Page 66 - GHES-2-1

Global Health Econ Sustain Quantum Data Lake for epidemic analysis

Table 5. (Continued) PT-symmetry. PT-symmetry is distinct from the condition
of Hermiticity, creating a new kind of quantum theory
Identifier Disease and symptoms with continuation from real-symmetric Hamiltonians to
In2 Oropharyngeal infection associated with head and neck SCC complex Hamiltonians (Bender et al., 2003; Bender, 2003;
In3 Oral cavity infections associated with oropharyngeal cancer Bender, 2005; Bender et al., 2005a; Bender, 2007; Bender
In4 Sporadic infections in mucocutaneous tissue & Darg, 2007; Bender et al., 2013; Bender, 2015; Bender
In5 Children with diarrhea et al., 2017; Bender et al., 2018; Bender, 2020; Bender
In6 Cervical infection et al., 2021). A Hamiltonian is a Dirac Hermitian, and its
In7 Febrile respiratory syndrome energy eigenvalues are always real. As indicated by Bender,
W1 Common warts (verruca vulgaris) a Dirac Hermitian Hamiltonian cannot have a phase
transition where its eigenvalues go from real to complex.
W2 Flat warts (verruca planae) However, PT-symmetric Hamiltonians have two regions
W3 Plantar warts regarding real energy parameter ε – a region of unbroken
W4 Mosaic warts PT-symmetry (ε ≥ 0), where the eigenvalues are all real,
W5 Anogenital warts (condyloma acuminata) and a region of spontaneously broken PT-symmetry (ε < 0),
W6 Butcher’s warts where real eigenvalues transform to the complex plane as
W7 Bowenoid papulosis complex conjugate pairs. If a Hamiltonian has an unbroken
W8 Cystic non-genital warts (plantar epidermoid cysts) PT-symmetry, every eigenstate of the PT-symmetric
non-Hermitian operator satisfies the PT-symmetry,
W9 Deep palmoplantar warts (myrmecia) and the energy levels are real and positive; the time-
W10 Palmoplantar pigmented warts with homogeneous evolution operator e -iHt/ħ is unitary without violating any
intracytoplasmic inclusion bodies of the physical axioms of quantum mechanics. If the
No1 No indication PT-symmetry is spontaneously broken, some eigenstates
No2 Detection on normal skin do not correspond to the eigenstates of the PT operator,
No3 Detection on normal genital area and some pairs of eigenvalues become complex conjugate
No4 Asymptomatic presence in healthy human to each other. PT-symmetric non-Hermitian Hamiltonians
No5 Detection on sun-exposed skin with complex potentials are denoted by Equations VII and
No6 Detection in the oropharynx of healthy human VIII.
S1 WHIM syndrome H = H PT (VII)
S2 Asymptomatic presence in Merkel cell carcinoma patients H = p + x (ix) (VIII)
2
PT
ε
2
(skin tumor, Human polyomavirus 5)
S3 Psoriatic lesions Bender et al. explained that PT-symmetric systems
S4 Pruritic and dyskeratotic dermatoses are intermediate between open (contact with an external
environment) and closed (isolated) systems. The unbroken
S5 Asymptomatic presence in HIV/AIDS patients PT-symmetry phase is in equilibrium and mimics a
S6 Asymptomatic presence in GATA2 deficiency patient closed system. The broken PT-symmetry phase is in non-
S7 Punctate palmoplantar keratoderma equilibrium, mimics an open system, and is characterized
S8 Glans lichen sclerosus by loss to or gain from its environment. The boundary
Abbreviations: AIDS: Acquired immunodeficiency syndrome, between these two regions corresponds to a phase
ASC-US: Atypical squamous cells of undetermined significance, transition (real-to-complex spectral transition) that is
CIN: Cervical intraepithelial neoplasia, HIV: Human called an exceptional point (or Bender-Wu singularity).
immunodeficiency virus, HPV: Human papillomavirus,
HSIL: High-grade squamous intraepithelial lesion, LSIL: Low-grade The phase transition with an exceptional point is of great
squamous intraepithelial lesion, SCC: Squamous cell carcinoma, interest for epidemic modeling.
VIN: Vulvar and vaginal intraepithelial neoplasia, WHIM: Warts,
hypogammaglobulinemia, immunodeficiency, and myelokathexis. 3. Discussion
3.1. Epidemic data complex structure
& Boettcher in 1998 (Bender & Boettcher, 1998). Since
then, this theory has been elaborated by Bender et al., Epidemic data have a very complex structure and the
demonstrating an alternative to the axiom of standard highest possible range of diversity. Raw data for epidemic
quantum mechanics that the Hamiltonian must be modeling are characterized by multidimensionality and
Hermitian. The axiom of Hermiticity may be replaced by uncertainty. While processing epidemic data, the machine’s
the physical condition of space-time reflection symmetry or rational, logical output inevitably comes into direct conflict

Volume 2 Issue 1 (2024) 15 https://doi.org/10.36922/ghes.2148