Recent Advances in Quantum Chaos of Generic Systems

Robnik, Marko

doi:10.1007/978-1-0716-0421-2_730

Cited by 3 publications

(2 citation statements)

References 41 publications

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“…Originally, it was first observed in periodically kicked rotors, and later it was also found in different systems, as the hydrogen atom in a monochromatic field and Rydberg atoms [3][4][5], as well as related to the Anderson localization present in one-dimensional disordered systems [6,7]. The phenomenon was also observed in conservative systems, such as the Band-random-matrix model and quantum billiards [8][9][10][11][12][13][14] and more recent studies have focused its onset on manybody systems [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Quantum localization measures in phase space

Villaseñor,

Pilatowsky-Cameo,

Bastarrachea-Magnani

et al. 2021

Preprint

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Measuring the degree of localization of quantum states in phase space is essential for the description of the dynamics and equilibration of quantum systems, but this is a topic far from understood. There is no unique way to measure localization, and individual measures can reflect different aspects of the same quantum state. Here, we present a general scheme to define localization in measure spaces, which is based on what we call Rényi occupations, and from which any measure of localization can be derived. We apply this scheme to the four-dimensional unbounded phase space of the interacting spin-boson Dicke model. In particular, we make a detailed comparison of two localization measures based on the Husimi function in the regime where the model is chaotic, namely one that projects the Husimi function over the finite phase space of the spin, and another one that uses the Husimi function defined over classical energy shells. We elucidate the origin of their differences, showing that in unbounded spaces, to define maximal delocalization requires a bounded reference subspace, with different selections leading to contextual answers.

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Section: Introductionmentioning

confidence: 99%

Quantum localization measures in phase space

Villaseñor,

Pilatowsky-Cameo,

Bastarrachea-Magnani

et al. 2021

Preprint

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“…This phenomenon has a dynamical counterpart originally studied in the context of the kicked rotor [3][4][5][6]. Localization is an extremely broad subject that extends to the hydrogen atom in a monochromatic field [7,8], Rydberg atoms [9], quantum billiards [10][11][12][13][14][15][16], banded random matrices [17], interacting systems [18][19][20][21][22], and kicked interacting systems [23][24][25][26], among others.…”

Section: Introductionmentioning

confidence: 99%

Identification of quantum scars via phase-space localization measures

Pilatowsky-Cameo,

Villaseñor,

Bastarrachea-Magnani

et al. 2021

Preprint

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There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the α-moments of the Husimi function and is known as the Rényi occupation of order α. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spinboson model with an unbounded four-dimensional phase space, we show that the Rényi occupations with large α are highly effective at revealing quantum scars. Furthermore, by analyzing the large moments of the Husimi function, we are able to find the unstable periodic orbits that scar some of the eigenstates of the model.

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Identification of quantum scars via phase-space localization measures

Santos

Pilatowsky-Cameo

̃nor

et al. 2022

Quantum

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There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the α-moments of the Husimi function and is known as the Rényi occupation of order α. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spin-boson model with an unbounded four-dimensional phase space, we show that the Rényi occupations with α>1 are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments (α>1) of the Husimi function, we are able to identify qualitatively and quantitatively the unstable periodic orbits that scar some of the eigenstates of the model.

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Recent Advances in Quantum Chaos of Generic Systems

Cited by 3 publications

References 41 publications

Quantum localization measures in phase space

Quantum localization measures in phase space

Identification of quantum scars via phase-space localization measures

Identification of quantum scars via phase-space localization measures

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