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Renormalization group in quantum mechanics at zero and finite temperature
P Gosselin1, H Mohrbach, A Bérard
1Université Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques, Boîte Postale 74, 38402 Saint Martin d'Hères Cedex, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
Summary
This study uses renormalization group methods to calculate quantum system energies at zero and finite temperatures. The approach provides a nonperturbative method for ground state energy and a variational method for free energy.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter theory
Background:
- Quantum fluctuations significantly impact the behavior of quantum mechanical systems.
- Accurate computation of ground state and free energies is crucial for understanding these systems.
- Traditional methods may face challenges in nonperturbative regimes or at finite temperatures.
Purpose of the Study:
- To develop and apply renormalization group (RG) methods for integrating quantum fluctuations in quantum mechanical systems.
- To compute the ground state energy at zero temperature using a nonperturbative RG approach.
- To compute the free energy at finite temperatures using a variational RG approach.
Main Methods:
- Application of the renormalization group formalism.
- Development of a nonperturbative renormalization group equation for zero temperature.
- Proposal of a variational renormalization group equation for finite temperature.
Main Results:
- The nonperturbative RG equation enables the computation of the ground state energy.
- The variational RG equation provides a method for calculating the free energy at finite temperatures.
- The RG approach effectively integrates quantum fluctuations across different temperature regimes.
Conclusions:
- The renormalization group formalism is a powerful tool for studying quantum mechanical systems.
- The proposed methods offer efficient ways to calculate key thermodynamic quantities.
- This work advances the understanding of quantum systems by incorporating quantum fluctuations systematically.