Relaxation dynamics of isolated quantum systems in the thermodynamic limit

Rikuya Kobashi

Uwe Holm

Barbara Fresch

Norayr Asriyan, Jan Meibohm, Vasco Cavina +1 more

We present a unifying description of dynamical phase transitions in the unitary evolution of an isolated quantum particle and the dissipative relaxation of a classical Brownian particle, based on a dynamical generat- ing function. In the semiclassical and weak-noise limits, Fisher zeros of this function condense in the complex- time plane and reach the corresponding physical axes, producing dynamical phase transitions through a competition between return trajectories. This establishes a direct connection between quantum and classical (finite-time) dynamical phase transitions, where the semiclassical limit plays the role of the thermodynamic limit. In particular, the established link naturally provides a classical version of the Loschmidt amplitude and shows how dynamical quantum phase transitions, typically associated with isolated many-body systems, can arise in a single-particle quantum system. The dynamical phases are distinguished by a unifying, trajectory- based order parameter, realized as a classical correlation function and a sequential quantum weak value.

Takashi Mori

時間反転対称性を持つミクロな力学法則からどのように熱平衡状態への緩和のような不可逆な現象が生じるかを説明することは理論物理学の大きな問題の一つである。近年、外界から孤立した量子系が熱平衡状態に緩和するための条件について理解が進んできたが、実際の物理系が熱平衡状態に緩和するまでにどの程度の時間がかかるかについては依然として難しい問題である。孤立量子系の熱平衡化の時間スケールの問題について理解を深めるため、孤立系に人工的に弱い散逸を加えた開放量子系の解析を行ない、その散逸ダイナミクスを記述するリンドブラディアンのスペクトルギャップの解析を行なった。理論的な予想によれば、スペクトルギャップは熱力学的極限において不連続性を示し、熱力学的極限の後に散逸を弱くする極限をとることによって、孤立量子系の熱平衡化に必要な緩和時間が定量的にわかるというものである。特に、着目系に粒子数一定などの保存量がある場合に、この予想が正しいことを確認した。さらに、このようなスペクトルギャップの不連続性を数学的にうまく利用することによって、開放量子系のダイナミクスを記述するリンドブラッド方程式の微視的導出が可能となることを明らかにし、プレプリントを公開した。 また、以上の理論的進展について、日本物理学会年次大会のシンポジウムで招待講演を行なった。 It is one of the most challenging problems in theoretical physics to elucidate how irreversible phenomena like the relaxation to thermal equilibrium arises from reversible microscopic law. In recent years, some progress has been made on our understanding of the condition under which a quantum system that is isolated from the surrounding environment relaxes towards thermal equilibrium. However, it is still a hard problem to evaluate how long time it takes for the system to thermalize. To get insights on the problem of timescale of thermalization in isolated quantum systems, we investigate an open quantum system, where artificial weak dissipation is introduced to the given isolated system. In particular, I focus on the spectral gap of the Lindbladian, which is the generator of the dissipative dynamics of such a system. According to the theoretical conjecture, the spectral gap shows discontinuity in the thermodynamic limit, and one can obtain the relaxation time by considering the double limit where the weak-dissipation limit is taken after the thermodynamic limit. I have confirmed that this conjecture is true when there are some conserved quantities like the number of particles. Moreover, I have shown that the discontinuity of the spectral gap allows us to microscopically derive the Lindblad equation, which is a fundamental equation describing the dynamics of open quantum systems, and this result is reported in the preprint. I also gave an invited talk on the above theoretical progress in the JPS annual meeting.

Daniel Matos