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Inclusion statistics and particle condensation in two dimensions
Stéphane Ouvry1, Alexios P Polychronakos1
1LPTMS, CNRS, Université Paris-Saclay, 91405 Orsay Cedex, France; Physics Department, the City College of New York, New York, New York 10031, USA; and The Graduate Center of CUNY, New York, New York 10016, USA.
Physical Review. E
|July 19, 2023
Summary
We introduce inclusion statistics, a novel quantum behavior where particles coalesce more than bosons. This leads to phenomena like condensation in lower dimensions, with potential experimental realization in attractive boson interactions.
Area of Science:
- Quantum mechanics
- Statistical physics
Background:
- Fermi statistics exhibit strong particle exclusion.
- Bose statistics allow particle coalescence.
- Existing quantum statistics do not fully capture strong attractive interactions.
Purpose of the Study:
- To propose and define a new quantum statistics: inclusion statistics.
- To explore the consequences of inclusion statistics on particle behavior and condensation.
- To investigate potential physical realizations of inclusion statistics.
Main Methods:
- Defining inclusion statistics by analogy with exclusion statistics, extrapolating beyond Bose statistics.
- Analyzing the conditions for particle condensation in different spatial dimensions.
- Considering attractive interactions between bosons as a potential mechanism.
Main Results:
- Inclusion statistics describe particles that coalesce more than bosons.
- Condensation in the absence of potentials occurs in d=2 dimensions for inclusion statistics, unlike d=3 for Bose-Einstein condensation.
- Stronger inclusion leads to a higher critical condensation temperature.
Conclusions:
- Inclusion statistics represent a novel framework for quantum systems with strong attractive interactions.
- The reduced dimensionality for condensation is a key characteristic of inclusion statistics.
- Experimental observation of inclusion statistics may be possible with systems exhibiting attractive boson interactions.
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