Optical properties of small polarons from dynamical mean-field theory

The optical properties of polarons are studied in the framework of the Holstein model by applying the dynamical mean-field theory. This approach allows to enlighten important quantitative and qualitative deviations from the limiting treatments of small polaron theory, that should be considered when interpreting experimental data. In the antiadiabatic regime, accounting on the same footing for a finite phonon frequency and a finite electron bandwidth allows to address the evolution of the optical absorption away from the well-understood molecular limit. It is shown that the width of the multiphonon peaks in the optical spectra depends on the temperature and on the frequency in a way that contradicts the commonly accepted results, most notably in the strong coupling case. In the adiabatic regime, on the other hand, the present method allows to identify a wide range of parameters of experimental interest, where the electron bandwidth is comparable or larger than the broadening of the Franck-Condon line, leading to a strong modification of both the position and the shape of the polaronic absorption. An analytical expression is derived in the limit of vanishing broadening, which improves over the existing formulas and whose validity extends to any finite-dimensional lattice. In the same adiabatic regime, at intermediate values of the interaction strength, the optical absorption exhibits a characteristic reentrant behavior, with the emergence of sharp features upon increasing the temperature -- polaron interband transitions -- which are peculiar of the polaron crossover, and for which analytical expressions are provided.Comment: 16 pages, 6 figure

Dielectric relaxation and intramolecular electron transfers

Intramolecular charge transfer are considered for the case that the motion of the system is on a single potential energy surface. The case where this motion occurred on two surfaces was considered elsewhere. The former is shown to be much preferable for studies of solvent dynamics. Several aspects of the relation between "constant charge" dielectric relaxation time of the polar solvent and the experimental decay time of emission from the polar excited state of the solute are discussed for hydrogen-bonded systems

Constraining the Location of Microlensing Objects by using the Finite Source Effect in EAGLE events

We propose a new method to constrain the location of microlensing objects using EAGLE (Extremely Amplified Gravitational LEnsing) events. We have estimated the rate of EAGLE events by taking the finite-source effect in to account. We found that the EAGLE event rate for using a 1-m class telescope w hose limiting magnitude is $V \sim 21$ is the same as or higher than that of the ordinary microlensing events which have been found to date. We have also found that the fraction of transit EAGLE events is large enough to detect: between $4 \sim 80$ depending on the lens location. Since the lens proper motion can be measured for a transit event, one can distinguish whether the lens is a MACHO (MAssive Compact Halo Object) in our hal o or one of the known stars in the Large Magellanic Cloud (LMC) from the proper motion measurement for each transit EAGLE event. Moreover, we show that the fraction of transit EAGLEs in all EAGLE events signif icantly depends on the lensing locations: the transit EAGLE fraction for the sel f-lensing case is $2 \sim 15$ times larger than that for halo MACHOs. Thus, one can constrain the location of lens objects by the statistics of the tr ansit events fraction. We show that we can reasonably expect $0 \sim 6$ transit events out of 21 EAGLE events in 3 years. We can also constrain the lens population properties at a gre ater than 99% confidence level depending on the number of transit events de tected. We also present the duration of EAGLE events, and show how an hourly ob servational mode is more suitable for an EAGLE event search program.Comment: 18 pages, 4 figures, accepted for publication in Ap

About the maximal rank of 3-tensors over the real and the complex number field

High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and Atkinson-Lloyd(1980). They treated the problem in the complex field, and we will present various bounds over the real field by proving several lemmas and propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen

Chebyshev approach to quantum systems coupled to a bath

We propose a new concept for the dynamics of a quantum bath, the Chebyshev space, and a new method based on this concept, the Chebyshev space method. The Chebyshev space is an abstract vector space that exactly represents the fermionic or bosonic bath degrees of freedom, without a discretization of the bath density of states. Relying on Chebyshev expansions the Chebyshev space representation of a bath has very favorable properties with respect to extremely precise and efficient calculations of groundstate properties, static and dynamical correlations, and time-evolution for a great variety of quantum systems. The aim of the present work is to introduce the Chebyshev space in detail and to demonstrate the capabilities of the Chebyshev space method. Although the central idea is derived in full generality the focus is on model systems coupled to fermionic baths. In particular we address quantum impurity problems, such as an impurity in a host or a bosonic impurity with a static barrier, and the motion of a wave packet on a chain coupled to leads. For the bosonic impurity, the phase transition from a delocalized electron to a localized polaron in arbitrary dimension is detected. For the wave packet on a chain, we show how the Chebyshev space method implements different boundary conditions, including transparent boundary conditions replacing infinite leads. Furthermore the self-consistent solution of the Holstein model in infinite dimension is calculated. With the examples we demonstrate how highly accurate results for system energies, correlation and spectral functions, and time-dependence of observables are obtained with modest computational effort.Comment: 18 pages, 13 figures, to appear in Phys. Rev.

Bandwidth-Controlled Insulator-Metal Transition and Correlated Metallic State in 5dd Transition Metal Oxides Srn+1_{n+1}Irn_{n}O3n+1_{3n+1} (nn=1, 2, and ∞\infty)

We investigated the electronic structures of the 5$d$ Ruddlesden-Popper series Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ ($n$=1, 2, and $\infty$) using optical spectroscopy and first-principles calculations. As 5$d$ orbitals are spatially more extended than 3$d$ or 4$d$ orbitals, it has been widely accepted that correlation effects are minimal in 5$d$ compounds. However, we observed a bandwidth-controlled transition from a Mott insulator to a metal as we increased $n$. In addition, the artificially synthesized perovskite SrIrO$_{3}$ showed a very large mass enhancement of about 6, indicating that it was in a correlated metallic state

Dynamical effects in electron transfer reactions

A theoretical treatment is given for the effect of intramolecular vibrational and diffusive solvent orientational motions on the rate of electron transfer reactions. Four limiting cases are considered for the two-electronic state problem: slow reaction, wide and narrow reaction window, and nondiffusing limits. With the aid of a decoupling approximation, an expression is derived for the reaction rate which reduces to the appropriate expression for each limiting case when the latter is approached. Under certain conditions the time dependence of the survival probability is multiexponential rather than single exponential. Because of this behavior two average survival times are defined and expressions for each are obtained. Experimental data are considered with the present treatment in mind. One feature of the present work is a more general analysis for the case that both vibrational and solvent diffusive motion contribute to the activation process. The relation to previous works in the literature is described