Dynamical Gauge Boson and Strong-Weak Reciprocity

It is proposed that asymptotically nonfree gauge theories are consistently interpreted as theories of composite gauge bosons. It is argued that when hidden local symmetry is introduced, masslessness and coupling universality of dynamically generated gauge boson are ensured. To illustrate these ideas we take a four dimensional Grassmannian sigma model as an example and show that the model should be regarded as a cut-off theory and there is a critical coupling at which the hidden local symmetry is restored. Propagator and vertex functions of the gauge field are calculated explicitly and existence of the massless pole is shown. The beta function determined from the $Z$ factor of the dynamically generated gauge boson coincides with that of an asymptotic nonfree elementary gauge theory. Using these theoretical machinery we construct a model in which asymptotic free and nonfree gauge bosons coexist and their running couplings are related by the reciprocally proportional relation.Comment: 19 pages, latex, 6 eps figures, a numbers of corrections are made in the tex

Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions

We explore and describe the roles of inter-molecular vibrations employing a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions, which we use to analyze two-dimensional (2D) THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In addition to linear absorption (1D IR), we calculated 2D Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and methanol using an equilibrium non-equilibrium hybrid MD simulation. The calculated 1D IR and 2D THz-Raman signals are compared with results obtained from the LL+SL BO model applied through use of hierarchal Fokker-Planck equations with non-perturbative and non-Markovian noise. We find that all of the qualitative features of the 2D profiles of the signals obtained from the MD simulations are reproduced with the LL+SL BO model, indicating that this model captures the essential features of the inter-molecular motion. We analyze the fitted 2D profiles in terms of anharmonicity, nonlinear polarizability, and dephasing time. The origins of the echo peaks of the librational motion and the elongated peaks parallel to the probe direction are elucidated using optical Liouville paths.Comment: 37 pages with 14 figures and 3 table

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two- dimensionalcorrelation spectroscopy

We theoretically investigate an electron transfer (ET) process in a dissipative environment by means of two-dimensional (2D) correlation spectroscopy. We extend the reduced hierarchy equations of motion approach to include both overdamped Drude and underdamped Brownian modes. While the overdamped mode describes the inhomogeneity of a system in the slow modulation limit, the underdamped mode expresses the primary vibrational mode coupled with the electronic states. We outline a procedure for calculating 2D correlation spectrum that incorporates the ET processes. The present approach has the capability of dealing with system-bath coherence under an external perturbation, which is important to calculate nonlinear response functions for non-Markovian noise. The calculated 2D spectrum exhibits the effects of the ET processes through the presence of ET transition peaks along the $\Omega_1$ axis, as well as the decay of echo signals.Comment: 28 pages, 8 figures; J. Chem. Phys. 137 (2012

Role of non-collective excitations in heavy-ion fusion reactions and quasi-elastic scattering around the Coulomb barrier

Despite the supposed simplicity of double-closed shell nuclei, conventional coupled-channels calculations, that include all of the known collective states of the target and projectile, give a poor fit to the fusion cross section for the $^{16}$O + $^{208}$Pb system. The discrepancies are highlighted through the experimental barrier distribution and logarithmic derivative, that are both well defined by the precise experimental fusion data available. In order to broaden our search for possible causes for this anomaly, we revisit this system and include in our calculations a large number of non-collective states of the target, whose spin, parity, excitation energy and deformation paramter are known from high-precision proton inelastic-scattering measurements. Although the new coupled-channels calculations modify the barrier distribution, the disagreemnt with experiment remains both for fusion and for quasi-elastic (QE) scattering. We find that the Q-value distributions for large-angle QE scattering become rapidly more important as the incident energy increases, reflecting the trend of the experimental data. The mass-number dependence of the non-collective excitations is discussed.Comment: 8 pages, 7 figure

Iterative solution of a Dirac equation with inverse Hamiltonian method

We solve a singe-particle Dirac equation with Woods-Saxon potentials using an iterative method in the coordinate space representation. By maximizing the expectation value of the inverse of the Dirac Hamiltonian, this method avoids the variational collapse, in which an iterative solution dives into the Dirac sea. We demonstrate that this method works efficiently, reproducing the exact solutions of the Dirac equation.Comment: 4 pages, 3 figure

Correlated fluctuations in the exciton dynamics and spectroscopy of DNA

The absorption of ultraviolet light creates excitations in DNA, which subsequently start moving in the helix. Their fate is important for an understanding of photo damage, and is determined by the interplay of electronic couplings between bases and the structure of the DNA environment. We model the effect of dynamical fluctuations in the environment and study correlation, which is present when multiple base pairs interact with the same mode in the environment. We find that the correlations strongly affect the exciton dynamics, and show how they are observed in the decay of the anisotropy as a function of a coherence and a population time in a non-linear optical experiment

An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

Hierarchical Equations of Motion Approach to Quantum Thermodynamics

We present a theoretical framework to investigate quantum thermodynamic processes under non-Markovian system-bath interactions on the basis of the hierarchical equations of motion (HEOM) approach, which is convenient to carry out numerically "exact" calculations. This formalism is valuable because it can be used to treat not only strong system-bath coupling but also system-bath correlation or entanglement, which will be essential to characterize the heat transport between the system and quantum heat baths. Using this formalism, we demonstrated an importance of the thermodynamic effect from the tri-partite correlations (TPC) for a two-level heat transfer model and a three-level autonomous heat engine model under the conditions that the conventional quantum master equation approaches are failed. Our numerical calculations show that TPC contributions, which distinguish the heat current from the energy current, have to be take into account to satisfy the thermodynamic laws.Comment: 9 pages, 4 figures. As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Recent Progress and Outlook", (Springer International Publishing

Direct observation of the proliferation of ferroelectric loop domains and vortex-antivortex pairs

We discovered "stripe" patterns of trimerization-ferroelectric domains in hexagonal REMnO3 (RE=Ho, ---, Lu) crystals (grown below ferroelectric transition temperatures (Tc), reaching up to 1435 oC), in contrast with the vortex patterns in YMnO3. These stripe patterns roughen with the appearance of numerous loop domains through thermal annealing just below Tc, but the stripe domain patterns turn to vortex-antivortex domain patterns through a freezing process when crystals cross Tc even though the phase transition appears not to be Kosterlitz-Thouless-type. The experimental systematics are compared with the results of our six-state clock model simulation and also the Kibble-Zurek Mechanism for trapped topological defects