PhD

No

mathematical physics

03years06months

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.

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 Membership in Academic Society

• international association of mathemtatical physics

Educational Activities