Collective dynamics of unstable quantum states

Соколов, В. В.; Zelevinsky, V. G.

doi:10.1016/0003-4916(92)90180-t

Cited by 175 publications

(200 citation statements)

References 25 publications

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“…The analogy between decay width segregation and Dicke superradiance [9] has been pointed out in Refs. [4,5], although Dicke superradiance is associated with many-body systems, while width segregation occurs also in the one-body case. We will refer to this phenomenon as the "superradiance transition" in the following.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, a consistent way to take the effect of the opening into account for arbitrary coupling strength between the system and the outside world is highly desirable. The effective non-Hermitian Hamiltonian approach to open quantum systems has been shown to be a very effective tool in addressing this issue [3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Elimination of the continuum leads to an effective non-Hermitian Hamiltonian [3,4,5,6,7]. Analysis of the complex eigenvalues of the effective Hamiltonian reveals a general phenomenon, namely the segregation of decay widths (corresponding to the imaginary part of the complex eigenvalues).…”

Section: Introductionmentioning

confidence: 99%

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Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

2009

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Using an energy-independent non-Hermitian Hamiltonian approach to open systems, we fully describe transport through a sequence of potential barriers as external barriers are varied. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian model, a transition to a superradiant regime is shown to occur. Transport properties undergo a strong change at the superradiance transition, where the transmission is maximized and a drastic change in the structure of resonances is demonstrated. Finally, we analyze the effect of the superradiance transition in the Anderson localized regime.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

2009

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“…Many properties are strongly dependent on the openness of the system and the way the system interacting with the environment around it. In order to take the influences of the environment into account, the effective non-Hermitian Hamiltonian approach has been used extensively in treating open systems [1][2][3][4][5][6]. By introducing imaginary parts to the Hamiltonian to represent the physical gain and loss of the system, one can study the open systems in an consistent way by analyzing the complex eigenvalues of the effective Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

2017

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We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

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“…n,λ is taken over the internal states n and all open scattering channels λ. For example, when the coupling constant (5) exceeds the critical value g = 1 and the number of scattering channels is small compared to the total number of states, a counterintuitive shrinking of the widths of most resonances with increasing coupling is observed [9,10,11]. For each attached scattering channel only one of the resonance widths grows further with the coupling g. The resulting redistribution of S-matrix poles was coined resonance trapping.…”

Section: Introductionmentioning

confidence: 99%

Effective coupling for open billiards

2001

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We derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard which is opened by attaching a waveguide. The Wigner time delay and the resonance positions resulting from the coupling constants are compared to an exact numerical calculation. Deviations can be attributed to evanescent modes in the waveguide and to the finite number of eigenstates taken into account. The influence of the shape of the billiard and of the boundary conditions at the mouth of the waveguide are also discussed. Finally we show that the mean value of the dimensionless coupling constants tends to the critical value when the eigenstates of the billiard follow random-matrix theory.

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Collective dynamics of unstable quantum states

Cited by 175 publications

References 25 publications

Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Effective coupling for open billiards

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