A new inequality for the von Neumann entropy

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent of strong subadditivity: it is an inequality which is true for any four party quantum state, provided that it satisfies three linear relations (constraints) on the entropies of certain reduced states.Comment: 8 pages, 1 eps figur

Vibrational Predissociation in Linear Hydrogen-Bonded Complexes

Dr. Shannon Lieb\u27s contribution to Volume 95 of the Proceedings of the Indiana Academy of Science

A SCC MO Calculation on the Tetracyanoethylene-benzene Complex

Dr. Shannon Lieb\u27s contribution to Volume 94 of the Proceedings of the Indiana Academy of Science

High‐Resolution ν1 Spectrum of Propyne: Application of a Microcomputer‐Controlled Infrared‐Acoustic Color Center Laser Spectrometer

Development of a microcomputer‐controlled infrared‐acoustic color center laserspectrometer capable of scanning in 100 cm−1 sections over the wavelength range 2.2–3.3 μm with a resolution of 0.01 cm−1 (300 MHz) is reported. Application of the spectrometer to investigation of the ν1spectrum of propyne is demonstrated

Molecular Dynamics in Hydrogen‐bonded Interactions: A Preliminary Experimentally Determined Harmonic Stretching Force Field for HCN‐‐‐HF

Observation of the 2ν1 overtone band in the hydrogen‐bonded complex HCN‐‐‐HF permits evaluation of the anharmonicity constant X 1 1=−116.9(1) cm− 1 and determination of the anharmonicity corrected fundamental frequency ω1. This information, and available data from previous rovibrational analyses in the common and perdeuterated isotopic species of HCN‐‐‐HF, offer an opportunity for calculation of an approximate stretching harmonic force field. With the assumptions f 1 2=f 2 4=0.0, the remaining force constants (in mdyn/Å) are evaluated as: f 1 1=8.600(20), f 2 2=6.228(9), f 3 3=19.115(40), f 4 4=0.2413(39), f 1 3=0.000(13), f 1 4=0.0343(2), f 2 3=−0.211(6), f 3 4=0.000(2). These compare to f 1 1=9.658(2) in the HF monomer and f 1 1=6.244(3) and f 3 3=18.707(16) in the HCN monomer. These results provide the information necessary to quantitatively assess the applicability of the Cummings and Wood approximation in this hydrogen‐bonded complex and also give an estimate of D e j , the equilibrium distortion constant in the harmonic limit. Comparisons of these experimentally determined parameters with the predictions of a b i n i t i o molecular orbital calculations at several levels of approximation are presented

Travelling-Wave Sub-Doppler Excited Molecule Energy Transfer Spectroscopy

A general formulation of traveling‐wave sub‐Doppler excited molecule energy transferspectroscopy is presented. The line profile analysis is applied to that determined experimentally for the R(22) ν3 HCN transition. Pn the noise equivalent power of the detector is demonstrated to be ⩽10−12 W. Finally, the technique is applied to resolve the KsR(7) ν1 transition head in NH3

The Spectroscopy and Molecular Dynamics of the High Frequency ν1 6 Intermolecular Vibrations in HCN‐‐‐HF and DCN‐‐‐DF

Gas phase rovibrational analysis of the high frequency intermolecular hydrogen bonded bending overtone 2ν0 6 [ν0=1132.4783(2) cm− 1] in HCN‐‐‐HF and its corresponding perdeuterated fundamental ν1 6 [ν0=409.1660(2) cm− 1] are reported. Evaluated rovibrational parameters provide the basis for quantitative modeling of the molecular dynamics associated with this vibration. A quantum mechanical calculation permits determination of the quadratic and quartic force constants K 6 6=537(17) and K 6 6 6 6=4.98(12) cm− 1 which in turn are used to estimate the pertinent cubic band stretching interaction constants K 4 6 6=−149.3(50) cm− 1 and account for the unexpected behavior in the rotational constantB 1 6. Second order expansion of the vibrational term energies, give X 4 6=−21.61(2), X 6 7=−7.694(1), X 6 6=−14.84(90), g 6 6=−31.04(90) cm− 1, neglecting corrections for Fermi resonance. The common isotopic species equilibrium rotational constantB e is evaluated to be 3681.1(11) MHz

Erratum: Determination of Dissociation Energies and Thermal Functions of Hydrogen Bond Formation Using High Resolution FTIR Spectroscopy [J. Chem. Phys. 8 7, 5674 (1987)]

Erratu