Chaos and complexity in quantum mechanics

Ali, Tibra; Bhattacharyya, Arpan; Haque, S. Shajidul; Kim, Eugene H.; Moynihan, Nathan; Murugan, Jeff

doi:10.1103/physrevd.101.026021

Cited by 93 publications

(117 citation statements)

References 79 publications

Supporting

Mentioning

106

Contrasting

Order By: Relevance

“…This approach was first applied to a concrete quantum field theory calculation in [57], where the authors adapted Nielsen's approach to evaluate the complexity of the vacuum state of a free scalar field theory. These calculations have been extended in a number of interesting ways in the past few years, e.g., [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], but we will be particularly interested in [65] where the same techniques were applied to explore the complexity of coherent states in the same QFT.…”

mentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We investigate the first law of complexity proposed in [1], i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.

show abstract

mentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…We can see the general behavior of the early-time solutions (18) and (19) and late-time solutions (22) and (23) in the numerical solutions to the equations of motion (16) and (17) in Fig. 1, shown for different choices of the equation of state w (equivalently different values of β).…”

Section: A Expanding Backgroundsmentioning

confidence: 97%

“…Recent studies have also explored different methods of calculating circuit complexity based on the position space wave function or covariance matrix [5][6][7][8][9][10][11], using the geometric technique pioneered by Nielsen [12], and they have extended the idea of complexity to quantum field theory [5,[13][14][15][16][17][18][19][20]. More generally, complexity can serve as one of several diagnostics for determining if a quantum system displays quantum chaos [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…For expanding de Sitter backgrounds, the cosmological complexity is small at early times while the mode is within the horizon, but it grows linearly with the logarithm of the scale factor after the mode exits the horizon. Because the linear growth of complexity is a characteristic [22] of quantum chaos, Ref. [28] proposed that cosmological perturbations in de Sitter space are (quantum) chaotic.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rise of cosmological complexity: Saturation of growth and chaos

Bhattacharyya

Das

Haque

et al. 2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

We compute the circuit complexity of scalar curvature perturbations on Friedmann-Lemaître-Robertson-Walker cosmological backgrounds with a fixed equation of state w using the language of squeezed vacuum states. Backgrounds that are accelerating and expanding, or decelerating and contracting, exhibit features consistent with chaotic behavior, including linearly growing complexity. Remarkably, we uncover a bound on the growth of complexity for both expanding and contracting backgrounds λ √ 2 |H |, similar to other bounds proposed independently in the literature. The bound is saturated for expanding backgrounds with an equation of state more negative than w = −5/3, and for contracting backgrounds with an equation of state larger than w = 1. For expanding backgrounds that preserve the null energy condition, de Sitter space has the largest rate of growth of complexity, and we find a scrambling time that is similar to other estimates up to order 1 factors.

show abstract

“…Compared with the case of single delayed feedback, the quantum dot laser with two delayed feedback proposed in this work will have more rich nonlinear dynamical behaviors by changing the systematical parameter. In reality, the nonlinear dynamics such as periodic and chaotic behaviors that are very significant research subject are also presented and demonstrated based on other interesting physical structures [31][32][33][34][35][36]. Compared with these reported nonlinear dynamical models, the semiconductor quantum dot laser-based periodic and chaotic phenomena will be more useful for the all-optical signal processing in optical communication technology.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics in Semiconductor Quantum Dot Laser Subject to Double Delayed Feedback: Numerical Analysis

Bao

2020

Braz J Phys

View full text Add to dashboard Cite

In this study, the research on the nonlinear dynamics of semiconductor quantum dot laser with two time-delayed optical feedbacks is numerically investigated. Results show that the nonlinear dynamics behaviors of the laser are very sensitive to the rich system parameters in which both feedback strength and bias current are easily controlled to significantly influence the nonlinear dynamics including the periodic state and chaotic state. By judiciously adjusting the bias current of the laser or the feedback strength in the external cavity, period one, period doubling, quasi-period, and chaos are achieved. The feedback levelrelated bifurcation diagrams are analyzed in detail while fixing another feedback level at a constant or varying the bias current. In addition, the translation variables of the 0-1 test method that are clearly bounded for regular behavior and exhibit the Brownian motion for irregular phenomenon are adopted to further evaluate the periodic state and the chaotic state. These results can give insight into the quantum dot laser-based applications in various optical technologies.

show abstract

Chaos and complexity in quantum mechanics

Cited by 93 publications

References 79 publications

Aspects of the first law of complexity

Aspects of the first law of complexity

Rise of cosmological complexity: Saturation of growth and chaos

Nonlinear Dynamics in Semiconductor Quantum Dot Laser Subject to Double Delayed Feedback: Numerical Analysis

Contact Info

Product

Resources

About