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Nanoscale Thermal Transport by QED Radiation trumps Phonon Theories
Thermal transport by QED radiation based on the creation of photons in nanostructures upon the absorption of EM energy is shown to supersede phonon based Non-Equilibrium Green’s Function
In 1822, the theory of thermal transport in solids began with Fourier’s transient heat conduction equation for temperatures in macroscopic systems. Quantum mechanics (QM) was introduced through the specific heat capacity in combination with phonons as heat carriers by Einstein and Debye [1,2] in 1907 and 1912. Over the past decade, anomalous thermal response of microsocpic systems prompted review of Fourier’s equation. Molecular dynamics (MD) based on classical statistical mechanics was found  to provide inaccurate results at low temperatures. The Boltzmann-Peierls equation  relying on the concept of a phonon distribution function could not be applied to discrete microscopic systems that lack translational invariance. Discrete microscopic systems have always posed difficulty for density functional theory (DFT). In fact, DFT coupled with MD was initially only intended  for microscopic ensembles of atoms under periodic boundary conditions. Recently, DFT combined with non-equilibrium Green's functions (NEGF) based on phonon interactions alone was proposed  to describe thermal transport in discrete microscopic systems. The NEGF model for thermal transport is analogous to that for electron transport depicted in the thumbnail and described in: http://smu.edu/
QM restricts the heat capacity of microscoic systems thereby significantly affecting thermal transport by phonons as heat carriers. Electron transport cannot be used as an analog for thermal transport by the NEGF because electron transport is not affected by heat capacity. Indeed, it is questionable whether thermal transport in microscopic systems exists at all. Indeed, QM embodied in the Einstein-Hopf relation for the harmonic oscillator precludes any and all thermal transport in discrete microscopic systems based on their submicron size alone. Hence, the problem is not one of whether NEGF theory replaces Fourier’s equation, but rather to overcome the notion that conduction by phonons is the only mechanism by which thermal transport may occur in microscopic systems. Arguments that NEGF theory agrees with experiments  should be set aside because the experiments may be explained with other theories. See references in: http://www.nanoqed.org
QED Induced Radiation
Classical physics by any theory cannot be applied to microscopic systems to derive the thermal response because of QM restrictions on heat capacity. Unlike classical physics that allows the atoms in microscopic systems to have heat capacity, QM requires the heat capacity of microscopic systems to vanish. Conservation of the absorbed EM energy (thermal, Joule, lasers) therefore cannot proceed by an increase in temperature. Hence, thermal gradients cannot exist, and therefore thermal conduciton does not occur in microscopic systems. Ibid
Lacking heat capacity, QM conserves the absorbed EM energy by the creation of QED radiation inside the microscopic system. QED stands for quantum electrodynamics. Creation is prompt with QED inducing the absorbed EM energy to coincide with the total internal reflection (TIR) resonance. The TIR confinement only occurring during EM absorption is a natural consequence of microscopic systems that have a high surface to volume ratio, i.e., the absorbed EM energy is almost totally confined to the surface of the microscopic system. But without heat capacity, there is no increase in temperature, and therefore conservation proceeds by the emission of QED induced radiation. E.g., consider the absorption of a single VIS photon by a nitrogen molecule. By NEGF, the nitrogen molecule having heat capacity is raised to a high temperature and vaporizes, but this is never observed. By QED, the nitrogen molecule lacking heat capacity is induced to emit QED radiation corresponding to its vibration spectra without any increase in temperature. Ibid
Thin Films Classically, Joule heat in thin films is conserved by an increase in temperature. But by QM, conservation proceeds by QED induced conversion of absorbed Joule heat to the TIR confinement frequency of the film. Experiments showing the thermal conductivity reduced  from bulk are erroneous because the QED radiation losses are excluded from the heat balance, but if included, the film maintains bulk conductivity.
Nanofluids Nanofluids comprising nanoparticles (NPs) in a solvent are found to increase thermal conductivity beyond that given by mixing rules. Classically, solvent molecule collisions increase the NP temperature and are absorbed and remitted as IR radiation. By QM, the collision energy  is reemitted in the VUV and penetrates farther than the IR, thereby enhancing heat transfer in proportion to the number of NPs without increasing the nanofluid conductivity. Nanofluid conductivity given by mixing rules is still valid and need not be modified.
Memristors Memristors  by QM conserve resistive heating by the QED induced creation of photons at UV levels that by the photoelectric effect create holes inside the memristor that decrease resistance only to be recovered later in the same cycle as the holes are attracted to and destroyed by the negative voltage terminals.
Graphene Graphene enhanced thermal management  of personal computers (PC) may have been overstated. Classically, almost all of the Joule heat loss from a PC s controlled by natural convection thereby negating any enhanced conductivity provided by graphene. QED differs. A single layer of graphene in intermittent contact with a PC component will not increase in temperature, and instead disspate heat by emitting QED radiation that is absorbed in the air surroundings. Similary, graphene nanoribbons dissipate Joule heat without danger of overheating.
1. DFT in combination with NEGF or any other exotic theory to derive the thermal transport by phonons in microscopic systems is meaningless because conduction is precluded by QM. In contrast, QED avoids conduction by conserving absorbed EM energy by the emission of QED radiation.
2. Phonons are unable to explain electrical charging of microscopic systems for the simple reason that there is no known phonon-electric effect. Only Einstein’s photo-electric effect will create charge from photons – not phonons. In microscopic systems, the photons are created naturally by QM and emitted by the microscopic system as QED radiation.
3. Implementation of QED radiation only requires the absorbed EM energy to be partitioned into the emission spectra of the microscopic system, the effect on the surroundings assessed by more conventional heat transfer methods.
 Einstein, A., The Planck Theory of Radiation and Theory of Specific Heat, Ann. der Physik, 22, 180-190, 1907.
 Debye, P., The Theory of Specific Heat, Ann. der Physik, 39, 789- 839, 1912.
 Lepri, S., et al., Thermal conduction in lattices, Physics Reports, 377, 1, 2003.
 Peirels, R. E., Quantum Theory of Solids, Oxford Clarendon Press, 1955.
 Car, R., Parinello, M., Unified Molecular Dynamics and Density Functional Theory, Phys. Rev. Lett., 55, 2471-4 1985.
 Tan, Z. W., Wang, J-S, and Gan, C. K. First-Principles Study of Graphene Nanoribbons,Nano Lett., 11, 214-?19 (2011).
 Pop, et al, Thermal Conductance of an Individual Single-Wall Carbon Nanotube, Nano Lett., 6, 96-100, 2006.
 Prevenslik, T., Heat Transfer in Thin Films,Third Int. Conf. Quant.Nano and Micro Tech., Cancun, February 1-6, 2009.
 Prevenslik, T., Nanofluids by Quantum Mechanics, Micro/Nano Heat & Mass Conf., Shanghai, December 18-21, 2009.
 Prevenslik, T., Memristors by Quantum Mechanics, Int. Conf. Intel. Comp. Zhengzhou, August 11-14, 2011.
 Prevenslik, T., See http://www.nanoqed.org
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About QED Induced EM Radiation: Classically, absorbed EM energy is conserved by an increase in temperature. But at the nanoscale, temperature increases are forbidden by quantum mechanics. QED radiation explains how absorbed EM energy is conserved at the nanoscale by the emission of nonthermal EM radiation.