Mean-field theory of the DNLS equation at positive and negative absolute temperatures
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917467173945344 |
|---|---|
| author | Giusfredi, Michele Iubini, Stefano Politi, Antonio Politi, Paolo |
| author_facet | Giusfredi, Michele Iubini, Stefano Politi, Antonio Politi, Paolo |
| contents | The Discrete Non Linear Schrödinger (DNLS) model, due to the existence of two conserved quantities, displays an equilibrium transition between a homogeneous phase at positive absolute temperature and a localized phase at negative absolute temperature. Here, we provide a mean-field theory of DNLS through a suitable approximation of the grandcanonical partition function which makes it factorizable and can be used to describe the equilibrium state at positive temperatures as well as the metastable state at negative temperatures. By comparing our mean-field results with numerically exact ones, we show that this approximation is good-to-excellent in the whole grandcanonical phase diagram. Explicit approximate expressions for equilibrium observables are provided in the high-temperature limit. Our theory represents a clear advancement over the model that neglects the interaction between sites. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean-field theory of the DNLS equation at positive and negative absolute temperatures Giusfredi, Michele Iubini, Stefano Politi, Antonio Politi, Paolo Statistical Mechanics Chaotic Dynamics The Discrete Non Linear Schrödinger (DNLS) model, due to the existence of two conserved quantities, displays an equilibrium transition between a homogeneous phase at positive absolute temperature and a localized phase at negative absolute temperature. Here, we provide a mean-field theory of DNLS through a suitable approximation of the grandcanonical partition function which makes it factorizable and can be used to describe the equilibrium state at positive temperatures as well as the metastable state at negative temperatures. By comparing our mean-field results with numerically exact ones, we show that this approximation is good-to-excellent in the whole grandcanonical phase diagram. Explicit approximate expressions for equilibrium observables are provided in the high-temperature limit. Our theory represents a clear advancement over the model that neglects the interaction between sites. |
| title | Mean-field theory of the DNLS equation at positive and negative absolute temperatures |
| topic | Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2511.09206 |