Energy as an entanglement witness for quantum many-body systems

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.

Highly efficient luminescence from a hybrid state found in strongly quantum confined PbS nanocrystals

We report that high quality PbS nanocrystals, synthesized in the strong quantum confinement regime, have quantum yields as high as 70% at room temperature. We use a combination of modelling and photoluminescence up-conversion to show that we obtain a nearly monodisperse size distribution. Nevertheless, the emission displays a large nonresonant Stokes shift. The magnitude of the Stokes shift is found to be directly proportional to the degree of quantum confinement, from which we establish that the emission results from the recombination of one quantum confined charge carrier with one localized or surface-trapped charge carrier. Furthermore, the surface state energy is found to lie outside the bulk bandgap so that surface-related emission only commences for strongly quantum confined nanocrystals, thus highlighting a regime where improved surface passivation becomes necessary.

Reducing the time period of steady state does not affect the accuracy of energy expenditure measurements by indirect calorimetry

Achievement of steady state during indirect calorimetry measurements of resting energy expenditure (REE) is necessary to reduce error and ensure accuracy in the measurement. Steady state is often defined as 5 consecutive min (5-min SS) during which oxygen consumption and carbon dioxide production vary by +/-10%. These criteria, however, are stringent and often difficult to satisfy. This study aimed to assess whether reducing the time period for steady state (4-min SS or 3-min SS) produced measurements of REE that were significantly different from 5-min SS. REE was measured with the use of open-circuit indirect calorimetry in 39 subjects, of whom only 21 (54%) met the 5-min SS criteria. In these 21 subjects, median biases in REE between 5-min SS and 4-min SS and between 5-min SS and 3-min SS were 0.1 and 0.01%, respectively. For individuals, 4-min SS measured REE within a clinically acceptable range of +/-2% of 5-min SS, whereas 3-min SS measured REE within a range of -2-3% of 5-min SS. Harris-Benedict prediction equations estimated REE for individuals within +/-20-30% of 5-min SS. Reducing the time period of steady state to 4 min produced measurements of REE for individuals that were within clinically acceptable, predetermined limits. The limits of agreement for 3-min SS fell outside the predefined limits of +/-2%; however, both 4-min SS and 3-min SS criteria greatly increased the proportion of subjects who satisfied steady state within smaller limits than would be achieved if relying on prediction equations.