Thermodynamics of the BCS-BEC crossover

We present a self-consistent theory for the thermodynamics of the BCS-BEC crossover in the normal and superfluid phase which is both conserving and gapless. It is based on the variational many-body formalism developed by Luttinger and Ward and by DeDominicis and Martin. Truncating the exact functional for the entropy to that obtained within a ladder approximation, the resulting self-consistent integral equations for the normal and anomalous Green functions are solved numerically for arbitrary coupling. The critical temperature, the equation of state and the entropy are determined as a function of the dimensionless parameter $1/k_Fa$, which controls the crossover from the BCS-regime of extended pairs to the BEC-regime of tightly bound molecules. The tightly bound pairs turn out to be described by a Popov-type approximation for a dilute, repulsive Bose gas. Even though our approximation does not capture the critical behaviour near the continuous superfluid transition, our results provide a consistent picture for the complete crossover thermodynamics which compare well with recent numerical and field-theoretic approaches at the unitarity point.Comment: published versio

Criticality and Superfluidity in liquid He-4 under Nonequilibrium Conditions

We review a striking array of recent experiments, and their theoretical interpretations, on the superfluid transition in $^4$He in the presence of a heat flux, $Q$. We define and evaluate a new set of critical point exponents. The statics and dynamics of the superfluid-normal interface are discussed, with special attention to the role of gravity. If $Q$ is in the same direction as gravity, a self-organized state can arise, in which the entire sample has a uniform reduced temperature, on either the normal or superfluid side of the transition. Finally, we review recent theory and experiment regarding the heat capacity at constant $Q$. The excitement that surrounds this field arises from the fact that advanced thermometry and the future availability of a microgravity experimental platform aboard the International Space Station will soon open to experimental exploration decades of reduced temperature that were previously inaccessible.Comment: 16 pages, 9 figures, plus harvard.sty style file for references Accepted for publication in Colloquia section of Reviews of Modern Physic

Brief increases in corticosterone affect morphology, stress responses, and telomere length, but not post-fledging movements, in a wild songbird

Organisms are frequently exposed to challenges during development, such as poor weather and food shortage. Such challenges can initiate the hormonal stress response, which involves secretion of glucocorticoids. Although the hormonal stress response helps organisms deal with challenges, long-term exposure to high levels of glucocorticoids can have morphological, behavioral, and physiological consequences, especially during development. Glucocorticoids are also associated with reduced survival and telomere shortening. To investigate whether brief, acute exposures to glucocorticoids can also produce these phenotypic effects in free-living birds, we exposed wild tree swallow (Tachycineta bicolor) nestlings to a brief exogenous dose of cort once per day for five days and then measured their morphology, baseline and stress-induced corticosterone levels, and telomere length. We also deployed radio tags on a subset of nestlings, which allowed us to determine the age at which tagged nestlings left the nest (fledged) and their pattern of presence and absence at the natal site during the post-breeding period. Corticosterone-treated nestlings had lower mass, higher baseline and stress-induced corticosterone, and reduced telomeres; other metrics of morphology were affected weakly or not at all. Our treatment resulted in no significant effect on survival to fledging, fledge age, or age at first departure from the natal site, and we found no negative effect of corticosterone on inter-annual return rate. These results show that brief acute corticosterone exposure during development can have measurable effects on phenotype in free-living tree swallows. Corticosterone may therefore mediate correlations between rearing environment and phenotype in developing organisms, even in the absence of prolonged stressors.Comment: 35 pages, 4 figures, 1 appendi

Liquid 4He near the superfluid transition in the presence of a heat current and gravity

The effects of a heat current and gravity in liquid 4He near the superfluid transition are investigated for temperatures above and below T_lambda. We present a renormalization-group calculation based on model F for the Green's function in a self-consistent approximation which in quantum many-particle theory is known as the Hartree approximation. The approach can handle a zero average order parameter above and below T_lambda and includes effects of vortices. We calculate the thermal conductivity and the specific heat for all temperatures T and heat currents Q in the critical regime. Furthermore, we calculate the temperature profile. Below T_lambda we find a second correlation length which describes the dephasing of the order parameter field due to vortices. We find dissipation and mutual friction of the superfluid-normal fluid counterflow and calculate the Gorter-Mellink coefficient A. We compare our theoretical results with recent experiments.Comment: 26 pages, 9 figure

Spectroscopy of Superfluid Pairing in Atomic Fermi Gases

We study the dynamic structure factor for density and spin within the crossover from BCS superfluidity of atomic fermions to the Bose-Einstein condensation of molecules. Both structure factors are experimentally accessible via Bragg spectroscopy, and allow for the identification of the pairing mechanism: the spin structure factor allows for the determination of the two particle gap, while the collective sound mode in the density structure reveals the superfluid state.Comment: 4 pages, 3 figure

Formation of magnetic impurities and pair-breaking effect in a superfluid Fermi gas

We theoretically investigate a possible idea to introduce magnetic impurities to a superfluid Fermi gas. In the presence of population imbalance ($N_\uparrow>N_\downarrow$, where $N_\sigma$ is the number of Fermi atoms with pseudospin $\sigma=\uparrow,\downarrow$), we show that nonmagnetic potential scatterers embedded in the system are magnetized in the sense that some of excess $\uparrow$-spin atoms are localized around them. They destroy the superfluid order parameter around them, as in the case of magnetic impurity effect discussed in the superconductivity literature. This pair-breaking effect naturally leads to localized excited states below the superfluid excitation gap. To confirm our idea in a simply manner, we treat an attractive Fermi Hubbard model within the mean-field theory at T=0. We self-consistently determine superfluid properties around a nonmagnetic impurity, such as the superfluid order parameter, local population imbalance, as well as single-particle density of states, in the presence of population imbalance. Since the competition between superconductivity and magnetism is one of the most fundamental problems in condensed matter physics, our results would be useful for the study of this important issue in cold Fermi gases.Comment: 27 pages, 14 figure

Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying

We study the problem of channel pairing and power allocation in a multichannel multihop relay network to enhance the end-to-end data rate. Both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. Given fixed power allocation to the channels, we show that channel pairing over multiple hops can be decomposed into independent pairing problems at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal, where each relay pairs its incoming and outgoing channels by their SNR order. For the joint optimization of channel pairing and power allocation under both total and individual power constraints, we show that the problem can be decoupled into two subproblems solved separately. This separation principle is established by observing the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution. It significantly reduces the computational complexity in finding the jointly optimal solution. It follows that the channel pairing problem in joint optimization can be again decomposed into independent pairing problems at each relay based on sorted channel gains. The solution for optimizing power allocation for DF relaying is also provided, as well as an asymptotically optimal solution for AF relaying. Numerical results are provided to demonstrate substantial performance gain of the jointly optimal solution over some suboptimal alternatives. It is also observed that more gain is obtained from optimal channel pairing than optimal power allocation through judiciously exploiting the variation among multiple channels. Impact of the variation of channel gain, the number of channels, and the number of hops on the performance gain is also studied through numerical examples.Comment: 15 pages. IEEE Transactions on Signal Processin