Computational Approaches to Time-Dependent Quantum Mechanics

Jincheng Zhang

Quantum state collapse is a fundamental process in quantum mechanics, leading to the emergence of classical reality. This paper explores the implications of non-linear collapse and proposes a time-geometry-based quantum computation framework leveraging quantum entanglement and time dilation. We investigate how time dependency affects the collapse process and design algorithms to exploit this dependency for enhanced quantum computational capabilities. The research introduces a novel time-geometric model, aiming to expand the potential of quantum computing beyond traditional qubit manipulation. This work presents a new approach to quantum algorithms, focusing on time-dependent optimization and utilizing quantum entanglement for computational advantage.

S V Mousavi, A S Majumdar, D Home

Abstract We study the effect of quantum statistics on the arrival time distribution of quantum particles computed through the probability current density. It is shown that symmetrization or asymmetrization of the wave function affects the arrival time distribution for even freely propagating particles. In order to investigate the effect of statistics on the weak equivalence principle in quantum mechanics (WEQ), we then compute the mean arrival time for wavepackets in free fall. The violation of WEQ through the effect of statistics on the mass dependence of the mean arrival time is clearly exhibited. We finally evaluate the effect of spin on the violation of WEQ using a different approach by including an explicit spin-dependence in the probability current distribution, and compare it with the approach using particle statistics. Our results show WEQ re-emerges smoothly in the limit of large mass.

Martin Formánek

Erik Lötstedt, Takanori Nishi, Kaoru Yamanouchi

R Wieser

The derivation of the time dependent Schrödinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schrödinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schrödinger equation.