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 -
TY - JOUR
AB - We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function λ {mapping} Tr exp(A - λB) is the Laplace transform of a positive measure supported on [0,∞].
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2401
IS - 1
JF - Journal of Statistical Physics
TI - Further implications of the Bessis-Moussa-Villani conjecture
VL - 149
ER -
TY - JOUR
AB - We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power.
AU - Frank, Rupert L
AU - Robert Seiringer
ID - 2402
IS - 9
JF - Journal of Mathematical Physics
TI - Lieb-Thirring inequality for a model of particles with point interactions
VL - 53
ER -
TY - JOUR
AB - We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval.
AU - Robert Seiringer
AU - Yngvason, Jakob
AU - Zagrebnov, Valentin A
ID - 2403
IS - 11
JF - Journal of Statistical Mechanics Theory and Experiment
TI - Disordered Bose-Einstein condensates with interaction in one dimension
VL - 2012
ER -
TY - JOUR
AB - The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over ℚ.
AU - de la Bretèche, Régis
AU - Timothy Browning
ID - 241
IS - 2
JF - Israel Journal of Mathematics
TI - Binary forms as sums of two squares and Châtelet surfaces
VL - 191
ER -
TY - JOUR
AB - The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses.
AU - Ebersberger, Ingo
AU - De Matos Simoes, Ricardo
AU - Kupczok, Anne
AU - Gube, Matthias
AU - Kothe, Erika
AU - Voigt, Kerstin
AU - Von Haeseler, Arndt
ID - 2411
IS - 5
JF - Molecular Biology and Evolution
TI - A consistent phylogenetic backbone for the fungi
VL - 29
ER -