# Semiclassical expansion of the Slater sum for position dependent mass distributions in d dimensions

Source: [Semiclassical expansion of the Slater sum for position dependent mass distributions in d dimensions](<https://www.sota2.com/research/paper/68fa2c241e209131ce84d35b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T15:08:32.018Z

Authors: K. Berkane, K. Bencheikh

Published: 2012-10-04T16:07:22.000Z

## Abstract

We consider hamiltonian systems with spatially varying effective mass and slowly varying local potential in d dimensions. The Slater sum is defined as the diagonal element of the Bloch propagator. We derive a gradient expansion of the Slater sum up to the second order. We will show that the derived analytical expression is valid for d=1,2,3 and 4. A numerical example is shown to highlight the effect of the spatially varying effective mass.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1210.1503>)

[PDF](<https://arxiv.org/pdf/1210.1503.pdf>)