[Submitted on 10 Nov 2022]

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    Abstract: The construction of exactly-solvable models has recently been advanced by
    considering integrable $T\bar{T}$ deformations and related Hamiltonian
    deformations in quantum mechanics. We introduce a broader class of
    non-Hermitian Hamiltonian deformations in a nonrelativistic setting, to account
    for the description of a large class of open quantum systems, which includes,
    e.g., arbitrary Markovian evolutions conditioned to the absence of quantum
    jumps. We relate the time evolution operator and the time-evolving density
    matrix in the undeformed and deformed theories in terms of integral transforms
    with a specific kernel. Non-Hermitian Hamiltonian deformations naturally arise
    in the description of energy diffusion that emerges in quantum systems from
    time-keeping errors in a real clock used to track time evolution. We show that
    the latter can be related to an inverse $T\bar{T}$ deformation with a purely
    imaginary deformation parameter. In this case, the integral transforms take a
    particularly simple form when the initial state is a coherent Gibbs state or a
    thermofield double state, as we illustrate by characterizing the purity,
    Rényi entropies, logarithmic negativity, and the spectral form factor. As the
    dissipative evolution of a quantum system can be conveniently described in
    Liouville space, we further discuss the spectral properties of the
    Liouvillians, i.e., the dynamical generators associated with the deformed
    theories. As an application, we discuss the interplay between decoherence and
    quantum chaos in non-Hermitian deformations of random matrix Hamiltonians and
    the Sachdev-Ye-Kitaev model.

    Submission history

    From: Apollonas S. Matsoukas-Roubeas [view email]

    Thu, 10 Nov 2022 09:25:59 UTC (6,801 KB)

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