Fano interference and cross-section fluctuations in molecular photodissociation

Alhassid, Y.; Fyodorov, Yan V.; Gorin, T.; Ihra, W.; Mehlig, B.

doi:10.1103/physreva.73.042711

Cited by 14 publications

(25 citation statements)

References 39 publications

(42 reference statements)

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“…It is the dip of the spectral form factor discussed in [44]. It has also been investigated in molecules [43,[45][46][47][48][49], random matrices [50][51][52][53][54], microwave billiards [55,56] and disordered spin models [19]. Here, we extend these studies to clean and disordered spin-1/2 models.…”

Section: Introductionmentioning

confidence: 86%

“…Contrary to signatures of chaos associated with the spacings of neighbouring levels, the level number variance detects long-range correlations between the eigenvalues. Correlations between energy levels are the source of the drop of P ini (t) belowP ini , which is known as the correlation hole [43,[45][46][47][48][49][50][51][52][53][54][55][56]. The correlation hole occurs at long times and disappears as we approach the Heisenberg time (the inverse of the mean level spacing [73]).…”

Section: (Iii) Survival Probability and Correlation Holementioning

confidence: 99%

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Dynamical manifestations of quantum chaos: correlation hole and bulge

Torres-Herrera

Santos

2017

Phil. Trans. R. Soc. A.

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A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and by a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. In contrast, the evolution of these quantities at shorter times reflect the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems.

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Section: Introductionmentioning

confidence: 86%

Section: (Iii) Survival Probability and Correlation Holementioning

confidence: 99%

Dynamical manifestations of quantum chaos: correlation hole and bulge

Torres-Herrera

Santos

2017

Phil. Trans. R. Soc. A.

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“…But before saturating, the dynamics resolves the discreteness of the spectrum. In the case of chaotic systems, the correlations between the eigenvalues are reflected in the evolution of the survival probability in the form of a dip below the saturation point, known as correlation hole [38][39][40][41][57][58][59][60][61][62][63][64][65][66]. The correlation hole was studied in the context of FRM, billiards, and molecules.…”

Section: Correlation Holementioning

confidence: 99%

Nonequilibrium Many-Body Quantum Dynamics: From Full Random Matrices to Real Systems

Santos

Torres-Herrera

2018

Fundamental Theories of Physics

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We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full random matrices can guide and support our studies of realistic systems. We show that features of the dynamics can be anticipated from a detailed analysis of the spectrum and the structure of the initial state projected onto the energy eigenbasis. On the other way round, if we only have access to the dynamics, we can use it to infer the properties of the spectrum of the system. Our focus is on the survival probability, but results for other observables, such as the spin density imbalance and Shannon entropy are also mentioned. *

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“…The use of complex energies allows for the combination of the energy of a resonance with its width [11]. Correspondingly, non-Hermitian Hamiltonians are commonly used to describe the dynamics of open systems [12][13][14][15][16]. In quantum optics the use of non-Hermitian Hamiltonians is put in a more rigorous form by the so-called quantum jump formalism, or Monte Carlo wave function method [12], which is equivalent to the evolution by a Markovian master equation.…”

Section: Introductionmentioning

confidence: 99%

Effective operator formalism for open quantum systems

Reiter¹,

Sørensen²

2012

Phys. Rev. A

275

319

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We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method with the hitherto existing concepts for effective interactions and present physical examples for the application of our formalism, including dissipative state preparation by engineered decay processes.

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Fano interference and cross-section fluctuations in molecular photodissociation

Cited by 14 publications

References 39 publications

Dynamical manifestations of quantum chaos: correlation hole and bulge

Dynamical manifestations of quantum chaos: correlation hole and bulge

Nonequilibrium Many-Body Quantum Dynamics: From Full Random Matrices to Real Systems

Effective operator formalism for open quantum systems

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