Nontrivial eigenvalues of the Liouvillian of an open quantum system

We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state and the ket state. We also introduce the integral equations equivalent to the original eigenvalue problem.Comment: 5 pages, 2 figures, proceeding

High-resolution glacial and deglacial record of atmospheric methane by continuous-flow and laser spectrometer analysis along the NEEM ice core

The Greenland NEEM (North Greenland Eemian Ice Drilling) operation in 2010 provided the first opportunity to combine trace-gas measurements by laser spectroscopic instruments and continuous-flow analysis along a freshly drilled ice core in a field-based setting. We present the resulting atmospheric methane (CH₄) record covering the time period from 107.7 to 9.5 ka b2k (thousand years before 2000 AD). Companion discrete CH₄ measurements are required to transfer the laser spectroscopic data from a relative to an absolute scale. However, even on a relative scale, the high-resolution CH₄ data set significantly improves our knowledge of past atmospheric methane concentration changes. New significant sub-millennial-scale features appear during interstadials and stadials, generally associated with similar changes in water isotopic ratios of the ice, a proxy for local temperature. In addition to the midpoint of Dansgaard–Oeschger (D/O) CH₄ transitions usually used for cross-dating, sharp definition of the start and end of these events brings precise depth markers (with ±20 cm uncertainty) for further cross-dating with other palaeo- or ice core records, e.g. speleothems. The method also provides an estimate of CH₄ rates of change. The onsets of D/O events in the methane signal show a more rapid rate of change than their endings. The rate of CH₄ increase associated with the onsets of D/O events progressively declines from 1.7 to 0.6 ppbv yr⁻¹ in the course of marine isotope stage 3. The largest observed rate of increase takes place at the onset of D/O event #21 and reaches 2.5 ppbv yr⁻¹

High-resolution glacial and deglacial record of atmospheric methane by continuous-flow and laser spectrometer analysis along the NEEM ice core

The Greenland NEEM (North Greenland Eemian Ice Drilling) operation in 2010 provided the first opportunity to combine trace-gas measurements by laser spectroscopic instruments and continuous-flow analysis along a freshly drilled ice core in a field-based setting. We present the resulting atmospheric methane (CH4) record covering the time period from 107.7 to 9.5 ka b2k (thousand years before 2000 AD). Companion discrete CH4 measurements are required to transfer the laser spectroscopic data from a relative to an absolute scale. However, even on a relative scale, the high-resolution CH4 data set significantly improves our knowledge of past atmospheric methane concentration changes. New significant sub-millennial-scale features appear during interstadials and stadials, generally associated with similar changes in water isotopic ratios of the ice, a proxy for local temperature. In addition to the midpoint of Dansgaard–Oeschger (D/O) CH4 transitions usually used for cross-dating, sharp definition of the start and end of these events brings precise depth markers (with ±20 cm uncertainty) for further cross-dating with other palaeo- or ice core records, e.g. speleothems. The method also provides an estimate of CH4 rates of change. The onsets of D/O events in the methane signal show a more rapid rate of change than their endings. The rate of CH4 increase associated with the onsets of D/O events progressively declines from 1.7 to 0.6 ppbv yr−1 in the course of marine isotope stage 3. The largest observed rate of increase takes place at the onset of D/O event #21 and reaches 2.5 ppbv yr−1