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Related Experiment Video

Updated: Jun 12, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Generalized Einstein relation in tilted periodic potential: a semiclassical approach.

Anindita Shit¹, Sudip Chattopadhyay, Suman Kumar Banik

¹Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.

The Journal of Physical Chemistry. B

|May 21, 2010

Summary

This summary is machine-generated.

We studied quantum motion in a heat bath using a quantum Langevin equation. Our findings show the diffusion rate is independent of potential shape in quantum and classical regimes.

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Area of Science:

Quantum mechanics
Statistical physics
Condensed matter physics

Background:

Understanding quantum systems interacting with their environment is crucial.
Dissipative effects and external fields significantly influence quantum dynamics.
The system-reservoir model is a standard approach for studying such interactions.

Purpose of the Study:

To investigate the quantum motion of a system in a dissipative Ohmic heat bath under an external field.
To develop a classical differential equation-based approach for quantum diffusion.
To calculate the Einstein relation for a quantum Brownian particle in a ratchet-type potential.

Main Methods:

Utilizing the traditional system-reservoir model.
Deriving the c-number of the generalized quantum Langevin equation from physically motivated initial conditions.
Employing a perturbation technique to calculate quantum correction terms.
Calculating the Einstein relation using a closed analytical form with approximations.

Main Results:

A classical differential equation-based approach is established for quantum diffusion in tilted periodic potentials.
Quantum correction terms are calculated.
The Einstein relation for a quantum Brownian particle in a ratchet-type potential is derived in a simple analytical form.
The diffusion rate is found to be independent of the potential's detailed form in both quantum and classical regimes.

Conclusions:

The developed approach simplifies the study of quantum diffusion.
The independence of the diffusion rate from potential shape is a key finding, unifying quantum and classical descriptions.
This work provides a valuable framework for analyzing quantum Brownian motion in complex potentials.