projection onto the F-adapted elements in a suitable Banach space of Lp-stochastically integrable ℒ(H, E)-valued processes.},
author = {van Neerven, Jan M and Jan Maas},
journal = {Electronic Communications in Probability},
pages = {151 -- 164},
publisher = {Institute of Mathematical Statistics},
title = {{A Clark-Ocone formula in UMD Banach spaces}},
volume = {13},
year = {2008},
}
@article{2146,
abstract = {We present an analytic model of thermal state-to-state rotationally inelastic collisions of polar molecules in electric fields. The model is based on the Fraunhofer scattering of matter waves and requires Legendre moments characterizing the “shape” of the target in the body-fixed frame as its input. The electric field orients the target in the space-fixed frame and thereby effects a striking alteration of the dynamical observables: both the phase and amplitude of the oscillations in the partial differential cross sections undergo characteristic field-dependent changes that transgress into the partial integral cross sections. As the cross sections can be evaluated for a field applied parallel or perpendicular to the relative velocity, the model also offers predictions about steric asymmetry. We exemplify the field-dependent quantum collision dynamics with the behavior of the Ne–OCS(Σ1) and Ar–NO(Π2) systems. A comparison with the close-coupling calculations available for the latter system [Chem. Phys. Lett.313, 491 (1999)] demonstrates the model’s ability to qualitatively explain the field dependence of all the scattering features observed.},
author = {Mikhail Lemeshko and Friedrich, Břetislav},
journal = {Journal of Chemical Physics},
number = {2},
publisher = {American Institute of Physics},
title = {{An analytic model of rotationally inelastic collisions of polar molecules in electric fields}},
doi = {10.1063/1.2948392},
volume = {129},
year = {2008},
}
@article{6146,
abstract = {Homeostasis of internal carbon dioxide (CO2) and oxygen (O2) levels is fundamental to all animals. Here we examine the CO2 response of the nematode Caenorhabditis elegans. This species inhabits rotting material, which typically has a broad CO2 concentration range. We show that well fed C. elegans avoid CO2 levels above 0.5%. Animals can respond to both absolute CO2 concentrations and changes in CO2 levels within seconds. Responses to CO2 do not reflect avoidance of acid pH but appear to define a new sensory response. Sensation of CO2 is promoted by the cGMP-gated ion channel subunits TAX-2 and TAX-4, but other pathways are also important. Robust CO2 avoidance in well fed animals requires inhibition of the DAF-16 forkhead transcription factor by the insulin-like receptor DAF-2. Starvation, which activates DAF-16, strongly suppresses CO2 avoidance. Exposure to hypoxia (<1% O2) also suppresses CO2 avoidance via activation of the hypoxia-inducible transcription factor HIF-1. The npr-1 215V allele of the naturally polymorphic neuropeptide receptor npr-1, besides inhibiting avoidance of high ambient O2 in feeding C. elegans, also promotes avoidance of high CO2. C. elegans integrates competing O2 and CO2 sensory inputs so that one response dominates. Food and allelic variation at NPR-1 regulate which response prevails. Our results suggest that multiple sensory inputs are coordinated by C. elegans to generate different coherent foraging strategies.},
author = {Bretscher, A. J. and Busch, K. E. and de Bono, Mario},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences},
number = {23},
pages = {8044--8049},
publisher = {Proceedings of the National Academy of Sciences},
title = {{A carbon dioxide avoidance behavior is integrated with responses to ambient oxygen and food in Caenorhabditis elegans}},
doi = {10.1073/pnas.0707607105},
volume = {105},
year = {2008},
}
@article{1460,
abstract = {We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of Mn: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2.},
author = {Tamas Hausel and Rodríguez Villegas, Fernando},
journal = {Inventiones Mathematicae},
number = {3},
pages = {555 -- 624},
publisher = {Springer},
title = {{Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz}},
doi = {10.1007/s00222-008-0142-x},
volume = {174},
year = {2008},
}
@article{1036,
abstract = {We report on the control of interaction-induced dephasing of Bloch oscillations for an atomic Bose-Einstein condensate in an optical lattice. We quantify the dephasing in terms of the width of the quasimomentum distribution and measure its dependence on time for different interaction strengths which we control by means of a Feshbach resonance. For minimal interaction, the dephasing time is increased from a few to more than 20 thousand Bloch oscillation periods, allowing us to realize a BEC-based atom interferometer in the noninteracting limit.},
author = {Gustavsson, Mattias and Haller, Elmar and Mark, Manfred and Danzl, Johann G and Rojas Kopeinig, Gabriel and Nägerl, Hanns},
journal = {Physical Review Letters},
number = {8},
publisher = {American Physical Society},
title = {{Control of interaction-induced dephasing of bloch oscillations}},
doi = {10.1103/PhysRevLett.100.080404},
volume = {100},
year = {2008},
}