Determinantal representations of closed orbits
نویسندگان
چکیده
منابع مشابه
Recurrences without closed orbits
The results of quantum photoabsorption calculations are presented for H, K, and Cs atoms in static electric fields. The recurrence spectra for ^Lz&Þ0 show features at scaled actions an order of magnitude shorter than for any classical closed orbit of this system. Two interesting manifestations are presented, and some of the systematics of the peak strengths are explored. These features suggest ...
متن کاملHermitian Determinantal Representations of Hyperbolic Curves
(1) f = det(xM1 + yM2 + zM3), where M1,M2,M3 are Hermitian d × d matrices. The representation is definite if there is a point e ∈ R for which the matrix e1M1+e2M2+e3M3 is positive definite. This imposes an immediate condition on the projective curve VC(f). Because the eigenvalues of a Hermitian matrix are real, every real line passing through e meets this hypersurface in only real points. A pol...
متن کاملRepresentations of Braid Groups via Determinantal Rings
We construct representations for braid groups Bn via actions of Bn on a determinantal ring, thus mirroring the setting of the classical representation theory for GLn. The representations that we construct fix a certain unitary form.
متن کاملPolynomials with and without Determinantal Representations
The problem of writing real zero polynomials as determinants of linear matrix polynomials has recently attracted a lot of attention. Helton and Vinnikov [9] have proved that any real zero polynomial in two variables has a determinantal representation. Brändén [2] has shown that the result does not extend to arbitrary numbers of variables, disproving the generalized Lax conjecture. We provide a ...
متن کاملDeterminantal Representations and the Hermite Matrix
We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the viewpoint of convex optimization. We relate the question to sums of squares decompositions of a certain Hermite matrix. If some power of a polynomial admits a de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.03.030