Fermi liquid features of the one-dimensional Luttinger liquid

We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Fermi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the 1D Fermi-liquid theory. Exact correspondence between the Landau parameters and Haldane parameters is established. The exponents of the dynamical correlation functions and the impurity problem are also discussed based on the finite size corrections of elementary excitations with the predictions of the conformal field theory, which provides a bridge between the 1D Fermi-liquid and the Luttinger liquid.Comment: RevTeX, 5 pages, published versio

Aharonov-Casher phase and persistent current in a polyacetylene ring

We investigate a polyacetylene ring in an axially symmetric, static electric field with a modified SSH Hamiltonian of a polyacetylene chain. An effective gauge potential of the single electron Hamiltonian due to spin-field interaction is obtained and it results in a Fr\"{o}hlich's type of superconductivity equivalent to the effect of travelling lattice wave. The total energy as well as the persistent current density are shown to be a periodic function of the flux of the gauge field embraced by the polyacetylene ring.Comment: 12 pages, 5 figure

On Macroscopic Energy Gap for qq-Quantum Mechanical Systems

The q-deformed harmonic oscillator within the framework of the recently introduced Schwenk-Wess $q$-Heisenberg algebra is considered. It is shown, that for "physical" values $q\sim1$, the gap between the energy levels decreases with growing energy. Comparing with the other (real) $q$-deformations of the harmonic oscillator, where the gap instead increases, indicates that the formation of the macroscopic energy gap in the Schwenk-Wess $q$-Quantum Mechanics may be avoided.Comment: 6 pages, TeX, PRA-HEP-92/1

Development of origin–destination matrices using mobile phone call data

In this research, we propose a methodology to develop OD matrices using mobile phone Call Detail Records (CDR) and limited traffic counts. CDR, which consist of time stamped tower locations with caller IDs, are analyzed first and trips occurring within certain time windows are used to generate tower-to-tower transient OD matrices for different time periods. These are then associated with corresponding nodes of the traffic network and converted to node-to-node transient OD matrices. The actual OD matrices are derived by scaling up these node-to-node transient OD matrices. An optimization based approach, in conjunction with a microscopic traffic simulation platform, is used to determine the scaling factors that result best matches with the observed traffic counts. The methodology is demonstrated using CDR from 2.87 million users of Dhaka, Bangladesh over a month and traffic counts from 13 key locations over 3 days of that month. The applicability of the methodology is supported by a validation study

Fermionic R-operator approach for the small-polaron model with open boundary condition

Exact integrability and algebraic Bethe ansatz of the small-polaron model with the open boundary condition are discussed in the framework of the quantum inverse scattering method (QISM). We employ a new approach where the fermionic R-operator which consists of fermion operators is a key object. It satisfies the Yang-Baxter equation and the reflection equation with its corresponding K-operator. Two kinds of 'super-transposition' for the fermion operators are defined and the dual reflection equation is obtained. These equations prove the integrability and the Bethe ansatz equation which agrees with the one obtained from the graded Yang-Baxter equation and the graded reflection equations.Comment: 10 page

Quantum Tunneling of Spin Particles in Periodic Potentials with Asymmetric Twin Barriers

The tunneling effect of a periodic potential with an asymmetric twin barrier per period is calculated using the instanton method. The model is derived from the Hamiltonian of a small ferromagnetic particle in an external magnetic field using the spin-coherent-state path integral. The instantons in two neighbouring barriers differ and lead to different level shifts $\triangle\epsilon_1, \triangle\epsilon_2$. We derive with Bloch theory the energy spectrum which has formally the structure of an energy band. The spectrum depends on both level shifts. The removal of Kramer's degeneracy by an external magnetic field is discussed. In addition we find a new kind of quenching of macroscopic quantum coherence which is irrelevant to Kramer's degeneracy.Comment: 18 pages, LaTex, one figur

Evidence of Rapid Phenocryst Growth of Olivine During Ascent in Basalts From the Big Pine Volcanic Field: Application of Olivine‐Melt Thermometry and Hygrometry at the Liquidus

The Quaternary Big Pine (BP) volcanic field in eastern California is notable for the occurrence of mantle xenoliths in several flows. This points to rapid ascent of basalt through the crust and precludes prolonged storage in a crustal reservoir. In this study, the hypothesis of phenocryst growth during ascent is tested for several basalts (13–7 wt% MgO) and shown to be viable. Phenocrysts of olivine and clinopyroxene frequently display diffusion‐limited growth textures, and clinopyroxene compositions are consistent with polybaric crystallization. When the most Mg‐rich olivine in each sample is paired with the whole‐rock composition, resulting Fe2+‐MgKD(olivine‐melt) values (0.31–0.36) match those calculated from literature models (0.32–0.36). Application of a Mg‐ and a Ni‐based olivine‐melt thermometer from the literature, both calibrated on the same experimental data set, leads to two sets of temperatures that vary linearly with whole‐rock MgO wt%. Because the Ni thermometer is independent of water content, it provides the actual temperature at the onset of olivine crystallization (1247–1097°C), whereas the Mg thermometer gives the temperature under anhydrous conditions and thus allows ΔT (=TMg − TNi = depression of liquidus due to water) to be obtained. The average ΔT for all samples is ~59°C, which is consistent with analyzed water contents of 1.5–3.0 wt% in olivine‐hosted melt inclusions from the literature. Because the application of olivine‐melt thermometry/hygrometry at the liquidus only requires microprobe analyses of olivine combined with whole‐rock compositions, it can be used to obtain large global data sets of the temperature and water contents of basalts from different tectonic settings.Plain Language SummaryBasaltic lavas are a window into their mantle source regions, which is why it is important to determine their temperatures and water contents. In this study, a new approach that allows these two parameters to be quantified is demonstrated for basalts from the Big Pine volcanic field, CA. They were targeted because many contain chunks of dense mantle rocks, which precludes storage in a crustal magma chamber and points to direct ascent from the mantle to the surface along fractures. Two hypotheses are proposed, tested, and shown to be viable in this study: (1) olivine crystallized in the basalts during ascent, and (2) the most Mg‐rich olivine analyzed in each basalt represents the first olivine to grow during ascent. This enables the most Mg‐rich olivine to be paired with the whole‐rock composition in the application of olivine‐melt thermometry and hygrometry. The results match those from published, independent studies. The success of this approach paves the way for the attainment of large, high‐quality data sets for basalts from a wide variety of tectonic settings. This, in turn, may allow global variations in mantle temperature and volatile content to be mapped in greater detail and better understood.Key PointsRapid phenocryst growth occurs during ascent in Mg‐rich basalts (some carry mantle xenoliths) from the Big Pine volcanic field, CAThe most Mg‐rich olivine can be paired with the whole‐rock composition to apply olivine‐melt thermometry/hygrometry at the liquidusLarge, high‐quality data sets on the temperature and water content of basalts from various tectonic settings can be obtained by this methodPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163434/3/ggge22329-sup-0001-2020GC009264-SI.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163434/2/ggge22329.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163434/1/ggge22329_am.pd