We present a conditional construction of candidate CSL-type collapse-noise correlators inspired by Generalized Trace Dynamics (GTD). The construction is not a parameter-free derivation from the minimal GTD Grassmann algebra. It rests on a chain of explicit structural postulates, listed in Section 1; within that auxiliary structure the spectral form and amplitude follow by computation rather than by phenomenological fitting. The resulting narrow-band spectrum at the Hubble scale lies outside the bands of current CSL bounds, so the framework is not in tension with existing high-frequency data. We compute the two-point function of a candidate collapse-noise operator associated with the GTD aikyon decomposition $q_i = q_B + a_0β_i q_F$ . In the minimal Grassmann algebra, $q_F$ appears only multiplied by Grassmann generators $β_i$ , the reduction of $\mathrm{Tr}(q_F^\daggerΓ^μq_F)$ to ghost-mode operators is obstructed by the nilpotent $δβ= β_2 - β_1$ , and the pure-fermion coefficient $β_1β_2$ has no ordinary sign, modulus, or inverse. We therefore introduce an auxiliary canonical fermionic Fock-space sector for $q_F$ , equivalently replacing the nilpotent pure-fermion coefficient by an ordinary effective scalar body parameter. This replacement is an independent structural postulate, not a consequence of the original minimal action. Under this auxiliary postulate, together with a scalar bilinear $J = \mathrm{Tr}(q_F^\dagger q_F)$ as bath operator, positive-norm canonical quantization, and an effective sign choice $σ= \pm1$ for the scalarized pure-fermion sector, elementary Wick contraction gives a Wightman line at $|ω| = 2ω_0$ with amplitude $A_J = (\hbar/2m_Rω_0 L_{\mathrm{aik}}^2)^2\cdot N\cdot D$ . The cosmological identification $ω_0 \sim H_0$ places the line at twice the Hubble scale. [truncated]We present a conditional construction of candidate CSL-type collapse-noise correlators inspired by Generalized Trace Dynamics (GTD). The construction is not a parameter-free derivation from the minimal GTD Grassmann algebra. It rests on a chain of explicit structural postulates, listed in Section 1; within that auxiliary structure the spectral form and amplitude follow by computation rather than by phenomenological fitting. The resulting narrow-band spectrum at the Hubble scale lies outside the bands of current CSL bounds, so the framework is not in tension with existing high-frequency data. We compute the two-point function of a candidate collapse-noise operator associated with the GTD aikyon decomposition $q_i = q_B + a_0β_i q_F$. In the minimal Grassmann algebra, $q_F$ appears only multiplied by Grassmann generators $β_i$, the reduction of $\mathrm{Tr}(q_F^\daggerΓ^μq_F)$ to ghost-mode operators is obstructed by the nilpotent $δβ= β_2 - β_1$, and the pure-fermion coefficient $β_1β_2$ has no ordinary sign, modulus, or inverse. We therefore introduce an auxiliary canonical fermionic Fock-space sector for $q_F$, equivalently replacing the nilpotent pure-fermion coefficient by an ordinary effective scalar body parameter. This replacement is an independent structural postulate, not a consequence of the original minimal action. Under this auxiliary postulate, together with a scalar bilinear $J = \mathrm{Tr}(q_F^\dagger q_F)$ as bath operator, positive-norm canonical quantization, and an effective sign choice $σ= \pm1$ for the scalarized pure-fermion sector, elementary Wick contraction gives a Wightman line at $|ω| = 2ω_0$ with amplitude $A_J = (\hbar/2m_Rω_0 L_{\mathrm{aik}}^2)^2\cdot N\cdot D$. The cosmological identification $ω_0 \sim H_0$ places the line at twice the Hubble scale. [truncated]

quant-pharXiv:2605.29374May 29, 20260 citations

Discrete Spectrum of the Three-Particle Hamiltonian Operator

Dimitri R. Yafaev

Soviet physics. DokladyMar 1, 19730 citations

Let the Qudit Do the Jacobi: A Structured Quantum Algorithm for Spectral Decomposition

A. Mandilara

Jacobi diagonalization is a long-established numerical algorithm for the spectral decomposition of Hermitian and, more generally, normal matrices. In this work, we develop a qudit-native quantum realization of the Jacobi diagonalization algorithm for unknown unitary operators. The proposed framework avoids explicit reconstruction of the operator and controlled-unitary operations. Each elementary two-parameter Givens rotation is implemented through two sequential single-parameter quantum variational optimizations that are directly accessible experimentally. An interferometric protocol is further introduced for extracting the eigenvalues of the diagonalized unitary, up to an overall global phase. Numerical simulations on ensembles of Haar-random unitary matrices demonstrate that the proposed algorithm preserves the characteristic convergence behavior of the classical Jacobi method and exhibits the expected quadratic scaling in the number of elementary operations with the dimension $d$ , comparable to its classical counterpart. The results establish the proposed algorithm as a structured quantum numerical linear algebra algorithm naturally suited to qudit architectures and provide a bridge between classical iterative matrix algorithms and their quantum realizations.Jacobi diagonalization is a long-established numerical algorithm for the spectral decomposition of Hermitian and, more generally, normal matrices. In this work, we develop a qudit-native quantum realization of the Jacobi diagonalization algorithm for unknown unitary operators. The proposed framework avoids explicit reconstruction of the operator and controlled-unitary operations. Each elementary two-parameter Givens rotation is implemented through two sequential single-parameter quantum variational optimizations that are directly accessible experimentally. An interferometric protocol is further introduced for extracting the eigenvalues of the diagonalized unitary, up to an overall global phase. Numerical simulations on ensembles of Haar-random unitary matrices demonstrate that the proposed algorithm preserves the characteristic convergence behavior of the classical Jacobi method and exhibits the expected quadratic scaling in the number of elementary operations with the dimension $d$, comparable to its classical counterpart. The results establish the proposed algorithm as a structured quantum numerical linear algebra algorithm naturally suited to qudit architectures and provide a bridge between classical iterative matrix algorithms and their quantum realizations.

quant-pharXiv:2607.13244Jul 16, 20260 citations

Calculation of the two-body correlation function for Fermion systems

Stefano Fantoni, Sergio Rosati

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJul 1, 197473 citations

Shiva and Kali diagrams for composite quantum particle many-body effects

Monique Combescot, Odile Betbeder-Matibet

For half a century, Feynman diagrams have provided an enlightening way of representing many-body effects between elementary fermions and bosons. They however are quite inappropriate to visualize fermion exchanges taking place between a large number of composite quantum particles. We propose to replace them by "Shiva diagrams" for cobosons made of two fermions and by Shiva-like and "Kali diagrams" for cofermions made of three fermions. We also show how these fermion exchanges formally appear in a many-body theory appropriate to composite quantum particles. This theory relies on an operator algebra based on commutators and anticommutators, the usual scalar algebra based on Green functions being valid for elementary bosons or fermions having strict commutation relations, only.For half a century, Feynman diagrams have provided an enlightening way of representing many-body effects between elementary fermions and bosons. They however are quite inappropriate to visualize fermion exchanges taking place between a large number of composite quantum particles. We propose to replace them by "Shiva diagrams" for cobosons made of two fermions and by Shiva-like and "Kali diagrams" for cofermions made of three fermions. We also show how these fermion exchanges formally appear in a many-body theory appropriate to composite quantum particles. This theory relies on an operator algebra based on commutators and anticommutators, the usual scalar algebra based on Green functions being valid for elementary bosons or fermions having strict commutation relations, only.

arXiv:0902.4588Feb 26, 20091 citation

Eigenvalues of fermion density matrices

不可止佐々木

Jan 1, 19640 citations

q_i = q_B + a_0β_i q_F

. In the minimal Grassmann algebra,

q_F

appears only multiplied by Grassmann generators

β_i

, the reduction of

\mathrm{Tr}(q_F^\daggerΓ^μq_F)

to ghost-mode operators is obstructed by the nilpotent

δβ= β_2 - β_1

, and the pure-fermion coefficient

β_1β_2

has no ordinary sign, modulus, or inverse. We therefore introduce an auxiliary canonical fermionic Fock-space sector for

q_F

, equivalently replacing the nilpotent pure-fermion coefficient by an ordinary effective scalar body parameter. This replacement is an independent structural postulate, not a consequence of the original minimal action. Under this auxiliary postulate, together with a scalar bilinear

J = \mathrm{Tr}(q_F^\dagger q_F)

as bath operator, positive-norm canonical quantization, and an effective sign choice

σ= \pm1

for the scalarized pure-fermion sector, elementary Wick contraction gives a Wightman line at

|ω| = 2ω_0

with amplitude

A_J = (\hbar/2m_Rω_0 L_{\mathrm{aik}}^2)^2\cdot N\cdot D

. The cosmological identification

ω_0 \sim H_0

places the line at twice the Hubble scale. [truncated]

d

, comparable to its classical counterpart. The results establish the proposed algorithm as a structured quantum numerical linear algebra algorithm naturally suited to qudit architectures and provide a bridge between classical iterative matrix algorithms and their quantum realizations.