[1]Abramowitz, M. and Stegun, I. A.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York, ninth dover printing, tenth gpo printing edition, 1964.

[2]Ancona, M. G. and Iafrate, G. J.Quantum correction to the equation of state of an electron gas in a semiconductor. Phys. Rev. B, 39(13):9536–9540,May 1989.

[3]Ancona, M. G. and Tiersten, H. F.Macroscopic physics of the silicon inversion layer. Phys. Rev. B, 35(15):7959–7965, May 1987.

[4]Bhatnagar, P. L., Gross, E. P., and Krook, M.A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Phys. Rev., 94(3):511–525, May 1954.

[5]Carrillo, J. A., Gamba, I. M., Majorana, A., and Shu, C.-W.A weno-solver for the 1d non-stationary boltzmann Vpoisson system for semiconductor devices. Journal of Computational Electronics, 1:365–370, 2002. 10.1023/A:1020751624960.

[6]Carrillo, J. A., Gamba, I. M., Majorana, A., and Shu, C.-W.A direct solver for 2d non-stationary boltzmann-poisson systems for semiconductor devices: A mesfet simulation by weno-boltzmann schemes. Journal of Computational Electronics, 2:375–380, 2003. 10.1023/B:JCEL.0000011455.74817.35.

[7]Carrillo, J. A., Gamba, I. M., Majorana, A., and Shu, C.-W.A weno-solver for the transients of boltzmann-poisson system for semiconductor devices: performance and comparisons with monte carlo methods. Journal of Computational Physics, 184(2):498 – 525, 2003.

[8]Chapman, S. and Cowling, T. G.The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases. Cambridge University Press, 1970.

[9]Chen, G.Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Mit-Pappalardo Series in Mechanical Engineering). Oxford University Press, USA, Mar. 2005.

[10]Deng, X. G. and Zhang, H. X.Developing high-order weighted compact nonlinear schemes. Journal of Computational Physics, 165:24–44, 2000.

[11]Fatemi, E. and Odeh, F.Upwind finite difference solution of boltzmann equation applied to electron transport in semiconductor devices. Journal of Computational Physics, 108(2):209 – 217, 1993.

[12]Gardner, C. L.The quantum hydrodynamic model for semiconductor devices. SIAM J. Appl. Math., 54(2):409–427, 1994.

[13]Harten, A.High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 49(3):357 – 393, 1983.

[14]Harten, A. and Lax, P. D.On a class of high resolution total-variation-stable finite-difference schemes. SIAM Journal on Numerical Analysis, 21(1):pp. 1–23, 1984.

[15]Hsieh, T.-Y. and Yang, J.-Y.Thermal conductivity modeling of circular-wire nanocomposites. Journal of Applied Physics, 108:044306, 2010.

[16]Huang, A. B. and Giddens, D. P.The Discrete Ordinate Method for the Linearized Boundary Value Problems in Kinetic Theory of Gases. In Brundin, C. L., editor, Rarefied Gas Dynamics, Volume 1, pages 481–+, 1967.

[17]Jiang, G.-S., Levy, D., Lin, C.-T., Osher, S., and Tadmor, E.High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws. SIAM Journal on Numerical Analysis, 35(6):pp. 2147–2168, 1998.

[18]Jin, S.Runge-kutta methods for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys, 122:51–67, 1995.

[19]Jin, S. and Levermore, C. D.Numerical schemes for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys, 126:449–467, 1996.

[20]Jin, S. and Xin, Z. P.The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Communications on Pure and Applied Mathematics, 48:235, 2006.

[21]Kadanoff, L. P. and Baym, G.Quantum Statistical Mechanics. Benjamin, New York, 1962.

[22]Lax, P. D. and Liu, X. D.Solution of two dimensional riemann problem of gas dynamics by positive schemes. SIAM J. Sci. Comput, 19:319–340, 1995.

[23]Li, Z.-H. and Zhang, H.-X.Numerical investigation from rarefied flow to continuum by solving the boltzmann model equation. Intern. J. Numer. Fluids, 42:361–382, 2003.

[24]Li, Z.-H. and Zhang, H.-X.Study on gas kinetic unified algorithm for flows from rarefied transition to continuum. Journal of Computational Physics, 193:708–738, 2004.

[25]Lundstrom, M.Fundamentals of Carrier Transport. Cambridge University Press, 2nd edition, 2000.

[26]Majorana, A. and Pidatella, R. M.A finite difference scheme solving the boltzmann-poisson system for semiconductor devices: Volume 174, number 2 (2001), pages 649–668. Journal of Computational Physics, 177(2):450 – 450, 2002.

[27]Markowich, P. A., Ringhofer, C. A., and Schmeiser, C.Semiconductor Equations. Springer, 1 edition, 2002.

[28]Nikuni, T. and Griffin, A.Hydrodynamic damping in trapped bose gases. Journal of Low Temperature Physics, 111:793–814, 1998.

[29]Pattamatta, A. and Madnia, C. K.Modeling electron-phonon nonequilibrium in gold films using boltzmann transport model. Journal of Heat Transfer, 131:082401–1, 2009.

[30]Scaldaferri, S., Curatola, G., and Iannaccone, G.Direct solution of the boltzmann transport equation and poisson schrodinger equation for nanoscale mosfets. IEEE Transaction on Electron Devices, 54:2901, 2007.

[31]Schultz-Rinne, C. W., Collins, J. P., and Glaz, H. M.Numerical solution of the riemann problem for two-dimensional gas dynamics. SIAM J. Sci. Comput., 14(6):1394–1414, 1993.

[32]Shi, Y. H. and Yang, J. Y.A gas kinetic bgk scheme for semiclassical boltzmann hydrodynamic transport. Journal of Computational Physics, 227(22):9389 – 9407, 2008.

[33]Shizgal, B.A gaussian quadrature procedure for use in the solution of the boltzmann equation and related problems. Journal of Computational Physics, 41(2):309 – 328, 1981.

[34]Uehling, E. A. and Uhlenbeck, G. E.Transport phenomena in einstein-bose and fermi-dirac gases. i. Phys. Rev., 43(7):552–561, Apr 1933.

[35]Leer, B. van. Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov’s method. Journal of Computational Physics, 32(1):101 – 136, 1979.

[36]Wigner, E.On the quantum correction for thermodynamic equilibrium. Phys. Rev., 40(5):749–759, Jun 1932.

[37]Woolard, D. L., Tian, H., Littlejohn, M. A., Kim, K. W., Trew, R. J., Ieong, M. K., and Tang, T. W.Construction of higher-moment terms in the hydrodynamic electron transport model. Journal of Applied Physics, 74(10):6197 –6207, nov 1993.

[38]Xu, Z. and Shu, C.-W.Anti-diffusive flux corrections for high order finite difference weno schemes. Journal of Computational Physics, 205(2):458 – 485, 2005.

[9]Yang, J. Y., Hsieh, T. Y., and Shi, Y. H.Kinetic flux vector splitting schemes for ideal quantum gas dynamics. SIAM J. Sci. Comput., 29(1):221–244,2007.

[40]Yang, J. Y. and Huang, J. C.Rarefied flow computations using nonlinear model boltzmann equations. Journal of Computational Physics, 120(2):323 – 339, 1995.

[41]Yang, J. Y. and Shi, Y. H.A kinetic beam scheme for ideal quantum gas dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 462(2069):1553–1572, 2006.

[42]Zhang, H.-X.Non-oscillatory and non-free-parameter dissipation difference scheme. Acta Aerodynamica Sinica, 9(6):143–165, 1988.