Inflationary Perturbations: the Cosmological Schwinger Effect

This pedagogical review aims at presenting the fundamental aspects of the theory of inflationary cosmological perturbations of quantum-mechanical origin. The analogy with the well-known Schwinger effect is discussed in detail and a systematic comparison of the two physical phenomena is carried out. In particular, it is demonstrated that the two underlying formalisms differ only up to an irrelevant canonical transformation. Hence, the basic physical mechanisms at play are similar in both cases and can be reduced to the quantization of a parametric oscillator leading to particle creation due to the interaction with a classical source: pair production in vacuum is therefore equivalent to the appearance of a growing mode for the cosmological fluctuations. The only difference lies in the nature of the source: an electric field in the case of the Schwinger effect and the gravitational field in the case of inflationary perturbations. Although, in the laboratory, it is notoriously difficult to produce an electric field such that pairs extracted from the vacuum can be detected, the gravitational field in the early universe can be strong enough to lead to observable effects that ultimately reveal themselves as temperature fluctuations in the Cosmic Microwave Background. Finally, the question of how quantum cosmological perturbations can be considered as classical is discussed at the end of the article.Comment: 49 pages, 6 figures, to appear in a LNP volume "Inflationary Cosmology

Bose-Einstein condensation with magnetic dipole-dipole forces

Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of the Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of e.g. chromium and a typical value of the scattering length all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region the ground state wavefunctions show internal structures not seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.Comment: final version, 4 pages, 4 figure

Predictors of combined cognitive and physical decline

OBJECTIVES: To determine the incidence and correlates of combined declines in cognitive and physical performance. DESIGN: Cohort study of community-dwelling older women with moderate to severe disability. SETTING: The community surrounding Baltimore, Maryland. PARTICIPANTS: Participants in the Women's Health and Aging Study I with Mini-Mental State Examination (MMSE) score or 24 or greater and walking speed greater than 0.4 m/s at baseline. MEASUREMENTS: Cognitive decline was defined as an MMSE score less than 24 and physical decline as a walking speed of 0.4 m/s or less in at least one of the three annual follow-up visits. Participants were stratified into groups based on cognitive or physical decline or both. Group characteristics were compared, and results were adjusted for age, race, education, and significant covariates. RESULTS: Of 558 women that met the baseline MMSE and walking speed inclusion criteria, 21% developed physical decline, 12% developed cognitive decline, and 11% experienced combined cognitive and physical decline. After adjustment, physical decline was associated with age, nonwhite race, former smoking, baseline walking speed, and instrumental activities of daily living (IADL) impairment. Cognitive decline was associated with age and baseline MMSE score. Combined decline was associated with age, baseline walking speed, MMSE score, IADL impairment, as well as current smoking (odds ratio (OR)=5.66, 95% confidence interval (CI)=1.49-21.54) and hemoglobin level (OR=0.68, 95% CI=0.47-0.98). CONCLUSION: Potential predictors of cognitive and physical performance decline were identified. The association between smoking and lower hemoglobin levels and combined cognitive and physical decline may represent potentially modifiable risk factors and should be confirmed in future studie

The influence of anxiety on the progression of disability

OBJECTIVES: To determine the influence of anxiety on the progression of disability and examine possible mediators of the relationship. DESIGN: Community-based observational study. SETTING: Women's Health and Aging Study I, a prospective observational study with assessments every 6 months for 3 years. PARTICIPANTS: One thousand two functionally limited women aged 65 and older. MEASUREMENTS: Anxiety symptoms were assessed using four questions from the Hopkins Symptom Checklist (nervous or shaky, avoidance of certain things, tense or keyed up, fearful). Participants who reported experiencing two or more of these symptoms at baseline were considered anxious. Anxiety as a predictor of the onset of four types of disability was examined using Cox proportional hazards models. Three models were tested: an unadjusted model, a model adjusted for confounding variables (age, race, vision, number of diseases, physical performance, depressive symptoms), and a mediational model (benzodiazepine and psychotropic medication use, physical activity, emotional support). RESULTS: Nineteen percent of women reported two or more symptoms of anxiety at baseline. Unadjusted models indicate that anxiety was associated with a greater risk of worsening disability: activity of daily living (ADL) disability (relative risk (RR)=1.40, 95% confidence interval (CI)=1.10-1.79), mobility disability (RR=1.41, 95% CI=1.06-1.86), lifting disability (RR=1.54, 95% CI=1.20-1.97), and light housework disability (RR=1.77, 95% CI=1.32-2.37). After adjusting for confounding variables, anxiety continued to predict the development of two types of disability: ADL disability (RR=1.41, 95% CI=1.08-1.84) and light housework disability (RR=1.56, 95% CI=1.14-2.14). Finally, benzodiazepine and psychotropic medication use, physical activity, and emotional support were not significant mediators of the effect of anxiety on the development of a disability. CONCLUSION: Anxiety is a significant risk factor for the progression of disability in older women. Studies are needed to determine whether treatment of anxiety delays or prevents disabilit

Coupled Bose-Einstein condensate: Collapse for attractive interaction

We study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two or three of the scattering lengths $a_{ij}$ for scattering of boson $i$ with $j$, $i,j = 1, 2$, are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.Comment: 5 pages and 9 figures, small changes mad

Mean-field analysis of collapsing and exploding Bose-Einstein condensates

The dynamics of collapsing and exploding trapped Bose-Einstein condensat es caused by a sudden switch of interactions from repulsive to attractive a re studied by numerically integrating the Gross-Pitaevskii equation with atomic loss for an axially symmetric trap. We investigate the decay rate of condensates and the phenomena of bursts and jets of atoms, and compare our results with those of the experiments performed by E. A. Donley {\it et al.} [Nature {\bf 412}, 295 (2001)]. Our study suggests that the condensate decay and the burst production is due to local intermittent implosions in the condensate, and that atomic clouds of bursts and jets are coherent. We also predict nonlinear pattern formation caused by the density instability of attractive condensates.Comment: 7 pages, 8 figures, axi-symmetric results are adde

Macroscopic Quantum Fluctuations in the Josephson Dynamics of Two Weakly Linked Bose-Einstein Condensates

We study the quantum corrections to the Gross-Pitaevskii equation for two weakly linked Bose-Einstein condensates. The goals are: 1) to investigate dynamical regimes at the borderline between the classical and quantum behaviour of the bosonic field; 2) to search for new macroscopic quantum coherence phenomena not observable with other superfluid/superconducting systems. Quantum fluctuations renormalize the classical Josephson oscillation frequencies. Large amplitude phase oscillations are modulated, exhibiting collapses and revivals. We describe a new inter-well oscillation mode, with a vanishing (ensemble averaged) mean value of the observables, but with oscillating mean square fluctuations. Increasing the number of condensate atoms, we recover the classical Gross-Pitaevskii (Josephson) dynamics, without invoking the symmetry-breaking of the Gauge invariance.Comment: Submitte

Collective dynamics of internal states in a Bose gas

Theory for the Rabi and internal Josephson effects in an interacting Bose gas in the cold collision regime is presented. By using microscopic transport equation for the density matrix the problem is mapped onto a problem of precession of two coupled classical spins. In the absence of an external excitation field our results agree with the theory for the density induced frequency shifts in atomic clocks. In the presence of the external field, the internal Josephson effect takes place in a condensed Bose gas as well as in a non-condensed gas. The crossover from Rabi oscillations to the Josephson oscillations as a function of interaction strength is studied in detail.Comment: 18 pages, 2 figure

Mean-field description of collapsing and exploding Bose-Einstein condensates

We perform numerical simulation based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. on the dynamics of collapsing and exploding Bose-Einstein condensates of $^{85}$Rb atoms. They manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one and vice versa. In the actual experiment they changed suddenly the scattering length of atomic interaction from positive to a large negative value on a pre-formed condensate in an axially symmetric trap. Consequently, the condensate collapses and ejects atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates.Comment: 9 Latex pages, 10 ps and eps files, version accepted in Physical Review A, minor changes mad

Spinor condensates and light scattering from Bose-Einstein condensates

These notes discuss two aspects of the physics of atomic Bose-Einstein condensates: optical properties and spinor condensates. The first topic includes light scattering experiments which probe the excitations of a condensate in both the free-particle and phonon regime. At higher light intensity, a new form of superradiance and phase-coherent matter wave amplification were observed. We also discuss properties of spinor condensates and describe studies of ground--state spin domain structures and dynamical studies which revealed metastable excited states and quantum tunneling.Comment: 58 pages, 33 figures, to appear in Proceedings of Les Houches 1999 Summer School, Session LXXI