DOCSLIB.ORG

Plasma Oscillations, Just Like Phonons Are Quantizations of Mechanical Vibrations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Plasma Oscillations, Just Like Phonons Are Quantizations of Mechanical Vibrations Optical Properties of Plasma Course: B.Sc. Physical Sciences Semester: VI, Section C Paper: Solid State Physics Instructor: Manish K. Shukla Plasma • Plasma is a gas of charge particles. • The plasma is overall neutral, i.e., the number density of the electrons and ions are the same. • Under normal conditions, there are always equal numbers positive ions and electrons in any volume of the plasma, so the charge density 휌 = 0, and there is no large scale electric field in the plasma. 22 April 2020 2 Plasma Oscillation 22 April 2020 3 Plasma Oscillation contd. Now imagine that all of the electrons are displaced to the right by a small amount x, while the positive ions are held fixed, as shown on the right side of the figure above. The displacement of the electrons to the right leaves an excess of positive charge on the left side of the plasma slab and an excess of negative charge on the right side, as indicated by the dashed rectangular boxes. The positive slab on the left and the negative slab on the right produce an electric field pointing toward the right that pulls the electrons back toward their original locations. However, the electric force on the electrons causes them to accelerate and gain kinetic energy, so they will overshoot their original positions. This situation is similar to a mass on a horizontal frictionless surface connected to a horizontal spring. In the present problem,. the electrons execute simple harmonic motion at a frequency that is called the “plasma frequency”. Derivation of Plasma frequency Derivation of Plasma frequency contd. Derivation of Plasma frequency 푓0= 8.98 푁 Plasmon o A plasmon is a quantum of plasma oscillation. o Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. o The plasmon can be considered as a quasiparticle since it arises from the quantization of plasma oscillations, just like phonons are quantizations of mechanical vibrations. o Thus, plasmons are collective (a discrete number) oscillations of the free electron gas density. o At optical frequencies, plasmons can couple with a photon to create another quasiparticle called a plasmon polariton. o The plasmon energy can often be estimated in the free electron model as, 퐸 = ℏ휔0(= ℎ푓0) where 휔0, 푓0 are plasma angular frequency and plasma frequency. Dispersion Relation for plasma o Recall the Lorentz Dispersion relation for gaseous medium 2 2 푁푞 푓푗 휖푟 표푟 푛 = 1 + 2 2 휖0푚 휔 − 휔 − 휄 훾휔 푗 푗 In plasma i. The electrons are free and not bound to ions by any kind of spring like force, so 훽 = 0 ⇒ 휔푗 = 0 ii. All electrons experience same force, so no summation required, iii. Also, q=e , and there is negligible damping in plasma: so, 훾 = 0. Thus, we have : 2 2 푁푒 1 2 2 휖푟 = 푛 = 1 − 2 . We know 휔0 = 푁푒 /푚휖0, 휖0푚 −휔 • Expression of dielectric constant and refractive index of 2 plasma. Thus, 2 휔0 휖 = 푛 = 1 − • 푟 휔2 This expression is also called the dispersion relation of plasma. • It is clear that refractive index of plasma n depends on the frequency (휔) of the wave passing through it. Surprise in Dispersion relation of plasma In this relation two surprising elements can be seen 휔2 휖 = 푛2 = 1 − 0 1. 푛2 < 1 푚푒푎푛푠 푐/푣 < 1 ⟹ 푣 > 푐, Surprising !!!! Is it violation of Einstein’s 푟 휔2 special relativity?? 2. For 휔 < 휔0, dielectric constant 휖푟 is negative and refractive index n is pure imaginary. • In the definition of n=c/v, v is in fact phase velocity of EM wave in a given medium. In above expression, putting n=c/v, 푐 we get 푣 = 휔2 1− 0 휔2 • As, 푣 = 푣푝 = 휔/푘, substitution of v gives, 2 2 2 푘 푐 휔 2 = 1 − 0 ⇒ 푘2푐2 = 휔2 − 휔 휔2 휔2 0 • Above expression is an alternate form of dispersion relation (DR) written in terms of wave vector k and angular freq. 휔. • Group velocity is the physical velocity which gives the rate of energy/signal transfer in a medium. 푑휔 • 푣 = : differentiation of DR w.r.t. k gives 푔 푑푘 푑휔 푘푐2 푐2 2푘푐2푑푘 = 2휔푑휔 ⟹ = = 푑푘 휔 푣푝 휔2 ⟹ 푣 = 푐 1 − 0 , now, 푣 < 푐 which is cosistant with Relativity 푔 휔2 푔 Imaginary Refractive index & Negative Dielectric constant: Physical meaning 2 2 휔0 2 2 2 2 2 2 휖 = 푛 = 1 − 푘 푐 = 휔 − 휔0 ⇒ 푘푐 = (휔 − 휔0) 푟 휔2 푖(푘푧−휔푡) • Wave Equation : 퐸 = 퐸0 푒 , • Waves can propagate through a medium only if k has a real part. • If 휔 < 휔0, dielectric constant 휖푟 is negative and refractive index n is pure imaginary. Also 푘 = 푘 i.e. k is also a pure imaginary number. 푖(푘푧−휔푡) −|푘|푧 −푖휔푡 • Hence wave equation becomes, 퐸 = 퐸0푒 = 퐸0푒 푒 . • Here the first term 푒−|푘|푧 is exponentially decaying with space while the second term 푒−푖휔푡 gives oscillation with time. Thus for 휔 < 휔0, wave take the form of decaying standing waves. • In fact, for 휔 < 휔0, the EM wave incident on plasma does not propagate in plasma , instead it will be totally reflected. (How ??) Answer comes from the EM theory. 퐸 2 • Energy flux of EM wave 푢 = Re(k). For 휔 < 휔0, i.e. k is pure imaginary, so, 푢 = 0 which means NO energy is 휇0휔 transferred in the plasma. Thus wave is completely reflected. Conclusion 2 휔0 2 2 2 2 Dispersion Relation 휖 = 푛2 = 1 − or 푘 푐 = 휔 − 휔0 푟 휔2 (DR) o Plasma frequency sets a lower cutoff for the frequencies of electromagnetic radiation. o Waves of frequencies lower than plasma frequency (휔 < 휔0), are reflected back by the plasma. o Only those radiations for which frequency is greater than plasma frequency (휔 > 휔0), can pass through a plasma. o For very high frequencies i.e. 휔 ≫ 휔0 plasma behaves as a transparent non-dispersive medium. How?? 2 2 2 o In the limit 휔 ≫ 휔0, 휖푟 ⟶ 1, 푛 ⟶ 1. DR becomes 푘 푐 = 휔 , where 푣푝 = 푣푔 = 푐. Since, dielectric constant, refractive index and phase velocity is independent of frequency, there is no dispersion of wave. Application of Plasma : Ionosphere Application of plasma II : Metals • The metals shine by reflecting most of light in visible range. • The concept of electron plasma oscillations can also be applied to the free electrons in a conductor. • The visible light can't pass through the metal because the plasma frequency of electrons in metal falls in ultraviolet region. • For frequencies in UV, metals are transparent. • For example, the free electron density in Cu is 8.4 × 1028 m−3. (By way of comparison, the density of air molecules at a pressure of one atmosphere and T = 300K is 2.4 × 1025 m−3.) 15 • In Cu, then plasma frequency, fo ≈ 2.6 × 10 Hz. • This is higher than the frequencies of visible light, and explains why metals are opaque to visible light and transparent to UV light..
Load more

Recommended publications
  • Plasma Oscillation in Semiconductor Superlattice Structure
    Memoirs of the Faculty of Engineering,Okayama University,Vol.23, No, I, November 1988 Plasma Oscillation in Semiconductor Superlattice Structure Hiroo Totsuji* and Makoto Takei* (Received September 30, 1988) Abstract The statistical properties of two-dimensional systems of charges in semiconductor superlattices are analyzed and the dispersion relation of the plasma oscillation is ealculated. The possibility to excite these oscillations by applying the electric field parallel to the structure is discussed. ]. Introduction The layered structure of semiconductors with thickness of the order of lO-6 cm or less is called semiconductor superlattice. The superlattice was first proposed by Esaki and Tsu [11 as a structure which has a Brillouin zone of reduced size and therefore allows to apply the negative mass part of the band structure to electronic devices through conduction of carriers perpendicular to the structure. The superlattice has been realized by subsequent developments of technologies such as molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD) in fabricating controlled fine structures. At the same time, many interesting and useful physical phenomena related to the parallel conduction have also been revealed in addition to the parallel conduction. From the view point of application to devices, the enhancement of the carrier mobility due to separation of channels from Ionized impurities may be one of the most important progresses. Some high speed devices are based on this technique. The superlattlce structure
    [Show full text]
  • Carbon Fiber Skeleton/Silver Nanowires Composites with Tunable Negative
    EPJ Appl. Metamat. 8, 1 (2021) © Y. An et al., published by EDP Sciences, 2021 https://doi.org/10.1051/epjam/2020019 Available online at: epjam.edp-open.org Metamaterial Research Updates from China RESEARCH ARTICLE Carbon fiber skeleton/silver nanowires composites with tunable negative permittivity behavior Yan An1, Jinyuan Qin1, Kai Sun1,*, Jiahong Tian1, Zhongyang Wang2,*, Yaman Zhao1, Xiaofeng Li1, and Runhua Fan1 1 College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, PR China 2 State Key Lab of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China Received: 13 November 2020 / Accepted: 25 December 2020 Abstract. With the development of periodic metamaterials, more attention has been paid to negative permittivity behavior due to great potential applications. In this paper, silver nanowires (AgNWs) were introduced to the porous carbon fibers (CFS) by an impregnation process to prepare CFS/AgNWs composites with different content of AgNWs and the dielectric property was investigated. With the formation of conductive network, the Drude-like negative permittivity was observed in CFS/AgNWs composites. With the increase of AgNWs, the connectivity of conductive network became enhanced, the conductivity gradually increases, and the absolute value of the negative dielectric constant also increases to 8.9 Â 104, which was ascribed to the enhancement of electron density of the composite material. Further investigation revealed that the inductive characteristic was responsible for the negative permittivity. Keywords: Negative permittivity / metacomposites / plasma oscillation / inductive characteristic 1 Introduction capacitors [10,11]. The electromagnetic metamaterials have a great value in the fields of wireless communication In the past decades, electromagnetic metamaterials with [12], electromagnetic absorption [13] and shielding [14], etc.
    [Show full text]
  • Solid State Physics II Level 4 Semester 1 Course Content
    Solid State Physics II Level 4 Semester 1 Course Content L1. Introduction to solid state physics - The free electron theory : Free levels in one dimension. L2. Free electron gas in three dimensions. L3. Electrical conductivity – Motion in magnetic field- Wiedemann-Franz law. L4. Nearly free electron model - origin of the energy band. L5. Bloch functions - Kronig Penney model. L6. Dielectrics I : Polarization in dielectrics L7 .Dielectrics II: Types of polarization - dielectric constant L8. Assessment L9. Experimental determination of dielectric constant L10. Ferroelectrics (1) : Ferroelectric crystals L11. Ferroelectrics (2): Piezoelectricity L12. Piezoelectricity Applications L1 : Solid State Physics Solid state physics is the study of rigid matter, or solids, ,through methods such as quantum mechanics, crystallography, electromagnetism and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic- scale properties. Thus, solid-state physics forms the theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors. Crystalline solids & Amorphous solids Solid materials are formed from densely-packed atoms, which interact intensely. These interactions produce : the mechanical (e.g. hardness and elasticity), thermal, electrical, magnetic and optical properties of solids. Depending on the material involved and the conditions in which it was formed , the atoms may be arranged in a regular, geometric pattern (crystalline solids, which include metals and ordinary water ice) , or irregularly (an amorphous solid such as common window glass). Crystalline solids & Amorphous solids The bulk of solid-state physics theory and research is focused on crystals.
    [Show full text]
  • Free Electron Lasers and High-Energy Electron Cooling*
    FREE ELECTRON LASERS AND HIGH-ENERGY ELECTRON COOLING* Vladimir N. Litvinenko, BNL, Upton, Long Island, NY, USA# Yaroslav S. Derbenev, TJNAF, Newport News, VA, USA) Abstract The main figure of merit of any collider is its average Cooling intense high-energy hadron beams remains a luminosity, i.e., its average productivity for an appropriate major challenge in modern accelerator physics. branch of physics. Cooling hadron beams at top energy Synchrotron radiation of such beams is too feeble to may further this productivity. provide significant cooling: even in the Large Hadron For a round beam, typical for hadron colliders, the Collider (LHC) with 7 TeV protons, the longitudinal luminosity is given by a simple expression: ' * damping time is about thirteen hours. Decrements of N1N2 & s traditional electron cooling decrease rapidly as the high L = fc * % h) * , (1) 4"# $ ( # + power of beam energy, and an effective electron cooling of protons or antiprotons at energies above 100 GeV where N1, N2 are the number of particles per bunch, fc is seems unlikely. Traditional stochastic cooling still cannot their collision frequency, !* is the transverse !-function catch up with the challenge of cooling high-intensity at the collision point, " is the transverse emittance of the bunched proton beams - to be effective, its bandwidth b!ea m, #s is the bunch length, and h ! 1 is a coefficient must be increased by about two orders-of-magnitude. accounting for the so-called hourglass effect [1]: Two techniques offering the potential to cool high- " 1/ x 2 h(x) = e erfc(1/ x). energy hadron beams are optical stochastic cooling (OSC) x and coherent electron cooling (CEC) – the latter is the The hourglass effect is caused by variations in the beam’s 2 focus of this paper.
    [Show full text]
  • The Effect Pressure on Wavelengths of Plasma Oscillations in Argon And
    AN ABSTRACT OF TI-lE TRESIS OF - ¡Idgar for Gold.an the ri,, s. in (Name) (Degree) (Najor) Date Thesis presented ia. i9i__ Title flTO PSDEo LPLASMA OSeILLATIos..iN - Abstract Approved (-(Najor Professor) Experiments on argon and. nitrogen are described. which show that the wave length of electromaetjc radiation emitted from a gas plasma in a magnetic field is a function of the pressure of the gas. This result is Consistent with the theory of plasma oscillation developed by Tonics and Langniir if the assumption is made that plasma electron density is a function of gas pressure. A lower limit of wave length plasma of oscillation is indicated by the experiments in qualitative agreement with the Debye length equation, No difference in the wave length-tressn, relationship between the two gases was observed. The experimental tube, which consisted of a gas filled cylindrical anode with an axial tungsten filament) was motmted. in a magnetic field parallel to the axis of the anode. Gas pressures between i and 50 microns and. magnetic fields between 500 and 1,000 gauss were used. The anode voltage was aplied. in short pulses in order to mini- mize heating of the cathode by ion bombardment and to make possible the use of alternating voltage amplifiers in the receiver. The receiver of electromagnetic radiation consisted. of a crystal- detector dipole, constructed from a 1N26 crystal cartridge, followed by a video amp1ifier The amplifier had a maximum gain of 1.6 X iO7, and. a bandwidth of 2 megacycles Wave lengths were measured by means of an interferometer.
    [Show full text]
  • Introduction to Metamaterials
    FEATURE ARTICLE INTRODUCTION TO METAMATERIALS BY MAREK S. WARTAK, KOSMAS L. TSAKMAKIDIS AND ORTWIN HESS etamaterials (MMs) are artificial structures LEFT-HANDED MATERIALS designed to have properties not available in To describe the basic properties of metamaterials, let us nature [1]. They resemble natural crystals as recall Maxwell’s equations M they are build from periodically arranged (e.g., square) unit cells, each with a side length of a. The ∂H ∂E ∇×E =−μμand ∇×H = εε (1) unit cells are not made of physical atoms or molecules but, 00rr∂tt∂ instead, contain small metallic resonators which interact μ ε with an external electromagnetic wave that has a wave- where the r and r are relative permeability and permit- λ ⎡ ∂ ∂ ∂ ⎤ length . The manner in which the incident light wave tivity, respectively, and L =⎢ ,,⎥ . From the above ⎣⎢∂xy∂ ∂z ⎦⎥ interacts with these metallic “meta-atoms” of a metamate- equations, one obtains the wave equation rial determines the medium’s electromagnetic proper- ties – which may, hence, be made to enter highly unusual ∂2E ∇=−2E εμεμ (2) regimes, such as one where the electric permittivity and 00rr∂t 2 the magnetic permeability become simultaneously (in the ε μ same frequency region) negative. If losses are ignored and r and r are considered as real numbers, then one can observe that the wave equation is ε The response of a metamaterial to an incident electromag- unchanged when we simultaneously change signs of r and μ netic wave can be classified by ascribing to it an effective r . (averaged over the volume of a unit cell) permittivity ε ε ε μ μ μ To understand why such materials are also called left- eff = 0 r and effective permeability eff = 0 r .
    [Show full text]
  • Plasma Waves
    Plasma Waves S.M.Lea January 2007 1 General considerations To consider the different possible normal modes of a plasma, we will usually begin by assuming that there is an equilibrium in which the plasma parameters such as density and magnetic field are uniform and constant in time. We will then look at small perturbations away from this equilibrium, and investigate the time and space dependence of those perturbations. The usual notation is to label the equilibrium quantities with a subscript 0, e.g. n0, and the pertrubed quantities with a subscript 1, eg n1. Then the assumption of small perturbations is n /n 1. When the perturbations are small, we can generally ignore j 1 0j ¿ squares and higher powers of these quantities, thus obtaining a set of linear equations for the unknowns. These linear equations may be Fourier transformed in both space and time, thus reducing the differential equations to a set of algebraic equations. Equivalently, we may assume that each perturbed quantity has the mathematical form n = n exp i~k ~x iωt (1) 1 ¢ ¡ where the real part is implicitly assumed. Th³is form descri´bes a wave. The amplitude n is in ~ general complex, allowing for a non•zero phase constant φ0. The vector k, called the wave vector, gives both the direction of propagation of the wave and the wavelength: k = 2π/λ; ω is the angular frequency. There is a relation between ω and ~k that is determined by the physical properties of the system. The function ω ~k is called the dispersion relation for the wave.
    [Show full text]
  • Inorganic Chemistry for Dummies® Published by John Wiley & Sons, Inc
    Inorganic Chemistry Inorganic Chemistry by Michael L. Matson and Alvin W. Orbaek Inorganic Chemistry For Dummies® Published by John Wiley & Sons, Inc. 111 River St. Hoboken, NJ 07030-5774 www.wiley.com Copyright © 2013 by John Wiley & Sons, Inc., Hoboken, New Jersey Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permis- sion of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley. com/go/permissions. Trademarks: Wiley, the Wiley logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries, and may not be used without written permission. All other trade- marks are the property of their respective owners. John Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book.
    [Show full text]
  • Chapter 6 Free Electron Fermi Gas
    理学院 物理系 沈嵘 Chapter 6 Free Electron Fermi Gas 6.1 Electron Gas Model and its Ground State 6.2 Thermal Properties of Electron Gas 6.3 Free Electrons in Electric Fields 6.4 Hall Effect 6.5 Thermal Conductivity of Metals 6.6 Failures of the free electron gas model 1 6.1 Electron Gas Model and its Ground State 6.1 Electron Gas Model and its Ground State I. Basic Assumptions of Electron Gas Model Metal: valence electrons → conduction electrons (moving freely) ü The simplest metals are the alkali metals—lithium, sodium, 2 potassium, cesium, and rubidium. 6.1 Electron Gas Model and its Ground State density of electrons: Zr n = N m A A where Z is # of conduction electrons per atom, A is relative atomic mass, rm is the density of mass in the metal. The spherical volume of each electron is, 1 3 1 V 4 3 æ 3 ö = = p rs rs = ç ÷ n N 3 è 4p nø Free electron gas model: Suppose, except the confining potential near surfaces of metals, conduction electrons are completely free. The conduction electrons thus behave just like gas atoms in an ideal gas --- free electron gas. 3 6.1 Electron Gas Model and its Ground State Basic Properties： ü Ignore interactions of electron-ion type (free electron approx.) ü And electron-eletron type (independent electron approx). Total energy are of kinetic type, ignore potential energy contribution. ü The classical theory had several conspicuous successes 4 6.1 Electron Gas Model and its Ground State Long Mean Free Path: ü From many types of experiments it is clear that a conduction electron in a metal can move freely in a straight path over many atomic distances.
    [Show full text]
  • Chapter 6 Free Electron Fermi
    Chapter 6 Free Electron Fermi Gas Free electron model: • The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. • The simplest metals are the alkali metals– lithium, sodium, potassium, Na, cesium, and rubidium. • The classical theory had several conspicuous successes, notably the derivation of the form of Ohm’s law and the relation between the electrical and thermal conductivity. • The classical theory fails to explain the heat capacity and the magnetic susceptibility of the conduction electrons. M = B • Why the electrons in a metal can move so freely without much deflections? (a) A conduction electron is not deflected by ion cores arranged on a periodic lattice, because matter waves propagate freely in a periodic structure. (b) A conduction electron is scattered only infrequently by other conduction electrons. Pauli exclusion principle. Free Electron Fermi Gas: a gas of free electrons subject to the Pauli Principle ELECTRON GAS MODEL IN METALS Valence electrons form the electron gas eZa -e(Za-Z) -eZ Figure 1.1 (a) Schematic picture of an isolated atom (not to scale). (b) In a metal the nucleus and ion core retain their configuration in the free atom, but the valence electrons leave the atom to form the electron gas. 3.66A 0.98A Na : simple metal In a sea of conduction of electrons Core ~ occupy about 15% in total volume of crystal Classical Theory (Drude Model) Drude Model, 1900AD, after Thompson’s discovery of electrons in 1897 Based on the concept of kinetic theory of neutral dilute ideal gas Apply to the dense electrons in metals by the free electron gas picture Classical Statistical Mechanics: Boltzmann Maxwell Distribution The number of electrons per unit volume with velocity in the range du about u 3/2 2 fB(u) = n (m/ 2pkBT) exp (-mu /2kBT) Success: Failure: (1) The Ohm’s Law , (1) Heat capacity Cv~ 3/2 NKB the electrical conductivity The observed heat capacity is only 0.01, J = E , = n e2 / m, too small.
    [Show full text]
  • What Is Plasma? Its Characteristics Plasma Oscillations Plasmon And
    Topics covered here are: What is Plasma? Its Characteristics Plasma Oscillations Plasmon and plasmon frequency Sources used here are: http://farside.ph.utexas.edu/teaching/plasma/Plasmahtml/node1.html https://www.britannica.com/science/plasma-state-of-matter/Plasma-oscillations- and-parameters What is Plasma The electromagnetic force is generally observed to create structure: e.g., stable atoms and molecules, crystalline solids. Structured systems have binding energies larger than the ambient thermal energy. Placed in a sufficiently hot environment, they decompose: e.g., crystals melt, molecules disassociate. At temperatures near or exceeding atomic ionization energies, atoms similarly decompose into negatively charged electrons and positively charged ions. These charged particles are by no means free: in fact, they are strongly affected by each others' electromagnetic fields. Nevertheless, because the charges are no longer bound, their assemblage becomes capable of collective motions of great vigor and complexity. Such an assemblage is termed a plasma. Of course, bound systems can display extreme complexity of structure: e.g., a protein molecule. Complexity in a plasma is somewhat different, being expressed temporally as much as spatially. It is predominately characterized by the excitation of an enormous variety of collective dynamical modes. Its occurrence and characteristics Since thermal decomposition breaks interatomic bonds before ionizing, most terrestrial plasmas begin as gases. In fact, a plasma is sometimes defined as a gas that is sufficiently ionized to exhibit plasma-like behavior. Note that plasma-like behavior ensues after a remarkably small fraction of the gas has undergone ionization. Thus, fractionally ionized gases exhibit most of the exotic phenomena characteristic of fully ionized gases.
    [Show full text]
  • Arxiv:2006.09236V4 [Quant-Ph] 27 May 2021
    The Free Electron Gas in Cavity Quantum Electrodynamics Vasil Rokaj,1, ∗ Michael Ruggenthaler,1, y Florian G. Eich,1 and Angel Rubio1, 2, z 1Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany 2Center for Computational Quantum Physics (CCQ), Flatiron Institute, 162 Fifth Avenue, New York NY 10010 (Dated: May 31, 2021) Cavity modification of material properties and phenomena is a novel research field largely mo- tivated by the advances in strong light-matter interactions. Despite this progress, exact solutions for extended systems strongly coupled to the photon field are not available, and both theory and experiments rely mainly on finite-system models. Therefore a paradigmatic example of an exactly solvable extended system in a cavity becomes highly desireable. To fill this gap we revisit Som- merfeld's theory of the free electron gas in cavity quantum electrodynamics (QED). We solve this system analytically in the long-wavelength limit for an arbitrary number of non-interacting elec- trons, and we demonstrate that the electron-photon ground state is a Fermi liquid which contains virtual photons. In contrast to models of finite systems, no ground state exists if the diamagentic A2 term is omitted. Further, by performing linear response we show that the cavity field induces plasmon-polariton excitations and modifies the optical and the DC conductivity of the electron gas. Our exact solution allows us to consider the thermodynamic limit for both electrons and photons by constructing an effective quantum field theory. The continuum of modes leads to a many-body renormalization of the electron mass, which modifies the fermionic quasiparticle excitations of the Fermi liquid and the Wigner-Seitz radius of the interacting electron gas.
    [Show full text]