Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow

TY - JOUR

T1 - Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow

AU - Jauslin, H. R.

AU - Sapin, O.

AU - Weigert, Stefan

PY - 2007/5

Y1 - 2007/5

N2 - We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapunov exponents are positive and equal to the Lyapunov exponent of the corresponding classical parametric oscillators. As second example, we show that the configurational quantum cat system satisfies quantum Anosov properties.

AB - We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapunov exponents are positive and equal to the Lyapunov exponent of the corresponding classical parametric oscillators. As second example, we show that the configurational quantum cat system satisfies quantum Anosov properties.

U2 - 10.1007/s10955-007-9310-4

DO - 10.1007/s10955-007-9310-4

M3 - Article

VL - 127

SP - 699

EP - 719

JO - J Stat. Phys.

JF - J Stat. Phys.

IS - 4

ER -