arXiv subjects

T. Koide

Publications and source records attributed to T. Koide.

At least 37 records · Page 2Linked to original sources

arXiv2020

Variational formulation of compressible hydrodynamics in curved spacetime and symmetry of stress tensor

Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation becomes asymmetric for the exchange of the indices, differently from the standard Euclidean one. Its incompressible limit suggests that the viscous term should be represented with the Bochner Laplacian. Moreover the modified Navier-Stokes-Fourier (NSF) equation proposed by Brenner can be considered even in the curved spacetime. To confirm the compatibility with the symmetry principle, SVM is applied to the gauge-invariant Lagrangian of a charged compressible fluid and then the Lorentz force is reproduced as the interaction between the Abelian gauge fields and the viscous charged fluid.

gr-qc↗

arXiv2019

Quantum Smooth Boundary Forces from Constrained Geometries

We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is illustrated with the basic example of the one-dimensional motion of a free particle in an interval, and yields a fuzzy boundary, a position-dependent mass (PDM), and an extra potential on the quantum level. The consistency of our quantization is discussed by analyzing the semi-classical phase space portrait of the derived quantum dynamics, which is obtained as a regularization of its original classical counterpart.

quant-ph↗

arXiv2019

Novel Effect Induced by Spacetime Curvature in Quantum Hydrodynamics

The interplay between quantum fluctuation and spacetime curvature is shown to induce an additional quantum-curvature (QC) term in the energy-momentum tensor of fluid using the generalized framework of the stochastic variational method (SVM). The QC term is necessary to satisfy the momentum conservation but the corresponding quantum hydrodynamics is not necessarily cast into the form of the Schrödinger equation, differently from the case of the Euclidean spacetime. This seems to suggest that the existence of the Hilbert space is not a priori requirement in the quantization of curved spacetime systems. As an example, we apply the Friedmann-Robertson-Walker (FRW) metric and show that this effect contributes to the cosmological acceleration although it is too small in the present non-relativistic toy model.

quant-ph↗

arXiv2018

Generalization of Uncertainty Relation for Quantum and Stochastic Systems

The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.

quant-ph↗

arXiv2018

Anisotropic spin-density distribution and magnetic anisotropy of strained La$_{1-x}$Sr$_x$MnO$_3$ thin films: Angle-dependent x-ray magnetic circular dichroism

Magnetic anisotropies of ferromagnetic thin films are induced by epitaxial strain from the substrate via strain-induced anisotropy in the orbital magnetic moment and that in the spatial distribution of spin-polarized electrons. However, the preferential orbital occupation in ferromagnetic metallic La$_{1-x}$Sr$_x$MnO$_3$ (LSMO) thin films studied by x-ray linear dichroism (XLD) has always been found out-of-plane for both tensile and compressive epitaxial strain and hence irrespective of the magnetic anisotropy. In order to resolve this mystery, we directly probed the preferential orbital occupation of spin-polarized electrons in LSMO thin films under strain by angle-dependent x-ray magnetic circular dichroism (XMCD). Anisotropy of the spin-density distribution was found to be in-plane for the tensile strain and out-of-plane for the compressive strain, consistent with the observed magnetic anisotropy. The ubiquitous out-of-plane preferential orbital occupation seen by XLD is attributed to the occupation of both spin-up and spin-down out-of-plane orbitals in the surface magnetic dead layer.

cond-mat.mtrl-sci↗

arXiv2018

Nonequilibrium Work Relation from Schroedinger's Unrecognized Probability Theory

Jarzynski's nonequilibrium work relation can be understood as the realization of the (hidden) time-generator reciprocal symmetry satisfied for the conditional probability function. To show this, we introduce the reciprocal process where the classical probability theory is expressed with real wave functions, and derive a mathematical relation using the symmetry. We further discuss that the descriptions by the standard Markov process from an initial equilibrium state are indistinguishable from those by the reciprocal process. Then the Jarzynski relation is obtained from the mathematical relation for the Markov processes described by the Fokker-Planck, Kramers and relativistic Kramers equations.

cond-mat.stat-mech↗

arXiv2017

Quantum Analysis and Thermodynamic Operator Relations in Stochastic Energetics

We introduce a model of the quantum Brownian motion coupled to a classical neat bath by using the operator differential proposed in the quantum analysis. We then define the heat operator by adapting the idea of the stochastic energetics. The introduced operator satisfies the relations which are analogous to the first and second laws of thermodynamics.

cond-mat.stat-mech↗

arXiv2017

Perturbative Expansion of Irreversible Work in Fokker-Planck Equation a la Quantum Mechanics

We discuss the systematic expansion of the solution of the Fokker-Planck equation with the help of the eigenfunctions of the time-dependent Fokker-Planck operator. The expansion parameter is the time derivative of the external parameter which controls the form of an external potential. Our expansion corresponds to the perturbative calculation of the adiabatic motion in quantum mechanics. With this method, we derive a new formula to calculate the irreversible work order by order, which is expressed as the expectation value with a pseudo density matrix. Applying this method to the case of the harmonic potential, we show that the first order term of the expansion gives the exact result. Because we do not need to solve the coupled differential equations of moments, our method simplifies the calculations of various functions such as the fluctuation of the irreversible work per unit time. We further investigate the exact optimized protocol to minimize the irreversible work by calculating its variation with respect to the control parameter itself.

cond-mat.stat-mech↗

arXiv2017

More quantum centrifugal effect in rotating frame

The behaviour of quantum systems in non-inertial frames is revisited from the point of view of affine coherent state (ACS) quantization. We restrict our approach to the one-particle dynamics confined in a rotating plane about a fixed axis. This plane is considered as punctured due to the existence of the rotation center, which is viewed as a singularity. The corresponding phase space is the affine group of the plane and the ACS quantization enables us to quantize the system by respecting the affine symmetry of the true phase space. Our formulation predicts the appearance of an additional quantum centrifugal term, besides the usual angular momentum one, which prevents the particle to reach the singular rotation center. Moreover it helps us to understand why two different non-inertial Schrödinger equations are obtained in previous works. The validity of our equation can be confirmed experimentally by observing the harmonic oscillator bound states and the critical angular velocity for their existence.

quant-ph↗

arXiv2016

Schroedinger Equation in Rotating Frame by using Stochastic Variational Method

We give a pedagogical introduction of the stochastic variational method by considering the quantization of a non-inertial particle system. We show that the effects of fictitious forces are represented in the forms of vector fields which behave analogous to the gauge fields in the electromagnetic interaction. We further discuss that the operator expressions for observables can be defined by applying the stochastic Noether theorem.

math-ph↗

arXiv2016

Memory Effect in Upper Bound of Heat Flux Induced by Quantum Fluctuations

Thermodynamic behaviors in a quantum Brownian motion coupled to a classical heat bath is studied. We then define a heat operator by generalizing the stochastic energetics and show the energy balance (first law) and the upper bound of the expectation value of the heat operator (second law). We further find that this upper bound depends on the memory effect induced by quantum fluctuations and hence the maximum extractable work can be qualitatively modified in quantum thermodynamics.

quant-ph↗

arXiv2016

Anisotropy of Low Energy Direct Photons in Relativistic Heavy Ion Collisions

We investigate the behavior of low energy photons radiated by the deceleration processes of two colliding nuclei in relativistic heavy ion collisions using the Wigner function approach for electromagnetic radiation fields. The angular distribution reveals the information of the initial geometric configurations. Such a property is reflected in the anisotropic parameter $v_{2}$, showing an increasing $v_{2}$ as energy decreases, which is a behavior qualitatively different from $v_{2}$ from hadrons produced in the collisions.

nucl-th↗

arXiv2016

Quantum-classical hybrids in a simplified model of QED and geometric phase induced by charged particle trajectory

We derive a model of quantum-classical hybrids for a simplified model of quantum electrodynamics in the framework of the stochastic variational method. In this model, charged particle trajectories are affected by the interaction with quantized electromagnetic fields, and this quantum-classical interaction induces a displacement current. We further investigate a geometric phase in the wave functional of the gauge field configuration, which is induced by adiabatic motions of the charged particles. This phase contains the quantum-classical backreaction effect and usual Berry's phase is reproduced in the vanishing limit of the fluctuation of the charged particle trajectories.

quant-ph↗

arXiv2015

Thickness-dependent magnetic properties and strain-induced orbital magnetic moment in SrRuO3 thin films

Thin films of the ferromagnetic metal SrRuO3 (SRO) show a varying easy magnetization axis depending on the epitaxial strain and undergo a metal-to-insulator transition with decreasing film thickness. We have investigated the magnetic properties of SRO thin films with varying thicknesses fabricated on SrTiO3(001) substrates by soft x-ray magnetic circular dichroism (XMCD) at the Ru M2,3 edge. Results have shown that, with decreasing film thickness, the film changes from ferromagnetic to non-magnetic around 3monolayer thickness, consistent with previous magnetization and magneto-optical Kerr effect measurements. The orbital magnetic moment perpendicular to the film was found to be ~ 0.1μB/Ru atom, and remained nearly unchanged with decreasing film thickness while the spin magnetic moment decreases. Mechanism for the formation of the orbital magnetic moment is discussed based on the electronic structure of the compressively strained SRO film.

cond-mat.str-el↗

arXiv2015

Classicalization of Quantum Variables and Quantum-Classical Hybrids

The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids) is derived. In this procedure, conservation laws such as energy are maintained, and Ehrenfest's theorem is still satisfied with modification. The criterion for the applicability of quantum-classical hybrids is also discussed.

quant-ph↗

arXiv2015

Electronic and magnetic properties of off-stoichiometric Co$_\mathrm{2}$Mn$_β$Si/MgO interfaces studied by x-ray magnetic circular dichroism

We have studied the electronic and magnetic states of Co and Mn atoms at the interface of the Co$_\mathrm{2}$Mn$_β$Si (CMS)/MgO ($β$=0.69, 0.99, 1.15 and 1.29) magnetic tunnel junction (MTJ) by means of x-ray magnetic circular dichroism. In particular, the Mn composition ($β$) dependences of the Mn and Co magnetic moments were investigated. The experimental spin magnetic moments of Mn, $m_\mathrm{spin}$(Mn), derived from XMCD weakly decreased with increasing Mn composition $β$ in going from Mn-deficient to Mn-rich CMS films. This behavior was explained by first-principles calculations based on the antisite-based site-specific formula unit (SSFU) composition model, which assumes the formation of only antisite defect, not vacancies, to accommodate off-stoichiometry. Furthermore, the experimental spin magnetic moments of Co, $m_\mathrm{spin}$(Co), also weakly decreased with increasing Mn composition. This behavior was consistently explained by the antisite-based SSFU model, in particular, by the decrease in the concentration of Co$_\mathrm{Mn}$ antisites detrimental to the half-metallicity of CMS with increasing $β$. This finding is consistent with the higher TMR ratios which have been observed for CMS/MgO/CMS MTJs with Mn-rich CMS electrodes.

cond-mat.str-el↗

arXiv2015

Variational Principle of Hydrodynamics and Quantization by Stochastic Process

The well-known hydrodynamical representation of the Schrödinger equation is reformulated by extending the idea of Nelson-Yasue's stochastic variational method. The fluid flow is composed by the two stochastic processes from the past and the future, which are unified naturally by the principle of maximum entropy. We show that this formulation is easily applicable to the quantization of scalar fields.

quant-ph↗

arXiv2014

Noether Theorem of Relativistic-Electromagnetic Ideal Hydrodynamics

We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conserved quantity derived from the Noether theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion.

hep-th↗