Monte Carlo Study of Real Time Dynamics on the Lattice

Area of Science:

• Computational Physics
• Quantum Mechanics
• Lattice Field Theory

Background:

• Monte Carlo simulations are crucial for studying quantum systems but face limitations due to the 'sign problem' in real-time dynamics.
• The sign problem arises from highly oscillatory phases in path integral calculations, hindering accurate simulations.

Purpose of the Study:

• To develop a new computational method for calculating real-time quantities in quantum systems using lattice simulations.
• To address and mitigate the sign problem in Monte Carlo simulations of real-time dynamics.

Main Methods:

• Utilizing the Schwinger-Keldysh formalism for real-time calculations.
• Deforming the path integration domain to a complex manifold to manage phase oscillations.
• Employing the 'contraction algorithm' to construct a Markov chain on the complex manifold.

Main Results:

• The proposed method successfully computes real-time quantities, as demonstrated with the quantum mechanical anharmonic oscillator.
• Results obtained using the new method align with exact solutions derived from Hamiltonian diagonalization.
• The approach is shown to be generalizable to quantum field theory, though currently computationally intensive.

Conclusions:

• The developed complex manifold deformation technique offers a viable solution to the sign problem in real-time Monte Carlo simulations.
• This method provides a pathway for more accurate lattice-based studies of quantum dynamics.
• Future work will focus on optimizing the algorithm to improve its efficiency for complex quantum field theory applications.