論文 / 著書情報
Article / Book Information
題目(和文)

開放量子系におけるパリティ・時間対称性由来 の散逸連続時間結晶

Title(English)

Dissipative continuous time crystals originating from parity-timesymmetry in open quantum systems

著者(和文)

中西優馬

Author(English)

Yuma Nakanishi

出典(和文)

学位:Doctor (Science),
学位授与機関:東京工業大学,
報告番号:甲第12640号,授与年月日:2024年3月26日,
学位の種別:課程博士,審査員:笹本 智弘,村上 修一,西田 祐介,石塚 大晃,納富 雅也

Citation(English)

Degree:博士(理学),Conferring organization: Tokyo Institute of Technology,
Report number:甲第12640号,
Conferred date:2024/3/26,
Degree Type:Course doctor,
Examiner:,,,,

学位種別(和文)博士論文Category(English)

Doctoral Thesis

種別(和文)

論文要旨

Type(English)

Summary

Powered by T2R2 (Tokyo Institute Research Repository)

（博士課程）Doctoral Program論 文 要 旨ＴＨＥＳＩＳ ＳＵＭＭＡＲＹ

系・コース：
Department of, Graduate major in

物理学
物理学

学生氏名：
Student’s Name

中西 優馬

系
コース

申請学位（専攻分野）：

博士

Academic Degree Requested

Doctor of

審査員主査：
Chief Examiner（ 理学 ）笹本 智弘

要旨（英文 800 語程度）
Thesis Summary （approx.800 English Words ）Exploration of novel non-equilibrium phases of matter or phase transitions and clarification of their mechanisms areimportant problems for non-equilibrium statistical physics. In particular, (continuous) time crystals that spontaneously breakcontinuous time-translation symmetry into discrete time-translation symmetry are a typical example, and these have beenobserved in open quantum systems but proved to be impossible to exist in closed quantum systems. Here, continuous timecrystals in open quantum systems are called dissipative continuous time crystals. In this thesis, we provide novel nonequilibrium phase transitions with anti-unitary symmetry breaking in Markovian open quantum systems and show that theycan explain the mechanism of a class of dissipative continuous time crystals in open collective spin systems.
First, we give a novel phase transition similar to the parity-time (PT) phase transitions, which are studied in non-Hermitiansystems well, for investigating a two-collective spin system with balanced gain and loss described by the GKSL (GoriniKossakowski-Sudarshan-Lindblad) equation. Here, a generator of the GKSL equation is called the Lindbladian. In the nonHermitian PT phase transitions, for the Hamiltonian with the PT symmetry, the eigenvalues change from real to complex
eigenvalues, thereby changing the dynamics from periodic oscillations to diverging or decaying dynamics, and the PT
symmetry of the eigenstate is broken at the same parameter point. On the other hand, for the Lindbladian case, we show thatwhen the Lindbladian has a PT symmetry, the Lindbladian spectrum transition, dynamics transition, and PT symmetry
breaking of the stationary state occur at the same parameter point. Also, in the non-Hermitian PT phase transition, thetransition point is known as the exceptional point where more than two eigenvectors coalesce. We will explain that thetransition point is expected to be an exceptional point in the Lindbladian case as well. These properties are similar to thoseof non-Hermitian PT phase transitions. This dissipative phase transition is called the Lindbladian PT phase transition.
Next, we show the physical origin of the boundary time crystal (BTC) for specific models, which is a dissipative time
crystal only in the thermodynamic limit. In particular, we focus on the dissipative one-collective spin model with transverse
magnetic field and excitation loss (hereafter, we refer to this model as the Driven Dicke model). In the Driven Dicke model,
the exact solution of the stationary state had already been found in 1979, and the static dissipative phase transition wasknown to occur. However, the mechanism of this phase transition is unclear. Also, the persistent oscillation appearing in thismodel was reaffirmed as the BTC in 2018, and this mechanism is also unclear.
In this thesis, we analytically show that the Driven Dicke model has the Lindbladian PT symmetry, and the PT symmetry
breaking of the stationary state occurs at the point where BTC breaks down. Also, we numerically show a similar statement
for another BTC (generalized Driven Dicke) model. Finally, using perturbation theory with degeneracy, we prove that BTC
arises under weak dissipation for a class of one-collective spin systems only when gain and loss are balanced. These results
indicate that there exist BTCs in collective spin systems originating from parity-time symmetry.
Furthermore, we give a simple and clear description of BTCs and the Lindbadian PT phase transitions using the Schwinger
boson transformation. In particular, we show that when the Lindbladian has PT symmetry at the microscopic level, theSchwinger boson mean-field equation becomes a nonlinear Schrodinger equation with U (1) symmetry. Then, the effective
nonlinear Hamiltonian has PT symmetry. Moreover, the continuous and discontinuous phase transitions can occur with nonlinear PT symmetry breaking. Then, we demonstrate that all collective excitation modes are shown to be destabilized at thetransition point using the linear stability analysis. As a result, the time-dependent phases appear, such as the swap or chiralphases, in which the amplitude or phase periodically oscillates, respectively. In particular, the phase where amplitudes aretime-dependent (e.g., swap phase) corresponds to the time-crystalline (Lindbladian PT) phase in the notation of collectivespin. Moreover, we show that critical exceptional points (CEPs), in which two excitation modes coalesce, emerge in thecase of continuous phase transitions. Finally, we confirm the validity of these analyses by comparing them with numericalcalculations. As a result, we can expect that the exceptional point also emerges for the Lindbladian.
Lastly, we summarize and mention the outlook on the BTCs and Lindbladian PT phase transitions. In particular, wemention the application of Lindbladian exceptional points. The PT phase transitions in non-Hermitian systems have been

used for many applications, such as sensors and lasers, by exploiting the properties of exceptional points. Then, theLindbladian exceptional points may extend these to quantum systems. Our thesis will further our understanding of nonequilibrium phase transitions or phases of matter and help us develop applied techniques using exceptional points in open
quantum systems. (794 words)

備考 : 論文要旨は、和文 2000 字と英文 300 語を 1 部ずつ提出するか、もしくは英文 800 語を 1 部提出してください。
Note : Thesis Summary should be submitted in either a copy of2000 Japanese Characters and 300 Words (Engｌish) or 1copy of 800

Words (English).
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Attention: Thesis Summary will be published on Tokyo Tech Research Repository

Website (T2R2).