Quantum coherence as a signature of chaos

Anand, Namit; Styliaris, Georgios; Kumari, Meenu; Zanardi, Paolo

doi:10.1103/physrevresearch.3.023214

Cited by 38 publications

(22 citation statements)

References 110 publications

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“…many-body systems and not in integrable systems. For the same type of physical systems, suppression of temporal variance of CGP has been noticed in [40]. These findings were used to suggest that both the bi-partite averaged OTOC and CGP can be used as diagnostic tools to detect some aspects of quantum chaotic behavior.…”

Section: D) Moreover the First Inequality Above Becomes An Equality I...mentioning

confidence: 85%

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Quantum scrambling of observable algebras

Zanardi

2022

Quantum

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In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by an hermitian-closed unital subalgebra A of operators evolving through a unitary channel. Qualitatively, quantum scrambling is defined by how the associated physical degrees of freedom get mixed up with others by the dynamics. Quantitatively, this is accomplished by introducing a measure, the geometric algebra anti-correlator (GAAC), of the self-orthogonalization of the commutant of A induced by the dynamics. This approach extends and unifies averaged bipartite OTOC, operator entanglement, coherence generating power and Loschmidt echo. Each of these concepts is indeed recovered by a special choice of A. We compute typical values of GAAC for random unitaries, we prove upper bounds and characterize their saturation. For generic energy spectrum we find explicit expressions for the infinite-time average of the GAAC which encode the relation between A and the full system of Hamiltonian eigenstates. Finally, a notion of A-chaoticity is suggested.

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Section: D) Moreover the First Inequality Above Becomes An Equality I...mentioning

confidence: 85%

“…The fact that the CGP is related to the distance between maximal abelian subalgebras was already established in [27]. CGP has been applied to the detection of the localization transitions in many-body systems [39], detection of quantum chaos in closed and open systems [40].…”

Section: Proposition 2 I) One Can Find An Orthogonal Basis Of a {E α ...mentioning

confidence: 99%

Quantum scrambling of observable algebras

Zanardi

2022

Quantum

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“…Quantum chaos plays a crucial role in many fields of physics, such as quantum statistics [1][2][3][4][5], quantum information science [6][7][8][9][10][11][12][13], and high-energy physics [14][15][16]. In particular, chaos of interacting quantum systems, dubbed as many-body quantum chaos, has attracted significant attention in recent years [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Wang

Robnik

2021

Entropy

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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

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“…Quantum chaos plays a crucial role in many fields of physics, such as quantum statistics [1][2][3][4][5], quantum information science [6][7][8][9][10][11][12][13], and high energy physics [14][15][16]. In particular, chaos of interacting quantum systems, dubbed as manybody quantum chaos, has attracted significant attention in recent years [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Multifractality in quasienergy space of coherent states as a signature of quantum chaos

Wang,

Robnik

2021

Preprint

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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase space averaged multifractal dimensions, which are well described by random matrix theory in strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

show abstract

Quantum coherence as a signature of chaos

Cited by 38 publications

References 110 publications

Quantum scrambling of observable algebras

Quantum scrambling of observable algebras

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Multifractality in quasienergy space of coherent states as a signature of quantum chaos

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