Robust quantum boomerang effect in non-Hermitian systems

Noronha, Flavio; Lourenço, José A. S.; Macrì, Tommaso

doi:10.1103/physrevb.106.104310

Cited by 7 publications

(3 citation statements)

References 63 publications

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“…This phenomenon was also shown to exist in higher-dimensional random or pseudo-random systems [15,16], as well as in kicked-rotor models [16], where it was recently demonstrated experimentally [17]. While originally described in timereversal-invariant (TRI) systems, recently QBE was also shown to exist in systems without time-reversal symmetry [18][19][20]. In [18], in addition, QBE was characterized in the presence of a spin-orbit coupling mechanism inducing left-right asymmetric scattering between different spin states.…”

Section: Introductionmentioning

confidence: 85%

Berezinskii Approach to Disordered Spin Systems with Asymmetric Scattering and Application to the Quantum Boomerang Effect

Janarek,

Cherroret,

Delande

2023

Acta Phys. Pol. A

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We extend the Berezinskii diagrammatic technique to one-dimensional disordered spin systems, in which time-reversal invariance is broken due to a spin-orbit coupling term inducing left-right asymmetric scattering. We then use this formalism to theoretically describe the dynamics of the quantum boomerang effect, a recently discovered manifestation of Anderson localization. The theoretical results are confirmed by exact numerical simulations of wave-packet dynamics in a random potential.

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Section: Introductionmentioning

confidence: 85%

Berezinskii Approach to Disordered Spin Systems with Asymmetric Scattering and Application to the Quantum Boomerang Effect

Janarek,

Cherroret,

Delande

2023

Acta Phys. Pol. A

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“…Non-Hermitian systems are naturally realizable in experiment, and non-Hermitian wave packet dynamics are studied in photonic lattices and electrical circuits [8][9][10][10][11][12][13][14]. The transition between propagating phases can be implemented as a switch tuned by a continuous parameter, with uses in control or sensor systems.…”

Section: Discussionmentioning

confidence: 99%

Phase transitions of wave packet dynamics in disordered non-Hermitian systems

Spring,

Könye,

Gerritsma

et al. 2024

SciPost Phys.

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Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition is close to 1/2 in propagating-propagating and (de)localization transitions.

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“…Despite extensive studies on Anderson localization [3][4][5][6][7][8], there are still several aspects that are not fully understood, and new types of localization phenomena continue to be discovered . Recent examples include unconventional transport in disordered quantum wires [9][10][11][12][13], localization in disordered non-Hermitian systems [14][15][16][17][18][19][20], and the quantum boomerang effect in both Hermitian and non-Hermitian systems [21][22][23][24][25]. Furthermore, the effect of interactions on Anderson localization and the related phenomenon of many-body localization has been an important and challenging research topic for many decades that still raises many open questions [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations

Nguyen,

Kim

2023

J. Phys. A: Math. Theor.

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We present a numerical study of the transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations. The model is characterized by the modulation period $\kappa$ and the disorder strength $W$. We calculate the disorder averages $\langle T\rangle$, $\langle \ln T\rangle$, and $\langle P\rangle$, where $T$ is the transmittance and $P$ is the participation ratio, as a function ofenergy $E$ and system size $L$, for different values of $\kappa$ and $W$. For excitations at quasiresonance energies determined by $\kappa$, we find power-law scaling behaviors of the form $\langle T \rangle \propto L^{-\gamma_{a}}$,$\langle \ln T \rangle \approx -\gamma_g \ln L$, and $\langle P \rangle \propto L^{\beta}$, as $L$ increases to a large value.In the strong disorder limit, the exponents are seen to saturate at the values $\gamma_a \sim 0.5$, $\gamma_g \sim 1$, and $\beta\sim 0.3$,regardless of the quasiresonance energy value. This behavior is in contrast to the exponentiallocalization behavior occurring at all other energies.The appearance of sharp peaks in the participation ratio spectrum at quasiresonance energies provides additional evidence for the existence of an anomalous power-law localization phenomenon.The corresponding eigenstates demonstrate multifractal behavior and exhibit unique node structures.In addition, we investigate the time-dependent wave packet dynamics and calculate the mean square displacement $\langle m^2(t) \rangle$, spatial probability distribution, participation number, and return probability.When the wave packet's initial momentum satisfies the quasiresonance condition, weobserve a subdiffusive spreading of the wave packet, characterized by $\langle m^2(t) \rangle\propto t^{\eta}$ where $\eta$ is always less than 1.We also note the occurrence of partial localization at quasiresonance energies, as indicated by the saturation of the participation number and a nonzero value for the return probability at long times.

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Robust quantum boomerang effect in non-Hermitian systems

Cited by 7 publications

References 63 publications

Berezinskii Approach to Disordered Spin Systems with Asymmetric Scattering and Application to the Quantum Boomerang Effect

Berezinskii Approach to Disordered Spin Systems with Asymmetric Scattering and Application to the Quantum Boomerang Effect

Phase transitions of wave packet dynamics in disordered non-Hermitian systems

Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations

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