Ulrich D. Jentschura, Andrey Surzhykov, Jean Zinn-Justin, “Generalized Nonanalytic Expansions, $\mathcal{PT}$-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators”, SIGMA, 2009, том 5,005, 10 стр.

Эта публикация цитируется в 6 статьях

Generalized Nonanalytic Expansions, $\mathcal{PT}$-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators

Ulrich D. Jentschura^a, Andrey Surzhykov^b, Jean Zinn-Justin^c

^a Department of Physics, Missouri University of Science and Technology, Rolla MO65409-0640, USA
^b Physikalisches Institut der Universität, Philosophenweg 12, 69120 Heidelberg, Germany
^c CEA, IRFU and Institut de Physique Théorique, Centre de Saclay, F-91191 Gif-Sur-Yvette, France

Аннотация: The concept of a generalized nonanalytic expansion which involves nonanalytic combinations of exponentials, logarithms and powers of a coupling is introduced and its use illustrated in various areas of physics. Dispersion relations for the resonance energies of odd anharmonic oscillators are discussed, and higher-order formulas are presented for cubic and quartic potentials.

Ключевые слова: $\mathcal{PT}$-symmetry; asymptotics; higher-order corrections; instantons.

MSC: 81Q15; 81T15

Поступила: 30 октября 2008 г.; в окончательном варианте 7 января 2009 г.; опубликована 13 января 2009 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2009.005