Complete particle-pair annihilation as a dynamical signature of the spectral singularity

Motivated by the physical relevance of a spectral singularity of interacting many-particle system, we explore the dynamics of two bosons as well as fermions in one-dimensional system with imaginary delta interaction strength. Based on the exact solution, it shows that the two-particle collision lead...

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Bibliographic Details
Published in:Annals of physics 2014-10, Vol.349, p.288-296
Main Authors: Li, G.R., Zhang, X.Z., Song, Z.
Format: Article
Language:English
Subjects:
ANNIHILATION
BOSONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COLLISIONS
DETECTION
Dynamical systems
Dynamics
EXACT SOLUTIONS
FERMIONS
Interacting many-particle system
MANY-BODY PROBLEM
Particle physics
Particle-pair annihilation
Signatures
Singularities
SINGULARITY
SPECTRA
Spectral singularity
SPIN
Strength
WAVE FUNCTIONS
WAVE PACKETS
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Summary:Motivated by the physical relevance of a spectral singularity of interacting many-particle system, we explore the dynamics of two bosons as well as fermions in one-dimensional system with imaginary delta interaction strength. Based on the exact solution, it shows that the two-particle collision leads to amplitude-reduction of the wave function. For fermion pair, the amplitude-reduction depends on the spin configuration of two particles. In both cases, the residual amplitude can vanish when the relative group velocity of two single-particle Gaussian wave packets with equal width reaches the magnitude of the interaction strength, exhibiting complete particle-pair annihilation at the spectral singularity. •We investigate the physical relevance of a spectral singularity.•The two-particle collision leads to amplitude-reduction of the wave function.•There is a singularity spectrum which leads to complete particle-pair annihilation.•Complete particle-pair annihilation can only occur for two distinguishable bosons and singlet fermions.•Pair annihilation provides a detection method of the spectral singularity in the experiment.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2014.06.022