arXiv subjects

Seyed Mahmoud Manjegani

Publications and source records attributed to Seyed Mahmoud Manjegani.

4 recordsLinked to original sources

arXiv2026

Local Determinant Defects and Low-Energy Subspace Stability in Semifinite von Neumann Algebras

We give a finite-temperature test for the stability of low-energy spectral subspaces. The test uses a local determinant defect for the alpha-z Renyi kernel of two Gibbs states and bounds the tracial L2 distance between their low-energy projections. The main tool is a spectral-flattening principle for bounded positive injective operators in a semifinite von Neumann algebra. It reduces the local product defect to an exact two-projection formula. The thermal result applies to lower-bounded affiliated Hamiltonians with trace-class Gibbs operators and does not require the Hamiltonians to be close in operator norm. We give an infinite-level example with unbounded Hamiltonians. For matrices, the result gives a sum of principal-angle remainders. For qubits, the defect and the thermal gaps determine the ground-state overlap exactly. The same estimate gives a uniform error bound for bounded observables in an effective low-energy model. We also prove the determinant inequalities, their equality cases, and z-monotonicity in matrix, finite, and semifinite settings.

math-ph↗

arXiv2026

Spectral Equality for Tropical Totally Nonnegative Matrices: Dominant Cancellation and Newton Polygons

Let $\mathbf A$ be a totally nonnegative matrix over a real closed non-Archimedean valued field, and suppose that its valuation $A$ is tropically totally nonnegative. Although the valuations of the classical eigenvalues are weakly majorized by the tropical eigenvalues of $A$, equality can fail through cancellation. We give a necessary and sufficient condition for equality. The only obstruction is dominant cancellation in the principal minors that give the essential coefficients of the tropical characteristic polynomial. In other words, equality holds exactly when the classical and tropical Newton polygons agree at the breakpoints determined by the diagonal entries. We describe the exceptional lifts by explicit polynomial equations in the leading coefficients. We also study these equations on each irreducible component of the admissible parameter space. Finally, we give a complete $3\times 3$ criterion and a family that contains both ordinary lifts with spectral equality and exceptional totally nonnegative lifts without it.

math.AC↗

arXiv2026

Trace-Norm Overlaps of Quantum States: Interpolation, Equality, and Data-Processing Rigidity

Let $ρ$ and $σ$ be density operators on a separable Hilbert space. For $0<α<1$, we study the directed trace-norm overlap $Φ_α(ρ,σ)=\|ρ^ασ^{1-α}\|_1$ and its symmetrized form $\mathcal F_α(ρ,σ)=\frac12\bigl(Φ_α(ρ,σ)+Φ_{1-α}(ρ,σ)\bigr)$. At $α=\tfrac12$, both quantities coincide with the root Uhlmann--Jozsa fidelity. Our aim is not to introduce a new notion of fidelity, but to understand how these overlaps vary with the parameter and when equality occurs in the resulting inequalities. We first prove that $α\mapstoΦ_α(ρ,σ)$ is log-convex. This yields a sharp lower bound for $\mathcal F_α$ in terms of the root fidelity, together with a stronger intermediate geometric-mean bound. We also show that $Φ_α$ is the trace functional $Q_{α,1/2}$ associated with the $α$-$z$ Renyi divergence, which connects the directed overlap with the known $α$-$z$ Renyi theory. We then determine the exact data-processing behavior of the symmetrized family. Universal monotonicity under quantum channels holds only at $α=\tfrac12$; for every other value of $α$, it already fails under diagonal pinching of faithful real qubit states. In finite dimensions, we give a complete spectral description of the equality cases and provide explicit noncommuting examples. We also discuss some natural questions about overlap-preserving maps. Finally, we prove that the difference between the Petz overlap and the directed trace-norm overlap vanishes exactly when $ρ$ and $σ$ commute, without requiring either faithfulness or any additional support assumption.

quant-ph↗

arXiv2022

Majorization and Semi-Doubly Stochastic Operators on $L^1(X)$

This article is devoted to a study of majorization based on semi-doubly stochastic operators (denoted by $S\mathcal{D}(L^1)$) on $L^1(X)$ when $X$ is a $σ$-finite measure space. We answered Mirsky's question and characterized the majorization by means of semi-doubly stochastic maps on $L^1(X)$. We collect some results of semi-doubly stochastic operators such as a strong relation of semi-doubly stochastic operators and integral stochastic operators, and relatively weakly compactness of $S_f=\{Sf: ~S\in S\mathcal{D}(L^1)\}$ when $f$ is a fixed element in $L^1(X)$ by proving equi-integrability of $S_f$.

quant-ph↗