Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong whereas at smaller interactions only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.Comment: 9 figures, corrected typo

Proceedings from the 1984 Tax Institute Symposium: Cash or Deferred Arrangements Under I.R.C. Section 401(k)

This article examines the reasons why an employer might consider a cash or deferred profit sharing or stock bonus plan. It looks at the rules for a cash or deferred arrangement (CODA) under Section 401(k) of the Internal Revenue Code. It covers the four primary requirements under the I.R.C., and then fifth, and biggest requirement, nondiscrimination

Observation of quantum spin noise in a 1D light-atoms quantum interface

We observe collective quantum spin states of an ensemble of atoms in a one-dimensional light-atom interface. Strings of hundreds of cesium atoms trapped in the evanescent fiel of a tapered nanofiber are prepared in a coherent spin state, a superposition of the two clock states. A weak quantum nondemolition measurement of one projection of the collective spin is performed using a detuned probe dispersively coupled to the collective atomic observable, followed by a strong destructive measurement of the same spin projection. For the coherent spin state we achieve the value of the quantum projection noise 40 dB above the detection noise, well above the 3 dB required for reconstruction of the negative Wigner function of nonclassical states. We analyze the effects of strong spatial inhomogeneity inherent to atoms trapped and probed by the evanescent waves. We furthermore study temporal dynamics of quantum fluctuations relevant for measurement-induced spin squeezing and assess the impact of thermal atomic motion. This work paves the road towards observation of spin squeezed and entangled states and many-body interactions in 1D spin ensembles

Systematic Search and Scoping Review of Physicians’ Intolerance of Uncertainty and Medical Decision-Making Uncertainties During the COVID-19 Pandemic: A Summary of the Literature and Directions for Future Research

Pandemic-related uncertainties and intolerance of uncertainty (IU) could negatively affect physicians’ well-being and functioning, being associated with experiences of distress and problematic decision-making processes. To summarize the available quantitative and qualitative evidence of physicians’ IU and decisional uncertainty during COVID-19 and problems associated with it, a systematic search was conducted to identify all relevant articles describing physician uncertainty with regard to medical decision making and well-being in COVID-19 pandemic conditions. Medical, psychological, and preprint databases were searched. Ten articles met all eligibility criteria, with eight describing quantitative and two describing qualitative research outcomes, assessed primarily in European regions and via online surveys. Associations between IU and symptoms of poor mental health and mental health risk factors were widespread, but inconsistencies emerged. Qualitative studies emphasized decisional uncertainty as a stressor for physicians, and quantitative studies suggest it may have fostered more unproven treatment choices. While the prevalence and impact of physician uncertainty under COVID-19 conditions requires further investigation, sighting available literature indicates that IU coincided with experiences of poor mental health and, at least towards the beginning of the pandemic, with willingness to endorse unproven treatments. Efforts to reduce uncertainty-related problems for physicians seem warranted, for example, through normalizing experiences of uncertainty or reducing avoidable uncertainty through maintaining open and timely communication channels

A new proof that alternating links are non-trivial

We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.Comment: Minor changes. To appear in Fundamenta Mathematica

Adjustable thermal ''tree''

Tree mounts 10 thermocouples on extensible arms to provide a reliable heat profile of conditions within heat treating devices, such as ovens and autoclaves, and within environmental test chambers

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Since the proof of the four color theorem in 1976, computer-generated proofs have become a reality in mathematics and computer science. During the last decade, we have seen formal proofs using verified proof assistants being used to verify the validity of such proofs. In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c

Bose-Einstein condensation of alkaline earth atoms: 40^{40}{Ca}

We have achieved Bose-Einstein condensation of $^{40}$Ca, the first for an alkaline earth element. The influence of elastic and inelastic collisions associated with the large ground state s-wave scattering length of $^{40}$Ca was measured. From these findings, an optimized loading and cooling scheme was developed that allowed us to condense about $2 \cdot 10^4$ atoms after laser cooling in a two-stage magneto-optical trap and subsequent forced evaporation in a crossed dipole trap within less than 3 s. The condensation of an alkaline earth element opens novel opportunities for precision measurements on the narrow intercombination lines as well as investigations of molecular states at the $^1$S--$^3$P asymptotes

Generation and detection of a sub-Poissonian atom number distribution in a one-dimensional optical lattice

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance $-14$ dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of $\pm 8$ atoms on an ensemble of some $10^3$ atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum non-demolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice