Differential equation for partition functions and a duality pseudo-forest
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2019
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917677183795200 |
|---|---|
| author | Vanchurin, Vitaly |
| author_facet | Vanchurin, Vitaly |
| contents | We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph which contains a necessary and sufficient information for computing the full quantum partition function. We derive a second-order differential equation for an extended partition function $z[β, β', J]$ which describes a transformation from a ``parent'' partition function $z[0, β', J]$ (or anti-commutativity graph) to a ``child'' partition function $z[β, 0, J]$ (or anti-commutativity graph). The procedure can be iterated and then one forms a pseudo-forest of duality transformations between quantum systems, i.e. a directed graph in which every vertex (or quantum system) has at most one incoming edge (from its parent system). The pseudo-forest has a single tree connected to a constant partition function, many pseudo-trees connected to self-dual systems and all other pseudo-trees connected to closed cycles of transformations between mutually dual systems. We also show how the differential equation for the extended partition function can be used to study disordered systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_11268 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Differential equation for partition functions and a duality pseudo-forest Vanchurin, Vitaly High Energy Physics - Theory Mathematical Physics Quantum Physics We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph which contains a necessary and sufficient information for computing the full quantum partition function. We derive a second-order differential equation for an extended partition function $z[β, β', J]$ which describes a transformation from a ``parent'' partition function $z[0, β', J]$ (or anti-commutativity graph) to a ``child'' partition function $z[β, 0, J]$ (or anti-commutativity graph). The procedure can be iterated and then one forms a pseudo-forest of duality transformations between quantum systems, i.e. a directed graph in which every vertex (or quantum system) has at most one incoming edge (from its parent system). The pseudo-forest has a single tree connected to a constant partition function, many pseudo-trees connected to self-dual systems and all other pseudo-trees connected to closed cycles of transformations between mutually dual systems. We also show how the differential equation for the extended partition function can be used to study disordered systems. |
| title | Differential equation for partition functions and a duality pseudo-forest |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/1910.11268 |