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Journal articles on the topic 'Umklapp Scattering'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Turlakov, Misha. "Umklapp scattering in cuprates." Journal of Physics A: Mathematical and General 36, no. 35 (2003): 9399–404. http://dx.doi.org/10.1088/0305-4470/36/35/324.

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2

Kumar, Deepak, and R. Rajaraman. "Umklapp Scattering in Fermi Liquids: A Renormalisation Group Approach." International Journal of Modern Physics B 11, no. 15 (1997): 1813–28. http://dx.doi.org/10.1142/s0217979297000939.

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The role of Umklapp scattering for electrons on a lattice is studied. Using renormalisation group methods it is shown that the effective low energy interaction involves not only forward scattering, but also non-forward Umklapp scattering. We show that the latter can happen to almost all of the electrons even when they have a filling of around one-half. The bahavior of these Umklapp couplings is studied in the loop expansion. It is shown that they remain marginal to all loop orders. The discussion is given in the context of two-dimensional lattices, but generalisation to three-dimensions is mentioned. We also briefly discuss the possible consequences of this on Fermi liquid theory and on physical properties of such electronic systems.

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3

Zülicke, U., and A. H. MacDonald. "Umklapp scattering at reconstructed quantum Hall edges." Physica E: Low-dimensional Systems and Nanostructures 6, no. 1-4 (2000): 104–7. http://dx.doi.org/10.1016/s1386-9477(99)00069-7.

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4

Dharma-wardana, M. W. C., D. J. Lockwood, J. M. Baribeau, and D. C. Houghton. "Raman scattering involving umklapp processes inSiGexSi1−xsuperlattices." Physical Review B 34, no. 4 (1986): 3034–36. http://dx.doi.org/10.1103/physrevb.34.3034.

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5

Wang, Zan. "Thermal Transport and Rectification Properties of Bamboo-Like SiC Polytypes Nanowires." Journal of Nanomaterials 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/5038978.

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Bamboo-like SiC nanowires (NWs) have specific geometric shapes, which have the potential to suppress thermal conductivity by phonon boundary scattering. In this work, phonon transport behaviors in the 3C-SiC, 4H-SiC, and 6H-SiC crystal lattices are studied by the Monte Carlo (MC) method, including impurity scattering, boundary scattering, and Umklapp scattering. Phonon relaxation times for Umklapp (U) scattering for the above three SiC polytypes are calculated from the respective phonon spectra, which have not been reported in the literature. Diffuse boundary scattering and thermal rectification with different aspect ratios are also studied at different temperatures. It is found that the thermal conductivities of the bamboo-like SiC polytypes can be lowered by two orders of magnitude compared with the bulk values by contributions from boundary scattering. Compared with bamboo-like 4H-SiC and 6H-SiC NWs, 3C-SiC has the largest U scattering relaxation rate and boundary scattering rate, which leads to its lowest thermal conductivities. The thermal conductivity in the positive direction is larger than that in the negative direction because of its lower boundary scattering relaxation rate.

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6

Suzumura, Y., M. Tsuchiizu, and G. Grüner. "Confinement by umklapp scattering in two coupled chains." Synthetic Metals 103, no. 1-3 (1999): 2191–92. http://dx.doi.org/10.1016/s0379-6779(98)00880-7.

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7

Lercher, M. J., and J. M. Wheatley. "Umklapp scattering from spin fluctuations in copper oxides." Physical Review B 52, no. 10 (1995): R7038—R7041. http://dx.doi.org/10.1103/physrevb.52.r7038.

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8

Zheng, X. H., and D. G. Walmsley. "Umklapp scattering of pairs in BCS superconductivity theory." Journal of Physics: Condensed Matter 16, no. 46 (2004): 8297–309. http://dx.doi.org/10.1088/0953-8984/16/46/016.

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9

Foret, M., B. Hehlen, G. Taillades, et al. "Neutron Brillouin and Umklapp Scattering from Glassy Selenium." Physical Review Letters 81, no. 10 (1998): 2100–2103. http://dx.doi.org/10.1103/physrevlett.81.2100.

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10

Maznev, A. A., and O. B. Wright. "Demystifying umklapp vs normal scattering in lattice thermal conductivity." American Journal of Physics 82, no. 11 (2014): 1062–66. http://dx.doi.org/10.1119/1.4892612.

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11

Buchenau, U., A. Wischnewski, M. Monkenbusch, and W. Schmidt. "Intensity sharing between Brillouin and Umklapp scattering in glasses." Philosophical Magazine B 79, no. 11-12 (1999): 2021–26. http://dx.doi.org/10.1080/13642819908223090.

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12

Buchenau, A. Wischnewski, M. Monken, U. "Intensity sharing between Brillouin and Umklapp scattering in glasses." Philosophical Magazine B 79, no. 11-12 (1999): 2021–26. http://dx.doi.org/10.1080/014186399256196.

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13

Cheung, J. Y., R. J. Stewart, and R. P. May. "Energy separation of neutrons scattered at small angles from silicon using time-of-flight techniques." Journal of Applied Crystallography 39, no. 1 (2006): 46–52. http://dx.doi.org/10.1107/s0021889805033698.

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The time-of-flight technique is used on a small-angle neutron scattering instrument to separate the energies of the scattered neutrons, in order to determine the origin of the temperature-dependent scattering observed from silicon atQ> ∼0.1 Å−1. A quantitative analysis of the results in comparison with the phonon dispersion curves, determined by Dolling using a triple-axis neutron spectrometer, shows that the temperature-dependent scattering can be understood in terms of Umklapp processes whereby neutrons gain energy from phonons.

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14

Sokolov, A. P., U. Buchenau, D. Richter, et al. "Brillouin and Umklapp scattering in polybutadiene: Comparison of neutron and x-ray scattering." Physical Review E 60, no. 3 (1999): R2464—R2467. http://dx.doi.org/10.1103/physreve.60.r2464.

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15

Fujimoto, Satoshi, and Norio Kawakami. "Effect of Umklapp Scattering on the Conductance in Quantum Wires." Journal of the Physical Society of Japan 65, no. 12 (1996): 3700–3703. http://dx.doi.org/10.1143/jpsj.65.3700.

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16

Murakami, Masakazu, and Hidetoshi Fukuyama. "Effects of Umklapp Scattering on Electronic States in One Dimension." Journal of the Physical Society of Japan 66, no. 8 (1997): 2399–409. http://dx.doi.org/10.1143/jpsj.66.2399.

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17

Hsin, Cheng-Lun, Yu-Ting Liu та Yue-Yun Tsai. "Suppressed Umklapp scattering ofβ-FeSi2thin film and single crystalline nanowires". Nanotechnology 28, № 48 (2017): 485702. http://dx.doi.org/10.1088/1361-6528/aa904a.

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18

Zülicke, U. "Exactly Soluble Model for Umklapp Scattering at Quantum Hall Edges." Physical Review Letters 83, no. 25 (1999): 5330–33. http://dx.doi.org/10.1103/physrevlett.83.5330.

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19

Tsuchiizu, M., and Y. Suzumura. "Confinement-deconfinement transition in two coupled chains with umklapp scattering." Physical Review B 59, no. 19 (1999): 12326–37. http://dx.doi.org/10.1103/physrevb.59.12326.

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20

Aleiner, Igor L., and Oded Agam. "Saturation of strong electron–electron umklapp scattering at high temperature." Annals of Physics 385 (October 2017): 716–28. http://dx.doi.org/10.1016/j.aop.2017.08.017.

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21

Wallbank, J. R., R. Krishna Kumar, M. Holwill, et al. "Excess resistivity in graphene superlattices caused by umklapp electron–electron scattering." Nature Physics 15, no. 1 (2018): 32–36. http://dx.doi.org/10.1038/s41567-018-0278-6.

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22

Suzumura, Y., M. Tsuchiizu, and G. Grüner. "Confinement of interchain hopping by umklapp scattering in two coupled chains." Physical Review B 57, no. 24 (1998): R15040—R15043. http://dx.doi.org/10.1103/physrevb.57.r15040.

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23

Sakurai, Hiroshi, and Akio Sakurai. "Electrical Resistivity Due to Electron-Electron Umklapp Scattering in Ferromagnetic Metals." Progress of Theoretical Physics Supplement 106 (1991): 119–28. http://dx.doi.org/10.1143/ptps.106.119.

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24

Sakurai, H., and A. Sakurai. "Electrical Resistivity Due to Electron-Electron Umklapp Scattering in Ferromagnetic Metals." Progress of Theoretical Physics Supplement 106 (May 16, 2013): 119–28. http://dx.doi.org/10.1143/ptp.106.119.

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25

Fujimoto, S., and N. Kawakami. "Universal conductance in quantum wires in the presence of Umklapp scattering." European Physical Journal B 5, no. 3 (1998): 389–93. http://dx.doi.org/10.1007/s100510050458.

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26

Mamand, S. M., and M. S. Omar. "Effect of Parameters on Lattice Thermal Conductivity in Germanium Nanowires." Advanced Materials Research 832 (November 2013): 33–38. http://dx.doi.org/10.4028/www.scientific.net/amr.832.33.

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Modified Callaway's theory was used to calculate lattice thermal conductivity (LTC) of Germanium nanowires. Results are compared to those of experimental values of the temperature dependence of LTC for nanowire diameters of 62, 19, and 15nm. In this calculation, both longitudinal and transverse modes are taken into account. Scattering of phonons is assumed to be by nanowire boundaries, imperfections, dislocations, electrons, and other phonons via both normal and Umklapp processes. Effect of parameters, phonon confinement and imperfections in limiting thermal conductivity for the nanowires under considerations are investigated. The suppression in thermal conductivity of these nanowires is arise from electron-phonon scattering and phonon-boundary scattering at low temperatures, while at high temperatures is due to imperfections and intrinsic properties.

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27

Grimm, H., H. Stiller, C. F. Majkrzak, A. Rupprecht, and U. Dahlborg. "Observation of acoustic umklapp-phonons in water-stabilized DNA by neutron scattering." Physical Review Letters 59, no. 15 (1987): 1780–83. http://dx.doi.org/10.1103/physrevlett.59.1780.

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28

Grimm, H., H. Stiller, C. F. Majkrzak, A. Rupprecht, and U. Dahlborg. "Observation of Acoustic Umklapp Phonons in Water-Stabilized DNA by Neutron Scattering." Physical Review Letters 60, no. 1 (1988): 76. http://dx.doi.org/10.1103/physrevlett.60.76.2.

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29

Jujo, Takanobu. "Effect of Umklapp Scattering on Magnetic Field Penetration Depth in High-TcCuprates." Journal of the Physical Society of Japan 71, no. 3 (2002): 888–904. http://dx.doi.org/10.1143/jpsj.71.888.

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30

PEREIRA, RODRIGO G. "LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS." International Journal of Modern Physics B 26, no. 22 (2012): 1244008. http://dx.doi.org/10.1142/s0217979212440080.

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An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga–Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density–density correlation due to umklapp scattering in lattice models.

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31

Mehri, Ali, Maryam Jamaati, and Moslem Moradi. "The effect of imposed temperature difference on thermal conductivity in armchair single-walled carbon nanotube." International Journal of Modern Physics C 26, no. 09 (2015): 1550105. http://dx.doi.org/10.1142/s0129183115501053.

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Thermal conductivity of carbon nanotubes depends on various factors. The simulation of heat transport in armchair single-walled carbon nanotube by direct nonequilibrium molecular dynamics (NEMD) method employing Tersoff–Brenner potential indicates that, thermal conductivity decreases with increase in temperature difference between two ends of the tube. Increasing the imposed temperature differential along the tube axis, leads to domination of Umklapp scattering and impacts the heat transport. The applied temperature difference does not influence the behavior of thermal conductivity vs. tube length, diameter and temperature, but changes its value.

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32

Cea, Tommaso, and Francisco Guinea. "Coulomb interaction, phonons, and superconductivity in twisted bilayer graphene." Proceedings of the National Academy of Sciences 118, no. 32 (2021): e2107874118. http://dx.doi.org/10.1073/pnas.2107874118.

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The polarizability of twisted bilayer graphene, due to the combined effect of electron–hole pairs, plasmons, and acoustic phonons, is analyzed. The screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron–hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among the different pockets of the Fermi surface.

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33

Lundmark, L. "The Umklapp scattering contribution to the electron-electron scattering part of the thermal resistivity in alkali metals." Journal of Physics: Condensed Matter 2, no. 47 (1990): 9309–22. http://dx.doi.org/10.1088/0953-8984/2/47/006.

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34

Kato, Mayumi, Makoto Sakairi, Akira Endo, Shingo Katsumoto, and Yasuhiro Iye. "Electron–electron umklapp scattering in two-dimensional electron gas under lateral magnetic periodicity." Physica B: Condensed Matter 284-288 (July 2000): 1902–3. http://dx.doi.org/10.1016/s0921-4526(99)02992-0.

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35

Hellman, E. S. "Umklapp electron-electron scattering resistivity of half-filled copper-oxygen chains and planes." Physical Review B 39, no. 13 (1989): 9604–6. http://dx.doi.org/10.1103/physrevb.39.9604.

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36

Fernández, V. I., and C. M. Naón. "Path-integral formulation of backward and umklapp scattering for one-dimensional spinless fermions." Theoretical and Mathematical Physics 118, no. 3 (1999): 385–91. http://dx.doi.org/10.1007/bf02557337.

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37

Sahoo, Sushant Kumar, Anju Pansari, and Bijaya Kumar Sahoo. "Built-in-polarization effect on relaxation time and mean free path of phonons in AlxGa1−xN/GaN heterostructure." Modern Physics Letters B 30, no. 08 (2016): 1650097. http://dx.doi.org/10.1142/s0217984916500974.

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In this paper, we have theoretically investigated the effect of built-in-polarization field on various phonon scattering mechanisms in Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure. The built-in-polarization field enhances the elastic constant, phonon velocity and Debye frequency of Al[Formula: see text]Ga[Formula: see text]N alloy. As a result, various phonon scattering mechanisms are modified. Important phonon scattering mechanisms such as normal scattering, Umklapp scattering, point defect scattering, dislocation scattering and phonon–electron scattering processes have been considered. The combined relaxation time due to above scattering mechanisms has also been computed as a function of phonon frequency for various Al contents at room temperature. Our result shows that built-in-polarization field suppresses scattering rates leading to enhanced combined relaxation time. Increased relaxation time implies longer phonon mean free path and enhanced optical and thermal transport properties. The result can be used to determine the effect of built-in-polarization field on optical and thermal properties of Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure and will be useful, particularly, for improvement of thermoelectric performance of Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure through polarization engineering.

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38

Maebashi, Hideaki, and Hidetoshi Fukuyama. "Electrical Conductivity of Interacting Fermions. II. Effects of Normal Scattering Processes in the Presence of Umklapp Scattering Processes." Journal of the Physical Society of Japan 67, no. 1 (1998): 242–51. http://dx.doi.org/10.1143/jpsj.67.242.

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39

Yu, Choongho, Sanjoy Saha, Jianhua Zhou, et al. "Thermal Contact Resistance and Thermal Conductivity of a Carbon Nanofiber." Journal of Heat Transfer 128, no. 3 (2005): 234–39. http://dx.doi.org/10.1115/1.2150833.

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We have measured the thermal resistance of a 152‐nm-diameter carbon nanofiber before and after a platinum layer was deposited on the contacts between the nanofiber and the measurement device. The contact resistance was reduced by the platinum coating for about 9–13% of the total thermal resistance of the nanofiber sample before the platinum coating. At a temperature of 300K, the axial thermal conductivity of the carbon nanofiber is about three times smaller than that of graphite fibers grown by pyrolysis of natural gas prior to high-temperature heat treatment, and increases with temperature in the temperature range between 150K and 310K. The phonon mean free path was found to be about 1.5nm and approximately temperature-independent. This feature and the absence of a peak in the thermal conductivity curve indicate that phonon-boundary and phonon-defect scattering dominate over phonon-phonon Umklapp scattering for the temperature range.

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40

Awad, Adil H. "Lattice Thermal Conductivity Modelling of a Diatomic Nanoscale Material." Nanoscience & Nanotechnology-Asia 10, no. 5 (2020): 602–9. http://dx.doi.org/10.2174/2210681209666190423142040.

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Introduction: A new approach for expressing the lattice thermal conductivity of diatomic nanoscale materials is developed. Methods: The lattice thermal conductivity of two samples of GaAs nanobeam at 4-100K is calculated on the basis of monatomic dispersion relation. Phonons are scattered by nanobeam boundaries, point defects and other phonons via normal and Umklapp processes. Methods: A comparative study of the results of the present analysis and those obtained using Callaway formula is performed. We clearly demonstrate the importance of the utilised scattering mechanisms in lattice thermal conductivity by addressing the separate role of the phonon scattering relaxation rate. The formulas derived from the correction term are also presented, and their difference from Callaway model is evident. Furthermore their percentage contribution is sufficiently small to be neglected in calculating lattice thermal conductivity. Conclusion: Our model is successfully used to correlate the predicted lattice thermal conductivity with that of the experimental observation.

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41

CHOUDHARY, K. K., N. KAURAV, and S. K. GHOSH. "OPTIMIZATION OF THERMOELECTRIC PROPERTIES BY Cu SUBSTITUTION IN LaCoO3 CERAMICS." International Journal of Modern Physics B 28, no. 09 (2014): 1450065. http://dx.doi.org/10.1142/s0217979214500659.

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The thermoelectric properties of LaCo 1-x Cu x O 3-δ ceramics are theoretically analyzed, it is observed that thermoelectric figure of merit ZT ( = S2σT/κ) is maximized by Cu substitution in LaCo 1-x Cu x O 3-δ at x = 0.15. The lattice thermal conductivity (κ ph ) and phonon drag thermoelectric power [Formula: see text] were estimated by the scattering of phonons with defects, grain boundaries, electrons and phonon umklapp scattering to evaluate the thermoelectric figure of merit ZT. The Mott expression is used to estimate the electron diffusive thermoelectric power [Formula: see text] using Fermi energy as electron free parameter, [Formula: see text] shows linear temperature dependence. The electron contribution to thermal conductivity (κe) is estimated using temperature-dependent electron relaxation time. We found that Cu substitution increases the phonon scattering with grain boundaries and defects which significantly decrease the thermal conductivity and subsequently increase the thermoelectric power. The present numerical analysis of thermoelectric properties will help in designing more efficient thermoelectric materials for thermoelectric applications.

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42

Murthy, J. Y., and S. R. Mathur. "Computation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method." Journal of Heat Transfer 124, no. 6 (2002): 1176–81. http://dx.doi.org/10.1115/1.1518495.

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An unstructured finite volume scheme is applied to the solution of sub-micron heat conduction problems. The phonon Boltzmann transport equation (BTE) in the relaxation time approximation is considered. The similarity between the radiative transfer equation (RTE) and the BTE is exploited in developing a finite volume scheme for the BTE. The spatial domain is divided into arbitrary unstructured polyhedra, the angular domain into control angles, and the frequency domain into frequency bands, and conservation equations for phonon energy are written. The unsteady wave propagation term, not usually present in thermal radiation problems, is differentiated using a fully implicit scheme. A sequential multigrid scheme is applied to solve the nominally linear set. Isotropic scattering due to a variety of mechanisms such as impurity and Umklapp scattering is considered. The numerical scheme is applied to a variety of sub-micron conduction problems, both unsteady and steady. Favorable comparison is found with the published literature and with exact solutions.

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43

Chen, Yunfei, Deyu Li, Jennifer R. Lukes, and Arun Majumdar. "Monte Carlo Simulation of Silicon Nanowire Thermal Conductivity." Journal of Heat Transfer 127, no. 10 (2005): 1129–37. http://dx.doi.org/10.1115/1.2035114.

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Monte Carlo simulation is applied to investigate phonon transport in single crystalline Si nanowires. Phonon-phonon normal (N) and Umklapp (U) scattering processes are modeled with a genetic algorithm to satisfy energy and momentum conservation. The scattering rates of N and U scattering processes are found from first-order perturbation theory. The thermal conductivity of Si nanowires is simulated and good agreement is achieved with recent experimental data. In order to study the confinement effects on phonon transport in nanowires, two different phonon dispersions, one from experimental measurements on bulk Si and the other solved from elastic wave theory, are adopted in the simulation. The discrepancy between simulations using different phonon dispersions increases as the nanowire diameter decreases, which suggests that the confinement effect is significant when the nanowire diameter approaches tens of nanometers. It is found that the U scattering probability in Si nanowires is higher than that in bulk Si due to the decrease of the frequency gap between different modes and the reduced phonon group velocity. Simulation results suggest that the dispersion relation for nanowires obtained from elasticity theory should be used to evaluate nanowire thermal conductivity as the nanowire diameter is reduced to the sub-100 nm scale.

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44

Sharma, Suresh C., Vivek Khichar, Hussein Akafzade, Douglas Zinn, and Nader Hozhabri. "Controlling Electrical Conduction through Noble Metal Thin Films by Surface Plasmon Resonance." Condensed Matter 5, no. 3 (2020): 52. http://dx.doi.org/10.3390/condmat5030052.

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We have conducted in situ measurements of the surface plasmons and electrical resistivity of noble metal thin films. We present results for the electrical resistivity of these materials as functions of the angle of incidence for p-polarized light of wavelength λ = 632 nm in the Kretschmann configuration optical system. We observe a significantly lower resistivity (higher conductivity) under resonance conditions for the surface plasmon polaritons. The resistivity data are supported by COMSOL simulations of the evanescent fields associated with the surface plasmons. We discuss the resistivity data in terms of the theoretical models, which suggest that the electrical conductivity of the transition metals is sensitive to Umklapp electron-electron scattering and attractive interactions between free electrons because of the screening of the d-band electrons by the s-band electrons.

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45

Robinson, Neil J., Peter D. Johnson, T. Maurice Rice, and Alexei M. Tsvelik. "Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering." Reports on Progress in Physics 82, no. 12 (2019): 126501. http://dx.doi.org/10.1088/1361-6633/ab31ed.

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46

Batistić, I., B. Korin-Hamzić, and J. R. Cooper. "Linear temperature dependence of the transverse electrical resistivity of organic metals arising from electron-electron umklapp scattering." Physical Review B 48, no. 22 (1993): 16849–52. http://dx.doi.org/10.1103/physrevb.48.16849.

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47

Kocharovsky, V. V., and VI V. Kocharovsky. "Origin of Bragg-Coulomb high-Tc superconductivity Green's function and diagram method for umklapp e−-e− scattering." Physica C: Superconductivity 200, no. 3-4 (1992): 385–402. http://dx.doi.org/10.1016/0921-4534(92)90392-p.

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48

Lucas, Andrew, and Sean A. Hartnoll. "Resistivity bound for hydrodynamic bad metals." Proceedings of the National Academy of Sciences 114, no. 43 (2017): 11344–49. http://dx.doi.org/10.1073/pnas.1711414114.

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We obtain a rigorous upper bound on the resistivity ρ of an electron fluid whose electronic mean free path is short compared with the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a nonthermal diffusion process—such as an imbalance mode between different bands—we show that the resistivity bound becomes ρ≲AΓ. The coefficient A is independent of temperature and inhomogeneity lengthscale, and Γ is a microscopic momentum-preserving scattering rate. In this way, we obtain a unified mechanism—without umklapp—for ρ∼T2 in a Fermi liquid and the crossover to ρ∼T in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides, and heavy fermion compounds and has presented a long-standing challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.

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49

Bondarev, I. V. "On the role of umklapp processes in the scattering of delocalized positronium by acoustic phonons in ionic crystals." Journal of Experimental and Theoretical Physics Letters 69, no. 3 (1999): 231–35. http://dx.doi.org/10.1134/1.568019.

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50

Dupuis, N., and V. M. Yakovenko. "Effect of umklapp scattering on the magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductors." Physical Review B 58, no. 13 (1998): 8773–92. http://dx.doi.org/10.1103/physrevb.58.8773.

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