Beyond Standard Solutions: Exploring Schrödinger’s Equation with Time Delays
New research delves into the existence and properties of complex solutions to the Schrödinger equation when faced with time-delayed potentials, expanding the possibilities for modeling quantum systems.
![Impurity challenges within thermal baths can be effectively modeled using a Wilson chain approach with a length cutoff [latex]\Lambda_{imp}[/latex] for non-interacting systems, but strongly-correlated baths necessitate representation via local tensors defined across impurity and bulk regions-also demarcated by [latex]\Lambda_{imp}[/latex]-allowing the impurity itself to function as a quantum probe for diagnosing quantum critical regions and associated crossovers during quantum phase transitions.](https://arxiv.org/html/2601.04729v1/main_text/Fig1.png)
![The proposed unified framework analyzes the unpredictability of [latex] \mathbf{Exp}\_{\mathbf{\mathcal{PUF},\mathcal{A}}}^{Unpredict}(\mathrm{N}) [/latex], offering a means to quantify inherent system decay through the evaluation of physical unpredictable functions.](https://arxiv.org/html/2601.04697v1/x3.png)

![Through native-frames analysis of [latex]CO^{3+}_{2}[/latex] breakup following collisions with Argon projectiles, the study disentangles sequential dissociation - where [latex]CO^{2+}[/latex] forms initially before yielding [latex]C^{+}[/latex] and [latex]O^{+}[/latex] - from concerted events, utilizing kinetic energy release and angular distributions to reconstruct the full process and establishing a framework for distinguishing decay pathways in complex molecular fragmentation.](https://arxiv.org/html/2601.03711v1/x2.png)

