Quantum interference from sums over closed paths for electrons on a three-dimensional lattice in a magnetic field: total energy, magnetic moment, and orbital susceptibility

We study quantum interference effects due to electron motion on a three-dimensional cubic lattice in a continuously-tunable magnetic field of arbitrary orientation and magnitude. These effects arise from the interference between magnetic phase factors associated with different electron closed paths. The sums of these phase factors, called lattice path-integrals, are ``many-loop" generalizations of the standard ``one-loop" Aharonov-Bohm-type argument. Our lattice path integral calculation enables us to obtain various important physical quantities through several different methods. The spirit of our approach follows Feynman's programme: to derive physical quantities in terms of ``sums over paths". From these lattice path-integrals we compute analytically, for several lengths of the electron path, the half-filled Fermi-sea ground-state energy of noninteracting spinless electrons in a cubic lattice. Our results are valid for any strength of the applied magnetic field in any direction. We also study in detail two experimentally important quantities: the magnetic moment and orbital susceptibility at half-filling, as well as the zero-field susceptibility as a function of the Fermi energy.Comment: 14 pages, RevTe

An exchange-correlation energy for a two-dimensional electron gas in a magnetic field

We present the results of a variational Monte Carlo calculation of the exchange-correlation energy for a spin-polarized two-dimensional electron gas in a perpendicular magnetic field. These energies are a necessary input to the recently developed current-density functional theory. Landau-level mixing is included in a variational manner, which gives the energy at finite density at finite field, in contrast to previous approaches. Results are presented for the exchange-correlation energy and excited-state gap at $\nu =$ 1/7, 1/5, 1/3, 1, and 2. We parameterize the results as a function of $r_s$ and $\nu$ in a form convenient for current-density functional calculations.Comment: 36 pages, including 6 postscript figure

Mobility impairment is associated with reduced microstructural integrity of the inferior and superior cerebellar peduncles in elderly with no clinical signs of cerebellar dysfunction☆

While the cerebellum plays a critical role in motor coordination and control no studies have investigated its involvement in idiopathic mobility impairment in community-dwelling elderly. In this study we tested the hypothesis that structural changes in the cerebellar peduncles not detected by conventional magnetic resonance imaging are associated with reduced mobility performance. The analysis involved eighty-five subjects (age range: 75–90 years) who had no clinical signs of cerebellar dysfunction. Based on the short physical performance battery (SPPB) score, we defined mobility status of the subjects in the study as normal (score 11–12, n = 26), intermediate (score 9–10, n = 27) or impaired (score < 9, n = 32). We acquired diffusion tensor imaging data to obtain indices of white matter integrity: fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD) and radial diffusivity (RD). Using a parcellation atlas, regional indices within the superior, middle, and inferior cerebellar peduncles (ICP, MCP, SCP) were calculated and their associations with mobility performance were analyzed. Subjects with impaired mobility showed reduced FA and AD values in the ICP and SCP but not in the MCP. The ICP-FA, ICP-AD and SCP-FA indices showed a significant association with the SPPB score. We also observed significant correlation between ICP-FA and walk time (r = − 0.311, p = 0.004), as well as between SCP-AD and self-paced maximum walking velocity (r = 0.385, p = 0.003) and usual walking velocity (r = 0.400, p = 0.002). In logistic regression analysis ICP-FA and ICP-AD together explained 51% of the variability in the mobility status of a sample comprising the normal and impaired subgroups, and correctly classified more than three-quarters of those subjects. Our findings suggest that presence of microstructural damage, likely axonal, in afferent and efferent connections of the cerebellum contributes to the deterioration of motor performance in older people

Exchange and correlation energies of ground states of atoms and molecules in strong magnetic fields

Using a Hartree-Fock mesh method and a configuration interaction approach based on a generalized Gaussian basis set we investigate the behaviour of the exchange and correlation energies of small atoms and molecules, namely th e helium and lithium atom as well as the hydrogen molecule, in the presence of a magnetic field covering the regime B=0-100a.u. In general the importance of the exchange energy to the binding properties of at oms or molecules increases strongly with increasing field strength. This is due to the spin-flip transitions and in particular due to the contributions of the tightly bound hydrogenic state s which are involved in the corresponding ground states of different symmetries. In contrast to the exchange energy the correlation energy becomes less relevant with increasing field strength. This holds for the individual configurations constituting the ground state and for the crossovers of the global ground state.Comment: 4 Figures acc.f.publ.in Phys.Rev.

Quantum Hall effect in single wide quantum wells

We study the quantum Hall states in the lowest Landau level for a single wide quantum well. Due to a separation of charges to opposite sides of the well, a single wide well can be modelled as an effective two level system. We provide numerical evidence of the existence of a phase transition from an incompressible to a compressible state as the electron density is increased for specific well width. Our numerical results show a critical electron density which depends on well width, beyond which a transition incompressible double layer quantum Hall state to a mono-layer compressible state occurs. We also calculate the related phase boundary corresponding to destruction of the collective mode energy gap. We show that the effective tunneling term and the interlayer separation are both renormalised by the strong magnetic field. We also exploite the local density functional techniques in the presence of strong magnetic field at $\nu=1$ to calculate renormalized $\Delta_{SAS}$. The numerical results shows good agreement between many-body calculations and local density functional techniques in the presence of a strong magnetic field at $\nu=1$. we also discuss implications of this work on the $\nu=1/2$ incompressible state observed in SWQW.Comment: 30 pages, 7 figures (figures are not included

Realistic Calculations of Correlated Incompressible Electronic States in GaAs--Al_{x}Ga_{1-x}As Heterostructures and Quantum Wells

We perform an exact spherical geometry finite-size diagonalization calculation for the fractional quantum Hall ground state in three different experimentally relevant GaAs-Al_{x}Ga_{1-x}As systems: a wide parabolic quantum well, a narrow square quantum well, and a heterostructure. For each system we obtain the Coulomb pseudopotential parameters entering the exact diagonalization calculation by using the realistic subband wave function from a self-consistent electronic structure calculation within the local density approximation (LDA) for a range of electron densities. We compare our realistic LDA pseudopotential parameters with those from widely used simpler model approximations in order to estimate the accuracies of the latter. We also calculate the overlap between the exact numerical ground state and the analytical Laughlin state as well as the excitation gap as a function of density. For the three physical systems we consider the calculated overlap is found to be large in the experimental electron density range. We compare our calculated excitation gap energy to the experimentally obtained activated transport energy gaps after subtracting out the effect of level broadening due to collisions. The agreement between our calculated excitation gaps and the experimental measurements is excellent.Comment: 24 pages, RevTex, 20 figure

A novel brain partition highlights the modular skeleton shared by structure and function

Elucidating the intricate relationship between brain structure and function, both in healthy and pathological conditions, is a key challenge for modern neuroscience. Recent progress in neuroimaging has helped advance our understanding of this important issue, with diffusion images providing information about structural connectivity (SC) and functional magnetic resonance imaging shedding light on resting state functional connectivity (rsFC). Here, we adopt a systems approach, relying on modular hierarchical clustering, to study together SC and rsFC datasets gathered independently from healthy human subjects. Our novel approach allows us to find a common skeleton shared by structure and function from which a new, optimal, brain partition can be extracted. We describe the emerging common structure-function modules (SFMs) in detail and compare them with commonly employed anatomical or functional parcellations. Our results underline the strong correspondence between brain structure and resting-state dynamics as well as the emerging coherent organization of the human brain.Work supported by Ikerbasque: The Basque Foundation for Science, Euskampus at UPV/EHU, Gobierno Vasco (Saiotek SAIO13-PE13BF001) and Junta de Andalucía (P09-FQM-4682) to JMC; Ikerbasque Visiting Professor to SS; Junta de Andalucía (P09-FQM-4682) and Spanish Ministry of Economy and Competitiveness (FIS2013-43201-P) to MAM; the European Union’s Seventh Framework Programme (ICT-FET FP7/2007-2013, FET Young Explorers scheme) under grant agreement n. 284772 BRAIN BOW (www.brainbowproject.eu) and by the Joint Italy—Israel Laboratory on Neuroscience to PB. For results validation (figure S8), data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University

Copy number deletion burden is associated with cognitive, structural, and resting-state network differences in patients with schizophrenia

Total burden of copy number deletions has been implicated in schizophrenia risk and has been associated with reduced cognitive functioning. The current study aims to replicate the cognitive findings and investigate regional grey and white matter volumes. Moreover, it will explore resting-state networks for correlations between functional connectivity and total deletion burden. All imaging differences will be investigated for correlations with cognitive differences. Seventy-eight patients with chronic schizophrenia, who formed a subset of a large genome-wide association study (GWAS), were assessed for intelligence, 34 had structural magnetic resonance imaging, 33 had resting-state functional magnetic resonance imaging, and 32 had diffusion tensor imaging (DTI). Total deletion burden was negatively associated with IQ performance and positively associated with regional volumes in the striatum bilaterally and in the right superior temporal gyrus and white-matter in the corpus callosum. Correlations were identified between deletion burden and both hyper and hypoconnectivity within the default-mode network and hypoconnectivity within the cognitive control network. The functional connectivity correlations with deletion burden were also correlated with the IQ differences identified. Total deletion burden affects regional volumes and resting-state functional connectivity in key brain networks in patients with schizophrenia. Moreover, effects of deletions on cognitive functioning in may be due to inefficiency of key brain networks as identified by dysconnectivity in resting-state networks

Integrating Functional and Diffusion Magnetic Resonance Imaging for Analysis of Structure-Function Relationship in the Human Language Network

The capabilities of magnetic resonance imaging (MRI) to measure structural and functional connectivity in the human brain have motivated growing interest in characterizing the relationship between these measures in the distributed neural networks of the brain. In this study, we attempted an integration of structural and functional analyses of the human language circuits, including Wernicke's (WA), Broca's (BA) and supplementary motor area (SMA), using a combination of blood oxygen level dependent (BOLD) and diffusion tensor MRI.Functional connectivity was measured by low frequency inter-regional correlations of BOLD MRI signals acquired in a resting steady-state, and structural connectivity was measured by using adaptive fiber tracking with diffusion tensor MRI data. The results showed that different language pathways exhibited different structural and functional connectivity, indicating varying levels of inter-dependence in processing across regions. Along the path between BA and SMA, the fibers tracked generally formed a single bundle and the mean radius of the bundle was positively correlated with functional connectivity. However, fractional anisotropy was found not to be correlated with functional connectivity along paths connecting either BA and SMA or BA and WA. for use in diagnosing and determining disease progression and recovery

Matter in Strong Magnetic Fields

The properties of matter are significantly modified by strong magnetic fields, $B>>2.35\times 10^9$ Gauss ($1 G =10^{-4} Tesla$), as are typically found on the surfaces of neutron stars. In such strong magnetic fields, the Coulomb force on an electron acts as a small perturbation compared to the magnetic force. The strong field condition can also be mimicked in laboratory semiconductors. Because of the strong magnetic confinement of electrons perpendicular to the field, atoms attain a much greater binding energy compared to the zero-field case, and various other bound states become possible, including molecular chains and three-dimensional condensed matter. This article reviews the electronic structure of atoms, molecules and bulk matter, as well as the thermodynamic properties of dense plasma, in strong magnetic fields, $10^9G << B < 10^{16}G$. The focus is on the basic physical pictures and approximate scaling relations, although various theoretical approaches and numerical results are also discussed. For the neutron star surface composed of light elements such as hydrogen or helium, the outermost layer constitutes a nondegenerate, partially ionized Coulomb plasma if $B<<10^{14}G$, and may be in the form of a condensed liquid if the magnetic field is stronger (and temperature $<10^6$ K). For the iron surface, the outermost layer of the neutron star can be in a gaseous or a condensed phase depending on the cohesive property of the iron condensate.Comment: 45 pages with 9 figures. Many small additions/changes. Accepted for publication in Rev. Mod. Phy