1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Quantization of a free particle interacting linearly with a harmonic oscillator
Rent:
Rent this article for
USD
10.1063/1.2819060
/content/aip/journal/chaos/17/4/10.1063/1.2819060
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/4/10.1063/1.2819060
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) The configuration space of the particle. Its position on the ring is denoted .

Image of FIG. 2.
FIG. 2.

(Color online) Lifting of the double degeneracy in the eigenenergies for .

Image of FIG. 3.
FIG. 3.

(Color online) (a) The first 100 energy levels as a function of the interaction strength for Eq. (5) with a noninteraction region of length . (b) Magnification of the avoided crossing between the 18th and 19th levels from panel (a). The inset shows a further magnification, and the labels designate where we calculated Husimi distributions (see Fig. 9 ).

Image of FIG. 4.
FIG. 4.

(Color online) (a) The first 100 energy levels as a function of for Eq. (5) with a noninteraction region of length . (b) Magnification of panel (a) illustrating broad avoided crossings.

Image of FIG. 5.
FIG. 5.

(Color online) An isolated cluster of two sharp avoided crossings and a broad avoided crossing between the 119th, 120th, and 121st energy levels for . The incoming slope of the 119th level is imparted to the outgoing slope of the 121st. The labels designate locations at which we calculated Husimi distributions (see Fig. 10 ).

Image of FIG. 6.
FIG. 6.

(Color) (a) Husimi distribution localized around quasiperiodic orbits in a KAM island. Lighter regions have higher probabilities and black regions are ones with zero probability. The classical SOS is plotted in turquoise. To facilitate the comparison between the quantum and classical dynamics, we include plots of a few of the orbits in the integrable region. (b) Husimi distribution localized around multiple KAM islands.

Image of FIG. 7.
FIG. 7.

(Color) (a) Husimi distribution delocalized throughout the chaotic sea on the left half of the plot. (b) Husimi distribution and classical SOS for the chaotic eigenstate in (a) taken on the surface defined by (one fourth of the way into the noninteraction region).

Image of FIG. 8.
FIG. 8.

(Color) (a) Husimi distribution and classical SOS for the chaotic eigenstate in Fig. 7(a) taken on the surface defined by (in the middle of the noninteraction region). (b) Husimi distribution showing both chaotic and integrable features while having only one connected component. The structure is relatively delocalized throughout the enclosed area on the left side of the available phase space.

Image of FIG. 9.
FIG. 9.

(Color) Husimi structure exchange through the sharp avoided crossing shown in Fig. 3(b) . The left and right columns show the Husimi distributions of the 18th and 19th levels, respectively. The harmonic oscillator momentum is on the vertical axis and the oscillator position is on the horizontal axis. During the structure exchange, probability flows continuously from the integrable region to the chaotic region for the 18th eigenstate (and vice-versa for the 19th).

Image of FIG. 10.
FIG. 10.

(Color) Mixing of Husimi structures through the avoided-crossing cluster of Fig. 5 . The left, center, and right columns show the Husimi distributions of the 119th, 120th, and 121st levels, respectively. The axes are as in Fig. 9 .

Loading

Article metrics loading...

/content/aip/journal/chaos/17/4/10.1063/1.2819060
2007-12-28
2014-04-18
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantization of a free particle interacting linearly with a harmonic oscillator
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/4/10.1063/1.2819060
10.1063/1.2819060
SEARCH_EXPAND_ITEM