Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

Miyamoto, Manabu

doi:10.1063/1.2227260

Cited by 9 publications

(14 citation statements)

References 29 publications

(69 reference statements)

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Section: Bound States In the Continuum (Bics)mentioning

confidence: 99%

“…In [33], the advantage of the FPO method as compared to the N-level Friedrichs model [2] in studying BICs for unstable multilevel systems is discussed. In contrast to the coupling matrix elements (25), the form factors ξ E C |V |φ B n 0 and φ B n 0 |V |ξ E C considered in [2] contain the basic wave functions φ B n of the Hamiltonian H B of the closed system. Since the eigenfunctions φ λ of H eff can be represented as φ λ = a λ,λ ′ φ B λ ′ with complex coefficients a λ,λ ′ [and φ B λ = b λn φ B n with real b λn and the basic wave functions φ B n of discrete states defining H 0 according to (2)], a sum of individual form factors vanishes at the position of a BIC according to (25),…”

Section: Bound States In the Continuum (Bics)mentioning

confidence: 99%

“…It is not easy to receive results that are of physical interest in a broad range of parameters. An example for the mathematical troubles appearing in direct solving the equations is the study of bound states in the continuum performed in [2].…”

Section: Introductionmentioning

confidence: 99%

“…It is however not easy to receive results that are of physical interest in a broad range of parameters. For an example of the troubles see the study on bound states in the continuum [2].…”

mentioning

confidence: 99%

“…The wave functions of the two subspaces can be obtained by standard methods: the Q subspace is described by the Hermitian Hamilton operator H B that characterizes the closed system with discrete states, while the P subspace is described by the Hermitian Hamilton operator H C that contains the continuum of scattering wave functions. Thus, H 0 = H B + H C in (2). The coupling matrix elements are calculated according to (3) by using the eigenfunctions λ of H B instead of the basic wave functions n that appear in (3).…”

mentioning

confidence: 99%

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A non-Hermitian Hamilton operator and the physics of open quantum systems

Rotter

2009

J. Phys. A: Math. Theor.

774

1,040

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A powerful method for the description of open quantum systems is the Feshbach projection operator (FPO) technique. In this formalism, the whole function space is divided into two subspaces that are coupled with one another. One of the subspaces contains the wave functions localized in a certain finite region while the continuum of extended scattering wave functions is involved in the other subspace. The Hamilton operator of the whole system is Hermitian, that of the localized part is, however, non-Hermitian. This non-Hermitian Hamilton operator H eff represents the core of the FPO method in present-day studies. It gives a unified description of discrete and resonance states. Furthermore, it contains the time operator. The eigenvalues z λ and eigenfunctions φ λ of H eff are an important ingredient of the S matrix. They are energy dependent. The phases of the φ λ are, generally, nonrigid. Most interesting physical effects are caused by the branch points in the complex plane. On the one hand, they cause the avoided level crossings that appear as level repulsion or widths bifurcation in approaching the branch points under different conditions. On the other hand, observable values are usually enhanced and accelerated in the vicinity of the branch points. In most cases, the theory is time asymmetric. An exception are the PT symmetric bound states in the continuum appearing in space symmetric systems due to the avoided level crossing phenomenon in the complex plane. In the paper, the peculiarities of the FPO method are considered and three typical phenomena are sketched: (i) the unified description of decay and scattering processes, (ii) the appearance of bound states in the continuum and (iii) the spectroscopic reordering processes characteristic of the regime with overlapping resonances.

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Section: Bound States In the Continuum (Bics)mentioning

confidence: 99%

Section: Bound States In the Continuum (Bics)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It is however not easy to receive results that are of physical interest in a broad range of parameters. For an example of the troubles see the study on bound states in the continuum [2].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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A non-Hermitian Hamilton operator and the physics of open quantum systems

Rotter

2009

J. Phys. A: Math. Theor.

774

1,040

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Negative ion of hydrogen in dense semi-classical plasmas: Stability and zero-energy resonances

2021

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The effects of dense semi-classical plasma (DSCP) on the ground state of the negative ion of hydrogen (H−) and on the dynamics of electron–hydrogen scattering have been investigated. DSCP is described by an effective potential which takes care of the collective effects of the plasma at large distances as well as the quantum mechanical effects of diffraction at small distances. An elaborative wave function is employed in the Rayleigh–Ritz variational method to compute the ground state energy of H− for various values of the plasma parameters. In particular, critical values of the plasma parameters are calculated accurately to make a detailed study on the stability of the ion embedded in DSCP. Furthermore, parameters related to the ground state of H− and H are used in the effective range theory to study the effects of DSCP on the dynamics of low-energy e − H(1s) scattering. Special emphasis is given to investigate the phenomenon of zero-energy resonances by computing the singlet scattering length near the critical values of the plasma parameters.

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Quantum decay in a topological continuum

Longhi

2019

Phys. Rev. A

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The quantum mechanical decay of two or more overlapped resonances in a common continuum is largely influenced by Fano interference, leading to important phenomena such as the existence of bound states in the continuum, fractional decay and quiescent dynamics for single particle decay, and signature of particle statistics in the many-body quantum decay. An overlooked yet essential requirement to observe Fano interference is time reversal symmetry of the bath. Here we consider multilevel quantum decay in a bath sustaining unidirectional (chiral) propagating states, such as in quantum Hall or in Floquet topological insulators, and show that the chiral nature of scattering states fully suppresses Fano interference among overlapping resonances. As a result, there are not bound states in the continuum, quantum decay is complete, and there is not any signature of particle statistics in the decay process. Nonetheless, some interesting features are disclosed in the multilevel decay dynamics in a topological bath, such as the appearance of high-order exceptional points, long quiescent dynamics followed by a fast decay, and the possibility to observe damped non-Hermitian Bloch oscillations.

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Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

Cited by 9 publications

References 29 publications

A non-Hermitian Hamilton operator and the physics of open quantum systems

A non-Hermitian Hamilton operator and the physics of open quantum systems

Negative ion of hydrogen in dense semi-classical plasmas: Stability and zero-energy resonances

Quantum decay in a topological continuum

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