Exact quantum states of a general time-dependent quadratic system from classical action

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous and one particular solutions. The kernels are then used to find wave functions which satisfy the Schr\"{o}dinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization which gives a rather complicated quadratic Hamiltonian is simply interpreted as acting an unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.

The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

Measuring non-extensitivity parameters in a turbulent Couette-Taylor flow

We investigate probability density functions of velocity differences at different distances r measured in a Couette-Taylor flow for a range of Reynolds numbers Re. There is good agreement with the predictions of a theoretical model based on non-extensive statistical mechanics (where the entropies are non-additive for independent subsystems). We extract the scale-dependent non-extensitivity parameter q(r, Re) from the laboratory data.Comment: 8 pages, 5 figure

Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedIn quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrodinger equation can be mapped to solutions of the Schrodinger equation for harmonic potentials, both the trapping oscillator and the inverted `oscillator'. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environmentPeer reviewe

Excited B mesons from the lattice

We determine the energies of the excited states of a heavy-light meson $Q\bar{q}$, with a static heavy quark and light quark with mass approximately that of the strange quark from both quenched lattices and with dynamical fermions. We are able to explore the energies of orbital excitations up to L=3, the spin-orbit splitting up to L=2 and the first radial excitation. These $b \bar{s}$ mesons will be very narrow if their mass is less than 5775 MeV -- the $BK$ threshold. We investigate this in detail and present evidence that the scalar meson (L=1) will be very narrow and that as many as 6 $b \bar{s}$ excited states will have energies close to the $BK$ threshold and should also be relatively narrow.Comment: 17 pages, 6 ps figure

Tribbles1 is host protective during in vivo mycobacterial infection

Tuberculosis is a major global health problem and is one of the top 10 causes of death worldwide. There is a pressing need for new treatments that circumvent emerging antibiotic resistance. Mycobacterium tuberculosis parasitises macrophages, reprogramming them to establish a niche in which to proliferate, therefore macrophage manipulation is a potential host-directed therapy if druggable molecular targets could be identified. The pseudokinase Tribbles1 (Trib1) regulates multiple innate immune processes and inflammatory profiles making it a potential drug target in infections. Trib1 controls macrophage function, cytokine production, and macrophage polarisation. Despite wide-ranging effects on leukocyte biology, data exploring the roles of Tribbles in infection in vivo are limited. Here, we identify that human Tribbles1 is expressed in monocytes and is upregulated at the transcript level after stimulation with mycobacterial antigen. To investigate the mechanistic roles of Tribbles in the host response to mycobacteria in vivo, we used a zebrafish Mycobacterium marinum (Mm) infection tuberculosis model. Zebrafish Tribbles family members were characterised and shown to have substantial mRNA and protein sequence homology to their human orthologues. trib1 overexpression was host-protective against Mm infection, reducing burden by approximately 50%. Conversely, trib1 knockdown/knockout exhibited increased infection. Mechanistically, trib1 overexpression significantly increased the levels of proinflammatory factors il-1β and nitric oxide. The host-protective effect of trib1 was found to be dependent on the E3 ubiquitin kinase Cop1. These findings highlight the importance of Trib1 and Cop1 as immune regulators during infection in vivo and suggest that enhancing macrophage TRIB1 levels may provide a tractable therapeutic intervention to improve bacterial infection outcomes in tuberculosis

Study of B→D∗∗πB\to D^{**} \pi decays

We investigate the production of the novel $P$-wave mesons $D^{*}_{0}$ and $D^{\prime}_{1} (D_{1})$, identified as $J^{P}=0^+$ and $1^+$, in heavy $B$ meson decays, respectively. With the heavy quark limit, we give our modelling wave functions for the scalar meson $D^{*}_{0}$. Based on the assumptions of color transparency and factorization theorem, we estimate the branching ratios of $B\to D^{*}_{0} \pi$ decays in terms of the obtained wave functions. Some remarks on $D^{(\prime)}_{1}$ productions are also presented.Comment: 16 pages, 2 figures, Revtex4, to be published in Phys. Rev.

Evidence for softening of first-order transition in 3D by quenched disorder

We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional 4-state Potts model which is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.Comment: LaTeX file with Revtex, 4 pages, 4 eps figure

A geometric approach to time evolution operators of Lie quantum systems

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.Comment: Accepted for publication in the International Journal of Theoretical Physic

Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte