What question did this study set out to answer?

The aim is to investigate effective mass renormalization's impact on tunneling and energy levels in quantum systems under non-equilibrium conditions.

April 12, 2026Open Access

Effective Mass Renormalization from Energy Allocation: Tunneling, Energy Levels, and Band Structure

Key Points

The aim is to investigate effective mass renormalization's impact on tunneling and energy levels in quantum systems under non-equilibrium conditions.
Derived tunneling probabilities for a rectangular barrier based on the energy ratio.
Analyzed energy levels for infinite square wells and harmonic oscillators using $eta$ dependence.
Examined periodic potentials to understand the relationship with the hopping parameter and bandwidth.
Tunneling enhances when $eta > 1$ and suppresses when $eta < 1$.
Energy levels scale differently depending on the system, with unique expressions for various potentials.
The hopping parameter shows exponential growth with $eta$, increasing bandwidth significantly.

Abstract

In the Energy-Efficiency Theory (EET), the energy ratio = Ėₑ₄ₒ₏/Ė₌₀₈₍ controls the balance between spatial exploration and localization. For a quantum system in a non-equilibrium steady state, this leads to a modified Schrödinger equation with an effective mass m^* = m/. This paper explores the physical consequences of this renormalization in condensed matter and cold atom systems. We derive -dependent tunneling probabilities through a rectangular barrier, showing that >1 enhances tunneling while <1 suppresses it. For an infinite square well, energy levels scale as Eₙ = Eₙ^ (0) ; for a harmonic oscillator, Eₙ = Eₙ^ (0). In periodic potentials, the hopping parameter increases exponentially with, dramatically broadening the bandwidth. We clarify that this effective mass renormalization does not modify the bare mass of elementary particles in vacuum, but rather parametrizes the non-equilibrium coupling between the charge carrier and the underlying lattice or confinement potential. Three falsifiable predictions with explicit statistical criteria are proposed, using semiconductor heterostructures, quantum dots, and GaAs/AlGaAs two-dimensional electron gases as experimental platforms. The framework is fully compatible with standard quantum mechanics at =1 and offers a controllable extension for driven non-equilibrium systems.

Effective Mass Renormalization from Energy Allocation: Tunneling, Energy Levels, and Band Structure

Key Points

Abstract

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