Mori's Langevin equation for a quantum harmonic oscillator coupled to infinitely many scalar Bosons

Aritra Ghosh, Sushanta Dattagupta

Lorenzo Galleani

Toshio Tsuzuki

Masao Hirokawa

For every system with a passably general Hamiltonian of a quantum harmonic oscillator coupled to infinitely many scalar bosons, we estimate Heisenberg pictures of the annihilation and creation operators, describing the quantum harmonic oscillator, from only data on the autocorrelation function of the operators such that the pictures restore their autocorrelation functions to original ones, by reconsidering Mori's theory of generalized Brownian motion. And we then investigate the Liouville space and Liouville operator associated with the estimation.

Nataliia Rozhenko

Shamik Gupta, Malay Bandyopadhyay

We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.