MATSUI TAKU | Last modified date：2023.04.10 |

Graduate School

Undergraduate School

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##### https://kyushu-u.pure.elsevier.com/en/persons/taku-matsui

Reseacher Profiling Tool Kyushu University Pure

Academic Degree

PhD

Country of degree conferring institution (Overseas)

No

Field of Specialization

mathematical physics

Total Priod of education and research career in the foreign country

03years06months

Outline Activities

We study structure of infinite volume ground states , limit theorem(central limit theorem)

of quantum spin systems by use of functional analysis. We initiated a mathematical study of uniqueness of equilibrium stets of anharmonic crystals.

of quantum spin systems by use of functional analysis. We initiated a mathematical study of uniqueness of equilibrium stets of anharmonic crystals.

Research

**Research Interests**

- analysis of statistical mechanics of quantum spin systems by functional analytic methods

keyword : quantum spin sysytems, functional analysis,NESS, 高次元スピン系のHaag daulity Gemetric Interpretation of Z_2

2009.04～2021.03* Spectral properties and symmetry breaking of Quantum systems with infinite degree of freedom.

**Current and Past Project**

- We analyse the type of various von Neumann sub-algebras appearing in GNS reprepresentations of gapped ground states of 2 dim quantum spin systems.
- We study KMS and ground states of Bosonic systems on lattices using the resolevent algebras

and we are trying to prove their uniqueness under physical natural situations. - We consider a generalization of Projected Entnagled Pair states and their symmetry.
- We try to prove Haag duality for quatum systems on lattices in various situtations and

we try to show that the presence of the spectral gap implies split property for one-dimensional systems.

We als try to prove relative Haag duality (duality for relative commutants) and consider application to

non-equilibrium steady states - In one-dimensional quantum spin systems, try to find a condition

for producing infinitely many maximally entangled pairs of q-bits

in pure states and investigate the relationship with split property. - * proof of absence of non-periodic ground states

for anithferromagnetic XXZ models

* clarify the relation between random partition and Bose-Einstein

condensation

**Academic Activities**

**Papers**

**Membership in Academic Society**

- international association of mathemtatical physics

Educational

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