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Updated: Jun 4, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Correlation functions for a strongly coupled boson system and plane partitions
Nikolay Bogoliubov1, Jussi Timonen
1Saint Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023 Saint Petersburg, Russia.
Summary
We introduce a quantum phase model derived from strongly correlated q-boson systems. Its correlation functions are solved exactly, revealing low-temperature amplitude relations to finite-size plane partitions.
Area of Science:
- Quantum physics
- Statistical mechanics
- Condensed matter theory
Background:
- Strongly correlated quantum systems exhibit complex behaviors.
- Boson hopping models are crucial for understanding interacting particles.
- Phase models offer simplified frameworks for studying quantum phenomena.
Purpose of the Study:
- Introduce a quantum phase model as a limit of a strongly correlated q-boson hopping model.
- Provide exact solutions for the phase model and its correlation functions.
- Analyze the low-temperature behavior of these correlation functions.
Main Methods:
- Derivation of a quantum phase model from a q-boson hopping model.
- Exact solution techniques applied to the phase model.
- Calculation of correlation functions and their low-temperature limits.
Main Results:
- An exact solution for the quantum phase model was obtained.
- Explicit expressions for two key correlation functions were derived.
- Low-temperature amplitudes were found to be proportional to the number of plane partitions within finite-sized boxes.
Conclusions:
- The quantum phase model provides a tractable framework for strongly correlated systems.
- The derived correlation functions offer insights into the model's thermodynamic properties.
- The connection to plane partitions suggests a link between quantum many-body physics and combinatorial structures.
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