arXiv subjects

Masahiro Kaminaga

Publications and source records attributed to Masahiro Kaminaga.

At least 19 recordsLinked to original sources

arXiv2026

Causality, Redshift, and Matching-Scale Cancellation for Reflective Black-Hole Horizons

The Boltzmann flux reflectivity used in quantum-horizon models does not by itself define a causal black-hole boundary response. We study two related questions for stationary Schwarzschild scattering. First, a classical Hardy-space condition excludes an exact Boltzmann modulus on the entire positive frequency axis for any nonzero bounded causal reflection amplitude at a fixed matching plane. We construct causal completions that preserve the modulus on any prescribed finite band. Second, we prove a low-frequency outer-phase expansion for a class of completions with fixed profiles and a common Boltzmann slope, including an exact-band completion and a smooth crossover completion. The logarithmic coefficient is common to this class, while the linear constant is an explicit functional of the completion. When the fixed proper-frame cutoff is redshifted to the matching surface and the local temperature is the Tolman redshift of the Hawking temperature, the outer phase cancels the leading logarithmic dependence of the propagation phase on the matching distance. The geometric remainder is quadratic in the proper distance, while a separate dispersive remainder depends on the completion. This is a low-energy comparison of specified response families, not an exact matching invariance or a phase fixed by causality alone. In an axial Schwarzschild example at a fixed matching plane, accounting for the predicted linear-delay difference reduces the maximum relative cavity-factor difference between two cutoffs from about $21\%$ to $0.11\%$ on the sampled frequency band. A passive quantum completion supplies the associated absorption-noise relation and checks the consistency of the asymptotic output.

gr-qc↗

arXiv2026

Optimal Sample Exponents for Direct Discrete-Gaussian SVP Search on Haar Random Lattices

We determine the optimal sample exponent for direct discrete Gaussian SVP search on Haar random unimodular lattices, counting zero outputs. The output is one sampled vector, optionally divided by the greatest common divisor of its lattice coordinates. For every fixed approximation factor $1\leqγ<\sqrt e$, the exponent is $γ^2/(2e)-\logγ$ in natural logarithmic units; it is zero for $γ\geq\sqrt e$. For exact SVP this gives $0.2653689\ldots$ in base two. The converse permits arbitrary positive widths chosen from the lattice and all previous outputs, and a fixed width attains every exponent above the threshold. Aggarwal, Dadush, Regev, and Stephens-Davidowitz already give a width within a factor two of optimal for exact SVP on each lattice. We determine the explicit Haar typical rate and show that primitive reduction preserves it. An explicit finite dimensional converse controls all widths simultaneously, including recovery from long multiples; together with finite attainment bounds, it yields query guarantees in both directions. The proof uses random lattice moments and a pointwise Gaussian bound optimized over the width. We account for sampling error and separate sample requirements from generation costs in comparisons with the random lattice search of Pouly and Shen and later algorithms.

math.PR↗

arXiv2026

Controlled atomic limit and analytic density of states in a strongly attractive random Kronig-Penney model

We study the negative-energy density of states of a one-dimensional random Kronig-Penney model with independent and identically distributed attractive delta interactions. Each isolated interaction of strength $q<0$ has a bound state of energy $-q^2/4$. Using the inverse coupling $V=-1/q$, the Krein resolvent formula reduces the continuum problem to a lattice operator with random diagonal entries and energy-dependent hopping. Under a local analyticity assumption on the coupling density, we prove a controlled atomic limit. After energy is divided by the square of the attraction strength, the scaled density of states approaches the density of isolated binding energies with an exponentially small error on compact interior intervals. An explicit strong-attraction condition also gives real-analyticity of the density of states and the integrated density of states on the corresponding negative-energy interval. A support condition ensures that this interval belongs to the almost-sure spectrum. For a uniform coupling law, we obtain a concrete sufficient threshold and illustrate the spectral profile with finite-volume calculations based on the exact point-interaction recurrence.

math-ph↗

arXiv2026

Landau-level splitting by a circular $δ$ interaction: boundary overlap and the hard-wall crossover

A thin circular barrier lifts the angular momentum degeneracy of Landau states according to their overlap with the barrier. We quantify this effect for the two-dimensional Landau Hamiltonian with a circular $δ$ interaction of radius $a$ and strength $α$. Starting from the known Kummer-function matching equation, we separate the contribution of one Landau level from the remaining radial spectrum. For fixed $n$, $B>0$, $a>0$, and $α\ne0$, we prove $$ E_{n,m}^{(α)}-B(2n+1) =αc_{n,m}\left[1-\frac{αa}{2m}+O(m^{-2})\right] $$ as $m\to+\infty$, where $c_{n,m}$ is an explicit boundary trace weight with factorial decay. The proof gives a uniform estimate of the regular part of the radial resolvent, including at the Landau energy. This estimate also yields an expansion uniform over all repulsive strengths, with crossover parameter $αa/(2m)$, and the exterior Dirichlet limit. Thus a small energy shift does not by itself guarantee relative accuracy of the projected energy shift: the correction depends on the wall strength compared with the local centrifugal scale. The state nevertheless remains close in norm to the chosen Landau subspace, uniformly for repulsion. We also obtain the boundary density from the response to $α$ and distinguish nodal Landau states from coupling-dependent level crossings. High-precision calculations test both the fixed-strength expansion and the crossover to a hard wall.

math-ph↗

arXiv2026

Collective Onset of Matter-Induced Scalarization around a Black Hole with Two Thin Shells

We study the linear onset of matter-induced scalarization for a static black hole surrounded by two spatially separated thin matter shells. We assume that the conformal matter coupling is unity on the scalar-free background and that its logarithmic derivative vanishes there. The scalar perturbation then decouples from the metric and matter perturbations at first order, while the invariant surface traces of the shells give singular terms in the scalar equation. For a static spherical black-hole exterior with no bulk scalar effective-mass term between the shells, the onset reduces to the finite-rank condition $$ 1-a_1-a_2+(1-χ)a_1a_2=0, \qquad χ=\frac{{\cal S}(R_2)}{{\cal S}(R_1)}, $$ where $a_j$ is the attractive strength of shell $j$ normalized by its one--shell threshold on the same background and ${\cal S}$ is the static radial resistance. This relation shows that two individually subcritical shells can collectively destabilize the scalar-free black hole. We derive the critical scalar cloud in closed form and verify numerically, in the Schwarzschild probe problem, that a growing mode with a finite growth rate appears beyond the threshold. For an exact scalar-free background consisting of three Schwarzschild regions joined by two Israel shells, we separately derive the static onset condition and the corresponding critical cloud. The exact Israel trace also exhibits a sign transition whose light-shell limit occurs at the Schwarzschild photon sphere.

gr-qc↗

arXiv2026

Black-Hole Echo Resonance Spectra and Source Dependence in a Controlled Transfer-Function Model

Echo models phenomenologically encode possible near-horizon structure by replacing the purely ingoing horizon-side condition with an effective reflecting inner boundary near the would-be horizon. We study this idea in a controlled transfer-function model consisting of a compactly supported one-dimensional barrier and a Robin wall at $x=-L$, where $L>0$ is the cavity length measured in the tortoise coordinate. The aim is not to propose a new echo mechanism or to make an observational claim, but to analyze the standard cavity denominator in a controlled model with explicit normalizations. For this model, we prove a local one-zero-per-cell result with an $O(L^{-2})$ localization error and derive a source-to-observer factorization which separates the homogeneous poles from the source-dependent residues. To test the physical robustness of the mechanism, we also perform direct numerical calculations for the untruncated axial Regge-Wheeler potential. The computed resonances form the same nearly equally spaced comb, their deviations from the first asymptotic centers are numerically consistent with $L^{-2}$ scaling, and smooth source profiles modify the peak weights without changing the homogeneous pole locations. The rigorous $O(L^{-2})$ theorem remains restricted to the compactly supported model.

gr-qc↗

arXiv2026

A Transmission Framework for Stark Operators with $δ$ Interactions on a Compact Lipschitz Interface

We study an elliptic transmission problem associated with a Stark operator and a $δ$ interaction on a compact Lipschitz interface in $\mathbb R^d$. The background differential expression contains the unbounded coefficient $-Fx_1$, and the interface strength is an arbitrary real function $α\in L^\infty(Σ)$. We introduce a transmission class with piecewise $H^1$ regularity near the interface and an $L^2$ action away from it. This setting gives Dirichlet traces in $H^{1/2}(Σ)$ and weak normal derivatives in $H^{-1/2}(Σ)$ without assuming smoothness of $Σ$. We prove that the transmission conditions define a self-adjoint realization of the formal operator $H_{F,0}+αδ_Σ$. We also obtain a boundary resolvent formula in terms of the free Stark resolvent and a bounded operator from $H^{-1/2}(Σ)$ to $H^{1/2}(Σ)$. The formula implies that the resolvent difference is compact on $L^2(\mathbb R^d)$. Consequently, if $F\ne0$, the essential spectrum of the interacting operator is $\mathbb R$. The result supplies a direct boundary reduction for an interface problem whose background potential is not bounded and is not translation invariant.

math-ph↗

arXiv2026

Thermal Concentration and Poisson-Dirichlet Edge Statistics for Random-Lattice Gibbs Ensembles

We study Gibbs measures on high-dimensional Haar-random unimodular lattices, where the energy of a lattice vector is its squared Euclidean norm. The random lattice is viewed as quenched geometric disorder, and $c>0$ denotes the scaled inverse temperature. We first analyze the edge window of vectors whose length is within the factor $e^{a/n}$ of the shortest length, with fixed $a$ as $n\to\infty$. For the full sign-class Gibbs ensemble, we prove a Poisson point process limit theorem for the Gibbs mass of this window. The mass vanishes in probability for $0 1$ it has a nontrivial Poisson limit, and the ranked Gibbs weights converge to the Poisson-Dirichlet distribution with parameter $1/c$. We then pass to a primitive-direction Gibbs ensemble and consider a fixed approximation factor $γ>1$. For this modified ensemble, we prove a weighted moment formula and a quenched thermal concentration result in the high-temperature range $0<c<1$. This yields the primitive fixed-factor visibility curve $c=γ^{-2}$ for approximate shortest directions. More precisely, the primitive Gibbs mass of the fixed-factor window tends to zero for $c<γ^{-2}$, to one for $γ^{-2}<c<1$, and to $1/2$ at the critical boundary $c=γ^{-2}$. Thus the fixed-factor theorem is a visibility statement for an idealized primitive target measure, not for the original full lattice Gibbs measure. The results provide a random-lattice thermodynamic reference model for Gibbs targets related to approximate shortest vectors, without implying an efficient algorithm for the shortest vector problem.

math.PR↗

arXiv2026

Strong-disorder expansion of the root-averaged density of states for the Anderson model on the Bethe lattice

We study the root-averaged density of states for the Anderson model on the Bethe lattice in the strong-disorder regime. Here the density of states means the root-averaged spectral measure, not a finite-volume eigenvalue counting limit. We assume that the single-site distribution has compact support and has a locally analytic density on an interval $I^\sharp$ containing a given interval $I$. Combining the random-walk expansion on the tree with a complex-analytic argument for the single-site Stieltjes transforms, we prove that the scaled averaged diagonal resolvent has a holomorphic continuation to a complex neighborhood of $I$ for all sufficiently large $λ$. By the Stieltjes inversion formula, the root-averaged density of states measure is absolutely continuous on the scaled energy window $λI$, and its density is real analytic and has a finite-order strong-disorder expansion there. In the scaled form $E=λξ$, the leading coefficient is the local density of the single-site distribution. All odd coefficients vanish, and the higher coefficients are finite sums determined by occupation profiles of short closed walks on the tree. For the uniform single-site distribution, we compute the first nonzero correction term explicitly.

math-ph↗

arXiv2026

Determinant Formulas for Scattering Matrices of Schrödinger Operators with Finitely Many Concentric $δ$-Shells

We study stationary scattering for Schrödinger operators in $\mathbb R^3$ with finitely many concentric $δ$--shell interactions of constant real strengths. Starting from the self--adjoint realization and the boundary resolvent formula for this model, we show that, after partial--wave reduction, the same finite-dimensional boundary matrices that arise in the resolvent formula also determine the channel scattering coefficients. More precisely, for each angular momentum $\ell$, the channel coefficient $S_\ell(k)$ satisfies $S_\ell(k)=\det K_\ell(k^2-i0)/\det K_\ell(k^2+i0)$ for almost every $k>0$, where $K_\ell(z)=I_N+m_\ell(z)Θ$ is the $\ell$--th reduced boundary matrix. Thus, in each channel, the positive--energy scattering problem is reduced to a finite-dimensional matrix problem, and the scattering phase is recovered from $\det K_\ell(k^2+i0)$. We then study the first nontrivial case of two concentric shells in the $s$--wave channel, where the interaction between the shells produces nontrivial threshold effects. We derive an explicit formula for $S_0(k)$ and analyze its behavior as $k\downarrow0$. In the regular threshold regime, we obtain an explicit scattering length. We further identify a threshold--critical configuration characterized by the existence of a nontrivial zero--energy radial solution, regular at the origin, whose exterior constant term vanishes. In the corresponding nondegenerate exceptional case, the usual finite scattering length breaks down, and instead $S_0(k)\to -1$ as $k\downarrow0$.

math-ph↗

arXiv2026

Schrödinger operators with concentric $δ$--shell interactions

We study Schrödinger operators on $\mathbb R^3$ with finitely many concentric spherical $δ$-shell interactions. The operators are defined by the quadratic form method and are described by continuity across each shell together with the usual jump condition for the radial derivative. Using a boundary integral approach based on the free Green kernel and single-layer potentials, we derive an explicit resolvent representation for an arbitrary number of shells with bounded coupling strengths. This yields a concrete Kre\uın-type formula and a boundary operator whose noninvertibility characterizes the discrete spectrum, and it is compatible with a partial-wave reduction under rotational symmetry. We then specialize to the two-shell case with constant couplings and obtain a detailed description of the negative spectrum. In particular, we show that the ground state (when it exists) lies in the $s$-wave sector and derive an explicit secular equation for bound states. For large shell separation, each bound level approaches the corresponding single-shell level with exponentially small corrections, while a genuine tunneling splitting appears when the single-shell levels are tuned to coincide. As a simple calibration, we relate the two-shell parameters to representative core-shell quantum dot scales. At the level of order-of-magnitude and qualitative trends, Type~I configurations yield a relatively strongly confined state, whereas Type~II configurations produce a comparatively shallow outer-shell state.

math-ph↗

arXiv2025

Integrated density of states for the Poisson point interactions on $\mathbf{R}^3$

We determine the principal term of the asymptotics of the integrated density of states (IDS) $N(λ)$ for the Schrödinger operator with point interactions on $\mathbf{R}^3$ as $λ\to -\infty$, provided that the set of positions of the point obstacles is the Poisson configuration, and the interaction parameters are bounded i.i.d.\ random variables. In particular, we prove $N(λ) =O(|λ|^{-3/2})$ as $λ\to -\infty$. In the case that all interaction parameters are equal to a constant, we give a more detailed asymptotics of $N(λ)$, and verify the result by a numerical method using R.

math-ph↗

arXiv2022

Perturbation of discriminant for one-dimensional discrete Schrödinger operator with sparse periodic potential

We consider the one-dimensional discrete Schrödinger operator with complex-valued sparse periodic potential. The spectrum for a complex-valued periodic potential is a complicated compact set in the complex plane represented by real intersections of algebraic curves determined by a discriminant. We represent the discriminant by Chebyshev polynomials and use perturbations of the discriminant to study the spectrum.

math-ph↗

arXiv2019

A self-adjointness criterion for the Schrödinger operator with infinitely many point interactions and its application to random operators

We prove the Schrödinger operator with infinitely many point interactions in $\mathbb{R}^d$ $(d=1,2,3)$ is self-adjoint if the support of the interactions is decomposed into uniformly discrete clusters. Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions on a random perturbation of a lattice or on the Poisson configuration. We also determine the spectrum of the Schrödinger operators with random point interactions of Poisson--Anderson type.

math-ph↗

arXiv2019

Determining the Optimal Random-padding Size for Rabin Cryptosystems

Rabin encryption and a secure ownership transfer protocol based on the difficulty of factorization of a public key use a small public exponent. Such encryption requires random number padding. The Coppersmith's shortpad attack works effectively on short padding, thereby allowing an adversary to extract the secret message. However, the criteria for determining the appropriate padding size remains unclear. In this paper, we derived the processing-time formula for the shortpad attack and determined the optimal random-padding size in order to achieve the desired security.

cs.CR↗

arXiv2019

A True Random Number Generator Method Embedded in Wireless Communication Systems

To increase the number of wireless devices, e.g., mobile or IoT terminals, cryptosystems are essential for secure communications. In this regard, random number generation is crucial because the appropriate function of cryptosystems relies on it to work properly. This paper proposes a true random number generator (TRNG) method capable of working in wireless communication systems. By embedding a TRNG in such systems, no additional analog circuits are required and working conditions can be limited as long as wireless communication systems are functioning properly, making TRNG method cost-effective. We also present some theoretical background and considerations. We next conduct experimental verification, which strongly supports the viability of the proposed method.

cs.IT↗

arXiv2016

Quantum diffusion in the Kronig-Penney model

In this paper we consider the 1D Schrödinger operator $H$ with periodic point interactions. We show an $L^1-L^\infty$ bound for the time evolution operator $e^{-itH}$ restricted to each energy band with decay order $O(t^{-1/3})$ as $t\to \infty$, which comes from some kind of resonant state. The order $O(t^{-1/3})$ is optimal for our model. We also give an asymptotic bound for the coefficient in the high energy limit. For the proof, we give an asymptotic analysis for the band functions and the Bloch waves in the high energy limit. Especially we give the asymptotics for the inflection points in the graphs of band functions, which is crucial for the asymptotics of the coefficient in our estimate.

math-ph↗

arXiv2016

Crashing Modulus Attack on Modular Squaring for Rabin Cryptosystem

The Rabin cryptosystem has been proposed protect the unique ID (UID) in radio-frequency identification tags. The Rabin cryptosystem is a type of lightweight public key system that is theoretetically quite secure; however it is vulnerable to several side-channel attacks. In this paper, a crashing modulus attack is presented as a new fault attack on modular squaring during Rabin encryption. This attack requires only one fault in the public key if its perturbed public key can be factored. Our simulation results indicate that the attack is more than 50\% successful with several faults in practical time. A complicated situation arises when reconstrucing the message, including the UID, from ciphertext, i.e., the message and the perturbed public key are not relatively prime. We present a complete and mathematically rigorous message reconstruction algorithm for such a case. Moreover, we propose an exact formula to obtain a number of candidate messages. We show that the number is not generally equal to a power of two.

cs.CR↗