Nonequilibrium Green’s function method for quantum thermal transport

This review deals with the nonequilibrium Green’s function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In particular, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statistics. In the case of nonlinear systems, we make general comments on the thermal expansion effect, phonon relaxation time, and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF, reduced density matrix, and master equation approaches to thermal transport.     

Dynamics of superhorizon photons during inflation with vacuum polarization

We study asymptotic dynamics of photons propagating in the polarized vacuum of a locally de Sitter Universe. The origin of the vacuum polarization is fluctuations of a massless, minimally coupled, scalar, which we model by the one-loop vacuum polarization tensor of scalar electrodynamics. We show that late time dynamics of the electric field on superhorizon scales approaches that of an Airy oscillator. The magnetic field amplitude, on the other hand, asymptotically approaches a nonvanishing constant (plus an exponentially small oscillatory component), which is suppressed with respect to the initial (vacuum) amplitude. This implies that the asymptotic photon dynamics is more intricate than that of a massive photon obeying the local Proca equation.     

电磁场的复矢量表示

在麦克斯韦方程组及洛伦兹力密度公式基础上引入电磁场复矢量,讨论了电磁场普遍规律的新公式,包括对复矢量电磁场的建立,电荷守恒定律,能量守恒定律,电磁场矢势与标势,电磁场动量、能量、张量、相对论协变性等的研究,并和电动力学相比较,得出一些结论.     

The Kirchhoff gauge

We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge, the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge.     

On the Diagonalization of the Bethe–Salpeter Equation for the Imaginary Part of the Scattering Amplitude

The Bethe–Salpeter (BS) equation for the imaginary part of the scattering amplitude is examined in the ladder approximation of scalar quantum electrodynamics (QED). Asymptotic solutions of the BS equation derived for the imaginary part of the scattering amplitude are shown to exhibit the Regge amplitude behavior for small momentum transfer and scattering in the forward direction and at arbitrary angles.     

Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics

Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that the Schrödinger equation admits an analogous treatment. We present a Lagrangian theory of a real scalar field φ whose equation of motion turns out to be equivalent to the Schrödinger equation with time independent potential. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics. The field φ is in the same relation to the real and imaginary part of a wave function as the vector potential is in respect to electric and magnetic fields. Preservation of quantum-mechanics probability is just an energy conservation law of the field φ.     

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.     

Twisted shear Alfvén waves with orbital angular momentum

It is shown that a dispersive shear Alfvén wave (DSAW) in a magnetized plasma can propagate as a twisted Alfvén vortex beam carrying orbital angular momentum (OAM). We obtain a wave equation from the generalized ion vorticity equation and the magnetic field-aligned electron momentum equation that couple the scalar and vector potentials of the DSAW. A twisted shear Alfvén vortex beam can trap and transport plasma particles and energy in magnetoplasmas, such as those in the Earth?s auroral zone, in the solar atmosphere, and in Large Plasma Device (LAPD) at University of California, Los Angeles.     

Transmission through biased graphene strip

We solve the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum. We use both a numerical Poincaré map approach, based on space discretization of the original Dirac equation, and a direct analytical method. These two approaches have been used to study tunneling phenomena through a biased graphene strip. The numerical results generated by the Poincaré map are in complete agreement with the analytical results.     

Quantum thermal transport in nanostructures

In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scattering boundary condition, mode-matching, Piccard and Caroli formulas) of calculating the phonon transmission coefficients are given. The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli formula is derived. We also give iterative methods and an algorithm based on a generalized eigenvalue problem for the calculation of surface Green's functions, which are starting point for an NEGF calculation. A systematic exposition for the NEGF method is presented, starting from the fundamental definitions of the Green's functions, and ending with equations of motion for the contour ordered Green's functions and Feynman diagrammatic expansion. In the later part, we discuss the treatments of nonlinear effects in heat conduction, including a phenomenological expression for the transmission, NEGF for phonon-phonon interactions, molecular dynamics (generalized Langevin) with quantum heat-baths, and electron-phonon interactions. Some new results are also shown. We briefly review the experimental status of the thermal transport measurements in nanostructures.     

Vector tadpole graphs in the Coleman-Weinberg model

In the Coleman-Weinberg model (massless scalar quantum electrodynamics), a gauge invariant approximation scheme is obtained by summing vector tadpole graphs to all loop orders. We investigate the influence of this summation on the masses of the scalar and vector particles in the model.     

Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals,implementation, and nano-optical applications

In recent years significant experimental advances in nano-scale fabrication techniques and in available light sources have opened the possibility to study a vast set of novel light-matter interaction scenarios, including strong coupling cases. In many situations nowadays, classical electromagnetic modeling is insufficient as quantum effects, both in matter and light, start to play an important role. Instead, a fully self-consistent and microscopic coupling of light and matter becomes necessary. We provide here a critical review of current approaches for electromagnetic modeling, highlighting their limitations. We show how to overcome these limitations by introducing the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli–Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit, the formalism reduces to coupled Ehrenfest–Maxwell–Pauli–Kohn–Sham equations. We present an implementation of the approach in the real-space real-time code Octopus using the Riemann–Silberstein formulation of classical electrodynamics to rewrite Maxwell's equations in Schrödinger form. This allows us to use existing very efficient time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We show how to couple the time-evolution of the electromagnetic fields self-consistently with the quantum time-evolution of the electrons and nuclei. This approach is ideally suited for applications in nano-optics, nano-plasmonics, (photo) electrocatalysis, light-matter coupling in 2D materials, cases where laser pulses carry orbital angular momentum, or light-tailored chemical reactions in optical cavities just to name but a few.     

A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach

With the rapidly increasing integration density and power density in nanoscale electronic devices, the thermal management concerning heat generation and energy harvesting becomes quite crucial. Since phonon is the major heat carrier in semiconductors, thermal transport due to phonons in mesoscopic systems has attracted much attention. In quantum transport studies, the nonequilibrium Green’s function (NEGF) method is a versatile and powerful tool that has been developed for several decades. In this review, we will discuss theoretical investigations of thermal transport using the NEGF approach from two aspects. For the aspect of phonon transport, the phonon NEGF method is briefly introduced and its applications on thermal transport in mesoscopic systems including one-dimensional atomic chains, multi-terminal systems, and transient phonon transport are discussed. For the aspect of thermoelectric transport, the caloritronic effects in which the charge, spin, and valley degrees of freedom are manipulated by the temperature gradient are discussed. The time-dependent thermoelectric behavior is also presented in the transient regime within the partitioned scheme based on the NEGF method.     

The Energy-Momentum Tensor for Electromagnetic Interactions

We compute the energy tensor and the energy-momentum tensor for electrodynamics coupled to the current of a charged scalar field and for electrodynamics coupled tothe current of a Dirac spinor field, without using the equations of motion.     

Simplified Bethe-Salpeter equation for positronium

The Bethe-Salpeter equation for a fermion-antifermion system, coupled by photons, is considered in the Feynman gauge. The kernel is that resulting from exchange of a single photon. The usual reduction of the sixteen B-S spinor amplitudes in terms of tensors leads to 16 coupled integro-differential equations. By straightforward application of charge conjugation-, parity-, and Lorentz-invariance, the system of coupled equations is reduced to ones involving no more than eight and as few as three scalar structure functions for the various parity, charge conjugation, and total angular momentum states. The results hold for arbitrary coupling strength. As a check of the equations obtained, a perturbation theory is carried out for the Coulomb interaction. It leads to effective potentials in agreement with those obtained previously to order mα⁴ for positronium.     

Some properties of evolving wormhole geometries within nonlinear electrodynamics

In this paper, we review some properties for the evolving wormhole solution of Einstein equations coupled to nonlinear electrodynamics. We integrate the geodesic equations in the effective geometry obeyed by photons; we check out the weak field limit and find the traversability conditions. Then we analyze the case when the lagrangian depends on two electromagnetic invariants and it turns out that there is not a more general solution within the assumed geometry.     

等离激元增强的石墨烯光吸收

石墨烯中等离激元具有特殊的光电性质,其和入射光的强烈耦合可以引起光吸收的增强.本文基于时域有限差分法和多体自洽场理论研究了等离激元对处于光学谐振腔中的石墨烯光吸收的影响.由于石墨烯中等离激元与入射光动量和能量不匹配而不能直接相互作用,因此石墨烯上施加了金属光栅结构.研究发现光栅结构能够对入射光进行动量补偿并且能够引起其下石墨烯中的电场强度产生很大程度增强,从而导致在该石墨烯结构中太赫兹等离激元和入射光发生强烈耦合而产生太赫兹等离极化激元,同时引起石墨烯光吸收的增强.希望本文能够加深对石墨烯光电特性的理解以及可以为基于石墨烯的太赫兹光电装置提供一定的理论依据.     

Putting mechanics into circuit quantum electrodynamics

We review the use of mechanical oscillators in circuit quantum electrodynamics. The capacitive coupling of nano-electromechanical systems with quantum bits and superconducting microwave resonators gives rise to a rich quantum physics involving electrons, photons and phonons. We focus in particular on the linear coupling between a mechanical oscillator and a microwave resonator and present the quantum dynamics that stems from the phonotonic Josephson junction. The microwave cavity turns out to be a powerful device to detect quantum phonon states and manipulate entangled states between phonons and photons.     

Breakdown of Casimir invariance in curved space‐time

It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincaré group does not satisfy the properties of Casimir invariance when applied to the non‐inertial motion of particles while in the presence of external gravitational and electromagnetic fields, where general curvilinear co‐ordinates are used to describe the momentum generators within a Fermi normal co‐ordinate framework. Specific expressions of the Casimir scalar properties are presented. While the Casimir scalar for linear momentum remains Lorentz invariant in the absence of external fields, this is no longer true for the spin Casimir scalar. Potential implications are considered for the propagation of photons, gravitons, and gravitinos as described by the spin‐3/2 Rarita‐Schwinger vector‐spinor field. In particular, it is shown that non‐inertial motion introduces a frame‐based effective mass to the spin interaction, with interesting physical consequences that are explored in detail.