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The semiclassical propagator in Fock space: dynamical echo and many-body interference
Thomas Engl1, Juan Diego Urbina2, Klaus Richter2
1Institut für Theoretische Physik, Universität Regensburg, Regensburg 93040, Germany thomas.engl@physik.uni-regensburg.de.
Summary
We developed a new semiclassical method for quantum many-body systems. It describes interference effects and a novel many-body echo phenomenon using classical wave equations.
Area of Science:
- Quantum mechanics
- Many-body physics
- Nonlinear dynamics
Background:
- Describing quantum many-body dynamics, especially interference effects, is computationally challenging.
- Existing methods often rely on mean-field approximations, neglecting beyond-mean-field phenomena.
Purpose of the Study:
- To present a novel semiclassical approach for quantum many-body propagation.
- To accurately describe interference effects in interacting bosonic systems.
- To introduce and analyze a many-body echo phenomenon.
Main Methods:
- Utilizing coherent sums over quantum amplitudes derived from classical nonlinear wave equations.
- Non-perturbatively constructing transition amplitudes between Fock states.
- Extending Gutzwiller's van Vleck propagator to symmetrized many-body states.
Main Results:
- The approach successfully describes interference effects in many-body systems.
- A genuine many-body echo phenomenon, or coherent backscattering in Fock space, is identified.
- This echo arises from quantum interference between time-reversed classical solutions.
Conclusions:
- The proposed semiclassical method offers a powerful tool for studying complex quantum many-body dynamics.
- It provides a pathway to understand phenomena beyond mean-field approximations.
- The discovery of the many-body echo highlights the importance of interference in quantum systems.
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