Proves explicit velocity upper bounds for periodic quantum walks including linear bottleneck effects for small transmission parameters and harmonic-mean bounds, plus a general lower bound.
Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
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abstract
We investigate quantum dynamics with the underlying Hamiltonian being a Jacobi or a block Jacobi matrix with the diagonal and the off-diagonal terms modulated by a periodic or a limit-periodic sequence. In particular, we investigate the transport exponents. In the periodic case we demonstrate ballistic transport, while in the limit-periodic case we discuss various phenomena such as quasi-ballistic transport and weak dynamical localization. We also present applications to some quantum many body problems. In particular, we establish for the anisotropic XY chain on $\mathbb{Z}$ with periodic parameters an explicit strictly positive lower bound for the Lieb-Robinson velocity.
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math-ph 2years
2026 2verdicts
UNVERDICTED 2roles
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Sufficient conditions are proven for zero velocity in position-dependent 1D quantum walks via an a priori velocity bound depending on sparse site sequences and local coin parameters, with extensions to random cases and CMV matrices.
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Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks
Proves explicit velocity upper bounds for periodic quantum walks including linear bottleneck effects for small transmission parameters and harmonic-mean bounds, plus a general lower bound.
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Absence of Ballistic Transport in Quantum Walks with Asymptotically Reflecting Sites
Sufficient conditions are proven for zero velocity in position-dependent 1D quantum walks via an a priori velocity bound depending on sparse site sequences and local coin parameters, with extensions to random cases and CMV matrices.