The system of a particle interacting with a Bose field is investigated. It is proven that the binding condition holds by the decay of particle's potential. As an application, the exponential decay of the ground state follows.
Abstract We hypothesize that the binding interactions among the components of bound systems and the background fields, sometimes known as virtual particle exchange, affect the state of the systems as do typical scattering interactions. Then with the assumption that the interior environment of unstable particles is disordered, we derive in the limit of continuous binding both an exactly exponential non-decay probability and Fermi's Golden Rule for the decay rates. The result suggests resolutions to several long-standing theoretical challenges associated with exponential decay in quantum mechanics, without appealing directly to non-Hermitian, approximate Hamiltonians or complex energies. It also contributes to a conceptual understanding of the apparent continuum between controlled interactions that induce deviations from exponential decay, such as those in the Quantum Zeno Effect, and the uncontrolled internal dynamics of excited atoms and nuclei, which exhibit no such deviations. Finally, we examine how the binding interactions responsible for the general exponential character of decay for bound systems differ from the couplings with decay products that control decay rates, providing insight into challenges in quantum computing and information processing.
We investigate the survival probability of a localized 1D quantum particle subjected to a time-dependent potential of the form rU ( x ) sin ω t with U ( x ) = 2δ( x − a ) or U ( x ) = 2δ( x − a ) − 2δ( x + a ). The particle is initially in a bound state produced by the binding potential −2δ( x ). We prove that this probability goes to zero as t → ∞ for almost all values of r , ω and a . The decay is initially exponential followed by a t −3 law if ω is not close to resonances and r is small; otherwise the exponential disappears and Fermi's golden rule fails. For exceptional sets of parameters r , ω and a the survival probability never decays to zero, corresponding to the Floquet operator having a bound state. We show similar behaviour even in the absence of a binding potential: permitting a free particle to be trapped by harmonically oscillating delta function potential.