The University of Tokyo · 물리·천문학
요시코 오가타 교수의 연구실은 양자 스핀 체계와 양자 many-body 시스템의 비평형 거동, 특히 비평형 상태에서의 열적 및 양자 위상 전이, 대칭 보호 위상 등에 중점을 두고 있습니다. C*-대수학적 방법과 브레이드된 C*-텐서 범주를 활용해 고립된 상태의 위상적 성질을 수학적으로 해석하며, 게이지 대칭성과 위상적 순서의 기초를 다룹니다. 특히, 열역학적 균형 상태와 비균형 동역학 간의 관계, 그리고 대규모 제곱 결과의 수학적 기반을 강화하는 데 기여하고 있습니다.
표시된 성과는 수집된 데이터 기준으로 산출되며, 일부 차이가 있을 수 있습니다.
We investigate the nonequilibrium properties of the transverse XX chain. The steady state can be interpreted as the equilibrium state or the ground state of the effective Hamiltonian, which depends on the initial state. We also study the physical properties of the state at various temperatures, in particular, the effects of quantum phase transition.
We investigate the magnetization profile in the intermediate time of diffusion by using the C*-algebraic method. We observe a transition from monotone profile to nonmonotone profile. This transition is purely thermal.
We consider a set <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper P upper G left-parenthesis script upper A right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>P</mml:mi> <mml:mi>G</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">A</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotati
We derive braided C*-tensor categories from gapped ground states on two-dimensional quantum spin systems satisfying some additional condition, which we call the approximate Haag duality.
Abstract We consider symmetry-protected topological phases with on-site finite group G symmetry $\beta $ for two-dimensional quantum spin systems. We show that they have $H^{3}(G,{\mathbb T})$ -valued invariant.
We recover, expand, and unify quantum (and classical) large deviation results for lattice Gibbs states. The main new ingredient in this paper is a control on the overlap of spectral projections for non-commutative observables. Our proof of large deviations is based on Ruelle–Lanford functions [20, 34] which establishes the existence of a rate function directly by subadditivity arguments, as done in the classical case in [23, 32], instead of relying on Gärtner–Ellis theorem, and cluster expansion
