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Map from one-dimensional quantum field theory to quantum chaos on a two-dimensional torus
1Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia.
Summary
Quantum field models on a 1D lattice are equivalent to chaotic one-body systems on a 2D torus. This mapping simplifies the study of quantum dynamics and their classical limits.
Area of Science:
- Quantum Field Theory
- Statistical Mechanics
- Quantum Chaos
Background:
- The study of quantum field models on lattices is crucial for understanding complex quantum systems.
- Mapping these models to simpler systems can reveal fundamental properties.
Purpose of the Study:
- To establish a mapping between quantum field models on a 1D lattice and one-body chaotic systems.
- To explore the relationship between the continuum field limit and the quasiclassical limit.
Main Methods:
- Utilizing the Heisenberg picture for the 1D lattice quantum field model.
- Employing the Schrödinger picture for the 2D torus one-body chaotic system.
- Analyzing the correspondence between the continuum field and quasiclassical limits.
Main Results:
- A direct mapping is established between quantum field dynamics on a 1D lattice and chaotic one-body systems on a 2D torus.
- The continuum field limit of the lattice model corresponds to the quasiclassical limit of the chaotic system.
Conclusions:
- The established mapping provides a powerful tool for investigating quantum field theory through the lens of quantum chaos.
- This work bridges the gap between different theoretical frameworks in quantum mechanics.