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Tomoi Koide

Publications and source records attributed to Tomoi Koide.

At least 19 recordsLinked to original sources
arXiv2026

Torsion-Induced Quantum Fluctuations in Metric-Affine Gravity using the Stochastic Variational Method

This review paper comprehensively examines the influence of spatial torsion on quantum fluctuations from the perspectives of Metric-Affine Gravity (MAG) and the Stochastic Variational Method (SVM). We first outline the fundamental framework of MAG, a generalized theory that includes both torsion and non-metricity, and discuss the geometrical significance of torsion within this context. Subsequently, we summarize SVM, a powerful technique that facilitates quantization while effectively incorporating geometrical effects. By integrating these frameworks, we evaluate how the geometrical structures originating from torsion affect quantum fluctuations, demonstrating that they induce non-linearity in quantum mechanics. Notably, torsion, traditionally believed to influence only spin degrees of freedom, can also affect spinless degrees of freedom via quantum fluctuations. Furthermore, extending beyond the results of previous work [Koide and van de Venn, Phys. Rev. A112, 052217 (2025)], we investigate the competitive interplay between the Levi-Civita curvature and torsion within the non-linearity of the Schr\"odinger equation. Finally, we discuss the structural parallelism between SVM and information geometry, highlighting that the splitting of time derivatives in stochastic processes corresponds to the dual connections in statistical manifolds. These insights pave the way for future extensions to gravity theories involving non-metricity and are expected to deepen our understanding of unresolved cosmological problems.

gr-qc↗
arXiv2025

The Gravitational Aspect of Information: The Physical Reality of Asymmetric "Distance"

We show that when a Brownian bridge is physically constrained to satisfy a canonical condition, its time evolution exactly coincides with an m-geodesic on the statistical manifold of Gaussian distributions. This identification provides a direct physical realization of a geometric concept in information geometry. It implies that purely random processes evolve along informationally straight trajectories, analogous to geodesics in general relativity. Our findings suggest that the asymmetry of informational ``distance" (divergence) plays a fundamental physical role, offering a concrete step toward an equivalence principle for information.

cond-mat.stat-mech↗
arXiv2025

The Geometry of Qubit Decoherence: Linear vs. Nonlinear Dynamics in the Bloch Ball

We present two complementary approaches to the GKSL equation for an open qubit. The first, based on linearity, yields solutions illustrated by mixed states trajectories in the Bloch ball, including non-random asymptotic fixed points, and exceptional points. The second, exploiting the SU(2) symmetry, leads to a nonlinear dynamical system that separates angular dynamics from radial dissipation. This symmetry-based perspective offers a promising route toward generalisation to open qudits.

quant-ph↗
arXiv2025

Torsion-Driven Nonlinearity in Spinless Quantum Mechanics

We investigate the previously unexplored quantum dynamics of non-relativistic, spinless particles propagating in curved spaces with torsion. Our findings demonstrate that while torsion has been predominantly associated with spin, it can also influence the quantum behavior of spinless particles by inducing a logarithmic nonlinearity in the Schroedinger equation through quantum fluctuations, even in flat space. To facilitate quantization in curved spaces, we introduce a novel stochastic variational method. Unlike canonical quantization, this approach is naturally suited to general coordinate systems, with quantum fluctuations arising from a noise term in the stochastic process that is directly influenced by torsion. By requiring consistency with quantum dynamics, we ultimately derive an upper bound on the magnitude of torsion. Our results reveal a previously unrecognized mechanism by which torsion, as predicted in certain extensions of general relativity, can influence quantum systems, with potential implications for early-universe physics and dark matter or energy models.

gr-qc↗
arXiv2024

A purely geometrical Aharonov-Bohm effect

We present an application of the affine covariant integral quantization (ACIQ) (Adv. Oper. Theory, 5, 2020; Adv. Oper. Theory, 7, 2022) to quantum mechanics on the punctured plane. The associated four-dimensional phase space is identified with the similitude group SIM(2), which comprises translations, rotations, and dilations of the plane. Due to the topology of the punctured plane, our quantization procedure gives rise to an affine vector potential. This potential can be interpreted as the Aharonov-Bohm (AB) gauge field produced by an infinite solenoid. This observation supports a reinterpretation of the AB effect: it emerges from the topological constraint imposed by the impenetrable coil rather than from an externally applied classical gauge field. In addition to this gauge structure, ACIQ also generates a repulsive, centrifugal-like scalar potential, a feature already encountered when applying ACIQ to motion on the half-line, whose phase space is the open half-plane. These results provide a new perspective on the AB effect, highlighting the central roles of topology and symmetry in quantum mechanics.

quant-ph↗
arXiv2019

2-D Covariant Affine Integral Quantization(s)

Covariant affine integral quantization is studied and applied to the motion of a particle in a punctured plane R^2_\ast=R^2\{0}, for which the phase space is R^2_\ast=R^2\{0}X R^2. We examine the consequences of different quantizer operators built from weight functions on this phase space. To illustrate the procedure, we examine two examples of weights. The first one corresponds to 2-D coherent state families, while the second one corresponds to the affine inversion in the punctured plane. The later yields the usual canonical quantization and a quasi-probability distribution (2-D affine Wigner function) which is real, marginal in both position and momentum.

math-ph↗
arXiv2015

Hydrodynamic Approaches in Relativistic Heavy Ion Reactions

We review several facets of the hydrodynamic description of the relativistic heavy ion collisions, starting from the historical motivation to the present understandings of the observed collective aspects of experimental data, especially those of the most recent RHIC and LHC results. In this report, we particularly focus on the conceptual questions and the physical foundations of the validity of the hydrodynamic approach itself. We also discuss recent efforts to clarify some of the points in this direction, such as the various forms of derivations of relativistic hydrodynamics together with the limitations intrinsic to the traditional approaches, variational approaches, known analytic solutions for special cases, and several new theoretical developments. Throughout this review, we stress the role of course-graining procedure in the hydrodynamic description and discuss its relation to the physical observables through the analysis of a hydrodynamic mapping of a microscopic transport model. Several questions to be answered to clarify the physics of collective phenomena in the relativistic heavy ion collisions are pointed out.

nucl-th↗
arXiv2014

Dynamics and Stability of Chiral Fluid

Starting from the linear sigma model with constituent quarks we derive the chiral fluid dynamics where hydrodynamic equations for the quark fluid are coupled to the equation of motion for the order-parameter field. In a static system at thermal equilibrium this model leads to a chiral phase transition which, depending on the choice of the quark-meson coupling constant, could be a crossover or a first order one. We investigate the stability of the chiral fluid in the static and expanding backgrounds by considering the evolution of perturbations with respect to the mean-field solution. In the static background the spectrum of plane-wave perturbations consists of two branches, one corresponding to the sound waves and another to the sigma-meson excitations. For large couplings these two branches "cross" and the excitation spectrum acquires exponentially growing modes. The stability analysis is also done for the Bjorken-like background solution by explicitly solving the time-dependent differential equation for perturbations in the eta-space. In this case the growth rate of unstable modes is significantly reduced.

nucl-th↗
arXiv2013

Bivelocity picture in the nonrelativistic limit of relativistic hydrodynamics

We discuss the nonrelativistic limit of the relativistic Navier-Fourier-Stokes (NFS) theory. The next-to-leading order relativistic corrections to the NFS theory for the Landau-Lifshitz fluid are obtained. While the lowest order truncation of the velocity expansion leads to the usual NFS equations of nonrelativistic fluids, we show that when the next-to-leading order relativistic corrections are included, the equations can be expressed concurrently with two different fluid velocities. One of the fluid velocities is parallel to the conserved charge current (which follows the Eckart definition) and the other one is parallel to the energy current (which follows the Landau-Lifshitz definition). We compare this next-to-leading order relativistic hydrodynamics with bivelocity hydrodynamics, which is one of the generalizations of the NFS theory and is formulated in such a way to include the usual mass velocity and also a new velocity, called the volume velocity. We find that the volume velocity can be identified with the velocity obtained in the Landau-Lifshitz definition. Then, the structure of bivelocity hydrodynamics, which is derived using various nontrivial assumptions, is reproduced in the NFS theory including the next-to-leading order relativistic corrections.

cond-mat.stat-mech↗
arXiv2012

Shear viscosity, Bulk viscosity and Relaxation Times of Causal Dissipative Relativistic Fluid-Dynamics at Finite Temperature and Chemical Potential

The microscopic formulas for the shear viscosity $η$, the bulk viscosity $ζ$, and the corresponding relaxation times $τ_π$ and $τ_Π$ of causal dissipative relativistic fluid-dynamics are obtained at finite temperature and chemical potential by using the projection operator method. The non-triviality of the finite chemical potential calculation is attributed to the arbitrariness of the operator definition for the bulk viscous pressure.We show that, when the operator definition for the bulk viscous pressure $Π$ is appropriately chosen, the leading-order result of the ratio, $ζ$ over $τ_Π$, coincides with the same ratio obtained at vanishing chemical potential. We further discuss the physical meaning of the time-convolutionless (TCL) approximation to the memory function, which is adopted to derive the main formulas. We show that the TCL approximation violates the time reversal symmetry appropriately and leads results consistent with the quantum master equation obtained by van Hove. Furthermore, this approximation can reproduce an exact relation for transport coefficients obtained by using the f-sum rule derived by Kadanoff and Martin. Our approach can reproduce also the result in Baier et al.(2008) Ref. \cite{con} by taking into account the next-order correction to the TCL approximation, although this correction causes several problems.

hep-th↗
arXiv2010

Transport coefficients of causal dissipative relativistic hydrodynamics in quenched lattice simulations

Transport coefficients of causal dissipative relativistic fluid dynamics (CDR) are studied in quenched lattice simulations. CDR describes the behavior of relativistic non-Newtonian fluids in which the relaxation time appears as a new transport coefficient besides the shear and bulk viscosities. It was recently shown that these coefficients can be given by the temporal-correlation functions of the energy-momentum tensors as in the case of the Green-Kubo-Nakano formula. By using the new formula in CDR, we study the transport coefficients with lattice simulations in pure SU(3) gauge theory. After defining the energy-momentum tensor on the lattice, we extract a ratio of the shear viscosity to the relaxation time which is given only in terms of the static correlation functions. The simulations are performed on $24^3 \times 4$--16 lattices with $β_{_{\rm LAT}} = 6.0$, which corresponds to the temperature range of $0.5 \simle T/T_c \simle 1.8$, where $T_c$ is the critical temperature.

hep-lat↗
arXiv2010

Bulk Viscosity and Relaxation Time of Causal Dissipative Relativistic Fluid Dynamics

The microscopic formulae of the bulk viscosity $ζ$ and the corresponding relaxation time $τ_Π$ in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulae to the pionic fluid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. In the leading order approximation in the chiral perturbation theory, the relaxation time is enhanced near the QCD phase transition and $τ_Π$ and $ζ$ are related as $τ_Π=ζ/[β\{(1/3-c_{s}^{2})(ε+P)-2(ε-3P)/9\}]$, where $ε$, $P$ and $c_{s}$ are the energy density, pressure and velocity of sound, respectively. The predicted $ζ$ and $% τ_Π$ should satisfy the so-called causality condition. We compare our result with the results of the kinetic calculation by Israel and Stewart and the string theory, and confirm that all the three approaches are consistent with the causality condition.

nucl-th↗
arXiv2010

Non-Newtonian Properties of Relativistic Fluids

We show that relativistic fluids behave as non-Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier-Stokes equation is inadequate as the theory of relativistic fluids. Finally, the new microscopic formula to calculate the transport coefficients of the CDR fluid dynamics is discussed. The result of the microscopic formula is consistent with that of the Boltzmann equation, i.e., Grad's moment method.

hep-ph↗
arXiv2010

Does stability of relativistic dissipative fluid dynamics imply causality?

We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic dissipative fluid dynamics are always stable. We then perform a linear stability analysis in a Lorentz-boosted frame. Provided that the ratio of the relaxation time for the shear stress tensor, $τ_π$, to the sound attenuation length, $Γ_s = 4η/3(\varepsilon+P)$, fulfills a certain asymptotic causality condition, the equations of motion give rise to stable solutions. Although the group velocity associated with perturbations may exceed the velocity of light in a certain finite range of wavenumbers, we demonstrate that this does not violate causality, as long as the asymptotic causality condition is fulfilled. Finally, we compute the characteristic velocities and show that they remain below the velocity of light if the ratio $τ_π/Γ_s$ fulfills the asymptotic causality condition.

hep-ph↗
arXiv2010

Consistency of field-theoretical and kinetic calculations of viscous transport coefficients for a relativistic fluid

The transport coefficients of causal relativistic dissipative fluid dynamics are calculated both in a field-theoretical and a kinetic approach. We find that the results from the traditional kinetic calculation by Israel and Stewart are modified. The new expressions for the viscous transport coefficients agree with the results obtained in the field-theoretical approach when the contributions from pair creation and annihilation are neglected.

hep-th↗
arXiv2007

Status and Promise of Particle Interferometry in Heavy-Ion Collisions

After five years of running at RHIC, and on the eve of the LHC heavy-ion program, we highlight the status of femtoscopic measurements. We emphasize the role interferometry plays in addressing fundamental questions about the state of matter created in such collisions, and present an enumerated list of measurements, analyses and calculations that are needed to advance the field in the coming years.

nucl-ex↗
arXiv2007

Fermionic Collective Modes in QGP near Critical Temperatures

We investigate the quark spectrum in the quark-gluon plasma phase near color superconducting (CS) and chiral phase transitions. Owing to the precursory soft modes of the phase transitions, there appear novel excitaion spectra: In the CS transition, the quark matter shows non-Fermi liquid behavior and leads to the pseudogap in the density of states of quarks. In the chiral transition, three collective excitations appear in the quark spectrum.

hep-ph↗