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arXiv:1911.05056 · Journal of Physics Conference Series

Effect of the resonance spectra in the propagation of two decaying entangled particles

Gastón García-Calderón, Roberto Romo, Miguel Ángel Terán

Published Sep 1, 2019• 2 citations
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Abstract

Abstract An exact analytical solution of the decaying wave function of two identical noninteracting particles, which are entangled by spatial symmetry, is used to analyze the effect of the resonance spectra in the propagation of the decaying probability density outside the interaction potential region. We find, using exactly solvable problems, that a usual approximation that considers the two resonance levels associated with the initial states, is affected substantially in the case of sharp high energy resonances by disrupting the pure exponential decaying regime exhibited by the two resonance level approximation, whereas for broad high energy resonances, we find that the probability density profile is well described by the two resonance approximation.

DOI
10.1088/1742-6596/1275/1/012029

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Abstract An exact analytical solution of the decaying wave function of two identical noninteracting particles, which are entangled by spatial symmetry, is used to analyze the effect of the resonance spectra in the propagation of the decaying probability density outside the interaction potential region. We find, using exactly solvable problems, that a usual approximation that considers the two resonance levels associated with the initial states, is affected substantially in the case of sharp high energy resonances by disrupting the pure exponential decaying regime exhibited by the two resonance level approximation, whereas for broad high energy resonances, we find that the probability density profile is well described by the two resonance approximation.
An analytical solution for the time evolution of decay of two identical noninteracting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states. It is shown that the wave function, and hence also the survival and nonescape probabilities, for factorized symmetric and entangled symmetric or antisymmetric initial states evolve in a distinctive form along the exponentially decaying and nonexponential regimes. Our findings show the influence of the Pauli exclusion principle on decay. We exemplify our results by solving exactly the sss-wave $\ensuremath{\delta}$ shell potential model.
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and nonescape probabilities for the initial state of a single particle and entangled symmetric and antisymmetric initial states of two identical particles evolve in a distinctive form along the exponential and long-time nonexponential decaying regimes. In particular, for the last regime, they exhibit different inverse power of time behaviors.
We study the nonescape probability for tunneling decay of two identical noninteracting particles which are entangled due to symmetrization. As a consequence, the two-particle nonescape probability, which gives the probability that the particles remain within the potential region, may be written as the sum of two terms: a direct term and an exchange term which is added or subtracted according to symmetrization. At the initial time the direct term decays exponentially in the usual way, but the exchange term vanishes due to the orthonormality of the initial states. As time evolves the exchange term builds up until it becomes comparable to the direct term at time t0{t}_{0}t0​. Thereafter, the symmetric and antisymmetric nonescape probabilities decay in a distinctive way. The buildup time typically lasts several lifetimes and implies that during the relevant exponentially decaying regime the probability of finding the particles within the interaction region is insensitive to the symmetry of the decaying particles. That is, the particles decay as if they were distinguishable. This might be experimentally verified in the tunneling decay of atoms in ultracold gases.
Abstract By using an exact analytical formalism for quantum tunneling decay we show the existence of a regime of purely nonexponential decay for the survival probability in the full time interval and a propagating probability density along the external interaction region that evolves as a spreading process having no wavefront. This decaying regime follows from a complex pole of the propagator which in the wave number plane possesses an imaginary part larger than the corresponding real part, which implies a negative resonance energy and a decaying width, together with a dominant large overlap of the initial decaying state with the corresponding resonant state of the problem.
Abstract In this article, we study an exponential decay for the gas of bosons with strong repulsive delta interactions from a double-well potential. We consider an exactly solvable model comprising an infinite wall and two Dirac delta barriers. We explore its features both within the exact method and with the resonance expansion approach. The study reveals the effect of the splitting barrier on the decay rate in dependence on the number of particles. Among other things, we find that the effect of the splitting barrier on the decay rate is most pronounced in systems with odd particle numbers. During exponential decay, the spatial correlations in an internal region are well captured by the “radiating state”.