Normalized Gaussian path integrals

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.


Published in:
Physical Review E, 102, 2, 022135
Year:
Aug 25 2020
Publisher:
College Pk, AMER PHYSICAL SOC
ISSN:
1539-3755
1550-2376
Keywords:




 Record created 2020-09-17, last modified 2020-10-29


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