arXiv subjects

Tomohiro Matsuda

Publications and source records attributed to Tomohiro Matsuda.

At least 19 recordsLinked to original sources

arXiv2025

Exact WKB analysis for dynamical and geometric exponents in generalized and nonlinear Landau-Zener transitions

The Berry phase is a geometric phase that is important in explaining topological quantum phenomena. The Berry phase is also important in non-perturbative phenomena, as the imaginary part of the phase explains the non-perturbative transitions. However, problems arose because the singular perturbation with respect to the Planck constant has not been treated adequately in conventional calculations, where the most serious problem is the arbitrariness of approximate calculations. To solve this problem, we consider the exact WKB, which is a mathematical method that treats perturbative expansion with respect to the Planck constant as a rigorous singular perturbation. This method is also a powerful computational tool that makes analytical computation much easier for mathematical software. Using the exact WKB, we analyze the derivation of the dynamical and the geometric exponents in generalized Landau-Zener models, highlighting the differences from other calculational methods. The discontinuity of complex geometric factor is a universal phenomenon that manifests itself in phase transitions, boundaries, particle generation, and topology changes. These phenomena are ``non-perturbative'' in physics, while mathematically, these discontinuities can be deeply related to the singular structure of complex analysis. The mathematical structure of these phenomena will be revealed by using the exact WKB.

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arXiv2025

Quantum field theory on curved manifolds

This paper discusses how particle production from the vacuum can be explained by local analysis when the field theory is defined by differential geometry on curved manifolds. We have performed the local analysis in a mathematically rigorous way, respecting the Markov property. The exact WKB is used as a tool for extracting non-perturbative effect from the local system. After a serious application of the differential geometry and the exact WKB to particle production, we show that entanglement does not appear in the Unruh effect as far as the standard formulation by the differential geometry is valid. This result should not be attributed to a consistency problem between the ``entanglement state'' and the ``standard field theory by differential geometry'', but to the fact that the conventional calculation of the Unruh effect is done by extrapolation which is not consistent with the differential geometry. The situation is similar to that of the Dirac monopole, but topology is not relevant and the basis for building field theories in differential geometry is strongly involved.

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arXiv2025

How to define the moving frame of the Unruh-DeWitt detector on manifolds

The physical phenomena seen by an observer are defined for a local inertial system that is subjective to the observer. Such a coordinate system is called a ``moving frame'' because it changes from time to time. However, unlike the Thomas precession, the Unruh-DeWitt detector has been discussed for a fixed frame. We discuss the Unruh-DeWitt detector by defining the vacuum for the moving frame, showing that the problem of the Stokes phenomenon can be solved by using the vierbeins and the exact WKB, to find factor 2 discrepancy from the standard result. Differential geometry is constructed in such a way that local calculations can be performed rigorously. If one expects Markov property, the calculation is expected to be local. The final piece that was missing was a local non-perturbative calculation, which is now complemented by the exact WKB. Our analysis defines a serious problem regarding the relationship between entanglement of the Unruh effect and differential geometry.

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arXiv2023

Schwinger-Unruh-Hawking radiation on manifolds

The whole picture of gauge theory is described by manifolds, while the field equation provides only a part (a section) of the manifold. Just as a three-dimensional object is reconstructed from two planar images, a monopole is constructed by combining two solutions. The Schwinger and the Unruh effects and the Hawking radiation are the production of particles out of the ``vacuum''. If the '''vacuum'' on the manifold is properly defined, these phenomena should be described as local phenomena. However, calculations using the field equations have so far resulted in unnatural extrapolations. We present a method for properly defining the ``vacuum'' and explain how to resolve the local particle production on manifolds. By defining the Stokes phenomena on the manifold, the Schwinger effect is naturally accompanied by the Unruh effect. Also, unlike the conventional Unruh effect, calculations on manifolds do not suffer from the entanglement between disconnected wedges.

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arXiv2023

Non-perturbative particle production and differential geometry

This paper proposes a basic method for understanding stationary particle production on manifolds by means of the Stokes phenomenon. We studied the Stokes phenomena of the Schwinger effect, the Unruh effect and Hawking radiation in detail focusing on the origin of their continuous particle production. We found a possibility that conventional calculations may not explain the experimental results.

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arXiv2022

The Exact WKB analysis and the Stokes phenomena of the Unruh effect and Hawking radiation

The physical observables of quantum theory can be described by perturbation theory, which is often given by diverging power series. This divergence is connected to the existence of non-perturbative phenomena, where resurgence allows us to study this connection. Applying this idea to the WKB expansion, the exact WKB analysis gives a clear connection to non-perturbative phenomena. In this paper, we apply the exact WKB analysis to the Unruh effect and Hawking radiation. The mechanism we found in this paper is similar to the Schwinger effect of a constant electric field, where the background is static but the Stokes phenomenon appears in the temporal part. Comparing this with a sonic black hole, our calculations show a clear discrepancy between them. Then, we briefly explain how quantum backreactions can be included in the exact WKB formalism.

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arXiv2022

The Exact WKB analysis for asymmetric scalar preheating

Using the exact WKB analysis of the higher-order differential equations, we analyze the asymmetry in dynamical particle production of a complex scalar field. The solution requires the Stokes phenomena of the fourth-order differential equation. We found that the interference of different types of the Stokes phenomena causes matter-antimatter asymmetry. We also showed a specific example where asymmetry is forbidden in the exact calculation, but a false asymmetry appears in the perturbative expansion.

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arXiv2022

The Exact WKB and the Landau-Zener transition for asymmetry in cosmological particle production

Cosmological particle production by a time-dependent scalar field is common in cosmology. We focus on the mechanism of asymmetry production when interaction explicitly violates symmetry and its motion is rapid enough to create particles by itself. Combining the exact WKB analysis and the Landau-Zener transition, we point out that perturbation before the non-perturbative analysis may drastically change the structure of the Stokes lines of the theory. The Exact WKB can play an important role in avoiding such discrepancies.

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arXiv2021

The exact WKB for cosmological particle production

The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of the corresponding ordinary differential equation. The calculation becomes very simple as far as the solution is described by a special function. Otherwise, the calculation requires more tactics, where the Exact WKB (EWKB) may be a powerful tool. Using the EWKB, we discuss cosmological particle production focusing on the effect of more general interaction and classical scattering. The classical scattering appears when the corresponding scattering problem of the Schrödinger equation develops classical turning points on the trajectory. The higher process of fermionic preheating is also discussed using the Landau-Zener model.

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arXiv2019

Baryogenesis with the Berry phase

The spontaneous baryogenesis scenario explains how a baryon asymmetry can develop while baryon violating interactions are still in thermal equilibrium. However, generation of the chemical potential from the derivative coupling is dubious since the chemical potential may not appear after the Legendre transformation. The geometric phase (Pancharatnam-Berry phase) results from the geometrical properties of the parameter space of the Hamiltonian, which is calculated from the Berry connection. In this paper, using the formalism of the Berry phase, we show that the chemical potential defined by the Berry connection is consistent with the Legendre transformation. The framework of the Berry phase is useful in explaining the mathematical background of the spontaneous baryogenesis, and also is useful for calculating the asymmetry of the non-thermal particle production in time-dependent backgrounds. Using the formalism, we show that the mechanism can be extended to more complex situations.

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arXiv2018

Asymmetric Preheating

We study the generation of the matter-antimatter asymmetry during bosonic preheating, focusing on the sources of the asymmetry. If the asymmetry appears in the multiplication factor of the resonant particle production, the matter-antimatter ratio will grow during preheating. On the other hand, if the asymmetry does not grow during preheating, one has to find out another reason. We consider several scenarios for the asymmetric preheating to distinguish the sources of the asymmetry. We also discuss a new baryogenesis scenario, in which the asymmetry is generated without introducing neither loop corrections nor rotation of a field.

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arXiv2016

Particle production with L-R neutrino oscillation

When the Higgs field starts oscillation after Higgs inflation, gauge bosons are produced non-perturbatively near the Enhanced Symmetry Point (ESP). Just after the particle production, when the Higgs field is going away from the ESP, these gauge bosons gain mass and decay or annihilate into Standard Model (SM) fermions. Left-handed neutrinos can be generated in that way. If one assumes the see-saw mechanism, the mass matrix of a pair of left and right-handed neutrinos is non-diagonal. Although their mixing in the mass eigenstates is negligible in the true vacuum, it could be significant near the edge of the Higgs oscillation, where the off-diagonal component is large. Therefore, the left-handed neutrinos generated from the gauge bosons can start neutrino oscillation between the right-handed neutrinos. We study the particle production when such L-R neutrino oscillation is significant. For a working example, the non-thermal leptogenesis scenario after Higgs inflation is examined, which cannot be realized without the L-R neutrino oscillation. The same mechanism could be applied to other singlet particles whose abundance has been neglected.

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arXiv2016

What we can learn from the spectral index of the tensor mode

If the beginning of inflation is defined at the moment when the vacuum energy of the inflaton starts to dominate, the energy density of the other fields at that moment is (by definition) comparable to the inflaton. Although the fraction will be small at the horizon exit due to the inflationary expansion, they can alter the scale dependence of the spectrum. At the same time, velocity of the inflaton field may not coincide with the slow-roll (attractor) velocity. Those dynamics could be ubiquitous but can easily alter the scale dependence of the spectrum. Since the scale dependence is currently used to constrain or even exclude inflation models, it is very important to measure its shift, which is due to the dynamics that does not appear in the original inflation model. Considering typical examples, we show that the spectral index of the tensor mode is a useful measure of such effect. Precise measurement of the higher runnings of the scalar mode will be helpful in discriminating the source.

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arXiv2015

Preheating with higher dimensional interaction

Particle production caused by the oscillation after inflation is important since it explains reheating after inflation. On the particle theory side, we know that effective action may have additional higher dimensional terms (usually called non-renormalizable terms) suppressed by the cut-off scale. Moreover, interaction between inflaton and so-called moduli field will be higher dimensional. Therefore, if such higher dimensional interaction is significant for resonant particle production, one cannot avoid the effect in preheating study. We explicitly calculated the required number of oscillation for the energy transfer. Consequently, cosmological history of an oscillating field and the moduli problem can be reconsidered.

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arXiv2015

Ambiguity in running spectral index with an extra light field during inflation

At the beginning of inflation there could be extra dynamical scalar fields that will soon disappear (become static) before the end of inflation. In the light of multi-field inflation, those extra degrees of freedom may alter the time-dependence of the original spectrum of the curvature perturbation. It is possible to remove such fields introducing extra number of e-foldings prior to $N_e\sim 60$, however such extra e-foldings may make the trans-Planckian problem worse due to the Lyth bound. We show that such extra scalar fields can change the running of the spectral index to give correction of $\pm 0.01$ without adding significant contribution to the spectral index. The corrections to the spectral index (and the amplitude) could be important in considering global behavior of the corrected spectrum, although they can be neglected in the estimation of the spectrum and its spectral index at the pivot scale. The ambiguity in the running of the spectral index, which could be due to such fields, can be used to nullify tension between BICEP2 and Planck experiments.

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arXiv2014

Scale-dependent CMB asymmetry from primordial configuration

We demonstrate that a topological defect can explain the hemispherical power asymmetry of the CMB. The first point is that a defect configuration, which already exists prior to inflation, can source asymmetry of the CMB. The second point is that modulation mechanisms, such as the curvaton and other modulation mechanisms, can explain scale-dependence of the asymmetry. Using a simple analysis of the $δN$ formalism, we show models in which scale-dependent hemispherical power asymmetry is explained by primordial configuration of a defect.

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arXiv2014

Beauty is more attractive: Particle Production and Moduli trapping with Higher Dimensional Interaction

We study quantum effects on moduli dynamics arising from particle production near the enhanced symmetry point (ESP). We focus on non-renormalizable couplings between the moduli field and the field that becomes light at the ESP. Considering higher dimensional interaction, we find that particle production is significant in a large area, which is even larger than the area that is expected from a renormalizable interaction. It is possible to find this possibility from a trivial adiabatic condition; however the quantitative estimation of particle production and trapping of the field in motion are far from trivial. In this paper we study particle production and trapping in detail, using both the analytical and numerical calculations, to find a clear and intuitive result that supports trapping in a vast variety of theories. Our study shows that trapping driven by a non-renormalizable interaction is possible. This possibility has not been considered in previous works. Some phenomenological models of particle physics will be mentioned to complement discussion.

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arXiv2013

Modulated decay in the multi-component Universe

The early Universe after inflation may have oscillations, kinations (nonoscillatory evolution of a field), topological defects, relativistic and non-relativistic particles at the same time. The Universe whose energy density is a sum of those components can be called the multi-component Universe. The components, which may have distinguishable density scalings, may decay modulated. In this paper we study generation of the curvature perturbations caused by the modulated decay in the multi-component Universe.

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