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Kenzo Ishikawa

Publications and source records attributed to Kenzo Ishikawa.

36 records · Page 2Linked to original sources

Anomalous radiative transitions

Anomalous transitions involving photons derived by many-body interaction of the form, $\partial_μ G^μ$, in the standard model are studied. This does not affect the equation of motion in the bulk, but makes wave functions modified, and causes the unusual transition characterized by the time-independent probability. In the transition probability at a time-interval $T$ expressed generally in the form $P=T Γ_0 +P^{(d)}$, now with $ P^{(d)} \neq 0 $. The diffractive term $P^{(d)}$ has the origin in the overlap of waves of the initial and final states, and reveals the characteristics of waves. In particular, the processes of the neutrino-photon interaction ordinarily forbidden by Landau-Yang's theorem ($Γ_0=0$) manifests itself through the boundary interaction. The new term leads to physical processes over a wide energy range to have finite probabilities. New methods of detecting neutrinos using laser are proposed that are based on this difractive term, which enhance the detectability of neutrinos by many orders of magnitude.

hep-ph↗

Matter-enhanced transition probabilities in quantum field theory

The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, $S[\text T]$, that satisfies the boundary condition at T. Using $S[\text T]$, the finite-size corrections of the form of ${1/\text T}$ are found. The corrections to the Fermi's golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths.

hep-ph↗

Finite-size corrections to Fermi's golden rule: I. Decay rates

A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schrödinger equation, it preserves the total energy but not the kinetic energy in the intermediate-time region of a decay process where those of the parent and daughters overlap. The decay rate computed with Fermi's golden rule requires corrections that vary with the distance between the initial and final states, and the energy distribution of the daughter is distorted from that of plane waves. The corrections have universal properties in relativistically invariant systems and reveal macroscopic quantum phenomena for light particles. The implications for precision experiments in beta decays and various radiative transitions are presented.

hep-ph↗

A new method for measuring the absolute neutrino mass

The probability of the event that a neutrino produced in pion decay is detected in the intermediate $T$ shorter than the life-time $τ_π$, $T \leq τ_π$, is sensitive to the absolute mass of the neutrino. With a newly formulated S-matrix $S[T]$ that satisfies the boundary conditions of the experiments at a finite $T$, the rate of the event is computed as $Γ_0+\tilde{g}(ω_ν, {T};τ_π) \tilde Γ_{1} $, where $\tilde{g}(ω_ν,{T};τ_π)$ depends weakly on $τ_π$ and $ω_ν={m_ν^2c^4}/{(2E_ν\hbar)}$, $c$ is the speed of light. $Γ_0$ is the standard one and the correction, $\tilde{g}(ω_ν, {T};τ_π) \tilde Γ_{1} $, reflects relativistic invariance and is rigorously computed via the light-cone singularity of the system and reveals the diffraction pattern of a single quantum. The formula explains unsolved anomalies of neutrino experiments and indicates the heavy neutrino mass, $0.098 \pm 0.022$ or $0.083 \pm 0.026$ {eV}/ $c^2$ for normal or inverted mass hierarchies, respectively.

hep-ph↗

On transition of non-stationary waves

The probability of the events that the final states are detected with or interact with the nucleus in a finite time interval T was found to be, $P=\text T Γ_0 +P^{(d)}$. $Γ_0$ is computed with Fermi's golden rule, and does not depend on the nuclear wave functions. $P^{(d)}$ is not given by Fermi's golden rule, and depends on the nuclear wave functions. In the electron mode of pion decays, $Γ_0$ is proportional to $m_e^2$ but $P^{(d)}$ for the event that the neutrino is detected is proportional to $m_ν^{-2}$. $P^{(d)}$ does not hold the helicity suppression satisfied in $Γ_0$ and is inevitable in non-stationary quantum phenomena.

hep-ph↗

Neutrino diffraction induced by many body interaction

The neutrino produced in the pion decay reveals a new diffraction phenomenon due to many-body interactions in an intermediate time region when wave functions of the parent and daughters overlap. Because of diffraction, the probability to detect the neutrino involves a large finite-size correction that depends on the neutrino mass, $m_ν$ and energy, $E_ν$, the speed of light, $c$, and the distance $L$ between the positions of the initial pion and final neutrino, ${m_ν^2c^4 L}/{(2E_ν\hbar)}$. The correction vanishes for the charged leptons and is finite for the neutrino at a macroscopic distance, $L$, of near-detector regions in ground experiments. A new method for determining the absolute neutrino mass is proposed.

hep-ph↗

Long-range correlations of neutrinos in hadron reactions and neutrino diffraction II: neutrino

In this II, a probability to detect the neutrino produced in a high-energy pion decay is shown to receive the large finite-size correction. The neutrino interacts extremely weakly with matters and is described with a many-body wave function together with the pion and charged lepton. This wave function slowly approaches to an asymptotic form, which is probed by the neutrino. The whole process is described by an S-matrix of a finite-time interval, which couples with states of non-conserving kinetic energy, and the final states of a broad spectrum specific to a relativistic invariant system contribute to the positive semi-definite correction similar to diffraction of waves through a hole. This diffraction component for the neutrino becomes long range and stable under changes of the pion's energy. Moreover, it has a universal form that depends on the absolute neutrino mass. Thus a new method of measuring the absolute neutrino mass is suggested.

hep-ph↗

Resolving LSND anomaly by neutrino diffraction

In the charged pion decay, a neutrino is produced in pair with a charged lepton and they have the same production rate. In this paper we show that neutrinos have their own space-time correlations in a wide area and are detected in a different manner from charged leptons, owing to extremely small mass. The neutrino flux reveals a unique interference effect in the form of diffraction of non-stationary waves. The diffraction component of the flux shows a slow position-dependence and leads to an electron neutrino at short base-line regions. The electron neutrino flux at short distances is attributed to the neutrino diffraction and the one at long distances is to the normal flavor oscillation. The former depends upon the average mass-squared $\bar m^2_ν$ and the latter depends upon the mass-squared difference $δm^2_ν$. The LSND and the two neutrino experiment (TWN) measure $\bar m^2_ν$ and the other experiments measure $δm^2_ν$. Hence they are consistent with each other. The neutrino diffraction would supply valuable information on the absolute neutrino mass.

hep-ph↗

Diffraction-corrected neutrino flux and $νN$ total cross section

A neutrino produced in a particle decay maintains an unusual wave nature that reveals a diffraction phenomenon in a large spatial region. Diffraction gives a new component to a neutrino flux in this region and modifies determinations of physical quantities in neutrino experiments. A total cross section of neutrino nucleon scattering at high energies is studied in this paper. A cross section is proportional to an energy in the quark-parton model and is modified with the energy-dependent neutrino flux induced by the diffraction component. A total number of events divided by the energy is not constant but has a slight energy dependence. Theoretical values agree well with the recent experiments.

hep-ph↗

Coherence length of cosmic background radiation enlarges the attenuation length of the ultra-high energy proton

It is pointed out that an agreement of the one particle energy spectrum of the cosmic background radiation (CMBR) with Plank distribution of 2.725 [K] does not give a strong constraint on the coherence length of CMBR if the mean free path of CMBR is very long. The coherence length in this situation is estimated as a few times of $k_BT$. Due to this finite coherence length, the attenuation length of ultra-high energy cosmic rays (UHECR) is reduced in the $Δ$ resonance region,i.e., around $10^{20}$ [eV]. The small attenuation length makes the suppression of the flux of cosmic rays in this energy region less prominent than the naive estimation

hep-ph↗

On coherence lengths of wave packets

Coherence lengths of one particle states described by quantum wave functions are studied. We show that one particle states in various situations are not described by simple plane waves but are described by wave packets that are superpositions of plane waves. Wave packet is an approximate eigenstate of the free Hamiltonian and has a finite spatial size which we call the coherence length. The coherence lengths in the coordinate space and in the momentum space are studied in the present paper. We investigate several mechanisms of forming wave packets, stabilities of wave packets, and transformations of wave packets.

quant-ph↗

Anisotropic ground states of the quantum Hall system with currents

Anisotropic states at half-filled higher Landau levels are investigated in the system with a finite electric current. We study the response of the striped Hall state and the anisotropic charge density wave (ACDW) state against the injected current using the effective action. Current distributions and a current dependence of the total energy are determined for both states. With no injected current, the energy of the ACDW state is lower than that of the striped Hall state. We find that the energy of the ACDW state increases faster than that of the striped Hall state as the injected current increases. Hence, the striped Hall state becomes the lower energy state when the current exceeds the critical value. The critical value is estimated at about 0.04-0.07 nA, which is much smaller than the current used in the experiments.

cond-mat.mes-hall↗

Current induced transition of anisotropic quantum Hall states

We compare the energies of the striped Hall state and the anisotropic charge density wave (ACDW) state at half-filled third and higher Landau levels in the system with injected currents. With no injected current, the ACDW state has a lower energy. We find that the striped Hall state becomes the lower energy state when the injected current exceeds a critical value. The critical value is estimated as about 0.04-0.05 nA.

cond-mat.mes-hall↗

Generalized S-matrix in Mixed Representations

A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring instruments where momenta and positions satisfy minimum uncertainty are studied with a use of minimum wave packets, coherent states. In the present work, we show general features of the generalized scattering amplitudes based on $ϕ^4$ theory. We give a proof of completeness of many body states, asymptotic behaviors in the large distance region, and factorization of the amplitudes. Despite of the non-orthogonal properties of wave packets, we found that the probability interpretation is verified. A differential probability depends upon the wave packet size but a total probability that is integrated in the final states is independent from the size of final state wave packet and becomes universal. Few body amplitudes are studied as examples.

hep-ph↗

Stability of the compressible quantum Hall state around the half-filled Landau level

We study the compressible states in the quantum Hall system using a mean field theory on the von Neumann lattice. In the lowest Landau level, a kinetic energy is generated dynamically from Coulomb interaction. The compressibility of the state is calculated as a function of the filling factor $ν$ and the width $d$ of the spacer between the charge carrier layer and dopants. The compressibility becomes negative below a critical value of $d$ and the state becomes unstable at $ν=1/2$. Within a finite range around $ν=1/2$, the stable compressible state exists above the critical value of $d$.

cond-mat.mes-hall↗

Theory of Current-Induced Breakdown of the Quantum Hall Effect

By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the breakdown of the quantum Hall effect. The Hall conductance agrees with a topological invariant that is quantized exactly below a critical field and is not quantized above a critical field. The critical field is proportional to $B^{3/2}$ and is enhanced substantially if the extended states occupy a small fraction of the system.

cond-mat.mes-hall↗

Flux State in von Neumann lattice and Fractional Hall Effect

Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based on flux condensation is proposed. Because our mean field Hamiltonian has the same form as Hofstadter Hamiltonian, it is possible to understand characteristic features of the fractional Hall effect from Hofstadter's spectrum. Energy gap and other physical quantities are computed and are compared with the experiments. A reasonable agreement is obtained.

cond-mat↗

A Mean Field Theory for the Quantum Hall Liquid. II --- The Vortex Solution

In the Fractional Quantum Hall state, we introduce a bi-local mean field and get vortex mean field solutions. Rotational invariance is imposed and the solution is constructed by means of numerical self-consistent method. It is shown that vortex has a fractional charge, a fractional angular momentum and a magnetic field dependent energy. In $ν=1/3$ state, we get finite energy gap at $B=10,15,20[T]$. We find that the gap vanishes at $B=5.5[T]$ and becomes negative below it. The uniform mean field becomes unstable toward vortex pair production below $B=5.5[T]$.

cond-mat↗