Strong chaos in one-dimensional quantum system

Yang, Ciann-Dong; Wei, Chia Hung

doi:10.1016/j.chaos.2008.01.017

Cited by 9 publications

(4 citation statements)

References 19 publications

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“…The highly nonlinear character of the Bohmian equations motivated several works studying the dynamics of Bohmian trajectories (see, e.g. [8][9][10][11][12][13][14][15]). In our previous works we studied the existence of order and chaos in Bohmian trajectories both in 2 and 3 dimensions and proposed a general theoretical framework describing the production of chaos in BQM [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Chaos and ergodicity in an entangled two-qubit Bohmian system

Tzemos

Contopoulos

2020

Phys. Scr.

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We study in detail the onset of chaos and the probability measures formed by individual Bohmian trajectories in entangled states of two-qubit systems for various degrees of entanglement. The qubit systems consist of coherent states of 1-d harmonic oscillators with irrational frequencies. In weakly entangled states chaos is manifested through the sudden jumps of the Bohmian trajectories between successive Lissajous-like figures. These jumps are succesfully interpreted by the ‘nodal point-X-point complex’ mechanism. In strongly entangled states, the chaotic form of the Bohmian trajectories is manifested after a short time. We then study the mixing properties of ensembles of Bohmian trajectories with initial conditions satisfying Born’s rule. The trajectory points are initially distributed in two sets S1 and S2 with disjoint supports but they exhibit, over the course of time, abrupt mixing whenever they encounter the nodal points of the wavefunction. Then a substantial fraction of trajectory points is exchanged between S1 and S2, without violating Born’s rule. Finally, we provide strong numerical indications that, in this system, the main effect of the entanglement is the establishment of ergodicity in the individual Bohmian trajectories as : different initial conditions result to the same limiting distribution of trajectory points.

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Section: Introductionmentioning

confidence: 99%

Chaos and ergodicity in an entangled two-qubit Bohmian system

Tzemos

Contopoulos

2020

Phys. Scr.

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“…In recent years, the complex quantum trajectory (CQT) is adopted to study some quantum phenomena in more detail, such as tunneling effect [22][23][24], quantum chaos [25][26][27], and scattering [28][29][30]. The significant benefits brought out by the CQT may be the manifestation of the matter-wave [31] and the properties of the interferences [32,33].…”

Section: Introductionmentioning

confidence: 99%

Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue

Yang

Han

2020

Found Phys

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The correspondence principle states that the quantum system will approach to the classical system in high quantum numbers. Indeed, the average of the probability density distribution reflects a classicallike distribution. However, the likelihood of finding a particle at node of the wave function is zero. This condition is recognized as the nodal issue. In this paper, we propose a solution for this issue by means of complex quantum random trajectories which are obtained by solving the stochastic differential equation under the optimal guidance law. It turns out that point set A which is collected by the intersections of complex random trajectories and the real axis can present the quantum mechanical compatible distribution of the quantum harmonic oscillator system. Meanwhile, the projections of complex quantum random trajectories on the real axis form point set B that gives a distribution without appearance of nodes.Moreover, point set B can represent the classical compatible distribution in high quantum numbers. Furthermore, the statistical distribution of point set B is verified by the solution of the Fokker-Planck equation.

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“…The highly nonlinear character of the Bohmian equations motivated several works studying the dynamics of Bohmian trajectories (see, e.g. [8,9,10,11,12,13,14,15]). In our previous works we studied the existence of order and chaos in Bohmian trajectories both in 2 and 3 dimensions and proposed a general theoretical framework describing the production of chaos in BQM [16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Bohmian trajectories in an entangled two-qubit system

2019

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We study in detail the onset of chaos and the probability measures formed by individual Bohmian trajectories in entangled states of two-qubit systems for various degrees of entanglement. The qubit systems consist of coherent states of 1-d harmonic oscillators with irrational frequencies. In weakly entangled states chaos is manifested through the sudden jumps of the Bohmian trajectories between successive Lissajous-like figures. These jumps are succesfully interpreted by the 'nodal point-X-point complex' mechanism. In strongly entangled states, the chaotic form of the Bohmian trajectories is manifested after a short time. We then study the mixing properties of ensembles of Bohmian trajectories with initial conditions satisfying Born's rule. The trajectory points are initially distributed in two sets S 1 and S 2 with disjoint supports but they exhibit, over the course of time, abrupt mixing whenever they encounter the nodal points of the wavefunction. Then a substantial fraction of trajectory points is exchanged between S 1 and S 2 , without violating Born's rule. Finally, we provide strong numerical indications that, in this system, the main effect of the entanglement is the establishment of ergodicity in the individual Bohmian trajectories as t → ∞: different initial conditions result to the same limiting distribution of trajectory points.

show abstract

Strong chaos in one-dimensional quantum system

Cited by 9 publications

References 19 publications

Chaos and ergodicity in an entangled two-qubit Bohmian system

Chaos and ergodicity in an entangled two-qubit Bohmian system

Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue

Bohmian trajectories in an entangled two-qubit system

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