On the Foundations of Fluctuation Forces

Size: px

Start display at page:

Download "On the Foundations of Fluctuation Forces"

Job Hopkins
5 years ago
Views:

1 On the Foundations of Fluctuation Forces Carsten Henkel 1 and Vanik E. Mkrtchian 2 1 Universität Potsdam, Germany 2 Academy of Sciences, Armenia Progress in Electromagnetic Research Symposium (Stockholm Aug 2013) thanks to: G. Pieplow, H. Haakh, J. Schiefele, network Casimir (ESF), DFG arxiv: , New J Phys 15 (2013) Institute of Physics and Astronomy, Universität Potsdam, Germany

2 en.wikipedia.org c ESPCI-CRH ru.wikipedia.org ( ) ( ) ( ) ( ) Paul Langevin Sergei Michailovich Rytov

3 Outline Why? Fluctuation interactions How? Langevin dialect of Maxwellian = Rytov theory Basic observables Local thermodynamic equilibrium For example? Non-equilibrium field theory Quantum friction (& Mkrtchian) (& Pieplow, Haakh, Schiefele) As time goes by... Potential conversations Forgotten references

4 Maxwell & Langevin Macroscopic electrodynamics t B + E = 0 B = 0 t D H = j D = ρ (inhomogeneous) material approximation: linear response... always matter that provides nonlinearity D = ε 0 ε(x, ω)e ε(ω), µ(ω) must be complex [ Wed 3P3b, Wed 3P5, ] H = µ 1 0 µ 1 (x, ω)b ε(x), µ(x) cannot be local Thu 4P4 Rytov: losses come with fluctuating sources (Langevin forces) 50mm[r]Principles Stat Radiophys (Springer 1989)

5 Maxwell & Langevin Macroscopic electrodynamics i ω c 2 ε(x, ω)e = µ 1 (x, ω)b µ 0 j(x, ω) iωb = E Rytov: losses come with fluctuating sources (Langevin forces) j = j free iωp(x, ω) + M(x, ω) noise polarization P ρ = ρ free P(x, ω) noise magnetization M Maxwell-Langevin equation: stochastic differential equation 0 = P(x, t) 0 P(x, t)p(x, t ) = dω 2π S P (x, x, ω) e iω(t t ) spectral density 50mm[r]Principles Stat Radiophys (Springer 1989)

6 Maxwell & Langevin Macroscopic electrodynamics i ω c 2 ε(x, ω)e = µ 1 (x, ω)b µ 0 j(x, ω) iωb = E Rytov: losses come with fluctuating sources (Langevin forces) j = j free iωp(x, ω) + M(x, ω) noise polarization P ρ = ρ free P(x, ω) noise magnetization M Maxwell-Langevin equation: stochastic differential equation 0 = P(x, t) 0 P(x, t)p(x, t ) = dω 2π S P (x, x, ω) e iω(t t ) spectral density Rytov: S P,ij (x, x, ω) 2 h N(ω)ε 0 Im ε ij (x, ω)δ(x x )... fluctuation-dissipation relation Bose-Einstein distribution N(ω), local equilibrium T T (x) 50mm[r]Principles Stat Radiophys (Springer 1989)

7 Fluctuation forces Field energy (density, in vacuum) u(x) = ε 0 2 µ 1 0 E(x) E(x) + 2 B(x) B(x) = + dω u(x, ω) thermal sources blackbody radiation (Planck 1900) near objects: non-universal spectrum, distance dependence (Planck, Purcell) Dorofeyev & Vinogradov (Phys Rep 2011) Force on rigid body in vacuum d dt (total momentum) i = surf da j T ij Maxwell stress tensor T ij = ε 0 E i E j δ ij 2 quantum fluctuations Casimir force E E + µ 1 0 B ib j δ ij 2 B B (cosmological constant?) T A > T B or T : Heat current (Poynting vector) (this session Mon 1P3)

8 Potential Conversations Dynamical fluctuations and static zero-point energy Stress tensor in a medium (in/homogeneous) T Philbin, Ch Raabe & D-G Welsch, M v Laue EM Fields: (retarded) link between charges R Feynman & J A Wheeler Linear macroscopic response: filter theory signal engineers Local equilibrium assumption: incoherent summation coherence from propagation (diffraction) FD relation valid for both bosonic and fermionic matter Ch Huyghens, T Young H. B. Callen & T. A. Welton, F. Garcia de Abajo Beyond local equilibrium: thermodynamic cut L Boltzmann, M Lax, U Weiss Quantum limit (T A, T B 0): establishing correlations (entanglement) between bodies J S Høye & I Brevik, I Klich, R Behunin

9 Example 1: Non-equilibrium field theory Goal: calculate field correlations with Schwinger-Keldysh technique diagrammatic formulation of density operator dynamics path integral evaluation of effective action Symmetrized correlations of vector potential ( Keldysh Green function ) D K (x, x ) = i {A(x), A(x )} =... = da da G(x, a)s J (a, a )G (a, x ) Mkrtchian & Henkel arxiv: Janowicz & Holthaus Phys Rev A 2003 Sherkunov Phys Rev A 2007/09 (retarded) Green function G(x, x ), surface current correlations S J (a, a ) Assumption: un-correlated surfaces (bodies) single-interface S J (a, a ) reproduces Rytov theory + arbitrary reflection matrices, + Lorentz transformation of surface currents planar surfaces (translation symmetry), stationary situation (spectra)

10 Example 2: Quantum friction near graphene 08/08/13 14:26 metallic nanoparticle at speed v c graphene sheet (dielectric substrate) friction ( Coulomb drag ) creation of excitations photons in substrate ( Cherenkov ) graphene plasmons Motivation Mon 1A1,... Tue 2AK, Wed 3AK giant anomalous Doppler shift: ω = γ(ω k v) < 0 bridge gap between metallic (UV) and graphene (IR) plasmons file:///users/carstenh/work/voyages/piers_stockholm_aug13/pics/surface.svg Page 1 sur 2 controversy on quantum friction (T 0 limit) years of discordant results (Teodorovich session Tue 2P4)

11 2 Radiation forces and friction Force on neutral, polarizable particle F (x, v) = d i E i + µ i B i }{{} dominates fluctuating particle dipole fluctuating field & substrate excitations Expansion in 4th order correlations: polarizability α(ω ) in co-moving frame: Doppler shift ω = γ(ω k v) dipole fluctuation spectrum S d (x A, ω ) in local equilibrium field response = Green function... Quantum friction force (substrate & field T F 0, particle T A 0) F x = h 2γ dω 2π Im α(ω ) d 2 k (2π) 2 k x (sgn ω sgn ω ) σ = s,p ( e 2κz A r σ (k, ω) φ σ (k, ω) Im κ ) Dedkov & Kyasov, Phys Solid St 2001; Pieplow & Henkel, New J Phys 2013

2 Resonant emission of graphene plasmons force density F x dω dk x frequency hω/ef 0.7 0.6 0.5 0.4 0.3 0.

0 5 wave vector k x /k F (v x = 0.22 c) 0.1 0.0 k x /k F (v x = 0.42 c) 4 E F = 0.5 ev, c 300 v F distance 100 nm gold particle plasmon hω 5.2 ev G.

12 2 Resonant emission of graphene plasmons force density F x dω dk x frequency hω/ef frequency hω/ef plasmon dispersion ω k ck shifted particle resonance Ω = ω = γ(ω k v) free-standing graphene film wave vector k x /k F (v x = 0.22 c) k x /k F (v x = 0.42 c) 4 E F = 0.5 ev, c 300 v F distance 100 nm gold particle plasmon hω 5.2 ev G. Pieplow, H. Haakh, J. Schiefele, work in progress giant anomalous Doppler shift: ω < 0 emission of 1st plasmon excites the particle: ω + Ω = 0 Frank & Tamm explain Cherenkov radiation (1937) review: Ginzburg (Phys Uspekhi 1996)

13 Appendix forgotten references von Laue: Thermal radiation in absorbing bodies (Ann. Phys. (Leipzig) 1910) Bakker & Heller: Quantum Brownian motion in electric resistances (Physica 1939) Jauch & Watson: Phenomenological Quantum-Electrodynamics (Phys Rev 1948) Callen & Welton: Irreversibility and generalized noise (Phys Rev 1951) De Groot & al: Series on relativistic thermodynamics (Physica 1953) V. L. Ginzburg: Electrical fluctuations (Fortschr Phys 1953) Linder: Thermal Van der Waals interactions (J Chem Phys 1960) van Kampen: FD relation in non-linear systems? (Physica 1960) vs Polevoi & Rytov (Theor Math Phys 1975) Morris & Fürth: Spatial field correlations near conducting surfaces (Physica 1960) see also Fuchs (Radiophys Quant Electr 1965) Jaynes & Cummings: Quantum vs semiclassical radiation theories (Proc. IEEE 1963) Agarwal: FD theorems and series on field quantization (Z Phys 1972; Phys Rev A 1975) Boyer: Connection between Rytov and quantum electrodynamics (Phys Rev D 1975) Ginzburg & Ugarov: Macroscopic stress tensor (Sov Phys Usp 1976) Polevoi: Tangential forces/friction in non-equilibrium fields (JETP 1985/90) Eckhart: Problems with FD relations for heat transfer (Opt Commun 1982) Henry & Kazarinov: Quantum noise in photonics (Rev Mod Phys 1996)

14 Summary Status of Learning Curve Rytov fluctuation electrodynamics Robust working horse as long as matter responds linearly Universal framework to recover: thermal radiation, heat transfer, Casimir-Lifshitz forces, quantum friction... beyond local equilibrium: non-local response Statistics (thermodynamics) vs quantum Intuitive picture for vacuum fluctuations semiclassical, dynamical Radiative infinities regularized by temperature and coupling to matter... non-equilibrium interactions entropy production entanglement production download slides (end of week)

Fluctuation Electrodynamics foundations

Fluctuation Electrodynamics foundations Carsten Henkel Universität Potsdam Les Houches, May 2013 thanks to: Martin Wilkens, Humboldt foundation, DFG Institute of Physics and Astronomy, Universität Potsdam,