We review universal relaxation dynamics in quantum systems by focusing on the Kibble–Zurek mechanism, coarsening dynamics, and non-thermal fixed points. The first two subjects have recently been applied to quantum systems to explore universal phenomena. The last one concerns universal scale-invariant relaxation dynamics in isolated quantum systems. We overview the theoretical foundations of the universal properties and recent experiments on these topics on the basis of a quantum spin model, the Gross–Pitaevskii theory, and kinetic equations.We review universal relaxation dynamics in quantum systems by focusing on the Kibble–Zurek mechanism, coarsening dynamics, and non-thermal fixed points. The first two subjects have recently been applied to quantum systems to explore universal phenomena. The last one concerns universal scale-invariant relaxation dynamics in isolated quantum systems. We overview the theoretical foundations of the universal properties and recent experiments on these topics on the basis of a quantum spin model, the Gross–Pitaevskii theory, and kinetic equations.

Nonlinear systems and complexityJan 1, 20201 citation

Pattern formation of quantum Kelvin-Helmholtz instability in binary superfluids

Haruya Kokubo, Kenichi Kasamatsu, Hiromitsu Takeuchi

We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number $We$ , clarifying the microscopic aspects unique to the quantum fluid system. For $We \lesssim 1$ , the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to $We$ . When $We \gtrsim 1$ in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number $We$, clarifying the microscopic aspects unique to the quantum fluid system. For $We \lesssim 1$, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to $We$. When $We \gtrsim 1$ in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.

arXiv:2104.13539Physical Review AAug 13, 202127 citations

Dynamics of Two-Dimensional Quantum Spin Systems

M. S. Makivić, Mark Jarrell

Springer proceedings in physicsJan 1, 19930 citations

Manipulation and dynamics of quantum spin systems

Kristel F. L. Michielsen

Jan 1, 20170 citations

Universal aspects of high-temperature relaxation dynamics in random spin models

Tian-Gang Zhou, Wei Zheng, Pengfei Zhang

Universality is a crucial concept in modern physics, allowing us to capture the essential features of a system’s behavior using a small set of parameters. In this work, we unveil universal spin relaxation dynamics in anisotropic random Heisenberg models with infinite-range interactions at high temperatures. Starting from a polarized state, the total magnetization can relax monotonically or decay with long-lived oscillations, determined by the sign of a universal single function A=-\xi_1^2+\xi_2^2-4\xi_2\xi_3+\xi_3^2 A = − ξ 1 2 + ξ 2 2 − 4 ξ 2 ξ 3 + ξ 3 2 . Here (\xi_1,\xi_3,\xi_3) ( ξ 1 , ξ 3 , ξ 3 ) characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for A>0 A > 0 , with frequency \Omega \propto \sqrt{A} Ω ∝ A . This result is derived from the Kadanoff-Baym equation under the melon diagram approximation, which is consistent with numerical solutions. Furthermore, we verify our theory and approximation using exact diagonalization, albeit for a small system size of N=8 N = 8 . Our study sheds light on the universal aspect of quantum many-body dynamics beyond low energy limit.Universality is a crucial concept in modern physics, allowing us to capture the essential features of a system’s behavior using a small set of parameters. In this work, we unveil universal spin relaxation dynamics in anisotropic random Heisenberg models with infinite-range interactions at high temperatures. Starting from a polarized state, the total magnetization can relax monotonically or decay with long-lived oscillations, determined by the sign of a universal single function A=-\xi_1^2+\xi_2^2-4\xi_2\xi_3+\xi_3^2 A = − ξ 1 2 + ξ 2 2 − 4 ξ 2 ξ 3 + ξ 3 2 . Here (\xi_1,\xi_3,\xi_3) ( ξ 1 , ξ 3 , ξ 3 ) characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for A>0 A > 0 , with frequency \Omega \propto \sqrt{A} Ω ∝ A . This result is derived from the Kadanoff-Baym equation under the melon diagram approximation, which is consistent with numerical solutions. Furthermore, we verify our theory and approximation using exact diagonalization, albeit for a small system size of N=8 N = 8 . Our study sheds light on the universal aspect of quantum many-body dynamics beyond low energy limit.

arXiv:2305.02359SciPost PhysicsApr 8, 20252 citations

We

, clarifying the microscopic aspects unique to the quantum fluid system. For

We \lesssim 1

, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to

We

. When

We \gtrsim 1

in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.