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Normalized Gaussian path integrals.

  • Corazza G Laboratory for Computation and Visualization in Mathematics and Mechanics (LCVMM) Institute of Mathematics, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland.
  • Fadel M Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland.
  • 2020-09-18
Published in:
  • Physical review. E. - 2020
English Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show a consistent approach to solve conditional and unconditional Euclidean (Wiener) Gaussian path integrals that allow us to compute transition probabilities in the semiclassical approximation from the solutions of a system of linear differential equations. Our method is particularly useful for investigating Fokker-Planck dynamics and the physics of stringlike objects such as polymers. To give some examples, we derive the time evolution of the d-dimensional Ornstein-Uhlenbeck process and of the Van der Pol oscillator driven by white noise. Moreover, we compute the end-to-end transition probability for a charged string at thermal equilibrium, when an external field is applied.
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  • English
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https://sonar.ch/global/documents/54078
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