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Ground-state fluctuations in finite Fermi systems.
M N Tran1, M V Murthy, R K Bhaduri
1Department of Physics and Astronomy, McMaster University Hamilton, Ontario, Canada L8S 4M1.
Summary
This study calculates fermion number fluctuation in a trap using microcanonical counting. Results differ significantly from canonical and grand canonical methods, especially at low excitation energies.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- Understanding particle behavior in confined systems is crucial.
- Ground state properties of fermions at zero temperature (T=0) are fundamental.
- Excitation pathways from the ground state influence system dynamics.
Purpose of the Study:
- To develop and implement a method for calculating number fluctuation in the ground state of trapped fermions.
- To compare microcanonical counting results with canonical and grand canonical ensemble averaging.
- To analyze the impact of excitation energy on fluctuation differences.
Main Methods:
- Formulation of a microcanonical counting method.
- Implementation for noninteracting fermions in harmonic confinement.
- Comparison with canonical and grand canonical ensemble averaging.
Main Results:
- Microcanonical counting yields significantly different number fluctuation results compared to other ensembles.
- These differences are expected to persist even for large fermion numbers at low excitation.
- Bosonic results are provided for comparative analysis.
Conclusions:
- Microcanonical counting offers a distinct perspective on fermion number fluctuation in traps.
- Ensemble choice critically impacts the calculation of fluctuations in quantum systems.
- The findings highlight the importance of the counting method in confined fermion systems.