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Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems.

Giovani E Morales-Hernández1, Juan C Castellanos1, José L Romero1

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Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

We developed a discretized Truncated Wigner Approximation (TWA) for variable-spin quantum systems. This method approximates quantum dynamics using effective classical methods, offering a new computational tool.

Keywords:
phase-spacesemiclassical evolutionvariable spin systems

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Area of Science:

  • Quantum mechanics
  • Mathematical physics
  • Computational physics

Background:

  • Representing variable-spin quantum systems is computationally challenging.
  • Semi-classical approximations offer a path to simplify complex quantum dynamics.
  • The Truncated Wigner Approximation (TWA) is a powerful tool for simulating quantum systems.

Purpose of the Study:

  • To develop a discretized version of the Truncated Wigner Approximation (TWA) for variable-spin systems.
  • To approximate quantum dynamics using effective classical methods on a symplectic manifold.
  • To compare the accuracy of different TWA versions for emblematic quantum systems.

Main Methods:

  • Applying the semi-classical limit of the generalized SO(3) map.
  • Utilizing the asymptotic form of the star-product for quantization.
  • Introducing a discretized Truncated Wigner Approximation (TWA).

Main Results:

  • Successfully "quantized" a classical dynamic variable using the star-product.
  • Developed and implemented a discretized TWA for quantum dynamics.
  • Compared exact, continuous, and discretized TWA results for a rotor and coupled spins.

Conclusions:

  • The discretized TWA provides an effective method for approximating quantum dynamics of variable-spin systems.
  • This approach bridges quantum and classical descriptions, enabling efficient computation.
  • The study validates the discretized TWA against exact solutions for benchmark problems.