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Many-body green function of degenerate systems
Christian Brouder1, Gianluca Panati, Gabriel Stoltz
1Institut de Minéralogie et de Physique des Milieux Condensés, CNRS UMR 7590, Universités Paris 6 et 7, IPGP, 140 rue de Lourmel, 75015 Paris, France.
Physical Review Letters
|April 7, 2010
Summary
Researchers derived a new approximation for degenerate systems, solving the problem of initial state selection. This leads to a proper definition and convergence of Green functions in many-body physics.
Area of Science:
- Many-body physics
- Quantum mechanics
- Condensed matter theory
Background:
- Degenerate systems pose challenges in accurately describing their quantum evolution.
- Selecting appropriate initial states is crucial for solving Hamiltonians (H(0) + V).
- Existing methods struggle with the complexities of degenerate eigenspaces.
Purpose of the Study:
- To derive a rigorous nonperturbative adiabatic approximation for the evolution operator in degenerate many-body systems.
- To resolve the long-standing issue of choosing initial states that lead to eigenstates of the full Hamiltonian.
- To establish proper definitions and convergence for various Green functions in these systems.
Main Methods:
- Development of a nonperturbative adiabatic approximation.
- Utilizing projection operators (P(0)) onto degenerate eigenspaces of the unperturbed Hamiltonian (H(0)).
- Defining and analyzing Green functions, including statistical and nonequilibrium variants.
Main Results:
- A rigorous approximation for the evolution operator in degenerate systems is established.
- Initial states are identified as eigenstates of P(0)VP(0), solving a key problem.
- Proper definitions for Green functions (Green function, statistical Green function, nonequilibrium Green function) are provided.
- Convergence of these Green functions is mathematically established.
Conclusions:
- The derived adiabatic approximation offers a robust framework for studying degenerate quantum systems.
- The identification of specific initial states simplifies the analysis of system evolution.
- The established Green function definitions and convergence are critical for theoretical advancements and future research in many-body physics.
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