Quantized baker map

• Marcos Saraceno*, Laboratorio Tandar, Comision Nacional de Energia Atomica, Buenos Aires
• Leonardo Ermann, Laboratorio Tandar, Comision Nacional de Energia Atomica, Buenos Aires

Dr. Leonardo Ermann accepted the invitation on 4 July 2011

Quantized baker map

The quantized baker's map is a simple mathematical model that is used to explore the relationship between classical and quantum mechanics in the semiclassical limit, when the dynamics is chaotic. The relative simplicity of the classical description - provided by symbolic dynamics - and the elegant quantization scheme devised by Balasz and Voros allow a very detailed comparison of classical and quantum invariant structures.

The classical map

The classical map is best described geometrically as in Fig.1.

Figure 1: The action of the baker's map on a basket of bread

The phase space coordinates \(p,q \in [0,1)\times[0,1)\) are transformed as

\[p^\prime=\frac{p+[2q]}{2}\]

\[q^\prime=2q-[2q] \]

The quantum map

See also

Sponsored by: Dima Shepelyansky, Laboratoire de Physique Théorique, CNRS, Université Paul Sabatier, Toulouse