Quantum dynamical phase transition in a system with many-body interactions

We introduce a microscopic Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency $\omega_{0}$. For weak interactions with the environment $1/\tau_{\mathrm{SE}}<2\omega_{0},$ we find a slower oscillation whose amplitude decays with a decoherence rate $1/\tau_{\phi}=1/(2\tau_{\mathrm{SE}})$. However, beyond a finite critical interaction with the environment, $1/\tau_{\mathrm{SE}}>2\omega_{0}$, the decoherence rate becomes $1/\tau_{\phi}\propto(\omega_{0}^{2})\tau_{\mathrm{SE}}$. The oscillation period diverges showing a \emph{quantum dynamical phase transition}to a Quantum Zeno phase.Comment: 5 pages, 3 figures, minor changes, fig.2 modified, added reference

Geometric approach to nonvariational singular elliptic equations

In this work we develop a systematic geometric approach to study fully nonlinear elliptic equations with singular absorption terms as well as their related free boundary problems. The magnitude of the singularity is measured by a negative parameter $(\gamma -1)$, for $0 < \gamma < 1$, which reflects on lack of smoothness for an existing solution along the singular interface between its positive and zero phases. We establish existence as well sharp regularity properties of solutions. We further prove that minimal solutions are non-degenerate and obtain fine geometric-measure properties of the free boundary $\mathfrak{F} = \partial \{u > 0 \}$. In particular we show sharp Hausdorff estimates which imply local finiteness of the perimeter of the region $\{u > 0 \}$ and $\mathcal{H}^{n-1}$ a.e. weak differentiability property of $\mathfrak{F}$.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis 201

Universality of the Lyapunov regime for the Loschmidt echo

The Loschmidt echo (LE) is a magnitude that measures the sensitivity of quantum dynamics to perturbations in the Hamiltonian. For a certain regime of the parameters, the LE decays exponentially with a rate given by the Lyapunov exponent of the underlying classically chaotic system. We develop a semiclassical theory, supported by numerical results in a Lorentz gas model, which allows us to establish and characterize the universality of this Lyapunov regime. In particular, the universality is evidenced by the semiclassical limit of the Fermi wavelength going to zero, the behavior for times longer than Ehrenfest time, the insensitivity with respect to the form of the perturbation and the behavior of individual (non-averaged) initial conditions. Finally, by elaborating a semiclassical approximation to the Wigner function, we are able to distinguish between classical and quantum origin for the different terms of the LE. This approach renders an understanding for the persistence of the Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our results in terms of the quantum--classical transition.Comment: 33 pages, 17 figures, uses Revtex

Becoming The Boss: Discretion And Postsuccession Success In Family Firms

Family firms can enjoy substantial longevity. Ironically, however, they are often imperiled by the very process that is essential to this longevity. Using the concept of managerial discretion as a starting point, we use a human agency lens to introduce the construct of successor discretion as a factor that affects the family business succession process. While important in general, successor discretion is positioned as a particularly relevant factor for productively managing organizational renewal in family businesses. This study represents a foundation for future empirical research investigating the role of agency in entrepreneurial action in the family business context, which consequently can contribute to the larger research literature on succession and change

New Results on Standard Solar Models

We describe the current status of solar modelling and focus on the problems originated with the introduction of solar abundance determinations with low CNO abundance values. We use models computed with solar abundance compilations obtained during the last decade, including the newest published abundances by Asplund and collaborators. Results presented here make focus both on helioseismic properties and the models as well as in the neutrino fluxes predictions. We also discuss changes in radiative opacities to restore agreement between helioseismology, solar models, and solar abundances and show the effect of such modifications on solar neutrino fluxes.Comment: 9 pages. Review talk presented at "Synergies between solar and stellar modelling", Rome, June 2009. To be published by Astrophysics and Space Scienc

Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory

The method of the quantum probability theory only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. In the present paper, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the quantum probability theory, we investigate quantum central limit theorem for continuous-time quantum walks on odd graphs.Comment: 19 page, 1 figure

Local time and the pricing of time-dependent barrier options

A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions $\phi$, barrier functions $b_\pm$ and linear diffusions $(S_t)_{t\in[0,T]}$. We show that the barrier premium can be expressed as a sum of integrals along the barriers $b_\pm$ of the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair of functions $(\Delta_+,\Delta_-)$ solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic

Selective quantum evolution of a qubit state due to continuous measurement

We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We discuss the Bayesian formalism for such ``selective'' evolution of an individual qubit and apply it to several solid-state setups. In particular, we show how to suppress the qubit decoherence using continuous measurement and the feedback loop.Comment: 15 pages (including 9 figures

Design of oversampled generalised discrete Fourier transform filter banks for application to subband-based blind source separation

A novel design of oversampled generalised discrete Fourier transform filter banks is proposed, with application to subband-based convolutive blind source separation (BSS), where either instantaneous BSS algorithms or joint BSS algorithms can be applied. Conventional filter banks design is usually focused on elimination of the overall aliasing error and the perfect reconstruction (PR) condition, which are required by traditional subband adaptive filtering applications. However, because of the unknown scaling factor, the traditional PR condition is not necessary in the context of subband BSS and can be relaxed in the design. Owing to the increased degrees of design freedom, the authors can introduce an additional cost function to enhance the mutual information between adjacent subband signals. Together with a reduced subband aliasing level, it leads to an improved subband permutation alignment result for instantaneous BSS and an overall better performance for the joint BSS