Chebyshev approach to quantum systems coupled to a bath

We propose a new concept for the dynamics of a quantum bath, the Chebyshev space, and a new method based on this concept, the Chebyshev space method. The Chebyshev space is an abstract vector space that exactly represents the fermionic or bosonic bath degrees of freedom, without a discretization of the bath density of states. Relying on Chebyshev expansions the Chebyshev space representation of a bath has very favorable properties with respect to extremely precise and efficient calculations of groundstate properties, static and dynamical correlations, and time-evolution for a great variety of quantum systems. The aim of the present work is to introduce the Chebyshev space in detail and to demonstrate the capabilities of the Chebyshev space method. Although the central idea is derived in full generality the focus is on model systems coupled to fermionic baths. In particular we address quantum impurity problems, such as an impurity in a host or a bosonic impurity with a static barrier, and the motion of a wave packet on a chain coupled to leads. For the bosonic impurity, the phase transition from a delocalized electron to a localized polaron in arbitrary dimension is detected. For the wave packet on a chain, we show how the Chebyshev space method implements different boundary conditions, including transparent boundary conditions replacing infinite leads. Furthermore the self-consistent solution of the Holstein model in infinite dimension is calculated. With the examples we demonstrate how highly accurate results for system energies, correlation and spectral functions, and time-dependence of observables are obtained with modest computational effort.Comment: 18 pages, 13 figures, to appear in Phys. Rev.

Considerations on the quantum double-exchange Hamiltonian

Schwinger bosons allow for an advantageous representation of quantum double-exchange. We review this subject, comment on previous results, and address the transition to the semiclassical limit. We derive an effective fermionic Hamiltonian for the spin-dependent hopping of holes interacting with a background of local spins, which is used in a related publication within a two-phase description of colossal magnetoresistant manganites.Comment: 7 pages, 3 figure

Mantle Layering across Central South America

Imaging of seismic velocity discontinuities along a 3000 km profile across central South America at 20°S suggests that the depth variations of the 410-km (d410) and 660-km (d660) discontinuities are closely associated with the high-velocity Nazca slab and juxtaposed low-velocity oceanic mantle beneath the slab. The mantle transition zone thickness ranges from 220 km in the oceanic mantle to 270 km in a 600-km-wide area occupied by the deflected Nazca slab. The slab deflection has also been suggested by previous studies of seismic tomography and seismicity. This 50 km difference in the thickness corresponds to a lateral temperature variation of about 370°C between the two areas. The depth of d410 shows a gradual eastward decrease of about 10 km along the profile, corresponding to a temperature that is about 75°C cooler to the east. This variation is probably related to changes in the upper mantle geotherms associated with the transition from tectonically active to stable upper mantle. A low-velocity anomaly in the upper mantle and mantle transition zone beneath eastern Brazil, previously detected by seismic tomography and interpreted as a fossil plume, produced no detectable perturbation in transition zone thickness. It is thus unlikely to extend to the transition zone or alternatively is not thermal in origin. Finally, we have observed several possible second-order discontinuities at the depths of 230, 500, 600, 840, and 915 km beneath the western part of the study area

Southern African Crustal Evolution and Composition: Constraints from Receiver Function Studies

Stacking of approximately 1500 radial receiver functions recorded at about 80 broadband seismic stations deployed in southern Africa reveals systematic spatial variations in the ratio of crustal P and S wave velocities (Φ), crustal thickness (H), and the amplitude of the converted Moho phases (R). The eastern Zimbabwe and the southern Kaapvaal cratons are characterized by small H (~38 km), small Φ (~1.73), and large R (~0.15) values, suggesting that the relatively undisturbed Archean crust beneath southern Africa is separated from the mantle by a sharp Moho and is felsic in composition. The Limpopo belt, which was created by a collisional event at 2.7 Ga, displays large H (~43 km) but similar Φ and R values relative to the cratonic areas. The Bushveld Mafic Intrusion Complex and its surrounding areas show large Φ (~1.78), large H (~43 km), and small R (~0.11) values, reflecting the intrusion of mafic material into the original crust as a result of the Bushveld event at 2.05 Ga. Excluding the Bushveld, the spatially consistent and age-independent low Φ accentuate the difference between felsic crustal composition and more mafic island arcs that are thought to be the likely source of continental material. Within such an island arc model, our data, combined with xenolith data excluding mantle delamination in cratonic environments, suggest that the modification to a felsic composition (e.g., by the partial melting of basalt and removal of residue by delamination) is restricted to have occurred during the collision between the arcs and the continent

Description of recent large-qq neutron inclusive scattering data from liquid 4^4He

We report dynamical calculations for large-$q$ structure functions of liquid $^4$He at $T$=1.6 and 2.3 K and compare those with recent MARI data. We extend those calculations far beyond the experimental range q\le 29\Ain in order to study the approach of the response to its asymptotic limit for a system with interactions having a strong short-range repulsion. We find only small deviations from theoretical $1/q$ behavior, valid for smooth $V$. We repeat an extraction by Glyde et al of cumulant coefficients from data. We argue that fits determine the single atom momentum distribution, but express doubt as to the extraction of meaningful Final State Interaction parameters.Comment: 37 pages, 13 postscript fig

K-shell dielectronic resonances in photoabsorption: differential oscillator strengths for Li-like C IV, O VI, and Fe XXIV

Recently X-ray photoabsorption in KLL resonances of O VI was predicted [Pradhan, Astrophys.J. Lett. 545, L165 (2000)], and detected by the Chandra X-ray Observatory [Lee et al, Astrophys. J. {\it Lett.}, submitted]. The required resonance oscillator strengths f_r, are evaluated in terms of the differential oscillator strength df/de that relates bound and continuum absorption. We present the f_r values from radiatively damped and undamped photoionization cross sections for Li-like C,O, and Fe calculated using relativistic close coupling Breit-Pauli R-matrix method. The KLL resonances of interest here are: 1s2p (^3P^o) 2s [^4P^o_{1/2,3/2}, ^2P^o_{1/2,3/2}] and 1s2p (^1P^o) 2s [^2P^o_{1/2,3/2}]. The KLL photoabsorption resonances in Fe XXIV are fully resolved up to natural autoionization profiles for the first time. It is demonstrated that the undamped f_r independently yield the resonance radiative decay rates, and thereby provide a precise check on the resolution of photoionization calculations in general. The predicted photoabsorption features should be detectable by the X-ray space observatories and enable column densities in highly ionized astrophysical plasmas to be determined from the calculated f_r. The dielectronic satellites may appear as redward broadening of resonances lines in emission and absorption.Comment: 9 pages, 2 figurs, Phys. Rev. A, Rapid Communication (submitted

An inquiry-based learning approach to teaching information retrieval

The study of information retrieval (IR) has increased in interest and importance with the explosive growth of online information in recent years. Learning about IR within formal courses of study enables users of search engines to use them more knowledgeably and effectively, while providing the starting point for the explorations of new researchers into novel search technologies. Although IR can be taught in a traditional manner of formal classroom instruction with students being led through the details of the subject and expected to reproduce this in assessment, the nature of IR as a topic makes it an ideal subject for inquiry-based learning approaches to teaching. In an inquiry-based learning approach students are introduced to the principles of a subject and then encouraged to develop their understanding by solving structured or open problems. Working through solutions in subsequent class discussions enables students to appreciate the availability of alternative solutions as proposed by their classmates. Following this approach students not only learn the details of IR techniques, but significantly, naturally learn to apply them in solution of problems. In doing this they not only gain an appreciation of alternative solutions to a problem, but also how to assess their relative strengths and weaknesses. Developing confidence and skills in problem solving enables student assessment to be structured around solution of problems. Thus students can be assessed on the basis of their understanding and ability to apply techniques, rather simply their skill at reciting facts. This has the additional benefit of encouraging general problem solving skills which can be of benefit in other subjects. This approach to teaching IR was successfully implemented in an undergraduate module where students were assessed in a written examination exploring their knowledge and understanding of the principles of IR and their ability to apply them to solving problems, and a written assignment based on developing an individual research proposal

An efficient scheme for numerical simulations of the spin-bath decoherence

We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of few coupled spins: (i) determining the pointer states of the system, and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For the problems of second type, the Chebyshev-based approach has been 3--4 times faster than the Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide spectrum of systems, with different spin baths and different Hamiltonians.Comment: 8 pages (RevTeX), 3 EPS figure