We report measurements of the flux-integrated $\overline{\nu}_\mu$ and $\overline{\nu}_\mu+\nu_\mu$ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam with a mean beam energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced $\mu^\pm$ and no detected charged pion or proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton Module. The phase space of muons is restricted to the high-detection efficiency region, $p_{\mu}>400~{\rm MeV}/c$ and $\theta_{\mu}<30^{\circ}$, in the laboratory frame. An absence of pions and protons in the detectable phase spaces of $p_{\pi}>200~{\rm MeV}/c$, $\theta_{\pi}<70^{\circ}$ and $p_{\rm p}>600~{\rm MeV}/c$, $\theta_{\rm p}<70^{\circ}$ is required. In this paper, both the $\overline{\nu}_\mu$ cross-sections and $\overline{\nu}_\mu+\nu_\mu$ cross-sections on water and hydrocarbon targets and their ratios are provided by using the D’Agostini unfolding method. The results of the integrated $\overline{\nu}_\mu$ cross-section measurements over this phase space are $\sigma_{\rm H_{2}O}=(1.082\pm0.068(\rm stat.)^{+0.145}_{-0.128}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, $\sigma_{\rm CH}=(1.096\pm0.054(\rm stat.)^{+0.132}_{-0.117}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, and $\sigma_{\rm H_{2}O}/\sigma_{\rm CH} = 0.987\pm0.078(\rm stat.)^{+0.093}_{-0.090}(\rm syst.)$. The $\overline{\nu}_\mu+\nu_\mu$ cross-section is $\sigma_{\rm H_{2}O} = (1.155\pm0.064(\rm stat.)^{+0.148}_{-0.129}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, $\sigma_{\rm CH}=(1.159\pm0.049(\rm stat.)^{+0.129}_{-0.115}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, and $\sigma_{\rm H_{2}O}/\sigma_{\rm CH}=0.996\pm0.069(\rm stat.)^{+0.083}_{-0.078}(\rm syst.)$.
We have studied the contribution of high-scale SUSY to the |$K_L \to \pi ^0 \nu {\bar {\nu }}$| and |$K^+ \to \pi ^+ \nu {\bar {\nu }}$| processes by correlating with the CP-violating parameter |$\epsilon _K$|. Taking account of the recent LHC results for Higgs discovery and SUSY searches, we consider high-scale SUSY at the |$10$|–|$50$|TeV scale in the framework of non-minimal squark (slepton) flavor mixing. The Z penguin mediated chargino dominates the SUSY contribution for these decays. At the |$10$|TeV SUSY scale, the chargino contribution can enhance the branching ratio of |$K_L \to \pi ^0 \nu {\bar {\nu }}$| by eight times compared with SM predictions, whereas the predicted branching ratio |${\textit {BR}}(K^+ \to \pi ^+ \nu {\bar {\nu }})$| increases by up to three times that of the SM. The gluino box diagram dominates the SUSY contribution of |$\epsilon _K$| up to |$30{\%}$|. If down-squark mixing is neglected compared with up-squark mixing, the Z penguin mediated chargino dominates both SUSY contributions of |${\textit {BR}}(K_L \to \pi ^0 \nu {\bar {\nu }})$| and |$\epsilon _K$|. Then, a correlation between them is found, but the chargino contribution to |$\epsilon _K$| is at most |$3{\%}$|. Even if the SUSY scale is |$50$|TeV, the chargino process still enhances the branching ratio of |$K_L \to \pi ^0 \nu {\bar {\nu }}$| from the SM prediction by a factor of two, and |$\epsilon _K$| is deviated from the SM prediction by |$\mathcal {O}(10{\%})$|. We also discuss the chargino contribution to the |$K_L \to \pi ^0 e^+e^-$| process.
Many particle quantum hydrodynamics based on the Darwin Hamiltonian (the Hamiltonian corresponding to the Darwin Lagrangian) is considered. A force field appearing in corresponding Euler equation is considered in details. Contributions from different terms of the Darwin Hamiltonian in the Euler equation are traced. For example, the relativistic correction to the kinetic energy of particles leads to several terms in the Euler equation, these terms have different form. One of them has a form similar to a term appearing from the Darwin term. Hence, the two different mechanisms give analogous contributions in wave dispersion. Microscopic analog of the Biot-Savart law, called the current-current interaction and describing an interaction of moving charges via the magnetic field, is also included in our description. The semi-relativistic generalization of the quantum Bohm potential is obtained. Contribution of the relativistic effects in the spectrum of plasma collective excitations is considered.
It has been shown three different views in relativistic thermodynamics can be derived from the basic formulation proposed by van Kampen and Israel. The way to decompose energy-momentum into work and heat is not uniquely determined; the different choices result in different views. Also the definition of three dimensional volume causes ambiguity of thermodynamical quantities. The present paper shows various theories are obtained depending on the choice of these two factors.
We review a general theory of thermodynamics of information processing. The background of this topic is the recently-developed nonequilibrium statistical mechanics and quantum (and classical) information theory. These theories are closely related to the modern technologies to manipulate and observe small systems; for example, macromolecules and colloidal particles in the classical regime, and quantum-optical systems and quantum dots in the quantum regime.First, we review a generalization of the second law of thermodynamics to the situations in which small thermodynamic systems are subject to quantum feedback control. The generalized second law is expressed in terms of an inequality that includes the term of information obtained by the measurement, as well as the thermodynamic quantities such as the free energy. This inequality leads to the fundamental upper bound of the work that can be extracted by a "Maxwell's demon", which can be regarded as a feedback controller with a memory that stores measurement outcomes.Second, we review generalizations of the second law of thermodynamics to the measurement and information erasure processes of the memory of the demon that is a quantum system. The generalized second laws consist of inequalities that identify the lower bounds of the energy costs that are needed for the measurement and the information erasure. The inequality for the erasure leads to the celebrated Landauer's principle for a special case. Moreover, these inequalities enable us to reconcile Maxwell's demon with the second law of thermodynamics.In these inequalities, thermodynamic quantities and information contents are treated on an equal footing. In fact, the inequalities are model-independent, so that they can be applied to a broad class of information processing. Therefore, these inequalities can be called the second law of "information thermodynamics".
We calculate massive string scattering amplitudes of compactified open string in the Regge regime. We extract the complete infinite ratios among high-energy amplitudes of different string states in the fixed angle regime from these Regge string scattering amplitudes. The complete ratios calculated by this indirect method include and extend the subset of ratios calculated previously [J. C. Lee and Y. Yang, Nucl. Phys. B 784 (2007), 22; J. C. Lee, T. Takimi and Y. Yang, Nucl. Phys. B 804 (2008), 250] by the more difficult direct fixed angle calculation. In this calculation of compactified open string scattering, we discover a realization of arbitrary real values L in the identity Eq. (4.18), rather than integer value only in all previous high-energy string scattering amplitude calculations. The identity in Eq. (4-18) was explicitly proved recently in [J. C. Lee, C. H. Yan and Y. Yang, SIGMA 8 (2012), 045, arXiv:1012.5225] to link fixed angle and Rogge string scattering amplitudes. In addition, we discover a kinematic regime with stringy highly winding modes, which shows the unusual exponential fall-off behavior in the Regge string scattering. This is complimentary with a kinematic regime discovered previously [J. C. Lee, T. Takimi and Y. Yang, Nucl. Phys. B 804 (2008), 2501 which shows the unusual power-law behavior in the high-energy fixed angle compactified string scatterings.
Nielsen et al. have introduced a Riemannian metric on the space of n-qubit unitary operators [M. A. Nielsen, M. R. Dowling, M. Gu and A. C. Doherty, Science 311 (2006), 1133]. The length of the shortest curve connecting the identity I and a desired unitary operator W defined by this metric is essentially equivalent to the quantum gate complexity of W . This metric, and thus, the Riemannian geodesic equation for this metric, has a parameter q called “penalty” that must be large enough. In this paper, we investigate the sub-Riemannian geodesic equation obtained by taking the limit of the Riemannian geodesic equation as q → ∞, and show that the Riemannian geodesics for finite q can be explicitly constructed from the sub-Riemannian geodesics. We also present a numerical algorithm for finding the (sub-)Riemannian geodesics connecting I and W , which is based on the Krotov method in optimal control theory. As an example, we give an exact sub-Riemannian geodesic connecting I and the controlled-controlled-Z gate, which is obtained by guessing from the numerical results of the algorithm.
The lowest scalar and pseudoscalar glueball masses are evaluated by means of the time-dependent variational approach to the Yang-Mills gauge theory without fermions in the Hamiltonian formalism within a Gaussian wavefunctional approximation. The glueball mass is calculated as a pole of the propagator for a composite glueball field which consists of two massless gluons. The glueball propagator is here evaluated by using the linear response theory for the composite external glueball field. As a result, a finite glueball mass is obtained through the interaction between two massless gluons, in which the glueball mass depends on the QCD coupling constant g in the nonperturbative form.
The energy eigenstates for the su(4)-algebraic model for many-quark system obtained by the present authors in the Schwinger boson space are reconsidered in the original fermion space. Through this task, the structures of the single-quark and the quark-triplet are clarified. Variations of the su(4)-generators which have been adopted by the present authors are discussed.
We consider a method of obtaining exact implicit relations governing stationary solutions to the Wadati-Konno-Ichikawa-Shimizu (WKIS) equation. After a suitable transform, we put the WKIS equation into the form of a nonlinear ordinary differential equation. This equation has exact first and second integrals of motion. From this second integral, the exact equation governing the stationary solution to the WKIS equation is obtained. This relation may easily be inverted and plotted, to give the exact solution profiles. Furthermore, an exact formula for the period of oscillation in terms of the model parameters is obtained.
A molecular model developed for resonances observed in medium light heavy-ion collisions is described. At high spins in Si-28 + Si-28 (oblate-oblate system), a stable dinuclear configuration is found to be equator-equator touching one. The normal modes around the equilibrium are investigated. These modes are expected to be the origin of a large number of resonances observed. Furthermore, due to the axially asymmetric shape of the stale configuration of Si-28 + Si-28, the system rotates preferentially around the axis with the largest moment of inertia, which gives rise to wobbling motion (K-mixing). Energy spectra for the normal modes and for the extended model including the wobbling motion are given.
We investigate the electromagnetic mass differences of SU(3) baryons, using an "model-independent approach" within a chiral soliton model. The electromagnetic self-energy corrections to the masses of the baryon are expressed as the baryonic two-point correlation function of the electromagnetic currents. Using the fact that the electromagnetic current can be treated as an octet operator, and considering possible irreducible representations of the correlation function, we are able to construct a general collective operator for the electromagnetic self-energies, which consists of three unknown parameters. These parameters are fixed, the empirical data for the electromagnetic mass differences of the baryon octet being employed. We predict those of the baryon decuplet and antidecuplet. In addition, we obtain various mass relations between baryon masses within the corresponding representation with isospin symmetry breaking considered. We also predict the physical mass differences of the baryon decuplet. The results are in good agreement with the exisiting data.
As is well-known, in the conventional formulation of Bogoliubov's theory of an interacting Bose gas, the Hamiltonian (H) over cap is written as a decoupled sum of contributions from different momenta of the form (H) over cap = Sigma(k not equal 0) (H) over cap (k). Then, each of the single-mode Hamiltonians (H) over cap (k) is diagonalized separately, and the resulting ground state wavefunction of the total Hamiltonian (H) over cap is written as a simple product of the ground state wavefunctions of each of the single-mode Hamiltonians (H) over cap (k). While this way of diagonalizing the total Hamiltonian (H) over cap may seem to be valid from the perspective of the standard, number non-conserving Bogoliubov's method, where the k = 0 state is removed from the Hilbert space and hence the individual Hilbert spaces where the Hamiltonians {(H) over cap (k)} are diagonalized are disjoint from one another, we argue that from a number-conserving perspective this diagonalization method may not be adequate since the true Hilbert spaces where the Hamiltonians {(H) over cap (k)} should be diagonalized all have the k = 0 state in common, and hence the ground state wavefunction of the total Hamiltonian (H) over cap may not be written as a simple product of the ground state wavefunctions of the (H) over cap (k)'s. In this paper, we give a thorough review of Bogoliubov's method, and discuss a variational and number-conserving formulation of this theory in which the k = 0 state is restored to the Hilbert space of the interacting gas, and where, instead of diagonalizing the Hamiltonians (H) over cap (k) separately, we diagonalize the total Hamiltonian (H) over cap as a whole. When this is done, we find that the ground state energy is lowered below the Bogoliubov result, and the depletion of bosons is significantly reduced with respect to the one obtained in the number non-conserving treatment. We also find that the spectrum of the usual alpha(k) excitations of Bogoliubov's method changes from a gapless one, as predicted by the standard, number non-conserving formulation of this theory, to one which exhibits a finite gap in the k -> 0 limit. We discuss the presence of a gap in the spectrum of the alpha(k)'s in light of Goldstone's theorem, and show that there is no contradiction with the latter.
In this paper, we study the nonlinear sin(4)(phi) system in 1+1 dimensions which exhibits interesting nonlinear properties. We have categorized the system as radiative, since the collision of a kink and an antikink with velocities less than a threshold velocity leads to the complete annihilation of the pair and production of two high-amplitude wave packets with zero topological charges. Our results show that the individual kinks and antikinks are stable even against strong (nonlinear) perturbations. Other radiative systems similar to the sin(4)(phi) system are also studied. Finally, linear perturbations about the kink solution are examined in relation to the relaxation problem, by looking for the bound states of the resulting Schrodinger-like equation. Interestingly enough, the sin(4)(phi) system has only one trivial bound state with the omega(2) eigenvalue residing exactly at the top of the potential well. The significance of this property on the relaxation of the kink in this system is examined and compared to other nonlinear systems.
