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Concept: Noether's theorem


The conservation laws, such as those of charge, energy and momentum, have a central role in physics. In some special cases, classical conservation laws are broken at the quantum level by quantum fluctuations, in which case the theory is said to have quantum anomalies. One of the most prominent examples is the chiral anomaly, which involves massless chiral fermions. These particles have their spin, or internal angular momentum, aligned either parallel or antiparallel with their linear momentum, labelled as left and right chirality, respectively. In three spatial dimensions, the chiral anomaly is the breakdown (as a result of externally applied parallel electric and magnetic fields) of the classical conservation law that dictates that the number of massless fermions of each chirality are separately conserved. The current that measures the difference between left- and right-handed particles is called the axial current and is not conserved at the quantum level. In addition, an underlying curved space-time provides a distinct contribution to a chiral imbalance, an effect known as the mixed axial-gravitational anomaly, but this anomaly has yet to be confirmed experimentally. However, the presence of a mixed gauge-gravitational anomaly has recently been tied to thermoelectrical transport in a magnetic field, even in flat space-time, suggesting that such types of mixed anomaly could be experimentally probed in condensed matter systems known as Weyl semimetals. Here, using a temperature gradient, we observe experimentally a positive magneto-thermoelectric conductance in the Weyl semimetal niobium phosphide (NbP) for collinear temperature gradients and magnetic fields that vanishes in the ultra-quantum limit, when only a single Landau level is occupied. This observation is consistent with the presence of a mixed axial-gravitational anomaly, providing clear evidence for a theoretical concept that has so far eluded experimental detection.

Concepts: Special relativity, Quantum mechanics, Spin, Noether's theorem, Physics, Standard Model, Quantum field theory, Fundamental physics concepts


In this work, we study the exciton states in a zincblende InGaN/GaN quantum well using a variational technique. The system is considered under the action of intense laser fields with the incorporation of a dc electric field as an additional external probe. The effects of these external influences as well as of the changes in the geometry of the heterostructure on the exciton binding energy are discussed in detail.

Concepts: Mass, Noether's theorem, 2DEG, Electron, Fundamental physics concepts, Nuclear fusion, Photon, Quantum mechanics


Two experiments tested the idea that the principle of resource conservation moderates and limits automaticity effects on effort mobilization. Effort-related cardiovascular response was assessed in cognitive tasks with different levels of task difficulty (Experiment 1) and success incentive (Experiment 2) during which participants were exposed to suboptimally presented action versus inaction primes. As expected, implicit activation of the action concept resulted in stronger effort-related cardiovascular response than activation of the inaction concept-but only when the task was feasible and success incentive was sufficiently high. Effects on task performance were compatible with those on effort. The findings indicate that the automaticity effect of action/inaction primes on effort mobilization is situated, sensitive to task context, and limited by extreme task difficulty and low incentive. The findings facilitate a theoretical integration of automaticity in effort mobilization with the principle of resource conservation. (PsycINFO Database Record © 2013 APA, all rights reserved).

Concepts: Science, Economics, Copyright, Theory, Experiment, Noether's theorem, Concept, All rights reserved


A new type of reaction pathway which involves a nontotally symmetric trifurcation was found and investigated for a typical SN 2-type reaction, NC(-)  + CH3 X → NCCH3  + X(-) (X = F, Cl). A nontotally symmetric valley-ridge inflection (VRI) point was located along the C3 v reaction path. For X = F, the minimum energy path (MEP) starting from the transition state (TS) leads to a second-order saddle point with C3 v symmetry, which connects three product minima of Cs symmetry. For X = Cl, four product minima have been observed, of which three belong to Cs symmetry and one to C3 v symmetry. The branching path from the VRI point to the lower symmetry minima was determined by a linear interpolation technique. The branching mechanism is discussed based on the reaction path curvature and net atomic charges, and the possibility of a nonotally symmetric n-furcation is discussed. © 2015 Wiley Periodicals, Inc.

Concepts: Maxima and minima, Symmetry, Noether's theorem, Optimization, Typography, Rolle's theorem, Critical point, Second derivative test


Saturn’s rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ∼ r(-q) with q ≈ 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 ≤ q ≤ 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn’s rings.

Concepts: Fundamental physics concepts, Derivative, Noether's theorem, Particle physics, Angular momentum, Scientific method, Momentum, Particle size distribution


In the bottom-up synthesis of graphene nanoribbons (GNRs) from self-assembled linear polymer intermediates, surface-assisted cyclodehydrogenations usually take place on catalytic metal surfaces. Here we demonstrate the formation of GNRs from quasi-freestanding polymers assisted by hole injections from a scanning tunnelling microscope (STM) tip. While catalytic cyclodehydrogenations typically occur in a domino-like conversion process during the thermal annealing, the hole-injection-assisted reactions happen at selective molecular sites controlled by the STM tip. The charge injections lower the cyclodehydrogenation barrier in the catalyst-free formation of graphitic lattices, and the orbital symmetry conservation rules favour hole rather than electron injections for the GNR formation. The created polymer-GNR intraribbon heterostructures have a type-I energy level alignment and strongly localized interfacial states. This finding points to a new route towards controllable synthesis of freestanding graphitic layers, facilitating the design of on-surface reactions for GNR-based structures.

Concepts: Electric charge, Scanning tunneling microscope, Atom, Electron, Chemical reaction, Symmetry, Polymer, Noether's theorem


Much efforts are devoted to material structuring in a quest to enhance the photovoltaic effect. We show that structuring light in a way it transfers orbital angular momentum to semiconductor-based rings results in a steady charge accumulation at the outer boundaries that can be utilized for the generation of an open circuit voltage or a photogalvanic (bulk photovoltaic) type current. This effect which stems both from structuring light and matter confinement potentials, can be magnified even at fixed moderate intensities, by increasing the orbital angular momentum of light which strengthens the effective centrifugal potential that repels the charge outwards. Based on a full numerical time propagation of the carriers wave functions in the presence of light pulses we demonstrate how the charge buildup leads to a useable voltage or directed photocurrent whose amplitudes and directions are controllable by the light pulse parameters.

Concepts: Effectiveness, Physical quantities, Atom, Electromagnetism, Noether's theorem, Fundamental physics concepts, Angular momentum, Quantum mechanics


Controlling the flow of light with nanophotonic waveguides has the potential of transforming integrated information processing. Due to the strong transverse confinement of the guided photons, their internal spin and their orbital angular momentum get coupled. Using this spin-orbit interaction of light, we break the mirror symmetry of the scattering of light by a gold nanoparticle on the surface of a nanophotonic waveguide, and realize a chiral waveguide coupler in which the handedness of the incident light determines the propagation direction in the waveguide. We control the directionality of the scattering process and can direct up to 94% of the incoupled light into a given direction. Our approach allows for the control and manipulation of light in optical waveguides and new designs of optical sensors.

Concepts: Photon, Quantum mechanics, Spin, Noether's theorem, Light, Fundamental physics concepts, Angular momentum, Optics


Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.

Concepts: Noether's theorem, T-symmetry, Hilbert space, Quantum mechanics, Classical mechanics, Photon, Symmetry, Physics


Mechanical systems can display topological characteristics similar to that of topological insulators. Here we report a large class of topological mechanical systems related to the BDI symmetry class. These are self-assembled chains of rigid bodies with an inversion centre and no reflection planes. The particle-hole symmetry characteristic to the BDI symmetry class stems from the distinct behaviour of the translational and rotational degrees of freedom under inversion. This and other generic properties led us to the remarkable conclusion that, by adjusting the gyration radius of the bodies, one can always simultaneously open a gap in the phonon spectrum, lock-in all the characteristic symmetries and generate a non-trivial topological invariant. The particle-hole symmetry occurs around a finite frequency, and hence we can witness a dynamical topological Majorana edge mode. Contrasting a floppy mode occurring at zero frequency, a dynamical edge mode can absorb and store mechanical energy, potentially opening new applications of topological mechanics.

Concepts: Fundamental physics concepts, Rotation, Noether's theorem, Rotational symmetry, Erlangen program, Group, Geometry, Energy