TY - JOUR
AB - 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.
AU - de la Bretèche, Régis
AU - Timothy Browning
AU - Peyre, Emmanuel
ID - 237
IS - 1
JF - Annals of Mathematics
TI - On Manin's conjecture for a family of Châtelet surfaces
VL - 175
ER -
TY - JOUR
AB - For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z2 to congruences ax + by2 ≡ 0 mod q.
AU - Baier, Stephan
AU - Timothy Browning
ID - 238
IS - 2
JF - Functiones et Approximatio, Commentarii Mathematici
TI - Inhomogeneous quadratic congruences
VL - 47
ER -
TY - JOUR
AB - 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.
AU - Freiji, Abraham
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2394
IS - 1
JF - Journal of Mathematical Physics
TI - The gap equation for spin-polarized fermions
VL - 53
ER -
TY - JOUR
AB - 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.
AU - Frank, Rupert L
AU - Hainzl, Christian
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2395
IS - 3
JF - Journal of the American Mathematical Society
TI - Microscopic derivation of Ginzburg-Landau theory
VL - 25
ER -
TY - JOUR
AB - 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.
AU - Landon, Benjamin
AU - Robert Seiringer
ID - 2396
IS - 3
JF - Letters in Mathematical Physics
TI - The scattering length at positive temperature
VL - 100
ER -
TY - JOUR
AB - 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.
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2397
IS - 2
JF - Letters in Mathematical Physics
TI - Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs
VL - 100
ER -
TY - GEN
AB - 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.
AU - Jakšić, Vojkan
AU - Ogata, Yoshiko
AU - Pillet, Claude A
AU - Robert Seiringer
ID - 2398
IS - 6
T2 - Reviews in Mathematical Physics
TI - Quantum hypothesis testing and non-equilibrium statistical mechanics
VL - 24
ER -
TY - CHAP
AB - 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.
AU - Robert Seiringer
ED - Rivasseau, Vincent
ED - Robert Seiringer
ED - Solovej, Jan P
ED - Spencer, Thomas
ID - 2399
T2 - Quantum Many Body Systems
TI - Cold quantum gases and bose einstein condensation
VL - 2051
ER -
TY - JOUR
AB - 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.
AU - Timothy Browning
AU - Valckenborgh, K Van
ID - 240
IS - 2
JF - Experimental Mathematics
TI - Sums of three squareful numbers
VL - 21
ER -
TY - JOUR
AB - 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.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2400
IS - 2
JF - Communications in Mathematical Physics
TI - Binding of polarons and atoms at threshold
VL - 313
ER -