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Time evolution of spread complexity and statistics of work done in quantum quenches
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abstract
We relate the probability distribution of the work done on a statistical system under a sudden quench to the Lanczos coefficients corresponding to evolution under the post-quench Hamiltonian. Using the general relation between the moments and the cumulants of the probability distribution, we show that the Lanczos coefficients can be identified with physical quantities associated with the distribution, e.g., the average work done on the system, its variance, as well as the higher order cumulants. In a sense this gives an interpretation of the Lanczos coefficients in terms of experimentally measurable quantities. Consequently, our approach provides a way towards understanding spread complexity, a quantity that measures the spread of an initial state with time in the Krylov basis generated by the post quench Hamiltonian, from a thermodynamical perspective. We illustrate these relations with two examples. The first one involves quench done on a harmonic chain with periodic boundary conditions and with nearest neighbour interactions. As a second example, we consider mass quench in a free bosonic field theory in $d$ spatial dimensions in the limit of large system size. In both cases, we find out the time evolution of the spread complexity after the quench, and relate the Lanczos coefficients with the cumulants of the distribution of the work done on the system.
Forward citations
Cited by 5 Pith papers
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Analytic Spread Complexity from Level Statistics: From Chaos to Integrability
The finite-time peak of spread complexity is controlled by the Fourier transform of the nearest-neighbour energy-level spacing distribution.
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In the brickwall model of a BTZ black hole, hand-tuned Gaussian randomness at a stretched horizon reproduces random-matrix-theory spectral statistics and Krylov complexity peaks for scalar and fermionic probes.
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Krylov Complexity in Mixed Phase Space
The Krylov complexity peak height correlates with the Brody parameter in mixed-phase-space quantum systems, diminishing as the spectrum becomes Poissonian.
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Statistics and Complexity of Wavefunction Spreading in Quantum Dynamical Systems
The moments of the spreading-operator measurement distribution are generalized spread complexities, which for GUE Hamiltonians peak more sharply at higher order and obey a norm bound.
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Revisit the relationship between spread complexity rate and radial momentum
The paper shows that two proposed bulk momentum and boundary spread complexity correspondences are consistent, and that the match extends to any particle mass in AdS3.
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