Untitled

Belobrov, Yu. N.; Pil’gaev, V. M.

doi:10.1023/a:1004888911166

Cited by 3 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerical investigations of the excited spectra of certain two-level one-and two-boson systems [e.g., exciton [3,4] and E⊗e Jahn-Teller (JT) model [5]] show the existence of level avoidings and related highly excited "exotic" (localized) states. Signatures of chaos in twolevel boson systems remain objects of interest since the early studies by Hamiltonian methods [6,7,8,9,10,11]. Later on statistical methods based on the random matrix theory -e.g., level spacing and level curvature probability distributions -were applied mostly for one-phononmode models.…”

Section: Introductionmentioning

confidence: 99%

Incipience of quantum chaos in the Jahn-Teller model

Majerníková

Shpyrko

2006

Phys. Rev. E

View full text Add to dashboard Cite

We studied complex spectra of a two-level electron system coupled to two phonon (vibron) modes represented by the product of E and e Jahn-Teller model. For particular rotation quantum numbers we found a coexistence of up to three regions of the spectra: (i) the dimerized region of long-range-ordered (extended) pairs of oscillating levels, (ii) the short-range-ordered (localized) "kink lattice" of avoiding levels, and (iii) the intermediate region of kink nucleation with variable range of ordering. This structure appears above a certain critical line as a function of interaction strength. The level clustering and level avoiding generic patterns reflect themselves in several intermittent regions between up to three branches of spectral entropies. Linear scaling behavior of the widths of level curvature probability distributions provides the conventionally adopted indication for the presence of quantum chaos. Level spacing probability distributions show peculiarities of the partial (for fixed quantum angular momentum) as well as of the cumulative (all angular momenta) case. The clustering of levels with two and three dominant spacings at fixed angular momenta causes notable deviations of the cumulative distributions from the Poissonian one.

show abstract

Section: Introductionmentioning

confidence: 99%

Incipience of quantum chaos in the Jahn-Teller model

Majerníková

Shpyrko

2006

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…(6) with the z and p operators replaced by classical variables and the spin replaced by a classical magnetic moment. The transverse magnetic field along x causes the Hamiltonian to become non-integrable and leads to chaotic dynamics [14]. Previous studies showed that a continuous position measurement resulted in quantum trajectories that exhibit classical chaos when the actions associated with the spin and harmonic motion are both large relative toh [15,16].…”

mentioning

confidence: 99%

Entanglement and the quantum-to-classical transition

et al. 2005

View full text Add to dashboard Cite

We analyze the quantum-to-classical transition (QCT) for coupled bipartite quantum systems for which the position of one of the two subsystems is continuously monitored. We obtain the surprising result that the QCT can emerge concomitantly with the presence of highly entangled states in the bipartite system. Furthermore the changing degree of entanglement is associated with the back-action of the measurement on the system and is itself an indicator of the QCT. Our analysis elucidates the role of entanglement in von Neumann's paradigm of quantum measurements comprised of a system and a monitored measurement apparatus.

show abstract

“…10 In general, the covariances in Eq. (2) are non-zero, so that the quantum expectation values do not follow the classical trajectories.…”

Section: A Spin System Coupled To a Harmonic Oscillator Apparatusmentioning

confidence: 99%

The quantum to classical transition in continuously measured bipartite entangled systems

Ghose

Alsing²,

Deutsch³

et al. 2005

SPIE Proceedings

View full text Add to dashboard Cite

We study the quantum to classical transition in bipartite entangled systems in which one system is continuously coupled to a measurement apparatus as in the von Neumann model of quantum measurement. As an example, we study the open system dynamics of a particle in a harmonic well whose motion in the well is coupled to the internal spin. This system provides a rich illustration of the quantum to classical transition in weakly measured coupled systems. We analyze and derive conditions for which the dual constraints of strong localization/small noise required for the quantum-classical transition are satisfied for both regular and chaotic dynamics. We also study the dynamics of bipartite entanglement in the regime where classical trajectories emerge in the measurement record. Our analysis shows the surprising result that bipartite entanglement can persist in the classical limit.

show abstract

Untitled

Cited by 3 publications

References 0 publications

Incipience of quantum chaos in the Jahn-Teller model

Incipience of quantum chaos in the Jahn-Teller model

Entanglement and the quantum-to-classical transition

The quantum to classical transition in continuously measured bipartite entangled systems

Contact Info

Product

Resources

About