One-dimensional quantum chaos: Explicitly solvable cases
نویسندگان
چکیده
منابع مشابه
Explicitly solvable cases of one-dimensional quantum chaos.
We identify a set of quantum graphs with unique and precisely defined spectral properties called regular quantum graphs. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact, convergent periodic orbit expansions for individual energy levels, thus obtaining an analytical solution f...
متن کاملA ug 2 00 1 One - dimensional quantum chaos : Explicitly solvable cases
We present quantum graphs with remarkably regular spectral characteristics. We call them regular quantum graphs. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansio...
متن کاملChaos in a One-dimensional Integrable Quantum System
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties are nontrivial. The level spacing distribution between its neighboring odd and even levels displays a surprising agreement with the prediction obtained for the...
متن کاملQuasi-Exactly Solvable One-Dimensional Equations
Quasi-exactly solvable one-dimensional Schrödinger equations can be specified in order to exhibit supplementary analytic eigenstates. While the usual solutions are preserved by the sl(2,R) generators, the additional ones are stabilized at the level of the universal enveloping algebra of this Lie structure. We discuss the square-integrability, the orthogonality of these supplementary solutions a...
متن کاملRandom string: an explicitly solvable model
We calculate exactly the Lyapunov exponent and the integrated density of states for the random string operator whose density and elastic compliance are functions of a binary Markov chain. For all values of interest short and long wave asymptotic expansions are obtained. Finally we discuss conditions of propagation and localization of waves in a binary random medium.
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: Journal of Experimental and Theoretical Physics Letters
سال: 2001
ISSN: 0021-3640,1090-6487
DOI: 10.1134/1.1413563