Wigner-function nonclassicality as indicator of quantum chaos

Kowalewska-Kudłaszyk, A.; Kalaga, J. K.; Leoński, W.

doi:10.1103/physreve.78.066219

Cited by 29 publications

(21 citation statements)

References 32 publications

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“…Another field where the anharmonic oscillator model has got application is the study of the quantum physics of systems showing up chaotic behaviour classically, ie. the study of quantum chaos [6], [7], [8]. Also the possibility of quantum effects induced chaos has recently been debated on the problem of the quantized Duffing oscillator [9].…”

Section: Introductionmentioning

confidence: 99%

Functional renormalization group for quantized anharmonic oscillator

Nagy

Sailer

2011

Annals of Physics

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Functional renormalization group methods formulated in the real-time formalism are applied to the $O(N)$ symmetric quantum anharmonic oscillator, considered as a $0+1$ dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The field-independent term of the wavefunction renormalization turned out to be negligible, but its field-dependent piece is noticeable. It is shown that the infrared limits of the running couplings depend on the renormalization group scheme used, when the perturbation expansion in the bare quartic coupling is truncated keeping the terms up to the second order.Comment: 30 pages, 11 figure

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Section: Introductionmentioning

confidence: 99%

Functional renormalization group for quantized anharmonic oscillator

Nagy

Sailer

2011

Annals of Physics

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“…In order to investigate the dynamical aspects, we use the quartic oscillator model (Kerr oscillator), which was the object of many investigations [12,19,21,22,25,33,[94][95][96][97][98][99][100] with expressive experimental results [101]. The Hamiltonian is given bŷ…”

Section: Dynamic Distance Measure: the Quartic Modelmentioning

confidence: 99%

Roughness as classicality indicator of a quantum state

et al. 2018

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We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L 2 (R 2 ) distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [0,1], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness reaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum.

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“…It is relevant for fundamental research into the thermalization of isolated quantum systems [33], localization phenomena, chaos [34,35], or decoherence.…”

Section: The Loschmidt Echomentioning

confidence: 99%

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

2016

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In the framework of the matrix product state representation the effect of a sudden turning on of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. Depending on the value of the uniaxial anisotropy parameter, the calculations were derived within (or outside) the region where the Haldane gap survives. An exact expression for the time evolution of the Loschmidt echo has been derived and, moreover, its collapse and revival behaviour was captured. In addition, the non-local order parameter of a time evolving state was tracked, revealing two types of relaxations.

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Wigner-function nonclassicality as indicator of quantum chaos

Cited by 29 publications

References 32 publications

Functional renormalization group for quantized anharmonic oscillator

Functional renormalization group for quantized anharmonic oscillator

Roughness as classicality indicator of a quantum state

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

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