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The ultimate goal of this project is to develop a systematic method for deriving quantum master equations that satisfy the requirements of a completely positive and trace-preserving (CPTP) map, further describing thermal relaxation processes. In this paper, we assume that the quantum master equation is obtained through the canonical quantization of the generalized Brownian motion proposed in [Physics Letters A, 494, 129277 (2024)]. At least classically, this dynamics describes the thermal relaxation process regardless of the choice of the system Hamiltonian. The remaining task is to identify the parameters ensuring that the quantum master equation meets complete positivity. We limit our discussion to many-body quadratic Hamiltonians and establish a CPTP criterion for our quantum master equation. This criterion is useful for applying our quantum master equation to models with interaction such as a network model, which has been used to investigate how quantum effects modify heat conduction., Comment: 9 pages, 1 figure

We introduce a generalized classical model of Brownian motion for describing thermal relaxation processes which is thermodynamically consistent. Applying the canonical quantization to this model, a quantum equation for the density operator is obtained. This equation has a thermal equilibrium state as its stationary solution, but the time evolution is not necessarily a Completely Positive and Trace-Preserving (CPTP) map. In the application to the harmonic oscillator potential, however, the requirement of the CPTP map is shown to be satisfied by choosing parameters appropriately and then our equation reproduces a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation satisfying the detailed balance condition. This result suggests a quantum-classical correspondence in thermal relaxation processes and will provide a new insight to the study of decoherence., Comment: 9 pages, no figure, the discussion of the local and global equations is added, Accepted for publication in Phys. Lett. A

We formulate thermodynamical relations based on the field degrees of freedom by introducing a work induced by the volume change in the function space, in addition to the usual work associated with the spatial volume change. The first and second laws of thermodynamics are defined for such a work inherent to the field theory by generalizing stochastic energetics (stochastic thermodynamics) to the classical real scalar field in contact with a heat bath. We further discuss the local equilibrium ansatz in the function space and show that it is possible to introduce a model of functional ideal hydrodynamics, which is consistent with the derived thermodynamical laws., Comment: 11 pages, one figure, typos were corrected

We propose new ideal hydrodynamics in the function space which describes a fluid composed of the 1+1 dimensional real scalar field in the framework of the stochastic variational method (SVM). In the derivation, the thermal equilibrium is assumed to the internal state of fluid elements in the function space of the scalar-field configuration. The deterministic trajectory of the functional fluid element is related to the functional generalization of the Bohmian trajectory in relativistic quantum field theory. To find the correspondence relation to standard hydrodynamics, a further coarse-graining should be introduced. Thus functional hydrodynamics is regarded as a mesoscopic theory such as the Boltzmann equation in the dynamical hierarchy of many-body systems. Functional hydrodynamics reproduces the exact behaviors of relativistic quantum field theory in a certain limit. We thus expect that our theory is applicable to study the influence of quantum-field theoretical fluctuation in collective flows of produced particles in relativistic heavy-ion collisions., Comment: 28 pages, one figure, typos were corrected

In the stochastic formulation of viscous hydrodynamics, the velocity of a fluid element fluctuates satisfying a similar relation to the quantum-mechanical uncertainty relation. Using a non-relativistic toy model, we show that the presence of such a velocity fluctuation increases the local anisotropy of the momentum distributions of produced hadrons, and thus the collective flow parameters such as $v_2$ is emphasized.

The prototypical diluted magnetic semiconductor Cd1-xMnxTe is a spin glass (x<0.6) or an antiferromagnet (x>0.6), but becomes ferromagnetic upon doping with a small amount of Cr atoms substituting for Mn. In order to investigate the origin of the ferromagnetism in Cd1-x-yMnxCryTe, we have studied its element specific magnetic properties by x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) at the Cr and Mn L2,3 edges. Thin films were grown by molecular beam epitaxy with a fixed Mn content of x = 0.2 and varying Cr content in the range of y = 0 - 0.04. Measured XAS and XMCD spectra indicate that both Cr and Mn atoms are divalent and that the ferromagnetic or superparamagnetic components of Cr and Mn are aligned in the same directions. The magnetization of Mn increases with increasing Cr content. These results can be explained if ferromagnetic interaction exists between neighboring Mn and Cr ions although interaction between Mn atoms is largely antiferromagnetic. We conclude that each ferromagnetic or superparamagnetic cluster consists of ferromagnetically coupled several Cr and a much larger number of Mn ions., Comment: 13 pages, 5 figures

The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work perturbatively which is applicable to systems with degeneracy in the eigenvalues of the Fokker-Planck operator. This method enables us to study how the geometrical symmetry affects thermodynamic description of a Brownian particle. To illustrate the application of the derived theory, we consider the Fokker-Planck equation with a two-dimensional harmonic potential. To investigate the effect of symmetry of the potential, we study thermodynamic properties in symmetric and asymmetric deformation processes of the potential: the rotational symmetry of the harmonic potential is held in the former, but it is broken in the latter. Optimized deformations in these processes are defined by minimizing mean works. Comparing these optimized processes, we find that the difference between the symmetric and asymmetric processes is maximized when the deformation time of the potential is given by a critical time which is characterized by the relaxation time of the Fokker-Planck equation. This critical time in the mean work is smaller than that of the change of the mean energy because of the hysteresis effect in the irreversible processes., Comment: 40 pages, 6 figures and 2 tables, typos were corrected

The van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$ (CGT) has a two-dimensional crystal structure where each layer is stacked through van der Waals force. We have investigated the nature of the ferromagnetism and the weak perpendicular magnetic anisotropy (PMA) of CGT by means of X-ray absorption spectroscopy and X-ray magnetic circular dichroism (XMCD) studies of CGT single crystals. The XMCD spectra at the Cr $L_{2,3}$ edge for different magnetic field directions were analyzed on the basis of the cluster-model multiplet calculation. The Cr valence is confirmed to be 3+ and the orbital magnetic moment is found to be nearly quenched, as expected for the high-spin $t_{2g}$$^3$ configuration of the Cr$^{3+}$ ion. A large ($\sim 0.2$ eV) trigonal crystal-field splitting of the $t_{2g}$ level caused by the distortion of the CrTe$_6$ octahedron has been revealed, while the single-ion anisotropy (SIA) of the Cr atom is found to have a sign {\it opposite} to the observed PMA and too weak compared to the reported anisotropy energy. The present result suggests that anisotropic exchange coupling between the Cr atoms through the ligand Te $5p$ orbitals having strong spin-orbit coupling has to be invoked to explain the weak PMA of CGT, as in the case of the strong PMA of CrI$_3$., Comment: 17 pages, 5 figures

A minimum uncertainty state for position and momentum of a fluid element is obtained. We consider a general fluid described by the Navier-Stokes-Korteweg (NSK) equation, which reproduces the behaviors of a standard viscous fluid, a fluid with the capillary action and a quantum fluid, with the proper choice of parameters. When the parameters of the NSK equation is adjusted to reproduce Madelung's hydrodynamic representation of the Schreodinger equation, the uncertainty relation of a fluid element reproduces the Kennard and the Robertson-Schreodinger inequalities in quantum mechanics. The derived minimum uncertainty state is the generalization of the coherent state and its uncertainty is given by a function of the shear viscosity. The viscous uncertainty can be smaller than the inviscid minimum value when the shear viscosity is smaller than a critical value which is similar in magnitude to the Kovtun-Son-Starinets (KSS) bound. This uncertainty reflects the information of the fluctuating microscopic degrees of freedom in the fluid and will modify the standard hydrodynamic scenario, for example, in heavy-ion collisions., Comment: 10 pages, 2 figures, discussions were added, accepted for the publication in JSTAT

We introduce the Poisson bracket operator which is an alternative quantum counterpart of the Poisson bracket. This operator is defined using the operator derivative formulated in quantum analysis and is equivalent to the Poisson bracket in the classical limit. Using this, we derive the quantum canonical equation which describes the time evolution of operators. In the standard applications of quantum mechanics, the quantum canonical equation is equivalent to the Heisenberg equation. At the same time, this equation is applicable to c-number canonical variables and then coincides with the canonical equation in classical mechanics. Therefore the Poisson bracket operator enables us to describe classical and quantum behaviors in a unified way. Moreover, the quantum canonical equation is applicable to non-standard system where the Heisenberg equation is not defined. As an example, we consider the application to the system where a c-number and a q-number particles coexist. The derived dynamics satisfies the Ehrenfest theorem and the energy and momentum conservations., Comment: 25 pages, no figure, the discussions of the Wigner function and Lindblad equation and references were added. Accepted for publication in Phys. Rev. A

The uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the paper by two of the present authors [Phys. Lett. A382, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in hydrodynamics. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid., Comment: 56 pages, 9 figures

We revisit the problem of the uncertainty relation for angle by using quantum hydrodynamics formulated in the stochastic variational method (SVM), where we need not define the angle operator. We derive both the Kennard and Robertson-Schroedinger inequalities for canonical variables in polar coordinates. The inequalities have state-dependent minimum values which can be smaller than \hbar/2 and then permit a finite uncertainty of angle for the eigenstate of the angular momentum. The present approach provides a useful methodology to study quantum behaviors in arbitrary canonical coordinates., Comment: 7 pages, no figure, discussions and references are added

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., Comment: 23 pages, no figure, discussions, comments and references are added

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., Comment: 22 pages, 14 figures, the title was changed, many references for the position-dependent mass were delited, the published version in J. Phys. A

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 Schr\"{o}dinger 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., Comment: 7 pages, no figure, one table. References were updated. Accepted for publication in Phys. Lett. A

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., Comment: 7 pages, no figure, the proceedings of DICE2016: Spacetime - Matter - Quantum Mechanics

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., Comment: 8 pages, no figure. Typos are corrected, and discussions and references are added. Accepted for publication in J. Phys. Commu

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., Comment: 20 pages, 4 figures

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 Schr\"{o}dinger 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., Comment: 5 pages, no figure, references are added

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., Comment: 28 pages, 4 figures, published version in J. Phys. A

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., Comment: 6 pages, no figure, the proceedings of 31st International Colloquium on Group Theoretical Methods in Physics

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., Comment: 7 pages,5 figures, one reference was added, accepted for publication in J. Phys. G

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., Comment: 6 pages, no figures, errors of equations and typo were corrected, references and discussion are added, accepted for publication in Phys. Rev. E

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., Comment: 7 pages, no figure

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 ~ 0.1{\mu}B/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., Comment: 6 pages, 6 figures, Submitted in Phys. Rev. B

We have studied the electronic and magnetic states of Co and Mn atoms at the interface of the Co$_\mathrm{2}$Mn$_{\beta}$Si (CMS)/MgO ($\beta$=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 ($\beta$) 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 $\beta$ 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 $\beta$. This finding is consistent with the higher TMR ratios which have been observed for CMS/MgO/CMS MTJs with Mn-rich CMS electrodes., Comment: 6 Pages, 4 figures, Submitted in J. Appl. Phys

The well-known hydrodynamical representation of the Schr\"{o}dinger 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., Comment: 13 pages, no figure, references were added

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., Comment: 6 pages, 5 figures, section 4.4 and two figures were added, typos were corrected

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., Comment: 13 pages, 2 figures

Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed directly from the gauge invariant Lagrangian. The gauge condition is used to choose dynamically independent variables. We verify that, in the Coulomb gauge condition, SVM result is completely equivalent to the traditional result. On the other hand, in the Lorentz gauge condition, SVM quantization can be performed without introducing the indefinite metric. The temporal and longitudinal components of the gauge filed, then, behave as c-number functionals affected by quantum fluctuation through the interaction with charged matter fields. To see further the relation between SVM and the canonical quantization, we quantize the usual gauge Lagrangian with the Fermi term and argue a stochastic process with a negative second order correlation is introduced to reproduce the indefinite metric., Comment: 20 pages, 1 figure

We have investigated the electronic and magnetic properties of Co-doped Pr0.8Ca0.2MnO3 thin films using various spectroscopic techniques. X-ray absorption and hard x-ray photoemission spectroscopy revealed that the substituted Co ions are in the divalent state, resulting in hole doping on the Mn atoms. Studies of element-selective magnetic properties by x-ray magnetic circular dichroism found a large orbital magnetic moment for the Co ions. These spectroscopic studies reveal that the substituted Co ions play several roles of hole doping for Mn, ferromagnetic superexchange coupling between the Co2+ and Mn4+ ions, and orbital magnetism of the Co2+ ions. Competition among these complex interactions produces the unique electronic and magnetic behaviors including enhanced coercivity of the Co-doped Pr0.8Ca0.2MnO3., Comment: 7 pages and 6 figures

In the perovskite-type Ca$_{1-x}$Ce$_{x}$MnO$_{3}$ (CCMO), one can control the transport and magnetic properties through varying Ce content. In the case of thin films, the properties can also be controlled by epitaxial strain from the substrate through changing it such as YAlO$_{3}$ (YAO), NdAlO$_{3}$ (NAO), and LaSrAlO$_{4}$ (LSAO). However, one cannot measure the magnetization of thin films on NAO substrates by conventional magnetization measurements because of the strong paramagnetic signals from the Nd$^{3+}$ ions. In order to eliminate the influence of Nd$^{3+}$ and to identify magnetic phases of the CCMO thin films, we have performed element-selective X-ray magnetic circular dichroism (XMCD) measurements of the Mn 2{\it p} core level. By studying the anisotropy of the XMCD intensity, we could unambiguously determine the magnetic phase diagram of the CCMO thin films., Comment: 8 pages, 3 figures, 1 table, accepted Solid State Communications

We address the physical meaning of hydrodynamic approach related with the coarse graining scale in the frame work of variational formulation. We point out that the local thermal equilibrium does not necessarily play a critical role in the description of the collective flow patterns. We further show that the effect of viscosity is also formulated in the form of the variational method including fluctuations., Comment: 5 pages, no figure, proceedings of SQM2013

The coercivity of La$_{1-x}$Sr$_x$MnO$_3$ thin films can be enhanced by Ru substitution for Mn. In order to elucidate its mechanism, we performed soft x-ray absorption and magnetic circular dichroism measurements at the Ru M$_{2,3}$ and Mn L$_{2,3}$ edges. We found that the spin direction of Ru and Mn are opposite and that Ru has a finite orbital magnetic moment. Cluster-model analysis indicated that the finite orbital magnetic moment as well as the reduced spin moment of Ru result from local lattice distortion caused by epitaxial strain from the SrTiO$_3$ substrate in the presence of spin-orbit interaction., Comment: 10 pages, 4 figures, 2 tables, accepted Applied Physics Letters

Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we discuss the complex Klein-Gordon equation. In this scheme, the Euler-Lagrangian equation for the stochastic fields leads to the functional Schroedinger equation, which in turn can be interpreted as the ideal fluid equation in the functional space. We show that the Fock state vector is given by the stationary solution of these differential equations and various results in the usual canonical quantization can be reproduced, including the effect of anti-particles. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, for example, in the definition of Noether charges., Comment: 38 pages, 4 figures, the errors of definitions are corrected and arguments are added

We report on x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) studies of the paramagnetic (Mn,Co)-co-doped ZnO and ferromagnetic (Fe,Co)-co-doped ZnO nano-particles. Both the surface-sensitive total-electron-yield mode and the bulk-sensitive total-fluorescence-yield mode have been employed to extract the valence and spin states of the surface and inner core regions of the nano-particles. XAS spectra reveal that significant part of the doped Mn and Co atoms are found in the trivalent and tetravalent state in particular in the surface region while majority of Fe atoms are found in the trivalent state both in the inner core region and surface region. The XMCD spectra show that the Fe$^{3+}$ ions in the surface region give rise to the ferromagnetism while both the Co and Mn ions in the surface region show only paramagnetic behaviors. The transition-metal atoms in the inner core region do not show magnetic signals, meaning that they are antiferromagnetically coupled. The present result combined with the previous results on transition-metal-doped ZnO nano-particles and nano-wires suggest that doped holes, probably due to Zn vacancy formation at the surfaces of the nano-particles and nano-wires, rather than doped electrons are involved in the occurrence of ferromagnetism in these systems., Comment: Proceedings of "XAFS theory and nanoparticles"

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., Comment: 11 pages, 1 figure, the Robertson-Schroedinger uncertainty relation is discussed. Accepted for publication in Phys, Lett. A

The hydrodynamic model including the spin degree of freedom and the electromagnetic field was discussed. In this derivation, we applied electromagnetism for macroscopic medium proposed by Minkowski. For the equation of motion of spin, we assumed that the hydrodynamic representation of the Pauli equation is reproduced when the many-body effect is neglected. Then the spin-magnetic interaction in the Pauli equation was converted to a part of the magnetization. The fluid and spin stress tensors induced by the many-body effect were obtained by employing the algebraic positivity of the entropy production in the framework of the linear irreversible thermodynamics, including the mixing effect of the irreversible currents. We further constructed the constitutive equation of the polarization and the magnetization. Our polarization equation is more reasonable compared to another result obtained using electromagnetism for macroscopic medium proposed by de Groot-Mazur., Comment: 24 pages, no figure, the discussion for the modifed thermodynamic relation is added, several errors are corrected, accepted for publication in PRC

We apply the stochastic variational method to the action of the ideal fluid and showed that the Navier-Stokes equation is derived. In this variational method, the effect of dissipation is realized as the direct consequence of the fluctuation dissipation theorem. Differently from the previous works \cite{kk1,kk2}, we parameterize the Lagrangian of SVM in more general form. The form of the obtained equation is not modified but the definition of the transport coefficients are changed. We further discuss the formulation of SVM using the Hamiltonian and show that the variation of the Hamiltonian gives the same result as the case of the Lagrangian., Comment: 9 pages, 3 figures, the proceeding of sigmaphi2011, Cyprus, 11, July, 2011

The stochastic variational method is applied to particle systems and continuum mediums. As the brief review of this method, we first discuss the application to particle Lagrangians and derive a diffusion-type equation and the Schr\"{o}dinger equation with the minimum gauge coupling. We further extend the application of the stochastic variational method to Lagrangians of continuum mediums and show that the Navier-Stokes, Gross-Pitaevskii and generalized diffusion equations are derived. The correction term for the Navier-Stokes equation is also obtained in this method. We discuss the meaning of this correction by comparing with the diffusion equation., Comment: 26 pages, no figures, Eq. (52) was corrected, references are added

We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term., Comment: 19 pages, 2 figures, Phys. Rev. E in press

We derive the equations of second order dissipative fluid dynamics from the relativistic Boltzmann equation following the method of W. Israel and J. M. Stewart. We present a frame independent calculation of all first- and second-order terms and their coefficients using a linearised collision integral. Therefore, we restore all terms that were previously neglected in the original papers of W. Israel and J. M. Stewart., Comment: 8 pages, added references and corrected typos; Proceedings for HCBM 2010: International Workshop on Hot and Cold Baryonic Matter 2010, 15-20 August 2010, Budapest, Hungary

We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation., Comment: 4 pages, 1 figure

In this work, we examine the effect of shear and bulk viscosities on elliptic flow by taking a realistic parameterization of the shear and bulk viscous coefficients, $\eta$ and $\zeta$, and their respective relaxation times, $\tau_{\pi}$ and $\tau_{\Pi}$. We argue that the behaviors close to ideal fluid observed at RHIC energies may be related to non-trivial temperature dependence of these transport coefficients., Comment: 6 pages, 4 figures, to appear in the proceedings of Strange Quark Matter 2009 (SQM09)

The effects of bulk viscosity on the elliptic flow $v_{2}$ are studied using realistic equation of state and realistic transport coefficients. We find that thebulk viscosity acts in a non trivial manner on $v_{2}$. At low $p_{T}$, the reduction of $v_{2}$ is even more effective compared to the case of shear viscosity, whereas at high $p_{T}$, an enhancement of $v_{2}$ compared to the ideal case is observed. We argue that this is caused by the competition of the critical behavior of the equation of state and the transport coefficients., Comment: 4 pages, 3 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee

We consider a stochastic model described by two stochastic differential equations of motion; one is for the stochastic evolution forward in time and the other for backward in time. We further introduce averaged quantities for the two processes and construct the extended thermodynamic relation following the strategy of Sekimoto. By using this relation, we derive the fluctuation theorems such as the Seifert relation, the Jarzynski relation and the Komatsu-Nakagawa non-equilibrium steady state with respect to the introduced averaged quantities., Comment: 14 pages, 1 figure

Effects of the bulk viscosity on the elliptic flow are studied. To introduce a realistic equation of state and transport coefficients, we apply the results of the lattice QCD and hadron resonance gas calculations for these quantities. We found that the bulk viscosity acts in a non trivial manner on the elliptic flow $v_{2}$. The reduction of $v_{2}$ is more effective at low $p_{T}$ compared to the case of shear viscosity, whereas at high $p_{T}$, the situation is reversed, leading to $v_{2}$ enhancement. We argue that this is caused by the competition of the critical behaviors of the equation of state and the transport coefficients. We further found that Grad's method with the 14 moments approximation is not applicable to estimate the viscous effects for the one-particle distribution function at the freeze out., Comment: 14 pages, 12 figures