From elongated spanning trees to vicious random walks

Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\nu} \log r$ with $\nu = (k^2-1)/2$. Considering the spanning forest stretched along the meridian of this watermelon, we see that the two--dimensional $k$--leg loop--erased watermelon exponent $\nu$ is converting into the scaling exponent for the reunion probability (at a given point) of $k$ (1+1)--dimensional vicious walkers, $\tilde{\nu} = k^2/2$. Also, we express the conjectures about the possible relation to integrable systems.Comment: 27 pages, 6 figure

Alpha-1–Adrenergic Receptors in Heart Failure: The Adaptive Arm of the Cardiac Response to Chronic Catecholamine Stimulation

Alpha-1-adrenergic receptors are G-protein coupled receptors (GPCRs) activated by catecholamines. The alpha-1A and alpha-1B subtypes are expressed in mouse and human myocardium, whereas the alpha-1D protein is found only in coronary arteries. There are far fewer alpha-1-ARs than beta-ARs in the non-failing heart, but their abundance is maintained or increased in the setting of heart failure, which is characterized by pronounced chronic elevation of catecholamines and b□eta-AR dysfunction. Decades of evidence from gain- and loss-of-function studies in isolated cardiac myocytes and numerous animal models demonstrate important adaptive functions for cardiac alpha-1-ARs, to include physiological hypertrophy, positive inotropy, ischemic preconditioning, and protection from cell death. Clinical trial data indicate that blocking alpha-1-ARs is associated with incident heart failure in patients with hypertension. Collectively, these findings suggest that alpha-1-AR activation might mitigate the well-recognized toxic effects of beta-ARs in the hyperadrenergic setting of chronic heart failure. Thus, exogenous cardioselective activation of alpha-1-ARs might represent a novel and viable approach to the treatment of heart failure

QuTiP: An open-source Python framework for the dynamics of open quantum systems

We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte-Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well-suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.Comment: 16 pages, 12 figure

Coupling ultracold atoms to mechanical oscillators

In this article we discuss and compare different ways to engineer an interface between ultracold atoms and micro- and nanomechanical oscillators. We start by analyzing a direct mechanical coupling of a single atom or ion to a mechanical oscillator and show that the very different masses of the two systems place a limit on the achievable coupling constant in this scheme. We then discuss several promising strategies for enhancing the coupling: collective enhancement by using a large number of atoms in an optical lattice in free space, coupling schemes based on high-finesse optical cavities, and coupling to atomic internal states. Throughout the manuscript we discuss both theoretical proposals and first experimental implementations.Comment: 19 pages, 9 figure

Light dark matter versus astrophysical constraints

Hints of direct dark matter detection coming from the DAMA, CoGeNT experiments point toward light dark matter with isospin-violating and possibly inelastic couplings. However an array of astrophysical constraints are rapidly closing the window on light dark matter. We point out that if the relic density is determined by annihilation into invisible states, these constraints can be evaded. As an example we present a model of quasi-Dirac dark matter, interacting via two U(1) gauge bosons, one of which couples to baryon number and the other which kinetically mixes with the photon. Annihilation is primarily into "dark neutrinos" that do not mix with the SM, but which could provide a small component of dark radiation. The model could soon be tested by several experiments searching for such light gauge bosons, and we predict that both could be detected. The model also requires a fourth generation of quarks, whose existence might increase the production cross section of Higgs bosons at the Tevatron and LHC.Comment: 11 pages, two figures; references added, published versio

Decoherence Suppression by Cavity Optomechanical Cooling

We consider a cavity optomechanical cooling configuration consisting of a mechanical resonator (denoted as resonator b) and an electromagnetic resonator (denoted as resonator a), which are coupled in such a way that the effective resonance frequency of resonator a depends linearly on the displacement of resonator b. We study whether back-reaction effects in such a configuration can be efficiently employed for suppression of decoherence. To that end, we consider the case where the mechanical resonator is prepared in a superposition of two coherent states and evaluate the rate of decoherence. We find that no significant suppression of decoherence is achievable when resonator a is assumed to have a linear response. On the other hand, when resonator a exhibits Kerr nonlinearity and/or nonlinear damping the decoherence rate can be made much smaller than the equilibrium value provided that the parameters that characterize these nonlinearities can be tuned close to some specified optimum values

V. Rondot, Tebytnis II, Le temple de Soknebtynis, Le Caire (2004)

OʼConnell Elisabeth R. V. Rondot, Tebytnis II, Le temple de Soknebtynis, Le Caire (2004). In: Topoi, volume 14/2, 2006. pp. 591-599

V. Rondot, Tebytnis II, Le temple de Soknebtynis, Le Caire (2004)

OʼConnell Elisabeth R. V. Rondot, Tebytnis II, Le temple de Soknebtynis, Le Caire (2004). In: Topoi, volume 14/2, 2006. pp. 591-599