A general method to describe intersystem crossing dynamics in trajectory surface hopping

Intersystem crossing is a radiationless process that can take place in a molecule irradiated by UV-Vis light, thereby playing an important role in many environmental, biological and technological processes. This paper reviews different methods to describe intersystem crossing dynamics, paying attention to semiclassical trajectory theories, which are especially interesting because they can be applied to large systems with many degrees of freedom. In particular, a general trajectory surface hopping methodology recently developed by the authors, which is able to include non-adiabatic and spin-orbit couplings in excited-state dynamics simulations, is explained in detail. This method, termed SHARC, can in principle include any arbitrary coupling, what makes it generally applicable to photophysical and photochemical problems, also those including explicit laser fields. A step-by-step derivation of the main equations of motion employed in surface hopping based on the fewest-switches method of Tully, adapted for the inclusion of spin-orbit interactions, is provided. Special emphasis is put on describing the different possible choices of the electronic bases in which spin-orbit can be included in surface hopping, highlighting the advantages and inconsistencies of the different approaches.Comment: 47 pages, 4 figure

K3 metrics from little string theory

Certain six-dimensional (1,0) supersymmetric little string theories, when compactified on $T^3$, have moduli spaces of vacua given by smooth K3 surfaces. Using ideas of Gaiotto-Moore-Neitzke, we show that this provides a systematic procedure for determining the Ricci-flat metric on a smooth K3 surface in terms of BPS degeneracies of (compactified) little string theories.Comment: 34 page

The gravitational S-matrix: Erice lectures

These lectures discuss an S-matrix approach to quantum gravity, and its relation to more local spacetime approaches. Prominent among the problems of quantum gravity are those of unitarity and observables. In a unitary theory with solutions approximating Minkowski space, the S-matrix (or, in four dimensions, related inclusive probabilities) should be sharply formulated and physical. Features of its perturbative description are reviewed. A successful quantum gravity theory should in particular address the questions posed by the ultrahigh-energy regime. Some control can be gained in this regime by varying the impact parameter as well as the collision energy. However, with decreasing impact parameter gravity becomes strong, first eikonalizing, and then entering the regime where in the classical approximation black holes form. Here one confronts what may be the most profound problem of quantum gravity, that of providing unitary amplitudes, as seen through the information problem of black hole evaporation. Existing approaches to quantum gravity leave a number of unanswered questions in this regime; there are strong indications that new principles and mechanisms are needed, and in particular there is a good case that usual notions of locality are inaccurate. One approach to these questions is investigation of the approximate local dynamics of spacetime, its observables, and its limitations; another is to directly explore properties of the gravitational S-matrix, such as analyticity, crossing, and others implied by gravitational physics.Comment: 44 pages, 15 figures; with exercises. Lectures presented at the 48th Course of the Erice International School of Subnuclear Physics, "What is known and unexpected at LHC," Aug./Sept. 2010. v2: repaired referenc

Extended orbital modeling of spin qubits in double quantum dots

Orbital modeling of two electron spins confined in a double quantum dot is revisited. We develop an extended Hund Mulliken approach that includes excited orbitals, allowing for a triplet configuration with both electrons residing in a single dot. This model improves the reliability and applicability of the standard Hund Mulliken approximation, while remaining largely analytical, thus it enables us to identify the mechanisms behind the exchange coupling dynamics that we find. In particular, our calculations are in close agreement with exchange values that were recently measured at a high interdot bias regime, where the double occupancy triplet configuration is energetically accessible, demonstrating reduced sensitivity to bias fluctuations, while maintaining the large exchange needed for fast gating.Comment: 13 pages, 9 figure

Quantum Decoherence During Inflation from Gravitational Nonlinearities

We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation $\zeta$ due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state $\Psi$ in the Schr\"odinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorterwavelength) modes of $\zeta$ as an environment. We show that inflation produces phase oscillations in the wave functional $\Psi[\zeta(\mathbf{x})]$, which suppress off-diagonal components of the reduced density matrix, leaving a diagonal mixture of different classical configurations. Gravitational nonlinearities thus provide a minimal mechanism for generating classical stochastic perturbations from inflation. We identify the time when decoherence occurs, which is delayed after horizon crossing due to the weak coupling, and find that Hubble-scale modes act as the decohering environment. We also comment on the observational relevance of decoherence and its relation to the squeezing of the quantum state.Comment: 32 pages, 10 figures. Comments welcom

The Cowl - v.82 - n.12 - Dec 7, 2017

The Cowl - student newspaper of Providence College. Volume 82, Number 12 - December 7, 2017. 28 pages

Chiral d-wave superconductivity in doped graphene

A highly unconventional superconducting state with a spin-singlet $d_{x^2-y^2}\pm id_{xy}$-wave, or chiral d-wave, symmetry has recently been proposed to emerge from electron-electron interactions in doped graphene. Especially graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverges, has been argued to likely be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.Comment: 51 pages, 8 figures. Invited topical review in J. Phys.:Condens. Matte

The calculation of expectation values in Gaussian random tensor theory via meanders

A difficult problem in the theory of random tensors is to calculate the expectation values of polynomials in the tensor entries, even in the large N limit and in a Gaussian distribution. Here we address this issue, focusing on a family of polynomials labeled by permutations, which naturally generalize the single-trace invariants of random matrix models. Through Wick's theorem, we show that the Feynman graph expansion of the expectation values of those polynomials enumerates meandric systems whose lower arch configuration is obtained from the upper arch configuration by a permutation on half of the arch feet. Our main theorem reduces the calculation of expectation values to those of polynomials labeled by stabilized-interval-free permutations (SIF) which are proved to enumerate irreducible meandric systems. This together with explicit calculations of expectation values associated to SIF permutations allows to exactly evaluate large N expectation values beyond the so-called melonic polynomials.Comment: 23 page

Voice Activity Detection: Merging Source and Filter-based Information

Voice Activity Detection (VAD) refers to the problem of distinguishing speech segments from background noise. Numerous approaches have been proposed for this purpose. Some are based on features derived from the power spectral density, others exploit the periodicity of the signal. The goal of this paper is to investigate the joint use of source and filter-based features. Interestingly, a mutual information-based assessment shows superior discrimination power for the source-related features, especially the proposed ones. The features are further the input of an artificial neural network-based classifier trained on a multi-condition database. Two strategies are proposed to merge source and filter information: feature and decision fusion. Our experiments indicate an absolute reduction of 3% of the equal error rate when using decision fusion. The final proposed system is compared to four state-of-the-art methods on 150 minutes of data recorded in real environments. Thanks to the robustness of its source-related features, its multi-condition training and its efficient information fusion, the proposed system yields over the best state-of-the-art VAD a substantial increase of accuracy across all conditions (24% absolute on average)

Boutroux curves with external field: equilibrium measures without a minimization problem

The nonlinear steepest descent method for rank-two systems relies on the notion of g-function. The applicability of the method ranges from orthogonal polynomials (and generalizations) to Painleve transcendents, and integrable wave equations (KdV, NonLinear Schroedinger, etc.). For the case of asymptotics of generalized orthogonal polynomials with respect to varying complex weights we can recast the requirements for the Cauchy-transform of the equilibrium measure into a problem of algebraic geometry and harmonic analysis and completely solve the existence and uniqueness issue without relying on the minimization of a functional. This addresses and solves also the issue of the ``free boundary problem'', determining implicitly the curves where the zeroes of the orthogonal polynomials accumulate in the limit of large degrees and the support of the measure. The relevance to the quasi--linear Stokes phenomenon for Painleve equations is indicated. A numerical algorithm to find these curves in some cases is also explained. Technical note: the animations included in the file can be viewed using Acrobat Reader 7 or higher. Mac users should also install a QuickTime plugin called Flip4Mac. Linux users can extract the embedded animations and play them with an external program like VLC or MPlayer. All trademarks are owned by the respective companies.Comment: 37 pages, 12 figures, 3 animations. Version 2: minor corrections and improved presentation. Version 3: small but critical correction on page 18-19. No change in conclusion