arXiv subjects

Kenzo Ishikawa

Publications and source records attributed to Kenzo Ishikawa.

At least 19 recordsLinked to original sources

arXiv2026

Wave Packet Sizes in Quantum Mechanical Scatterings: New Perspective

Particles exist with a probability of 1 and are represented by wave packets in quantum mechanics. These wave packets satisfy the Schrödinger equation and are classified as either bound states or continuum states with finite coherence lengths. They undergo transitions according to unambiguous absolute probabilities, the magnitudes of which depend on the sizes of the wave packets. Because these sizes are not universal constants but depend on the environment and experimental conditions, their accurate estimation is essential. The sizes of propagating wave packets are determined by their environmental coherence lengths, whereas those of bound states are determined by their wave functions. Here, we present a systematic analysis of wave-packet sizes.

quant-ph↗

arXiv2026

New class of quantum transitions exhibiting large-scale intercorrelations: Color of the sky

The absolute value of the transition probability of the Rayleigh scattering is computed for the first time and applied to the scattering of solar light with molecules in the atmosphere and to the laser scattering with nanopartilces. The probability has a new contribution of unique properties from long-range correlations specific to the quantum mechanics. The magnitude is sufficient to resolve longstanding puzzle on diffusion lights in the sky and anomalous photon spectrum in laser experiments. The earth's albedo from the new calculations on Rayleigh scattering agrees with observations with satelites.

physics.optics↗

arXiv2026

B-H hysteresis in itinerant Feromagnetism from Chern-Simons Gauge theory

The log H term is derived in the free energy of many-electron system from Chern-Simons gauge theory. Owing to the singularity at $H=0$, this leads the first order transition and B-H hysteresis to many-electron systems of symmetric and single domain. This has the origin in quantum mechanics and is irrelevant to non-invertible motions of domains. This transition appears in single and symmetric domain.

cond-mat.str-el↗

arXiv2024

Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary states

Orthogonality of eigenstates of different energies and its implications in potential scattering are unlabeled. Scalar products of scattering states of different energies are found to have finite non-orthogonal terms in potentials of finite widths. Their superpositions have time-dependent norms, and are not suitable for isolate states. In these systems, a perturbative method and a variational method are viable methods for finding a rigorous transition probability that describes phenomena completely. In various exceptional potentials, an orthogonality is satisfied.

quant-ph↗

arXiv2024

Overlap integral of stationary scattering states

The overlap integrals of scattering states in potentials of finite widths are expressed with their asymptotic behaviors and those of energies $E_1$ and $E_2$ consist of diagonal terms that are proportional to $δ(E_1-E_2)$ and nondiagonal terms. Owing to the composition of nondiagonal terms, superpositions of stationary states have time-dependent norms and finite probability currents. These do not represent isolate states. In various exceptional potentials and in free theory, nondiagonal terms do not exist, and the superpositions of states with different energies represent isolate particles that exactly describe scattering processes.

quant-ph↗

arXiv2024

Magnetization without spin: effective Lagrangian of itinerant electrons

Effective Lagrangian of itinerant electron system of finite density at finite magnetic field is found to include Chern-Simons term of electromagnetic potentials of lower scale dimension than those studied before. This term has an origin in many-body wave function and unique topological property that is independent of a spin degree of freedom. The coupling strength is proportional to $\fracρ{eB}$, which is singular at $B=0$ for a constant charge density. The effective Lagrangian at a finite $B$ represents physical effects at $ B \neq 0$ properly. A universal shift of the magnetic field known as Slater-Pauling curve is derived from the effective Lagrangian.

cond-mat.str-el↗

arXiv2024

Topological interaction of neutrino with photon in the magnetic field -- Electroweak Hall effect

The effective interaction of a neutrino with a photon in magnetized plasma is obtained from a strong field expansion in the electroweak standard model. The interaction is expressed by a Chern-Simons form of the neutrino current and the electromagnetic vector potential of the coupling strength proportional to $\frac{n_e}{B} \times e G_F$. The derivation of the interaction Lagrangian and its properties are presented.

hep-ph↗

arXiv2023

Potential scattering in $L^2$ space: (2) Rigorous scattering probability of wave packets

In this study, potential scatterings are formulated in experimental setups with Gaussian wave packets in accordance with a probability principle and associativity of products. A breaking of an associativity is observed in scalar products with stationary scattering states in a majority of short-range potentials. Due to the breaking, states of different energies are not orthogonal and their superposition is not suitable for representing a normalized isolate state. Free wave packets in perturbative expansions in coupling strengths keep the associativity, and give a rigorous amplitude that preserves manifest unitarity and other principles of the quantum mechanics. An absolute probability is finite and comprises cross sections and new terms of unique properties. The results also demonstrate an interference term displaying unique behavior at an extreme forward direction.

quant-ph↗

arXiv2023

Wave-Packet Effects: A Solution for Isospin Anomalies in Vector-Meson Decay

There is a long-standing anomaly in the ratio of the decay width for $ψ(3770)\to D^0\overline{D^0}$ to that for $ψ(3770)\to D^+D^-$ at the level of $9.5\,σ$. A similar anomaly exists for the ratio of $ϕ(1020)\to K_\text{L}^0K_\text{S}^0$ to $ϕ(1020)\to K^+K^-$ at $2.1\,σ$. In this study, we reassess the anomaly through the lens of Gaussian wave-packet formalism. Our comprehensive calculations include the localization of the overlap of the wave packets near the mass thresholds as well as the composite nature of the initial-state vector mesons. The results align within $\sim 1 σ$ confidence level with the Particle Data Group's central values for a physically reasonable value of the form-factor parameter, indicating a resolution to these anomalies. We also check the deviation of a wave-packet resonance from the Briet-Wigner shape and find that wide ranges of the wave-packet size are consistent with the experimental data.

hep-ph↗

arXiv2023

New effect in wave-packet scattering of quantum fields

We report calculations of a wave-packet amplitude of the two-body scattering $ϕϕ\to Φ\to ϕϕ$, which leads to the measured probability in realistic experiments. We elucidate the decay amplitude of $ Φ\rightarrow ϕϕ$ from this. In such an amplitude of wave packets, there are in and out time boundaries for the initial $Φ$ and final $ϕϕ$ configurations, respectively. In this paper, we prove that the effect of the in time boundary of $Φ\toϕϕ$ emerges from $ϕϕ\toΦ\toϕϕ$ without assuming any time boundary \emph{a priori}. This effect has been overlooked in the standard plane-wave formulation and can exhibit distinct phenomena in wide areas of science. We confirm the result in different integration orders. The result is also interpreted as a Stokes phenomenon in the Lefschetz-thimble decomposition.

hep-th↗

arXiv2021

Particle decay in Gaussian wave-packet formalism revisited

We derive the Fermi's golden rule in the Gaussian wave-packet formalism of quantum field theory, proposed by Ishikawa, Shimomura, and Tobita, for the particle decay within a finite time interval. We present a systematic procedure to separate the bulk contribution from those of time boundaries, while manifestly maintaining the unitarity of the $S$-matrix unlike the proposal by Stueckelberg in 1951. We also revisit the suggested deviation from the golden rule and clarify that it indeed corresponds to the boundary contributions, though their physical significance is yet to be confirmed.

hep-ph↗

arXiv2020

Scalar scattering amplitude in Gaussian wave-packet formalism

We compute an $s$-channel $2\to2$ scalar scattering $ϕϕ\toΦ\toϕϕ$ in the Gaussian wave-packet formalism at the tree-level. We find that wave-packet effects, including shifts of the pole and width of the propagator of $Φ$, persist even when we do not take into account the time-boundary effect for $2\to2$, proposed earlier. The result can be interpreted that a heavy scalar $1\to2$ decay $Φ\toϕϕ$, taking into account the production of $Φ$, does not exhibit the in-state time-boundary effect unless we further take into account in-boundary effects for the $2\to2$ scattering. We also show various plane-wave limits.

hep-th↗

arXiv2020

Finite-size corrections to Fermi's Golden rule II: Quasi-stationary composite states

Many-body states described by a Schrödinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component to the transition probability. The probability is computed rigorously following the von Neumann's fundamental principle of quantum mechanics with an S-matrix that is defined with normalized functions, instead of plane waves. That includes the intriguing correction term to the Fermi's golden rule, in which a visible energy is smaller than the initial energy, and reveals macroscopic quantum phenomena for light particles. Processes in Quantum Electrodynamics are analyzed and the sizable corrections are found in the dilute systems. The results suggest that these states play important roles in natural phenomena, and the verification in laboratory would be possible with recent advanced technology.

hep-ph↗

arXiv2019

On Experimental Confirmation of the Corrections to the Fermi's golden rule

Standards calculations by the Fermi's Golden rule involve approximations. These approximations could lead to deviations from the predictions of the standard model as discussed in another paper. In this paper we propose experimental searches for such deviations in the two photon spectra from the decay of the neutral pion in the process $ϕ\rightarrow π^{+} π^{-} π^{0}$ and in the annihilation of the positron from nclear $β$ decay.

hep-ph↗

arXiv2017

Interaction of the SN1987A Neutrino with the Galaxy

In previous publications we have shown that long-ignored approximations in standard model calculations could have significant implications for very low mass particles such as neutrinos and photons. In particular we showed that, in a dilute plasma such as that in the solar corona, a significant decay probability of $ν' \rightarrow ν+ γ$ will be possible as a consequence of the terms ignored in making the approximations. Here the $ν'$ and $ν$ are high and low mass eigenstates of the neutrino. In this paper, we investigate the effect in the vicinity of an expanding supernovae remnant such as SN1987A. We show that, in the dilute plasma external to the remnant, such decays are possible and significant. We describe a calculation of effects of such decays on the anti-neutrinos from SN1987A. The calculated anti-neutrino energy against arrival time agrees reasonably well with that observed, assuming that the expansion velocity of the remnant is $\approx 0.2 c$ and that the plasma density is high within the expanding remnant.

hep-ph↗

arXiv2017

Finite-Size Corrections to the Excitation Energy Transfer in a Massless Scalar Interaction Model

We study the excitation energy transfer (EET) for a simple model in which a massless scalar particle is exchanged between two molecules. We show that a finite-size effect appears in EET by the interaction energy due to overlapping of the quantum waves in a short time interval. The effect generates finite-size corrections to Fermi's golden rule and modifies EET probability from the standard formula in the Forster mechanism. The correction terms come from transition modes outside the resonance energy region and enhance EET probability substantially.

physics.chem-ph↗

arXiv2017

Transition Probability for the Neutrino Wave in Muon Decay and Oscillation Experiments

This paper elucidates the anomalous decay of the muon ascribed to extended waves. Due to a large overlap of the parent and daughters, the transition amplitude and probability for the neutrinos are modified from the standard formula. A rigorous probability from the von Neumann's fundamental principle of the quantum mechanics at a large time interval $T$ is, $P=TΓ+ P^{(d)}$, where $Γ$ is derived from the Fermi's golden rule, and $P^{(d)}$ is a correction term. A new term $P^{(d)}$ has origins in the overlapping waves, and influences the determinations of physical parameters. By including $P^{(d)}$, short-baseline neutrino experiments with LSND, KARMEN, and MiniBooNE become consistent each other and with the solar, long-baseline, and reactor experiments within the three neutrinos. Byproduct is that the absolute neutrino mass of the neutrinos can be measured.

hep-ph↗

arXiv2015

Electroweak Hall Effect of Neutrino and Coronal Heating

The inversion of temperature at the solar corona is hard to understand from classical physics, and the coronal heating mechanism remains unclear. The heating in the quiet region seems contradicting with the thermodynamics and is a keen problem for physicists. A new mechanism for the coronal heating based on the neutrino radiative transition unique in the corona region is studied. The probability is enormously amplified by an electroweak Chern-Simons form and overlapping waves, and the sufficient energy is transfered. Thus the coronal heating is understood from the quantum effects of the solar neutrino.

hep-ph↗