dorsal/arxiv
View SchemaGeneral conditions for a quantum adiabatic evolution
| Authors | Daniel Comparat |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607118 |
| URL | https://arxiv.org/abs/quant-ph/0607118 |
Abstract
The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively valid for scaled timed hamiltonian and resonance processes as well as off resonance possible constructive St\"{u}ckelberg interference effects violate this usual condition for general hamiltionian. More general adiabatic condition and exact bounds for adiabatic quantum evolution are derived and studied in the framework of a two-level system. The usual criterion is restored for real two level hamiltonian with small number of monotonicity changes of the hamiltonian matrix elements and its derivative.
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"abstract": "The smallness of the variation rate of the hamiltonian matrix elements\ncompared to the (square of the) energy spectrum gap is usually believed to be\nthe key parameter for a quantum adiabatic evolution. However it is only\nperturbatively valid for scaled timed hamiltonian and resonance processes as\nwell as off resonance possible constructive St\\\"{u}ckelberg interference\neffects violate this usual condition for general hamiltionian. More general\nadiabatic condition and exact bounds for adiabatic quantum evolution are\nderived and studied in the framework of a two-level system. The usual criterion\nis restored for real two level hamiltonian with small number of monotonicity\nchanges of the hamiltonian matrix elements and its derivative.",
"arxiv_id": "quant-ph/0607118",
"authors": [
"Daniel Comparat"
],
"categories": [
"quant-ph"
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"title": "General conditions for a quantum adiabatic evolution",
"url": "https://arxiv.org/abs/quant-ph/0607118"
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