Session Y26: General Theory / Computational Physics I

Computation of Collision-Induced Absorption by dense Hydrogen-Helium gas mixtures up to Thousands of Kelvin, for Astrophysical Applications

The interaction-induced absorption by collisional pairs of H$_{2}$ molecules is an important opacity source in the atmospheres of the outer planets and cool stars. The emission spectra of cool white dwarf stars differ significantly in the infrared from the expected blackbody spectra of their cores, which is largely due to absorption by collisional H$_{2}$--H$_{2}$, H$_{2}$--He, and H$_{2}$--H complexes in the stellar atmospheres. Using quantum-chemical methods we compute the atmospheric absorption from hundreds to thousands of kelvin, as required, for example, in astrophysical analyses of objects, including cool white dwarf stars, brown dwarf stars, M dwarfs, cool main sequence stars, solar and extra-solar planets, and the formation of so-called first stars [1]. Comparisons of our calculations with laboratory measurements, which exist only at room temperature and below, show close agreement. \\[4pt] [1] Martin Abel, Lothar Frommhold, Xiaoping Li, and Katharine L. C. Hunt, ``Collision-Induced Absorption by H$_{2}$ pairs: From Hundreds to Thousands of Kelvin,'' J. Phys. A, 2011, 115 (25), pp 6805-6812   

Microcanonical entropy inflection points and their relationship to cooperative behavior

We discuss a method for the systematic classification of the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. The microcanonical entropy as the logarithm of the density of states is the fundamental quantity of statistical mechanics and can directly be obtained by means of contemporary generalized-ensemble computer simulation methodologies. Nowadays, the statistics achieved by employing these methods is sufficiently high such that the accuracy of the data allows for a very precise microcanonical analysis of ``phase'' transitions, even in mesoscopic systems, where finite-size and surface effects are significant. This can hardly be achieved by the far more prevalent conventional canonical approach. We demonstrate the power of this method in exemplified applications to long-standing problems of polymer and protein nucleation transitions.   

Improving Event Identification in the HF Calorimeter of CMS

The Forward Hadron Calorimeter (HF) of the Compact Muon Solenoid (CMS) at the Large Hadron Collider (LHC) lies in a region not covered by an inner tracking system, and we can rely only on the shapes of showers that hit the HF to determine whether or not they are due to electromagnetic particles. We review the current method of distinguishing shower types in the HF, and we bring attention to a drawback that will become present as the luminosity of the LHC increases and creates a need for tighter shower-shape cuts. We provide a method to correct this drawback, and we analyze the effectiveness of various tight cuts at isolating signal from background.   

The Effect of White Nonstationary and Colored Nonstationary Noise on Signal Detection

We analyze the effect of non-stationary noise on the detection of signals on unevenly sampled data. Initial frequency estimation is obtained from a Lomb-Scargle periodogram; which is followed by a global multi-start optimization, as working on a dense local Nelder-Mead iterator for parameter estimates. It has been found that a varying white noise level has no effect on the required relative signal-to-noise ratio for detection in the proposed algorithm, though affecting the absolute amplitude strength of the signal recording. Further analysis has been done on realistic colored noise. Different whitening routines have been incorporated to the proposed algorithm. Detection efficiency is compared for these different routines.   

Deteriorated Quality of Phase Distorted Gaussian Beams

The divergence of coherent optical beam is often characterized by the parameter $M^{2}$. For one transverse axis, this beam quality parameter is proportional to the product of the minimal observed beam size divided by the wavelength and multiplied by the divergence angle. Furthermore, $M^{2}$ is normalized such that its minimum value equals unity, which is achievable only by a Gaussian beam. An arbitrary phase distortion of a Gaussian beam increases $M^{2}$. Self-phase modulation is a common distortion in which the phase difference across the beam aperture is proportional to the beam intensity profile. For self-phase modulation, the deterioration of the beam quality parameter will depend on only one parameter, the phase at the center of the beam. We have found this dependence analytically. A general phase distortion profile can be represented by higher-order radial phase modes. We have also found the analytical dependence of $M^{2}$ in this generalized case. In addition, we derived expressions for beam quality deterioration of super-Gaussian beams due to phase distortions. If the waists of Gaussian and super-Gaussian beams are defined by a residual power criterion, which means both beams outside the same radius have the same amount of residual power, then a super-Gaussian beam will better tolerate phase distortions. It is important that all of our results cannot be efficiently reproduced by the traditional approach, based on the polynomial representation of aberrations, due to the poor convergence of power series for Gaussian profiles.   

Exponential tails near the band edges of a one-dimensional disordered exciton system in the Coherent Potential Approximation

We report the results of studies of the tails near the band edges of a one-dimensional Frenkel exciton system in the Coherent Potential Approximation (CPA). A Gaussian distribution of the transition frequencies with rms width $\sigma $ (0.1 $\le \sigma \le $ 2.0) is used. We found that the tails obey two different exponential power laws depending on the value of $\sigma $. In the weak disorder limit 0.1 $\le \sigma <$ 0.5, the tails of the absorption line shape and the density of states behave like $exp(-k|E|^{3/2} / \sigma^2)$, and in the strong disorder limit,\textit{0.5 $< \sigma \le $ 2.0}, the tails behave like $exp(-|E|^2 / \sigma^2)$. In the weak disorder limit, our CPA results are in excellent agreement with previous investigations.   

Elastic impurity scattering and relaxation in electronic lattice under finite electric-field

From the birth of solid state physics, understanding electron transport in solids has been one of the central questions. Recently, rigorous quantum mechanical treatments of solid nonequilibrium have been sought by many groups. Here, we discuss electron transport in tight-binding lattice with disordered potential scatterers when driven by a finite electric field. Based on Floquet formalism with non-perturbative treatment of the electric field, we investigate how the spectral properties evolve when the system is non-dissipative, governed by a \textit{closed} Hamiltonian. As the disorder becomes stronger, the spectra evolve from $\delta$-peaks representing Bloch oscillations to a continuous spectral distribution which is distinctly different from the non-interacting limit. We investigate the fate of electric current in the steady-state nonequilibrium. Finally, we discuss an implementation of energy dissipation channels and the way that the conventional Drude picture is recovered within the Floquet method as a function of Bloch oscillation frequency and electron relaxation-time.   

Universal resistance quantum in multichannel transport and dissipative field theory

The Landauer formula for coherent DC transport lies at the heart of nanoelectronics and embodies a startling prediction: the quantization of the conductance in one-dimensional metallic wires for ballistic transport, in steps of $R_q^{-1}=e^2/h$ for each channel. Scattering proccesses undergone by the electrons cause a deviation from this result. The resistance then depends on the transparency of the channel and assumes a nonuniversal value. Recently, the unit of resistance $R_q$ has been shown to be a universal feature for AC transport through a single-channel quantum RC circuit with a large cavity. This result can be understood by mapping the system to the one-channel Kondo model and the emergent low-energy Fermi-liquid theory. In a different context $R_q$ arises in a certain nonequilibrium setting for the multichannel quantum RC circuit. In this work, we study AC transport in the many-channel quantum RC circuit. Under certain well-defined conditions the charge relaxation resistance remains universal and equals $R_q$. We study the emergence of this universal resistance in the multi-channel limit by using the mapping with a dissipative particle on a ring and making an analogy with the Kondo model.   

Holon-Doublon Dynamics in Hubbard Ladders

Studies of the dynamics of holon-doublon pairs in Mott insulators have unveiled interesting and contrasting results with their band-insulator counterparts [1,2]. In the 1D Hubbard model, a paradigm for a Mott insulator, numerical evidence suggests that the mechanism for exciton decay into magnetic excitations is inefficient [1]. However, transition metal oxides are usually grown in layered superlattices and a real-time study of the holon-doublon propagation on ladders and other layered structures is therefore needed. In this talk, we present results for the real-time dynamics of holon-doublon pairs propagating in a \textit{two-leg} Hubbard ladder, a more realistic model for several SCMs. We use the time-dependent density matrix renormalization group (tDMRG) algorithm with a time-step-targetting Krylov method. We find that the ladder geometry changes the dynamics of the holon-doublon pair. A ``transfer" of the excitation between the ladder legs is seen, depending on the ratio between the couplings in the two leg directions. Furthermore, the time decay of the total double occupation is modified in the ladder as compared to the 1D case. \\[4pt] [1] K.A. Al-Hassanieh et al., PRL {\bf 100} 166403 (2008).\\[0pt] [2] L. Dias da Silva et al., PRB {\bf 81} 125113 (2010).   

First principles study of the spin-orbit coupling effect on the Tl-Pb superconducting alloy

We have studied the influence of spin-orbit coupling (SOC) on the phonon dispersion, the electron-phonon (e-ph) coupling and on the superconducting properties for the Pb-Tl alloy in the stable fcc-phase doping regime. This system have been studied within the framework of density functional perturbation theory, using a mixed-basis pseudopotential method and the virtual crystal approximation (VCA) for modeling the alloy. The Eliashberg spectral function ($\alpha^{2}F(\omega)$) and the electron-phonon coupling parameter ($\lambda$) have been calculated with and without SOC. The observed effects of SOC in the full phonon dispersion and $\alpha^{2}F(\omega)$ consist in a softening of the phonon frequencies and an increase of the e-ph coupling matrix elements, which become weaker on the Tl-rich side. SOC enhances $\lambda$ by as much as 48\% in some cases and improves its overall behavior as a function of the concentration for the alloy, leading to a very nice agreement with experimental data from tunneling measurements.   

Critical point of phase transitions of fractional order at Superconductors

This paper describes the behavior of thermodynamic values superconducting transition at temperature, tending to absolute zero. Using the thermodynamic arguments we demonstrate that superconductors can undergo third, fourth-, fifth- and higher (including fractional) order phase transitions (PT's) within the meaning of Baxter [1] (or Ehrenfest) as the temperature tending to zero. It is proved that the order of PT can be any real (fractional) number at some interval (from 2 to 8). It is established relation between critical exponent of specific heat and critical magnetic field for superconductor as the temperature tending to zero. It is proved that Ehrenfest classification of phase transitions does not work with a zero critical temperature. Note that the results are valid only in the case of thermodynamic equilibrium, making it difficult to reach experimentally at very low temperatures.\\[4pt] [1] Baxter R.J. Exactly Solved Models In Statistical Mechanics. -- London, New York, Sydney, Tokyo, Toronto. -- Academic press. -- 1982.   

Numerical simulation of dynamical response in superconducting quantum detectors

We numerically study the dynamical response of superconducting quantum detectors such as a single-photon detector, using the time-dependent Ginzburg-Landau equation coupled with heat diffusion and Maxwell equations. Our simulation shows a dynamical transition to a resistive state via an incident particle with energy higher than $T_{\rm c}$. We find that such a transition is associated with the generation of vortex-antivortex pairs and the occurrence of a normal-state region within the superconductor. We also discuss the applicability of this approach to a superconducting single-photon detector.   

Quantitative examination of out-of-phase mixed holographic gratings

Modern holographic applications require advanced photosensitive materials that particularly obey alterations of the complex permittivity with pronounced amplitudes of both real and imaginary parts on the sub-ps-time scale. Promising candidates such as amorphous and crystalline materials remarkably show a mutual phase-shift between phase and absorption gratings that complicates the analysis of the underlying wave-coupling mechanisms. Hence, theoretical descriptions that are simply based on Kogelnik's coupled-wave theory can not be applied, i.e., a formal approach to systematically derive the full parameter space of the gratings from diffraction efficiency measurements is missing in literature. We revised the analysis of the wave-coupling theory omitting former approximations or applying them later. As a result we derived a formal description for mixed gratings allowing for a full description of beam-coupling experiments. Both the modulations of the refractive index and the absorption coefficient as well as the phase shift between these gratings can be determined through measurements of the angular dependent diffraction efficiency around the positive and the negative Bragg angle. Our approach and results are demonstrated along a mixed grating with a most common parameter set.   

Extended phase diagram of ASEP with two types of particles

First introduced by Evans et al. (PR E, 74 208, (1995)), the Asymmetric Simple Exclusion Process (ASEP) has become an important model in the field. The model is simple in structure, however it offers an oppurtunity to study some of the basic characteristics of nonequilibrium systems. We use mean field, Monte Carlo, and RG methods to present a detailed phase diagram of the ASEP with two types of particles moving in opposite directions. The nature of the spontaneous symmetry broken phases will also be discussed.   

Non-Equilibrium Phase Transitions in the Baxter Model

The Baxter model in equilibrium is an exactly solved model for which the universality of the static critical phenomena does not hold [1]. The free energy has a branch-point singularity at a phase transition. The exponent of this singularity can range continuously from one to infinity. That is to say, this model has non-universal equilibrium critical exponents [2]. In our study, the non-equilibrium critical dynamics of the Baxter model which is in contact with two thermal baths is analyzed. Monte Carlo methods are applied to the system in which one of the bath is fixed at infinite temperature. The Baxter model is formulated as two interlacing spin-$1/2$ Ising models on a square lattice, interacting through a four spin coupling. The dynamics of the system is taken to be driven by ``spin exchanges'' of the neighbor spins in each lattice. We focus on the phase transitions of the system under this spin exchange dynamics. Preliminary results on the universality class properties of the non equilibrium phase transitions is presented. \\[4pt] [1] R.J. Baxter, Phys. Rev. Lett., {\bf 26}, 14 (1971).\\[0pt] [2] R.J. Baxter, J. Stat. Phys., {\bf 8}, 25 (1973).