Invariant variational principle for Hamiltonian mechanics

It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some 1-form $\gamma$, such that $\omega= d \gamma$, which is not unique and does not even generally exist in a global sense.Comment: final version; to appear in J.Phys.A; 17 pages, 2 figure

Patterns of change in subjective cognitive complaints are associated with cognitive decline and dementia risk: Findings from the Sydney Memory and Ageing Study

Background Subjective cognitive complaints (SCCs) are now an established risk factor for dementia, however, little is known about whether changing patterns in SCCs over time are associated with cognitive decline and dementia risk. We examine the trajectory of SCCs over a 6‐year period to determine whether intraindividual patterns of reporting SCCs over time is related to cognitive decline and incident dementia. Method Participants were 1037 older adults without dementia (M age = 78.65 years; 55% females) from the Sydney Memory and Ageing Study who were followed‐up biennially. Global cognition was measured using a comprehensive neuropsychological battery, and clinical diagnoses were made by an expert consensus panel. SCCs were obtained as participants’ response to a single question concerning their subjective report of memory decline. Patterns of SCCs over time were modelled by conducting categorical latent growth curve analysis using the logit transformation (Figure 1). We examined the associations between average level of SCC likelihood and change in SCC likelihood, with global cognition over six years using latent growth curve analysis, and with risk of incident dementia over 10 years using Cox regression. Result In this community‐dwelling older adult sample, there was an annual 10% increase in the odds of reporting SCCs (Figure 2). After controlling for demographics, depression, and personality, results revealed a negative longitudinal association between the slope of SCCs and the slope of global cognition scores, such that participants with an increasing propensity of reporting SCCs over time also showed a steeper rate of decline in global cognition (Figure 4). Cox regression revealed an association between increased SCCs and incident dementia risk (Table 1). That is, participants with an increasing propensity of reporting SCCs over time are also at greater risk for developing dementia (Figure 5). Conclusion This is the first study to use latent growth curve analysis to examine patterns of change in SCCs overtime. Traditionally, studies examining SCCs longitudinally categorise people as ‘stable’ versus ‘not stable’, however, important information may be lost this way. Understanding patterns of change in SCC reporting over time has significant potential to identify individuals at greater risk of cognitive decline and incident dementia

Electronic Spin Transport in Dual-Gated Bilayer Graphene

The elimination of extrinsic sources of spin relaxation is key in realizing the exceptional intrinsic spin transport performance of graphene. Towards this, we study charge and spin transport in bilayer graphene-based spin valve devices fabricated in a new device architecture which allows us to make a comparative study by separately investigating the roles of substrate and polymer residues on spin relaxation. First, the comparison between spin valves fabricated on SiO2 and BN substrates suggests that substrate-related charged impurities, phonons and roughness do not limit the spin transport in current devices. Next, the observation of a 5-fold enhancement in spin relaxation time in the encapsulated device highlights the significance of polymer residues on spin relaxation. We observe a spin relaxation length of ~ 10 um in the encapsulated bilayer with a charge mobility of 24000 cm2/Vs. The carrier density dependence of spin relaxation time has two distinct regimes; n<4 x 1012 cm-2, where spin relaxation time decreases monotonically as carrier concentration increases, and n>4 x 1012 cm-2, where spin relaxation time exhibits a sudden increase. The sudden increase in the spin relaxation time with no corresponding signature in the charge transport suggests the presence of a magnetic resonance close to the charge neutrality point. We also demonstrate, for the first time, spin transport across bipolar p-n junctions in our dual-gated device architecture that fully integrates a sequence of encapsulated regions in its design. At low temperatures, strong suppression of the spin signal was observed while a transport gap was induced, which is interpreted as a novel manifestation of impedance mismatch within the spin channel

The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.Comment: 16 pages, 4 figure

Social cognitive abilities in older adults with mild cognitive impairment and dementia

Background Aging is associated with changes in general cognition and social cognition. Many studies have detailed these functions in isolation, comparing young and older adults. More information is needed on how social cognition, including theory of mind (ToM), affective empathy (AE), social perception (SP), and social behavior (SB), is affected at different cognitive stages in older adults. Method Cross‐sectional study of 305 older adults from the Sydney Memory and Ageing Study. Dementia was classified based on clinical consensus using DSM‐IV criteria, while mild cognitive impairment (MCI) was classified using the International Working Group criteria. Cognitively normal (CN), MCI, and dementia participants were compared on social cognitive domains including: ToM, via the Reading the Mind in the Eyes Test (RMET) and the Interpersonal Reactivity Index – Perspective Taking subscale (IRI‐PT); AE, via the IRI – Empathic Concern subscale (IRI‐EC); and SP, via the Emotion Recognition Task (ERT). Apathy, which is related to SB, was measured via the Apathy Evaluation Scale (AES). Result Mean age 87.00 ± 4.05 years, mean education 11.89 ± 3.36 years, 60.3% female. 141 were CN, 103 had MCI, and 61 had dementia. Across cognitive groups, significant differences were observed for the RMET, ERT (specifically for the recognition of anger, disgust, and happiness), AES, IRI‐PT, and IRI‐EC. In posthoc comparisons, RMET and ERT were significantly poorer in MCI and dementia compared to CN, but not between MCI and dementia. IRI ratings and AES were poorer for dementia compared to MCI and CN, but not between MCI and CN (Table 1). In multivariable logistic regression adjusting for significant risk factors for cognitive impairment, RMET and ERT disgust performance were associated with lower risk of MCI over CN. Only AES significantly differentiated dementia from MCI (Table 2). Conclusion Neurocognitive disorders are associated with social cognition changes. ToM and SP appear to be affected in MCI relative to CN. Apathy, known to be linked to SB, appears to be affected in dementia. MCI seems to be associated with impaired ability to recognize specific social cognitive cues, while dementia may be more associated with overall worse social cognitive functioning and observed behavioral changes

Two-atom dark states in electromagnetic cavities

The center-of-mass motion of two two-level atoms coupled to a single damped mode of an electromagnetic resonator is investigated. For the case of one atom being initially excited and the cavity mode in the vacuum state it is shown that the atomic time evolution is dominated by the appearance of dark states. These states, in which the initial excitation is stored in the internal atomic degrees of freedom and the atoms become quantum mechanically entangled, are almost immune against photon loss from the cavity. Various properties of the dark states within and beyond the Raman-Nath approximation of atom optics are worked out.Comment: 8 pages, 4 figure

The HMW effect in Noncommutative Quantum Mechanics

The HMW effect in non-commutative quantum mechanics is studied. By solving the Dirac equations on non-commutative (NC) space and non-commutative phase space, we obtain topological HMW phase on NC space and NC phase space respectively, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.Comment: 8 Latex page

A direct approach to the construction of standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients

We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and find Lagrangian formulations which seem to be new. Some of the considered systems (e.g., motions with the friction proportional to the velocity and to the square of the velocity) admit infinite families of different Lagrangian formulations.Comment: 17 page

Gate-tunable black phosphorus spin valve with nanosecond spin lifetimes

Two-dimensional materials offer new opportunities for both fundamental science and technological applications, by exploiting the electron spin. While graphene is very promising for spin communication due to its extraordinary electron mobility, the lack of a band gap restricts its prospects for semiconducting spin devices such as spin diodes and bipolar spin transistors. The recent emergence of 2D semiconductors could help overcome this basic challenge. In this letter we report the first important step towards making 2D semiconductor spin devices. We have fabricated a spin valve based on ultra-thin (5 nm) semiconducting black phosphorus (bP), and established fundamental spin properties of this spin channel material which supports all electrical spin injection, transport, precession and detection up to room temperature (RT). Inserting a few layers of boron nitride between the ferromagnetic electrodes and bP alleviates the notorious conductivity mismatch problem and allows efficient electrical spin injection into an n-type bP. In the non-local spin valve geometry we measure Hanle spin precession and observe spin relaxation times as high as 4 ns, with spin relaxation lengths exceeding 6 um. Our experimental results are in a very good agreement with first-principles calculations and demonstrate that Elliott-Yafet spin relaxation mechanism is dominant. We also demonstrate that spin transport in ultra-thin bP depends strongly on the charge carrier concentration, and can be manipulated by the electric field effect

The latent construct of dementia phenotype: Validation and longitudinal examination in the Sydney Memory and Ageing Study

Background The latent continuous construct delta (δ) has been proposed as a novel approach to model dementia phenotype using structural equation modelling that reflects the “cognitive correlates of functional status” (Royall &amp; Palmer, 2012. J Neuropsychiatry Clin Neurosci; Royall et al., 2012. J Alzheimers Dis). This δ factor has been demonstrated to be associated with clinically diagnosed dementia status and severity of dementia. However, thus far there are few studies validating the model longitudinally and these are in American samples. To establish the potential research and clinical utility of δ, the current research constructs and validates this latent dementia factor over a 6‐year period in a community sample of Australian older adults. Method A community‐dwelling sample of Australian older adults without dementia (at baseline) from the Sydney Memory and Ageing Study was used (n = 1037; M age = 78.65 years; 55% females). Biennially, participants completed a battery of neuropsychological tests measuring performance in four major cognitive domains, and informants rated their functional status on instrumental activities of daily living. Dementia status and severity were established through consensus diagnosis by an expert panel of clinicians and the Clinical Dementia Rating Scale Sum of Boxes (CDR‐SOB), respectively. Result A latent growth curve model of δ and Spearman’s general intelligence factor (g) built on four waves of cognitive and function data revealed good fit: CFI = 0.97, RMSEA = 0.04, SRMR = 0.06. A significant increase in δ over time was observed, and this latent change in δ (Δδ) was significantly associated with CDR‐SOB at wave 4 after controlling for demographics, APOE*4, and baseline CDR‐SOB. Cox regression revealed a significant association between Δδ and incident dementia. Further, Δδ accurately discriminated diagnosed dementia cases at wave 4 (ROC area under the curve = 0.91, 95% CI [0.88, 0.95]). Conclusion This study tests and validates the δ framework in Australian older adults by demonstrating that the change in δ over 6 years is associated with dementia risk and prospective severity of dementia. Future research should further test the model using longitudinal data from geographically and ethnoculturally diverse samples