@article{237,
abstract = {The Manin conjecture is established for Châtelet surfaces over Q aris-ing as minimal proper smooth models of the surface Y 2 + Z 2 = f(X) in A 3 Q, where f ∈ Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation.},
author = {de la Bretèche, Régis and Timothy Browning and Peyre, Emmanuel},
journal = {Annals of Mathematics},
number = {1},
pages = {297 -- 343},
publisher = {Princeton University Press},
title = {{On Manin's conjecture for a family of Châtelet surfaces}},
doi = {10.4007/annals.2012.175.1.8},
volume = {175},
year = {2012},
}
@article{238,
abstract = {For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z2 to congruences ax + by2 ≡ 0 mod q.},
author = {Baier, Stephan and Timothy Browning},
journal = {Functiones et Approximatio, Commentarii Mathematici},
number = {2},
pages = {267 -- 286},
publisher = {Adam Mickiewicz University Press},
title = {{Inhomogeneous quadratic congruences}},
doi = {10.7169/facm/2012.47.2.9},
volume = {47},
year = {2012},
}
@article{2394,
abstract = {We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δ μ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.},
author = {Freiji, Abraham and Hainzl, Christian and Robert Seiringer},
journal = {Journal of Mathematical Physics},
number = {1},
publisher = {American Institute of Physics},
title = {{The gap equation for spin-polarized fermions}},
doi = {10.1063/1.3670747},
volume = {53},
year = {2012},
}
@article{2395,
abstract = {We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. },
author = {Frank, Rupert L and Hainzl, Christian and Robert Seiringer and Solovej, Jan P},
journal = {Journal of the American Mathematical Society},
number = {3},
pages = {667 -- 713},
publisher = {American Mathematical Society},
title = {{Microscopic derivation of Ginzburg-Landau theory}},
doi = {10.1090/S0894-0347-2012-00735-8},
volume = {25},
year = {2012},
}
@article{2396,
abstract = {A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of -Δ and, with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range.},
author = {Landon, Benjamin and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {3},
pages = {237 -- 243},
publisher = {Springer},
title = {{The scattering length at positive temperature}},
doi = {10.1007/s11005-012-0566-5},
volume = {100},
year = {2012},
}
@article{2397,
abstract = {We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs.},
author = {Hainzl, Christian and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {2},
pages = {119 -- 138},
publisher = {Springer},
title = {{Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs}},
doi = {10.1007/s11005-011-0535-4},
volume = {100},
year = {2012},
}
@misc{2398,
abstract = {We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.},
author = {Jakšić, Vojkan and Ogata, Yoshiko and Pillet, Claude A and Robert Seiringer},
booktitle = {Reviews in Mathematical Physics},
number = {6},
publisher = {World Scientific Publishing},
title = {{Quantum hypothesis testing and non-equilibrium statistical mechanics}},
doi = {10.1142/S0129055X12300026},
volume = {24},
year = {2012},
}
@inbook{2399,
abstract = {Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures.
},
author = {Robert Seiringer},
booktitle = {Quantum Many Body Systems},
editor = {Rivasseau, Vincent and Robert Seiringer and Solovej, Jan P and Spencer, Thomas},
pages = {55 -- 92},
publisher = {Springer},
title = {{Cold quantum gases and bose einstein condensation}},
doi = {10.1007/978-3-642-29511-9_2},
volume = {2051},
year = {2012},
}
@article{240,
abstract = {We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior.},
author = {Timothy Browning and Valckenborgh, K Van},
journal = {Experimental Mathematics},
number = {2},
pages = {204 -- 211},
publisher = {Taylor & Francis},
title = {{Sums of three squareful numbers}},
doi = {10.1080/10586458.2011.605733},
volume = {21},
year = {2012},
}
@article{2400,
abstract = {If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2.},
author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer},
journal = {Communications in Mathematical Physics},
number = {2},
pages = {405 -- 424},
publisher = {Springer},
title = {{Binding of polarons and atoms at threshold}},
doi = {10.1007/s00220-012-1436-9},
volume = {313},
year = {2012},
}