The Brillouin zone is a primitive cell (more specifically a Wigner–Seitz cell) of the reciprocal lattice, which plays an important role in solid state physics due to Bloch's theorem. The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where k on the reciprocal lattice does always take this form, this derivation is motivational, rather than rigorous, because it has omitted the proof that no other possibilities exist.) The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). In physics, the reciprocal lattice represents the Fourier transform of another lattice. ![]() A two-dimensional crystal and its reciprocal lattice (2003) Zbl1027.11075 MR1980849 DOI10.Fourier transform of a real-space lattice, important in solid-state physics The computer-generated reciprocal lattice of a fictional monoclinic 3D crystal. 1 The rst way of thinking about Minkowski’s theorem, even for the analysis-inclined people, would still be to draw a picture for the two-dimensional case and see if any property of the Euclidean plane would give the existence of the non-zero lattice point inside K. (1999) MR1708625ġ0.4064/aa109-1-1, Acta Arithm. lattice point, we mean a point from the integer lattice. On the number of coprime integer pairs within a circle, Acta Arithm. Wolfram Research, Inc., Mathematica 4.1,, Champaign, 2001.On the zeros of zeta-functions of quadratic forms, Trudy Mat.The Theory of the Riemann zeta-function, 2nd ed, Clarendon Press, Oxford, 1986.On the Zeros of Riemann’s zeta-function, Skr.Approximate equations for the Epstein zeta-function, Proc.On the distribution of square-free numbers, J. London Math. Soc.Lattice points in convex planar domains: Power moments with an application to primitive lattice points, In: Proc.Analytische Funktionen in der Zahlentheorie, Teubner, Wiesbaden, 2000.Lattice Points, Kluwer Academic Publishers, Berlin, 1988.The Riemann zeta-function, Wiley & Sons, New York, 1985.Exponential sums and lattice points III, Proc.Area, Lattice Points, and Exponential Sums. For large real x, one may ask for the number B (x) of primitive lattice points (integer points (m, n) with gcd (M, n) 1) in the ellipse disc Q (u, v) x, in particular, for the remainder term R (x) in the asymptotics for B (x).Exponential sums and lattice points II, Proc.Table of Integrals, Series, and Products, 5th ed., A. Jeffrey (ed.), Academic Press, San Diego, 1994. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |