Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

AbstractWe study the isotropic XY quantum spin chain with a time-periodic transverse magnetic field acting on a single site. The asymptotic dynamics is described by a highly resonant Floquet–Schrödinger equation, for which we show the existence of a periodic solution if the forcing frequency is away from a discrete set of resonances. This in turn implies the state of the quantum spin chain to be asymptotically a periodic function synchronised with the forcing, also at arbitrarily low non-resonant frequencies. The behaviour at the resonances remains a challenging open problem.

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Exact solution of an integrable quantum spin chain with competing interactions

Chinese Physics B ◽

10.1088/1674-1056/abfa0a ◽

2021 ◽

Author(s):

Jian Wang ◽

Yi Qiao ◽

Junpeng Cao ◽

Wen-Li Yang

Keyword(s):

Exact Solution ◽

Spin Chain ◽

Quantum Spin ◽

Quantum Spin Chain ◽

Competing Interactions ◽

Integrable Quantum

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Long-time dynamics of a class of nonlocal extensible beams with time delay

Mathematics and Mechanics of Solids ◽

10.1177/10812865211019457 ◽

2021 ◽

pp. 108128652110194

Author(s):

Fengjuan Meng ◽

Cuncai Liu ◽

Chang Zhang

Keyword(s):

Time Delay ◽

Stability Property ◽

Beam Equation ◽

Exponential Attractors ◽

Time Dynamics ◽

Bounded Smooth Domain ◽

Finite Dimensional ◽

Long Time ◽

Bounded Smooth ◽

Long Time Dynamics

This work is devoted to the following nonlocal extensible beam equation with time delay: [Formula: see text] on a bounded smooth domain [Formula: see text]. The main purpose of this paper is to consider the long-time dynamics of the system. Under suitable assumptions, the quasi-stability property of the system is established, based on which the existence and regularity of a finite-dimensional compact global attractor are obtained. Moreover, the existence of exponential attractors is proved.

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T − W relation and free energy of the Heisenberg chain at a finite temperature

Journal of High Energy Physics ◽

10.1007/jhep07(2021)133 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Pengcheng Lu ◽

Yi Qiao ◽

Junpeng Cao ◽

Wen-Li Yang ◽

Kang jie Shi ◽

...

Keyword(s):

Free Energy ◽

Spin Chain ◽

Quantum Spin ◽

Heisenberg Chain ◽

Quantum Spin Chain ◽

Heisenberg Spin ◽

Heisenberg Spin Chain ◽

Lattice Quantum ◽

Quantum Integrable Models ◽

Invariant Quantum

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

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