English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Given a time-independent Hamiltonian $\widetilde H$, one can construct atime-dependent Hamiltonian $H_t$ by means of the gauge transformation $H_t=U_t\widetilde H \, U^\dagger_t-i\, U_t\, \partial_t U_t^\dagger$. Here $U_t$ isthe unitary transformation that relates the solutions of the correspondingSchrodinger equations. In the many-body case one is usually interested inHamiltonians with few-body (often, at most two-body) interactions. We refer tosuch Hamiltonians as "physical". We formulate sufficient conditions on $U_t$ensuring that $H_t$ is physical as long as $\widetilde H$ is physical (and viceversa). This way we obtain a general method for finding such pairs of physicalHamiltonians $H_t$, $\widetilde H$ that the driven many-body dynamics governedby $H_t$ can be reduced to the quench dynamics due to the time-independent$\widetilde H$. We apply this method to a number of many-body systems. First wereview the mapping of a spin system with isotropic Heisenberg interaction andarbitrary time-dependent magnetic field to the time-independent system withouta magnetic field [F. Yan, L. Yang, B. Li, Phys. Lett. A 251, 289 (1999); Phys.Lett. A 259, 207 (1999)]. Then we demonstrate that essentially the same gaugetransformation eliminates an arbitrary time-dependent magnetic field from asystem of interacting fermions. Further, we apply the method to the quantumIsing spin system and a spin coupled to a bosonic environment. We also discussa more general situation where $\widetilde H = \widetilde H_t$ istime-dependent but dynamically integrable.

A map between time-dependent and time-independent quantum many-body Hamiltonians