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
s-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.
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.
We study the evolution of quantum correlations in two-particle discrete-time non-unitary quantum walks on a line with gain and loss. The two particles are initially prepared in a maximally entangled state and evolve independently. Using numerically exact calculations of position probability densities, average interparticle distance, entanglement entropy, and concurrence, we examine how dissipation and particle-exchange symmetry of the state (symmetric or antisymmetric) influence the resulting correlations. Notably, we find that the entanglement entropy of the antisymmetric state decays slower than that of the symmetric state at the exceptional point of the model. We also show that, in the antisymmetric state, the concurrence measured on the one-particle reduced density operator is unaffected by dissipation. Furthermore, we discuss how these correlations indicate quantum-to-classical transitions through the appearance of Gaussian position probability densities, sub-linear growth of average interparticle distance after a few steps, and decay of the entanglement entropy. On the other hand, the robustness of the qubit entanglement entropy can differentiate the model's topological phases better than in the one-particle quantum walk scenario.
Entanglement of identical massive particles recently gained attention, because of its relevance in highly controllable systems, e.g. , ultracold gases. It accounts for correlations among modes instead of particles, providing a different paradigm for quantum information. We prove that the entanglement of almost all states rarely vanishes in the presence of noise, and analyse the most relevant noise in ultracold gases: dephasing and particle losses. Furthermore, when the particle number increases, the entanglement decay can turn from exponential into algebraic.
Quantum entanglement in systems of identical particles is often obscured by the interplay between exchange-induced correlations and the operational framework used to define entanglement. To study the role of exchange statistics, we propose a scheme using two \textit{distinguishable} particles where an exchange symmetry is artificially engineered via a relative phase
θ in the initial state. This approach allows continuous tuning from bosonic (
θ=0) to fermionic (
θ=π) statistics. By monitoring the interplay between purity and coherence, we uncover distinct dynamical regimes dictated by the interaction strength
U and the phase
θ. For particles initially loaded in a bound state, strong
U suppresses coherence development by avoiding the scattering band, reducing the purity toward its minimum. For particles initially on neighboring sites, coherence grows linearly in time. While non-symmetric inputs feature a sharp purity reduction at intermediate
U, due to the competition between bound and unbound states, symmetric initial conditions produce transient coherence bursts that significantly enhance the purity. More generally, tuning the phase
θ reveals a high-purity region over a range of
θ at intermediate interactions, with the purity collapsing to
1/2 as
θ approaches the fermionic limit. Our results show that the imposed statistics, or lack thereof, reshapes the entanglement dynamics and its response to the interaction
U.