121 research outputs found
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
HighâResolution ν1 Spectrum of Propyne: Application of a MicrocomputerâControlled InfraredâAcoustic Color Center Laser Spectrometer
Development of a microcomputerâcontrolled infraredâacoustic color center laserspectrometer capable of scanning in 100 cmâ1 sections over the wavelength range 2.2â3.3 Îźm with a resolution of 0.01 cmâ1 (300 MHz) is reported. Application of the spectrometer to investigation of the ν1spectrum of propyne is demonstrated
Molecular Dynamics in Hydrogenâbonded Interactions: A Preliminary Experimentally Determined Harmonic Stretching Force Field for HCNâââHF
Observation of the 2ν1 overtone band in the hydrogenâbonded complex HCNâââHF permits evaluation of the anharmonicity constant X 1 1=â116.9(1) cmâ 1 and determination of the anharmonicity corrected fundamental frequency Ď1. This information, and available data from previous rovibrational analyses in the common and perdeuterated isotopic species of HCNâââHF, 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/Ă
) 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=â0.211(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 hydrogenâbonded 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 travelingâwave subâDoppler 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 ⊽10â12âW. 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 HCNâââHF and DCNâââDF
Gas phase rovibrational analysis of the high frequency intermolecular hydrogen bonded bending overtone 2ν0 6 [ν0=1132.4783(2) cmâ 1] in HCNâââHF and its corresponding perdeuterated fundamental ν1 6 [ν0=409.1660(2) cmâ 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) cmâ 1 which in turn are used to estimate the pertinent cubic band stretching interaction constants K 4 6 6=â149.3(50) cmâ 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=â21.61(2), X 6 7=â7.694(1), X 6 6=â14.84(90), g 6 6=â31.04(90) cmâ 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)]
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