Conduction Electrons in Materials — Quantum Corrections

This chapter contains the essential statistical mechanics required to understand the inner workings of, and interpretation of results from, computer simulations. The microcanonical, canonical, isothermal–isobaric, semigrand and grand canonical ensembles are defined. Thermodynamic, structural, and dynamical properties of simple and complex liquids are related to appropriate functions of molecular positions and velocities. A number of important thermodynamic properties are defined in terms of fluctuations in these ensembles. The effect of the inclusion of hard constraints in the underlying potential model on the calculated properties is considered, and the addition of long-range and quantum corrections to classical simulations is presented. The extension of statistical mechanics to describe inhomogeneous systems such as the planar gas–liquid interface, fluid membranes, and liquid crystals, and its application in the simulation of these systems, are discussed.

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Gauge invariance, polar coordinates and inflation

Journal of High Energy Physics ◽

10.1007/jhep03(2021)096 ◽

2021 ◽

Vol 2021 (3) ◽

Cited By ~ 1

Author(s):

Ali Akil ◽

Xi Tong

Keyword(s):

Coordinate System ◽

Effective Potential ◽

Gauge Invariance ◽

Polar Coordinates ◽

Quantum Corrections ◽

Background Current ◽

Gauge Invariant ◽

Gauge Dependence ◽

Current Term ◽

Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

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Quantum corrections to slow-roll inflation: scalar and tensor modes

Journal of High Energy Physics ◽

10.1007/jhep04(2021)273 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Jens O. Andersen ◽

Magdalena Eriksson ◽

Anders Tranberg

Keyword(s):

Scalar Field ◽

Quantum Corrections ◽

Tree Level ◽

Field Equations ◽

Slow Roll ◽

Scalar Field Equations ◽

Slow Rolling ◽

Different Sources ◽

Suitable Potential ◽

Quadratic Order

Abstract Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified with the expectation value of a quantum field, evolving in a quantum effective potential. The shape of this potential is determined by the underlying tree-level potential, dressed by quantum corrections from the scalar field itself and the metric perturbations. Following [1], we compute the effective scalar field equations and the corrected Friedmann equations to quadratic order in both scalar field, scalar metric and tensor perturbations. We identify the quantum corrections from different sources at leading order in slow-roll, and estimate their magnitude in benchmark models of inflation. We comment on the implications of non-minimal coupling to gravity in this context.

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Quantum corrections to generic branes: DBI, NLSM, and more

Journal of High Energy Physics ◽

10.1007/jhep01(2021)159 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Garrett Goon ◽

Scott Melville ◽

Johannes Noller

Keyword(s):

Sigma Models ◽

Quantum Corrections ◽

Higher Dimensional ◽

Symmetry Properties ◽

Non Linear ◽

Quantum Action ◽

Manifest Covariance ◽

Linear Sigma Models ◽

Scalar Sector ◽

Explicit Comparison

Abstract We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

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Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

Canadian Journal of Physics ◽

10.1139/p95-048 ◽

1995 ◽

Vol 73 (5-6) ◽

pp. 344-348 ◽

Cited By ~ 2

Author(s):

Yeong-Chuan Kao ◽

Hsiang-Nan Li

Keyword(s):

Effective Action ◽

Background Field ◽

Landau Gauge ◽

Quantum Corrections ◽

Simons Theory ◽

Loop Correction ◽

Loop Contribution ◽

Yang Mills ◽

Chern Simons ◽

Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

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An interpretation on the thermodynamic properties of liquid Pb–Te alloys

High Temperature Materials and Processes ◽

10.1515/htmp-2020-0068 ◽

2020 ◽

Vol 39 (1) ◽

pp. 297-303

Author(s):

Toru Akasofu ◽

Masanobu Kusakabe ◽

Shigeru Tamaki

Keyword(s):

Thermodynamic Properties ◽

Electron Affinity ◽

Ionization Energy ◽

Narrow Band ◽

Structural Information ◽

Lead Telluride ◽

Liquid Lead ◽

Metallic State ◽

Ternary Solution ◽

Conduction Electrons

AbstractThe bonding character of liquid lead telluride \text{PbTe} is thermodynamically investigated in detail. Its possibility as an ionic melt composed of cation {\text{Pb}}^{2+} and anion {\text{Te}}^{2-} is not acceptable, by comparing the ionization energy of \text{Pb} atom, electron affinity of \text{Te} atom and the ionic bonding energy due to the cation {\text{Pb}}^{2+} and anion {\text{Te}}^{2-} with the help of structural information. Solid lead telluride PbTe as a narrow band gap semiconductor might yield easily the overlapping of the tail of valence band and that of conduction one. And on melting, it becomes to an ill-conditioned metallic state, which concept is supported by the electrical behaviors of liquid Pb–Te alloys observed by the present authors. As structural information tells us about the partial remain of some sorts of covalent-type mono-dipole and poly-dipole of the molecule \text{PbTe}, all systems are thermodynamically explained in terms of a mixture of these molecules and cations {\text{Pb}}^{4+} and {\text{Te}}^{2+} and a small amount of the conduction electrons are set free from these elements based on the ternary solution model.

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Ruderman–Kittel–Kasuya–Yosida-type interfacial Dzyaloshinskii–Moriya interaction in heavy metal/ferromagnet heterostructures

Nature Communications ◽

10.1038/s41467-021-23586-y ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Taehyun Kim ◽

In Ho Cha ◽

Yong Jin Kim ◽

Gyu Won Kim ◽

Andrey Stashkevich ◽

...

Keyword(s):

Heavy Metal ◽

Exchange Coupling ◽

Spin Orbit Coupling ◽

Conduction Electrons ◽

Indirect Exchange ◽

Metal Atoms ◽

Technological Potential ◽

Interfacial Modification ◽

Coupling Phenomena ◽

Moriya Interaction

AbstractThe manipulation of magnetization with interfacial modification using various spin-orbit coupling phenomena has been recently revisited due to its scientific and technological potential for next-generation memory devices. Herein, we experimentally and theoretically demonstrate the interfacial Dzyaloshinskii–Moriya interaction characteristics penetrating through a MgO dielectric layer inserted between the Pt and CoFeSiB. The inserted MgO layer seems to function as a chiral exchange interaction mediator of the interfacial Dzyaloshinskii–Moriya interaction from the heavy metal atoms to ferromagnet ones. The potential physical mechanism of the anti-symmetric exchange is based on the tunneling-like behavior of conduction electrons through the semi-conductor-like ultrathin MgO. Such behavior can be correlated with the oscillations of the indirect exchange coupling of the Ruderman–Kittel–Kasuya–Yosida type. From the theoretical demonstration, we could provide approximate estimation and show qualitative trends peculiar to the system under investigation.

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