Escape behavior of quantum two-particle systems with Coulomb interactions
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Quantum escapes of two particles with Coulomb interactions from a confined one-dimensional region to a semi-infinite lead are discussed by using the probability of finding all particles within the confined region, that is, the survival probability, in comparison with free particles. By taking into account the quantum effects of two identical particles, such as the Pauli exclusion principle, it is shown analytically that for two identical free fermions (bosons), the survival probability decays asymptotically in power ~t(-10) (~t(-6)) as a function of time t, although it decays in power ~t(-3) for one free particle. On the other hand, for two particles with attractive Coulomb interactions it is shown numerically that the survival probability decays in power ~t(-3) after a long time. Moreover, for two particles with repulsive Coulomb interactions it decays exponentially in time ~exp (-αt) with a constant α, which is almost independent of the initial energy of particles.
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Following Khalfin, the survival amplitude A(β,t) is the Fourier transform of a function with support on the half energy axis.
“Following Khalfin [23, 29], we note that A ( β, t ) is then the Fourier transform of a function with support on the half energy axis, ˜ ρ ( E ) ≡ ρ ( E )Θ( E -E 0 ).”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [29]
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- Authors
- Taniguchi, T., & Sawada, S.-I.
- Affiliations
- Kwansei Gakuin University (JP)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2011-02-28
- Volume
- 83
- Issue
- 2
- Pages
- 026208-026208
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2074719688
- Cited by
- 30
- References
- 56
- Citations by year
- 2022: 2 · 2020: 1 · 2019: 3 · 2018: 6 · 2017: 2 · 2016: 2 · 2015: 3 · 2014: 2 · 2013: 3 · 2012: 3
- FWCI
- 2.69
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Keywords
- survival probability, two-particle systems, electrostatic interactions, identical particles, Pauli exclusion principle, fermions, bosons, attractive interactions, repulsive interactions, one-dimensional confinement, power-law decay, exponential decay
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