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Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
1Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia.
Summary
We studied current fluctuations in quantum spin chains, finding that the additivity principle applies even in non-stochastic quantum systems. This principle accurately predicts fluctuations in large systems, mirroring classical models.
Area of Science:
- Quantum physics
- Statistical mechanics
- Condensed matter theory
Background:
- Understanding nonequilibrium quantum systems is crucial.
- Current fluctuations provide insights into system dynamics.
- The applicability of classical statistical principles to quantum systems is an open question.
Purpose of the Study:
- To investigate current fluctuations in a diffusive nonequilibrium quantum spin chain.
- To determine if the additivity principle holds for quantum systems.
- To compare quantum system fluctuations with classical models.
Main Methods:
- Utilized the large-deviation formalism.
- Analytically calculated the second current moment for arbitrary system lengths.
- Employed numerical methods to study the thermodynamic limit.
Main Results:
- Derived an exact expression for the second current moment.
- Demonstrated that higher-order cumulants and the large-deviation function can be calculated using the additivity principle in the thermodynamic limit.
- Showed that current fluctuations in large quantum systems are analogous to the classical symmetric simple exclusion process.
Conclusions:
- The additivity principle is valid in nonequilibrium quantum systems, not just purely stochastic ones.
- Macroscopic hydrodynamic theory can describe quantum system fluctuations.
- Quantum spin chain fluctuations exhibit universality, connecting to classical statistical mechanics.
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