Description of simple physical models which account for electrical conductivity and thermal properties of solids. Basic crystal lattice structures, X-ray diffraction and dispersion curves for phonons and electrons in reciprocal space. Energy bands, Fermi surfaces, metals, insulators, semiconductors, superconductivity and ferromagnetism. Fall semester.
Typical text: Kittel, Introduction to Solid State Physics.
Vectors, kinetics, Newton’s laws, dynamics or particles, work and energy, friction, conserverative forces, linear momentum, center-of-mass and relative motion, collisions, angular momentum, static equilibrium, rigid body rotation, Newton’s law of gravity, simple harmonic motion, wave motion and sound.
Coulomb’s law, concepts of electric field and potential, Gauss’ law, capacitance, current and resistance, DC and R-C transient circuits, magnetic fields, Ampere’s law, Faraday’s law of induction, inductance, A/C circuits, electromagnetic oscillations, Maxwell’s equations and electromagnetic waves.
Simple harmonic motion, oscillations and pendulums; Fourier analysis; wave properties; wave-particle dualism; the Schrödinger equation and its interpretation; wave functions; the Heisenberg uncertainty principle; quantum mechanical tunneling and application; quantum mechanics of a particle in a "box," the hydrogen atom; electronic spin; properties of many electron atoms; atomic spectra; principles of lasers and applications; electrons in solids; conductors and semiconductors; the n-p junction and the transistor; properties of atomic nuclei; radioactivity; fusion and fission.
Vector and tensor fields and transformation properties under rotation of axes, vector identities, gradient, divergence, curl, tensor contraction, geometric interpretation of symmetric and antisymmetric tensors, divergence-Gauss' theorem for tensor fields and Stokes' theorem, Helmholtz' theorem, and scalar and vector potentials. Applications to inertia tensor, particle mechanics, transport, electromagnetism (Maxwell's equations), and viscous fluid dynamics (the Navier-Stokes equation, Euler equation, and the Bernoulli equation). Introduction to the Dirac delta-function and Greenís function technique for solving linear inhomogeneous equations. Orthogonal curvilinear coordinates (general, also spherical, and cylindrical). N-dimensional complex space and unitarity, matrix notation, inverse of matrix, Pauli spin matrices, relativity, and Lorentz transformation. Tensors and pseudotensors in n-dimensions. Similarity transformations and diagonalization of Hermitian and unitary matrices, eigenvectors, and eigenvalues of Hermitian and unitary matrices, and Schmidt orthogonalization. Applications to coupled oscillators, rigid body dynamics, etc. Linear independence and completeness. Functions of a complex variable, analyticity, Cauchyís theorem, Residue theorem, Taylor and Laurent expansions, classification of singularities, analytic continuation, Liouvilleís theorem, multiple-valued functions, contour integration, Jordanís lemma, applications, and asymptotics. Fall Semester.
PEP 528:Mathematical Methods of Science and Engineering II
Vector and Tensor Fields: transformation properties, algebraic and differential operators and identities, geometric interpretation of tensors, integral theorems. Dirac delta-function and Green's function technique for solving linear inhomogeneous equations. N-dimensional complex space: rotations, unitary and hermitian operators, matrix-dyadic-Dirac notation, similarity transformations and diagonalization, Schmidt orthogonalization. Introduction to functions of a complex variable: analyticity, Cauchy's theorem, Taylor and Laurent expansions, analytic continuation, multiple- valued functions, residue theorem, contour integration, asymptotics. As techniques are developed, they are applied to examples in mechanics, electromagnetism and/or transport theory.
Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations.
PEP 544:Introduction to Plasma Physics and Controlled Fusion
Plasmas in nature and application of plasma physics; single particle motion; plasma fluid theory; waves in plasmas; diffusion and resistivity; equilibrium and stability; nonlinear effects and thermonuclear reactions; the Lawson condition; magnetic confinement fusion; and laser fusion. Fall semester.
Lagrangian and Hamiltonian formulations of mechanics, rigid body motion, elasticity, mechanics of continuous media, small vibration theory, special relativity, canonical transformations, and perturbation theory. Typical text: Goldstein, Classical Mechanics.
Electrostatics, boundary value problems, Green’s function techniques, methods of image, inversion, and conformal mapping; multipole expansion. Magnetostatics, vector potential. Maxwell’s equations and conservation laws. Electromagnetic wave propagation in media. Crystal optics. Fall semester. Typical texts: Jackson, Classical Electrodynamics; Landau and Lifshitz, Electrodynamics in Continuous Media.
Interaction of electromagnetic waves with matter, dispersion, waveguides and resonant cavities, radiating systems, scattering and diffraction, covariant electromagnetic theory, motion of relativistic particles in electromagnetic fields, relativistic radiation theory, radiation damping, and self-fields. Spring semester. Typical texts: Jackson, Classical Electrodynamics and Landau and Lifshitz, The Classical Theory of Fields, Electrodynamics in Continuous Media.
PEP 700:Quantum Electron Physics and Technology Seminar
This seminar is focused on nanostructure-scale electron systems that are so small that their dynamic and statistical properties can only be properly described by quantum mechanics. This includes many submicron semiconductor devices based on heterostructures, quantum wells, superlattices, etc., and it interfaces solid state physics with surface physics and optics. Outstanding visiting scientists make presentations, as well as some faculty members and doctoral research students discussing their thesis work and related journal articles. Participation in these seminars is regarded as an important part of the research education of a physicist working in condensed matter physics and/or surface physics and optics.
This course is an introduction to relativistic quantum mechanics and quantum field theory. Relativistic wave equations, including the Klein-Gordon equation and the Dirac equation. Commutation relation and canonical quantization of free fields. Spin and statistics of Bose and Fermi fields. Interacting quantum fields: interaction representation and S-matrix perturbation theory, Feynman diagrams, and renormalization theory with applications to quantum electrodynamics. Typical texts: Advanced Quantum Mechanics by J. J. Sakurai and Quantum Field Theory by F. Mandl and G. Shaw.
PEP 757:Quantum Field Theory Methods in Statistical and Many-Body Physics
Dirac notation; Transformation theory; Second quantization; Particle creation and annihilation operators; Schrodinger, Heisenberg and Interaction Pictures; Linear response; S-matrix; Density matrix; Superoperators and non-Markovian kinetic equations; Schwinger Action Principle and variational calculus; Quantum Hamilton equations; Field equations with particle sources, potential and phonon sources; Retarded Green's functions; Localized state in continuumand chemisorption; Dyson equation; T-matrix; Impurity scattering; Self-consistent Born approximation;Density-of-states;Greens function matching; Ensemble averages and statistical thermodynamics, Bose and Fermi distributions, Bose condensation; Thermodynamic Green's functions; Lehmann spectral representation; periodicity/antipeiodicity in imaginary time and Matsubara Fourier series/frequencies; Anallytic continuation to real time; Multiparticle Green's functions; Electromagnetic current-current correlation response; Exact variational relations for multiparticle Green's functions; Cumulants; Linked cluster theorem; Random phase approximation; Perturbation theory for green's functions, self-energy and vertex functions by variational differential formulation; Shielded potential perturbation theory;Imaginary time contour ordering Langreth algebra and the GKB Ansatz.
Typical texts: Kadanoff and Baym, Quantum Statistical Mechanics, and Inkson, Many-Body Theory of Solids.
The course features the application of modern field theory methods and especially Feynman diagrams to fermion and boson system and critical phenomena. The initial text will be Quantum field theory and statistical physic by Abrikosov, Gorkov and Dzyalizhinski. Also discussed will be an introduction to scaling and the renormalization group (Wilson papers, texts of Pfeuty and Toulose, Ma and Reichl). Other topics will include broken symmetry non-phonon mechanisms in fermion superconductivity, field theory generalizations of the independent particle or Hartree-Fock model for non-homogeneous Fermion systems, Feynman path integrals and Wiener measure in statistical physics, exact properties of the Ising model,Feynman path integrals and Wiener measure in statistical physics, onset of ferromagnetism and spin-fluctuations.
Original experimental or theoretical research undertaken under the guidance of the faculty of the department which may serve as the basis for the dissertation required for the degree of Doctor of Philosophy. Hours and credits to be arranged. This course is open to students who have passed the doctoral qualifying examination; a student who has already taken the required doctoral courses may register for this in the term in which s/he intends to take the qualifying examination.
PEP 527:Mathematical Methods of Science and Engineering I
Fourier series, Bessel functions, and Legendre polynomials as involved in the solution of vibrating systems; tensors and vectors in the theory of elasticity; applications of vector analysis to electrodynamics; vector operations in curvilinear coordinates; numerical methods of interpolation and of integration of functions and differential equations.
School: Schaefer School of Engineering & Science
Department: Physics and Engineering Physics
Program: Physics / Nanotechnology
Research & Education
Quantum Field Theoretic Green's Function Methods in Many-Body Problems, Solid State and Surface Physics
Correlation Phenomena, Collective Modes in Low Dimensional Systems
Quantum Transport Theory for Semiconductor Nanostructures, Superlattices
Staff Physicist: US Naval Research Lab, Washington, D.C., 1966
Stevens Inst. of Tech: Assistant, Associate & Full Professor, 1966-Present
Director, Academic Support Center, Stevens Inst. of Tech., 1987-1993
Consultant to Dean of Faculty, Stevens Inst. of Tech., 1986-1992
Elderhostel Coordinator, Stevens Inst. of Tech., 1978-1989
Chair, Consultant to Graduate Academic Standards Comm. 2007-present
Over 315 peer reviewed publications in physics research journals. A full list of publications is available in the Resume/Bio link found under the photo at the top of the page.
Advisor to over 15 PhD Theses in Theoretical Condensed Matter Physics at Stevens and 3 PhD Theses in Europe (two at Humboldt University, Berlin, Germany, and one at University of Paris, France).
PhD Thesis Committee Member for many doctoral theses.
Supervisor of over 10 Postdoctoral Researchers and Visiting Scholars at Stevens.
Consultant US Army Electronics Command, Fort Monmouth, NJ, 1971
US Naval Research Res. Lab, Semicond Branch, Wash. DC, 1966-1971
Consultant to NEC Research Inst., Princeton, NJ, 1990-1995
Innovation and Entrepreneurship
Research and Course Development to Support Technogenesis Activities
Achievements & Professional Societies
Honors & Awards
Fellow of the New York Academy of Sciences, 2006
Henry Morton Distinguished Teaching Professor Award, 2005
Research Recognition Award, Stevens Inst. of Tech, 2004
Advisory Comm., Phys. & Astron. Sect., NY Acad. of Sci., 1988-1989
Jess H. Davis Research Prize, Stevens Inst. of Tech., 1986
M. Engr. (Honorary Degree) Stevens Inst. Tech., Hoboken, NJ, 1982
American Physical Society
New York Academy of Sciences
Society of the Sigma Xi: Vice President of Stevens Chapter, 1993
IEEE, Materials Research Society
European Physical Society
Grants, Contracts & Funds
DURINT Program of the ARO 2001-2006: $500,000
N.J.M. Horing. (2010). "Aspects of the Theory of Graphene", Philosophical Transactions of the Royal Society, Royal Society Publishing Org. ,. A 368 5525-5556 .
N.J.M. Horing. (2010). "Quantum Effects in Plasma Dielectric Response: Plasmons and Shielding in Normal Systems and Graphene", Eds: M. Bonitz, N.J.M. Horing & P. Ludwig, Introduction to Complex Plasmas (Book), Springer,. 109-132.
N.J.M. Horing, and S.Y. Liu. (2009). "Green's functions for a graphene sheet and quantum dot in a normal magnetic field", J. Phys. A. (42), 225301 .
S.Y. Liu, X.L. Lei, N.J.M. Horing. (2008). "Diffusive Transport in Graphene: The Role of Interband Correlation", J. Appl. Phys., 104 043705.
S.Y. Liu, N.J.M. Horing, & X.L. Lei. (2010). "Dynamic Conductivity of Graphene in a Terahertz AC Electric Field", IEEE Sensors Journal, IEEE. 10 681.
B. Dong B, H.Y. Fan, X.L. Lei, N.J.M. Horing. (2009). "Counting statistics of tunneling through a single molecule: Effect of distortion and displacement of vibrational potential surface", J. Appl. Phys. . 105 113702.
N.J.M. Horing, T. Yu. Bagaeva & V.V. Popov. "Excitation of Radiative Polaritons in a 2D Excitonic Layer by a Light Pulse", J. Optical Soc. America, B24, 2428 , AIP (2007).
N.J.M. Horing & L.Y. Chen. "Inverse Dielectric Function of a Lateral Quantum Wire Superlattice Parallel to the Interface of a Plasma-Like Semiconductor", Phys. Rev. B 74, 195336, AIP (2006) :[Also reprinted in the Virtual Journal of Nanoscale Science of Technology, Dec. 11, 2006].
N. J. M. Horing, M. L. Glasser & B. Dong. "Dynamic & Statistical Thermodynamic Properties of Electrons in a Thin Quantum Well in a Parallel Magnetic Field", J. Phys. C: Condensed Matter, 18, p. 2573, IOP (2006).
N. J. M. Horing & L. Y. Chen. "Magneto-Image Effects in the van der Waals Interaction of an Atom and a Bounded Dynamic Nonlocal Plasma-like Medium", Phys. Rev. A66, p. 042905, AIP (2002).
N.J.M. Horing. "Quantum Theory of Electron Gas Plasma Oscillations in a Magnetic Field", Annals of Physics (NY) 31, 1 (1965).
N.J.M. Horing, M.M. Yildiz. "Quantum-Theory of Longitudional Dielectric Response Properties of a 2-Dimensional Plasma in a Magnetic-Field", Annals of Physics (NY) 97, 216 (1976).
X. L. Lei, N. J. M. Horing & Hl Cui. "Theory of Negative Differential Conductivity In a Superlattice Miniband", Physical Review Letters 66 (25), 3277, AIP (1991) .
H.L. Cui, V. Fessatidis & N.J.M. Horing. "Commensurability Oscillations in Magnetoplasmons of a Density-Modulated Two-Dimensional Electron-Gas", Phys. Rev. Lett. 63, 2598, AIP (1989).
B. Dong, N. J. M. Horing & H. L. Cui. "Inelastic Cotunneling-Induced Decoherence & Relaxation, Charge & Spin Currents in an Interacting Quantum Dot Under a Magnetic Field", Physical Review B72, 165326, AIP (2005); [Also reprinted in the Virtual Journal of Nanoscale Science and Technology, October 31, 2005].
B. Dong, N.J.M. Horing and X.L. Lei. "Qubit Measurement by a Quantum Point Contact: a Quantum Langevin Equation Apporach", Phys. Rev. B 74, 033303, AIP (2006): [Also reprinted in the Virtual Journal of Nanoscale Science and Technology, July 18, 2006; and in the Virtual Journal of Quantum Information, July 2006].
X. L. Lei and N. J. M. Horing. (1992). "Balance Equation Approach to Hot-Carrier Transport in Semiconductors", Editor C. S. Ting, Physics of Hot Electron Transport in Semiconductors (Book), World Scientific Press, Singapore. 1-132 .
N. J. M. Horing , H. L. Cui & X. L. Lei. (1992). "Recent Developments in Hot Electron Magnetotransport Theory", Editor C. S. Ting, Physics of Hot Electron Transport in Semiconductors (Book), World Scientific Press, Singapore. 133-169 .