Emergence of singularities from decoherence: Quantum catastrophes

Goldberg, Aaron Z.; Al-Qasimi, Asma; Mumford, J.; O’Dell, D. H. J.

doi:10.1103/physreva.100.063628

Cited by 13 publications

(13 citation statements)

References 129 publications

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“…The apparently purely numerical, non-separable partial-differential nature of such a schematic bound state project redirected, presumably, attention of may interested researchers to the study of the full-fledged, realistic quantum systems in which the cusp-catastrophic phenomena only re-emerged as a consequence of their constructive analysis. For an illustration of this trend let us only recall the very recent study [17] in which the term "quantum catastrophe" has been attributed to an open quantum system (sampled by a Josephson junction made of two Bose-Einstein condensates) in which the authors apply the Thom's concepts of the fold and cusp catastrophes to the caustics in the number-difference probability distribution.…”

Section: Cusp Potentials In More Than One Dimensionmentioning

confidence: 99%

Polynomial potentials and coupled quantum dots in two and three dimensions

Znojil

2020

Annals of Physics

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Keywords:.coupled quantum dots; two-and three-dimensional models; non-separable polynomial potentials; probability density bifurcations; PACS number: PACS 03.65.Ge -Solutions of wave equations: bound states 1 znojil@ujf.cas.cz AbstractPolynomial potentials V (x) = x 4 + O(x 2 ) and V (x) = x 6 + O(x 4 ) were introduced, in the Thom's purely geometric classification of bifurcations, as the benchmark models of the so called cusp catastrophes and of the so called butterfly catastrophes, respectively. Due to their asymptotically confining property, these two potentials are exceptional, viz., able to serve similar purposes even after quantization, in the presence of tunneling. In this paper the idea is generalized to apply also to quantum systems in two and three dimensions. Two related technical obstacles are addressed, both connected with the non-separability of the underlying partial differential Schrödinger equations. The first one [viz., the necessity of a non-numerical localization of the extremes (i.e., of the minima and maxima) of V (x, y, . . .)] is resolved via an ad hoc reparametrization of the coupling constants. The second one [viz., the necessity of explicit construction of the low lying bound states ψ(x, y, . . .)] is circumvented by the restriction of attention to the dynamical regime in which the individual minima of V (x, y, . . .) are well separated, with the potential being locally approximated by the harmonic oscillator wells simulating a coupled system of quantum dots (a.k.a. an artificial molecule). Subsequently it is argued that the measurable characteristics (and, in particular, the topologically protected probability-density distributions) could bifurcate in specific evolution scenarios called relocalization catastrophes.

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Section: Cusp Potentials In More Than One Dimensionmentioning

confidence: 99%

Polynomial potentials and coupled quantum dots in two and three dimensions

Znojil

2020

Annals of Physics

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“…In this domain it offers, first of all, a systematic classification of structures and of the possible changes of structures of the long-term classical equilibria 5 . The applicability and/or an immediate transfer of these ideas to quantum systems are limited 6 – 10 .…”

Section: Introductionmentioning

confidence: 99%

Confluences of exceptional points and a systematic classification of quantum catastrophes

Znojil

2022

Sci Rep

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In the problem of classification of the parameter-controlled quantum phase transitions, attention is turned from the conventional manipulations with the energy-level mergers at exceptional points to the control of mergers of the exceptional points themselves. What is obtained is an exhaustive classification which characterizes every phase transition by the algebraic and geometric multiplicity of the underlying confluent exceptional point. Typical qualitative characteristics of non-equivalent phase transitions are illustrated via a few elementary toy models.

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“…Inspired by ideas from quantum optics [126,127], we have initiated a theory of many-body (second quantized) caustics in a series of papers on spin chains [128] and the BH dimer model [64][65][66]129]. In the former case, the celebrated "light-cones" observed [32,55,56] to govern the propagation of correlations following a quench are shown to in fact be caustics akin to ship wakes.…”

Section: Introductionmentioning

confidence: 99%

Caustics in quantum many-body dynamics

Kirkby,

Yee,

Shi

et al. 2021

Preprint

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Caustics are a striking phenomena in natural optics and hydrodynamics: high-amplitude characteristic patterns that are singular in the short wavelength limit. We use exact numerical and approximate semiclassical analytic methods to study quantum versions of caustics that form in Fock space during far-from-equilibrium dynamics following a quench in the Bose Hubbard dimer and trimer models. Due to interparticle interactions, both models are nonlinear and the trimer is also nonintegrable. The caustics exhibit a hierarchy of morphologies described by catastrophe theory that are stable against perturbations and hence occur generically. The dimer case gives rise to discretized versions of folds and cusps which are the simplest two of Thom's catastrophes. The extra dimension available in the trimer case allows for higher catastrophes including the codimension-3 hyperbolic umbilic and elliptic umbilic catastrophes which we argue are organized by, and projections of, an 8-dimensional corank-2 catastrophe known as X9. These results indicate a hitherto unrecognized form of universality in quantum many-body dynamics organized by singularities.

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Emergence of singularities from decoherence: Quantum catastrophes

Cited by 13 publications

References 129 publications

Polynomial potentials and coupled quantum dots in two and three dimensions

Polynomial potentials and coupled quantum dots in two and three dimensions

Confluences of exceptional points and a systematic classification of quantum catastrophes

Caustics in quantum many-body dynamics

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