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Non-equilibrium systems contain a rich variety of physical phenomena that do not exist in equilibrium. Even for such phenomena, some kind of universality (i.e., properties that are independent of the details of the system) is expected to exist.
・Exceptional dynamical quantum phase transition in periodically driven systems
Phase transitions at equilibrium are characterized by the singularity of the free energy. Recently, it has been discovered that "dynamical free energy", defined using imaginary time instead of the inverse temperature, can be singular. This quantity corresponds to the recurrence probability after time evolution in quantum systems.
As a new mechanism for this transition in unitary periodically driven systems, I proposed an "exceptional point dynamical phase transition" due to the spontaneous breaking of the hidden anti-unitary symmetry. This transition is accompanied by strong singularities of the dynamical free energy that cannot exist in the equilibrium state, divergence of the correlation length with respect to a quantity called the generalized correlation, and oscillatory long-range order. When the original periodically driven system satisfies certain parameter conditions, an anti-unitary symmetry appears for a non-unitary operator obtained by the technique called the space-time duality. When this hidden anti-unitary symmetry is spontaneously broken, a spectral singularity called an exceptional point appears and induces a dynamical phase transition of the original model reflecting its universality.
(a) Schematic diagram of the non-thermal fixed point. When strongly quenched from an initial state, dynamical scaling appears for intermediate time regime. (b), (c) The process for which two magnetic solitons of different signs intertwine with time and form a bound state. The vertical axis is space and the horizontal axis is time.
In a one-dimensional antiferromagnetic Spinor gas, magnetic solitons form a bound state with time, and relaxation proceeds as the bound solitons disappear.
・Dynamical scalings in ultracold atomic gases
Dynamic scaling in non-equilibrium dynamics of classical systems, especially dissipative systems and stochastic processes, has long been studied as a universal phenomenon that appears regardless of the details of the system. For example, when multiple order parameters in a system (e.g., in a symmetry-breaking phase) form a domain, the domain size grows over time due to e.g., collisions. This phenomenon is called the phase-ordering process. For such a phenomenon, equal-time correlation function is known to obey a dynamical scaling law characterized by a characteristic time-dependent length scale L(t). The time dependence of L(t) can be used to characterize the universality class of the phase-ordering process. More generally, such a kind of dynamical scaling is called a non-thermal fixed point and has attracted a lot of attention in various fields.
We have shown that there emerges a similar universal dynamical scaling of the correlation function in isolated quantum systems. For example, for a one-dimensional ferromagnetic spinor Bose gas, we showed that the newly found universality is unique to one-dimensional isolated quantum systems. Furthermore, in an antiferromagnetic spinor Bose gas, we found that there is a dynamical scaling reflecting the non-thermal fixed point due to the novel bound state of magnetic solitons (see figure in the left).
Phys. Rev. Lett. 120, 073002 (2018). [arxiv:1707.03615]
Phys. Rev. Lett. 122, 173001 (2019). [arxiv:1812.03581]
Magnetic solitons, which also play an important role in the latter study mentioned above, were observed in a cold atomic system in collaboration with an experimental group at Georgia Tech.
As a concept distinct from the non-thermal fixed point, it is known that the height fluctuation of interface growth in classical systems exhibits a spatio-temporal dynamical scaling law called the Family-Vicsek scaling.
We have shown for the first time that the Family-Vicsek scaling also appears in quantum many-body systems, such as the Bose-Hubbard model and disordered Fermionic systems.
Phys. Rev. Lett. 124, 210604 (2020). [arXiv:1911.10707]
Phys. Rev. Lett. 127, 090601 (2021). [arXiv:2101.08148]
Furthermore, we have shown that the Family-Vicsek scaling appears in an open quantum free fermionic system with dephasing. In this case, the scaling exponent changes from ballistic to diffusive by the inclusion of dephasing, but the scaling function becomes new and different from that of the Edwards-Wilkinson equation. This can be analytically shown by the renormalization group technique.
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