A Langevin approach to fermion and quantum spin correlation functions

John R. Klauder

By using spin-coherent states, the author shows that correlation functions for fermions or quantum spins follow from solutions to Langevin equations associated with a functional integral representation of the partition function. His method is applicable to any number of dimensions, may also be combined with boson variables, and is suitable for computer simulations.

J. Rae

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

Suraka Bhattacharjee, Koushik Mandal, Supurna Sinha

We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and coupled to a bath. We have considered two models for the bath: an Ohmic bath model and a non-Markovian Drude bath model with finite memory. The effect of finite memory on the dynamics of the quantum spin is studied in detail. In particular, we have studied the effect of memory on the expectation values of the magnetic moment and the spin correlation functions. The time evolution study of the spin correlation functions shows that the correlation functions exhibit a damped oscillatory behavior with the randomization time being determined by the damping rate. We have analytically shown that the damping gets affected by the finite memory time when the bath retains memory of the interaction with the system. We also analyze the spin response function of the system for the Ohmic bath. Our results qualitatively agree with the findings in spin noise spectroscopy experiments and our predictions can be tested in future ultracold atom experiments.

Bryan J. Dalton, John Jeffers, Stephen Mark Barnett

Abstract This chapter provides an overview of the phase space method for treating the physics of systems of bosons and fermions in regimes where quantum degeneracy occurs. Key concepts such as modes, creation and annihilation operators, distribution functions in phase space depending on c-number (bosons) or Grassmann (fermions) phase space variables, quantum correlation functions, and phase space integrals are introduced, together with how the dynamics of the system density operator as described via Liouville–von Neumann or master equations is translated into Fokker–Planck equations for the distribution function, and then how phase space integrals for quantum correlation functions can be determined via Langevin stochastic equations that are equivalent to the Fokker–Planck equations, and which involve stochastic phase space variables. The extension of the phase space approach to systems with large mode numbers, involving field annihilation and creation operators, distribution functionals, and functional Fokker–Planck and Langevin stochastic field equations is also reviewed.

Guo-Feng Zhang, Heng Fan, Ai-Ling Ji +3 more