PT-Symmetric Electronics

We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT-symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT-dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT-symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT-symmetric electronics offers new insights into the properties of PT-symmetric systems which are at the forefront of the research in mathematical physics and related fields.Comment: 17 pages, 7 figure

PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring

We study the properties of an N-site tight-binding ring with parity and time-reversal (PT) symmetric, Hermitian, site-dependent tunneling and a pair of non-Hermitian, PT-symmetric, loss and gain impurities $\pm i\gamma$. The properties of such lattices with open boundary conditions have been intensely explored over the past two years. We numerically investigate the PT-symmetric phase in a ring with a position-dependent tunneling function $t_\alpha(k)=[k(N-k)]^{\alpha/2}$ that, in an open lattice, leads to a strengthened PT-symmetric phase, and study the evolution of the PT-symmetric phase from the open chain to a ring. We show that, generally, periodic boundary conditions weaken the PT-symmetric phase, although for experimentally relevant lattice sizes $N \sim 50$, it remains easily accessible. We show that the chirality, quantified by the (magnitude of the) average transverse momentum of a wave packet, shows a maximum at the PT-symmetric threshold. Our results show that although the wavepacket intensity increases monotonically across the PT-breaking threshold, the average momentum decays monotonically on both sides of the threshold.Comment: 11 pages, 5 figures, preprin

An exactly solvable quantum-lattice model with a tunable degree of nonlocality

An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose spectrum is known as equal to the set of zeros of the N-th Laguerre polynomial. The two key problems (viz., the one of the ambiguity and the one of the closed-form construction of all of the eligible inner products which make $H$ Hermitian in the respective {\em ad hoc} Hilbert spaces) are discussed. Then, for illustration, the first four simplest, $k-$parametric definitions of inner products with $k=0,k=1,k=2$ and $k=3$ are explicitly displayed. In mathematical terms these alternative inner products may be perceived as alternative Hermitian conjugations of the initial N-plet of Laguerre polynomials. In physical terms the parameter $k$ may be interpreted as a measure of the "smearing of the lattice coordinates" in the model.Comment: 35 p

Electrical manipulation of spin states in a single electrostatically gated transition-metal complex

We demonstrate an electrically controlled high-spin (S=5/2) to low-spin (S=1/2) transition in a three-terminal device incorporating a single Mn2+ ion coordinated by two terpyridine ligands. By adjusting the gate-voltage we reduce the terpyridine moiety and thereby strengthen the ligand-field on the Mn-atom. Adding a single electron thus stabilizes the low-spin configuration and the corresponding sequential tunnelling current is suppressed by spin-blockade. From low-temperature inelastic cotunneling spectroscopy, we infer the magnetic excitation spectrum of the molecule and uncover also a strongly gate-dependent singlet-triplet splitting on the low-spin side. The measured bias-spectroscopy is shown to be consistent with an exact diagonalization of the Mn-complex, and an interpretation of the data is given in terms of a simplified effective model.Comment: Will appear soon in Nanoletter

Model parameterization to simulate and compare the PAR absorption potential of two competing plant species

Mountain pastures dominated by the pasture grass Setaria sphacelata in the Andes of southern Ecuador are heavily infested by southern bracken (Pteridium arachnoideum), a major problem for pasture management. Field observations suggest that bracken might outcompete the grass due to its competitive strength with regard to the absorption of photosynthetically active radiation (PAR). To understand the PAR absorption potential of both species, the aims of the current paper are to (1) parameterize a radiation scheme of a two-big-leaf model by deriving structural (LAI, leaf angle parameter) and optical (leaf albedo, transmittance) plant traits for average individuals from field surveys, (2) to initialize the properly parameterized radiation scheme with realistic global irradiation conditions of the Rio San Francisco Valley in the Andes of southern Ecuador, and (3) to compare the PAR absorption capabilities of both species under typical local weather conditions. Field data show that bracken reveals a slightly higher average leaf area index (LAI) and more horizontally oriented leaves in comparison to Setaria. Spectrometer measurements reveal that bracken and Setaria are characterized by a similar average leaf absorptance. Simulations with the average diurnal course of incoming solar radiation (1998–2005) and the mean leaf–sun geometry reveal that PAR absorption is fairly equal for both species. However, the comparison of typical clear and overcast days show that two parameters, (1) the relation of incoming diffuse and direct irradiance, and (2) the leaf–sun geometry play a major role for PAR absorption in the two-big-leaf approach: Under cloudy sky conditions (mainly diffuse irradiance), PAR absorption is slightly higher for Setaria while under clear sky conditions (mainly direct irradiance), the average bracken individual is characterized by a higher PAR absorption potential. (∼74 MJ m−2 year−1). The latter situation which occurs if the maximum daily irradiance exceeds 615 W m−2 is mainly due to the nearly orthogonal incidence of the direct solar beam onto the horizontally oriented frond area which implies a high amount of direct PAR absorption during the noon maximum of direct irradiance. Such situations of solar irradiance favoring a higher PAR absorptance of bracken occur in ∼36% of the observation period (1998–2005). By considering the annual course of PAR irradiance in the San Francisco Valley, the clear advantage of bracken on clear days (36% of all days) is completely compensated by the slight but more frequent advantage of Setaria under overcast conditions (64% of all days). This means that neither bracken nor Setaria show a distinct advantage in PAR absorption capability under the current climatic conditions of the study area

Structure formation in active networks

Structure formation and constant reorganization of the actin cytoskeleton are key requirements for the function of living cells. Here we show that a minimal reconstituted system consisting of actin filaments, crosslinking molecules and molecular-motor filaments exhibits a generic mechanism of structure formation, characterized by a broad distribution of cluster sizes. We demonstrate that the growth of the structures depends on the intricate balance between crosslinker-induced stabilization and simultaneous destabilization by molecular motors, a mechanism analogous to nucleation and growth in passive systems. We also show that the intricate interplay between force generation, coarsening and connectivity is responsible for the highly dynamic process of structure formation in this heterogeneous active gel, and that these competing mechanisms result in anomalous transport, reminiscent of intracellular dynamics

Effects of repetitive exposure to pain and morphine treatment on the neonatal rat brain

Background: Untreated exposure to pain in preterm neonates might damage the vulnerable premature brain and alter development. Pain treatment is limited because analgesic agents may also have adverse neurodevelopmental consequences in newborns. Objective: To study the effects of neonatal pain and morphine treatment on the developing brain in a n

Physical activity in pregnancy:a mixed methods process evaluation of the FitMum randomised controlled trial interventions

BACKGROUND: Physical activity (PA) at moderate intensity is recommended for healthy pregnant women. The three-arm FitMum randomised controlled trial showed that it was possible to increase PA level during pregnancy with structured supervised exercise training (EXE) compared to standard care. Motivational counselling on PA (MOT) did not increase PA. This process evaluation aims to understand the implementation and mechanisms of impact of EXE and MOT. METHODS: A mixed methods process evaluation was conducted using the UK Medical Research Council’s process evaluation framework by assessing implementation (reach, fidelity, and dose) and mechanisms of impact of the two interventions provided to pregnant women in FitMum. Data was collected both quantitatively (n = 220) and qualitatively (n = 20). RESULTS: The FitMum trial reached educated pregnant women (80% having an educational level ≥ bachelor’s degree) with high autonomy of everyday life. Most participants (58%) were recruited at their first-trimester ultrasonic scan. Reasons to participate were personal (91%) and altruistic (56%). The intervention dose was delivered as intended with high fidelity in the original physical intervention setup and in the altered online setup during the COVID-19 restrictions. A low dose received in EXE (1.3 [95% CI, 1.1; 1.5] sessions/week) was partly explained by the pre-scheduled EXE sessions favouring participants with a flexible everyday life and a supportive social network. Dose received in EXE increased during online intervention delivery. Participants in MOT received 5.2 [4.7; 5.7] of 7 sessions. Mechanisms of impact comprised a perception of intervention commitment among participants in EXE due to the scheduled EXE sessions, whereas participants in MOT considered themselves as PA self-determined. PA was considered as constrained activities in EXE and included in daily activities in MOT. CONCLUSION: The FitMum interventions was delivered with high fidelity. During COVID-19, the dose received in EXE increased compared to the previous physical setup. Mechanisms of impact as commitment, perception of empowerment and perception of PA as well as the paradox between prioritising PA and family and the need of a flexible everyday life need to be considered when offering pregnant women PA interventions. Future interventions should consider a combination of physical and online exercise training for pregnant women. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12889-022-14717-1