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

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.

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

Density-functional calculation of ionization energies of current-carrying atomic states

Current-density-functional theory is used to calculate ionization energies of current-carrying atomic states. A perturbative approximation to full current-density-functional theory is implemented for the first time, and found to be numerically feasible. Different parametrizations for the current-dependence of the density functional are critically compared. Orbital currents in open-shell atoms turn out to produce a small shift in the ionization energies. We find that modern density functionals have reached an accuracy at which small current-related terms appearing in open-shell configurations are not negligible anymore compared to the remaining difference to experiment.Comment: 7 pages, 2 tables, accepted by 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

EEG-Based Functional Brain Networks: Does the Network Size Matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks – whose nodes can vary from tens to hundreds – are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies

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

Modeling the Impact of Lesions in the Human Brain

Lesions of anatomical brain networks result in functional disturbances of brain systems and behavior which depend sensitively, often unpredictably, on the lesion site. The availability of whole-brain maps of structural connections within the human cerebrum and our increased understanding of the physiology and large-scale dynamics of cortical networks allow us to investigate the functional consequences of focal brain lesions in a computational model. We simulate the dynamic effects of lesions placed in different regions of the cerebral cortex by recording changes in the pattern of endogenous (“resting-state”) neural activity. We find that lesions produce specific patterns of altered functional connectivity among distant regions of cortex, often affecting both cortical hemispheres. The magnitude of these dynamic effects depends on the lesion location and is partly predicted by structural network properties of the lesion site. In the model, lesions along the cortical midline and in the vicinity of the temporo-parietal junction result in large and widely distributed changes in functional connectivity, while lesions of primary sensory or motor regions remain more localized. The model suggests that dynamic lesion effects can be predicted on the basis of specific network measures of structural brain networks and that these effects may be related to known behavioral and cognitive consequences of brain lesions