Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas

We propose a non-singular representation for a non-Hermitian operator even if the parameter space contains exceptional points (EPs), at which the operator cannot be diagonalized and the usual spectral representation ceases to exist. Our representation has a generalized Jordan block form and is written in terms of extended pseudo-eigenstates. Our method is free from a divergence in the spectral representation at EPs, at which multiple eigenvalues and eigenvectors coalesce and the eigenvectors cannot be normalized. Our representation improves the accuracy of numerical calculations of physical quantities near EPs. We also find that our method is applicable to various problems related to EPs in the parameter space of non-Hermitian operators. We demonstrate the usefulness of our representation by investigating Boltzmann's collision operator in a one-dimensional quantum Lorentz gas in the weak coupling approximation

Lower bounds for the mean dissipated heat in an open quantum system

Landauer's principle provides a perspective on the physical meaning of information as well as on the minimum working cost of information processing. Whereas most studies have related the decrease in entropy during a computationally irreversible process to a lower bound of dissipated heat, recent efforts have also provided another lower bound associated with the thermodynamic fluctuation of heat. The coexistence of the two conceptually independent bounds has stimulated comparative studies of their close relationship or tightness; however, these studies were concerned with finite quantum systems that allowed the revival of erased information because of a finite recurrence time. We broaden these comparative studies further to open quantum systems with infinite recurrence times. By examining their dependence on the initial state, we find the independence of the thermodynamic bound from the initial coherence, whereas the entropic bound depends on both the initial coherence and population. A crucial role is indicated by the purity of the initial state: the entropic bound is tighter when the initial condition is sufficiently mixed, whereas the thermodynamic bound is tighter when the initial state is close to a pure state. These trends are consistent with previous results obtained for finite systems

Thermodynamic stability of H2 + tetrahydrofuran mixed gas hydrate in nonstoichiometric aqueous solutions

Phase equilibria (pressure - temperature relations) of the H2 + tetrahydrofuran mixed gas hydrate system have been measured for various concentrations of tetrahydrofuran aqueous solutions. The three-phase equilibrium lines obtained in the present study are shifted to the low-temperature or high-pressure side from that of the stoichiometric THF solution. Each three-phase equilibrium line of H2 + tetrahydrofuran hydrate converges at the three-phase equilibrium line of the pure tetrahydrofuran hydrate. At the cross point on the lines, the tetrahydrofuran concentration of mother aqueous solution agrees with each other. The Raman spectra of H 2 and tetrahydrofuran for the H2 + tetrahydrofuran mixed gas hydrate do not change with the variation of tetrahydrofuran mole fraction from 0.010 to 0.130 in the aqueous solution. © 2007 American Chemical Society.Shunsuke Hashimoto, Takeshi Sugahara, Hiroshi Sato et al. Thermodynamic Stability of H2 + Tetrahydrofuran Mixed Gas Hydrate in Nonstoichiometric Aqueous Solutions. Journal of Chemical & Engineering Data, 52 (1), 517-520, March 1, © 2007 American Chemical Society. https://doi.org/10.1021/je060436

Phase equilibria for H2 + CO2 + H2O system containing gas hydrates

Isothermal phase equilibrium (pressure-composition in the gas phase) for the ternary system of H2 + CO2 + H2O has been investigated in the presence of gas hydrate phase. Three-phase equilibrium pressure increases with the H2 composition of gas phase. The Raman spectra suggest that H2 is not enclathrated in the hydrate-cages and behaves only like the diluent gas toward the formation of CO2 hydrate. This fact is also supported by the thermodynamic analysis using Soave-Redlich-Kwong equation of state. © 2005 Elsevier B.V. All rights reserved