Transport in Transitory Dynamical Systems

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case. This requires knowing only the "action" of relevant heteroclinic orbits at the intersection of invariant manifolds of "forward" and "backward" hyperbolic orbits. These manifolds can be easily computed by leveraging the autonomous nature of the vector fields on either side of the time-dependent transition. As illustrative examples we consider a two-dimensional fluid flow in a rotating double-gyre configuration and a simple one-and-a-half degree of freedom model of a resonant particle accelerator. We compare our results to those obtained using finite-time Lyapunov exponents and to adiabatic theory, discussing the benefits and limitations of each method.Comment: Updated and corrected version. LaTeX, 29 pages, 21 figure

New Class of Eigenstates in Generic Hamiltonian Systems

In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as $\hbar^{-\alpha}$ and relate the exponent $\alpha=1-1/\gamma$ to the decay of the classical staying probability $P(t)\sim t^{-\gamma}$. This is numerically confirmed for the kicked rotor by studying the influence of hierarchical states on eigenfunction and level statistics.Comment: 4 pages, 3 figures, Phys. Rev. Lett., to appea

Improvement of antitumor therapies based on vaccines and immune-checkpoint inhibitors by counteracting tumor-immunostimulationw

Immune-checkpoint inhibitors and antitumor vaccines may produce both tumor-inhibitory and tumor-stimulatory effects on growing tumors depending on the stage of tumor growth at which treatment is initiated. These paradoxical results are not necessarily incompatible with current tumor immunology but they might better be explained assuming the involvement of the phenomenon of tumor immunostimulation. This phenomenon was originally postulated on the basis that the immune response (IR) evoked in Winn tests by strong chemical murine tumors was not linear but biphasic, with strong IR producing inhibition and weak IR inducing stimulation of tumor growth. Herein, we extended those former observations to weak spontaneous murine tumors growing in pre-immunized, immune-competent and immune-depressed mice. Furthermore, we demonstrated that the interaction of specifical T cells and target tumor cells at low stimulatory ratios enhanced the production of chemokines aimed to recruit macrophages at the tumor site, which, upon activation of toll-like receptor 4 and p38 signaling pathways, would recruit and activate more macrophages and other inflammatory cells which would produce growth-stimulating signals leading to an accelerated tumor growth. On this basis, the paradoxical effects achieved by immunological therapies on growing tumors could be explained depending upon where the therapy-induced IR stands on the biphasic IR curve at each stage of tumor growth. At stages where tumor growth was enhanced (medium and large-sized tumors), counteraction of the tumor-immunostimulatory effect with anti-inflammatory strategies or, more efficiently, with selective inhibitors of p38 signaling pathways enabled the otherwise tumor-promoting immunological strategies to produce significant inhibition of tumor growth.Fil: Chiarella, Paula. Academia Nacional de Medicina de Buenos Aires; ArgentinaFil: Vermeulen, Mónica. Academia Nacional de Medicina de Buenos Aires; ArgentinaFil: Montagna, Daniela R.. Academia Nacional de Medicina de Buenos Aires; ArgentinaFil: Vallecorsa, Pablo. Academia Nacional de Medicina de Buenos Aires; ArgentinaFil: Strazza, Ariel Ramiro. Academia Nacional de Medicina de Buenos Aires; ArgentinaFil: Meiss, Roberto P.. Academia Nacional de Medicina de Buenos Aires; ArgentinaFil: Bustuoabad, Oscar D.. Retired; ArgentinaFil: Ruggiero, Raúl A.. Academia Nacional de Medicina de Buenos Aires; ArgentinaFil: Prehn, Richmond T.. University Of Washington, Seattle

Fractal Conductance Fluctuations in a Soft Wall Stadium and a Sinai Billiard

Conductance fluctuations have been studied in a soft wall stadium and a Sinai billiard defined by electrostatic gates on a high mobility semiconductor heterojunction. These reproducible magnetoconductance fluctuations are found to be fractal confirming recent theoretical predictions of quantum signatures in classically mixed (regular and chaotic) systems. The fractal character of the fluctuations provides direct evidence for a hierarchical phase space structure at the boundary between regular and chaotic motion.Comment: 4 pages, 4 figures, data on Sinai geometry added to Fig.1, minor change

Quantum Poincar\'e Recurrences

We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal value p=1 due to tunneling and localization effects. Experimental evidence of such decay should be observable in mesoscopic systems and cold atoms.Comment: revtex, 4 pages, 4 figure

Ulam method for the Chirikov standard map

We introduce a generalized Ulam method and apply it to symplectic dynamical maps with a divided phase space. Our extensive numerical studies based on the Arnoldi method show that the Ulam approximant of the Perron-Frobenius operator on a chaotic component converges to a continuous limit. Typically, in this regime the spectrum of relaxation modes is characterized by a power law decay for small relaxation rates. Our numerical data show that the exponent of this decay is approximately equal to the exponent of Poincar\'e recurrences in such systems. The eigenmodes show links with trajectories sticking around stability islands.Comment: 13 pages, 13 figures, high resolution figures available at: http://www.quantware.ups-tlse.fr/QWLIB/ulammethod/ minor corrections in text and fig. 12 and revised discussio

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

Asymptotic Statistics of Poincar\'e Recurrences in Hamiltonian Systems with Divided Phase Space

By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincar\'e recurrences P(\tau) and correlations C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p=3 should be also valid for a general chaos border.Comment: revtex, 4 pages, 3 ps-figure

Decay of Classical Chaotic Systems - the Case of the Bunimovich Stadium

The escape of an ensemble of particles from the Bunimovich stadium via a small hole has been studied numerically. The decay probability starts out exponentially but has an algebraic tail. The weight of the algebraic decay tends to zero for vanishing hole size. This behaviour is explained by the slow transport of the particles close to the marginally stable bouncing ball orbits. It is contrasted with the decay function of the corresponding quantum system.Comment: 16 pages, RevTex, 3 figures are available upon request from [email protected], to be published in Phys.Rev.

Integrability and Ergodicity of Classical Billiards in a Magnetic Field

We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not trivially integrable can be described by a "bouncing map". We compute a general expression for the Jacobian matrix of this map, which allows to determine stability and bifurcation values of specific periodic orbits. In some cases, the bouncing map is a twist map and admits a generating function which is useful to do perturbative calculations and to classify periodic orbits. We prove that billiards in convex domains with sufficiently smooth boundaries possess invariant tori corresponding to skipping trajectories. Moreover, in strong field we construct adiabatic invariants over exponentially large times. On the other hand, we present evidence that the billiard in a square is ergodic for some large enough values of the magnetic field. A numerical study reveals that the scattering on two circles is essentially chaotic.Comment: Explanations added in Section 5, Section 6 enlarged, small errors corrected; Large figures have been bitmapped; 40 pages LaTeX, 15 figures, uuencoded tar.gz. file. To appear in J. Stat. Phys. 8