Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment

Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates

One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of chaotic systems is proportional to the hole size and independent of position. Here we give exact formulas for the subsequent terms, as sums of correlation functions; these depend on hole size and position, hence yield information on the closed system dynamics. Conversely, the theory can be readily applied to experimental design, for example to control escape rates.Comment: Originally 4 pages and 2 eps figures incorporated into the text; v2 has more numerical results and discussion: now 6 pages, 4 figure

Normal-Superfluid Interface Scattering For Polarized Fermion Gases

We argue that, for the recent experiments with imbalanced fermion gases, a temperature difference may occur between the normal (N) and the gapped superfluid (SF) phase. Using the mean-field formalism, we study particle scattering off the N-SF interface from the deep BCS to the unitary regime. We show that the thermal conductivity across the interface drops exponentially fast with increasing $h/k_B T$, where $h$ is the chemical potential imbalance. This implies a blocking of thermal equilibration between the N and the SF phase. We also provide a possible mechanism for the creation of gap oscillations (FFLO-like states) as seen in recent studies on these systems.Comment: 4 pages, 3 figure

Escape Rates and Physically Relevant Measures for Billiards with Small Holes

We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the scatterers. For a large class of smooth initial distributions, we establish the existence of a common escape rate and normalized limiting distribution. This limiting distribution is conditionally invariant and is the natural analogue of the SRB measure of a closed system. Finally, we prove that as the size of the hole tends to zero, the limiting distribution converges to the smooth invariant measure of the billiard map.Comment: 39 pages, 4 figure

Majorana spinors and extended Lorentz symmetry in four-dimensional theory

An extended local Lorentz symmetry in four-dimensional (4D) theory is considered. A source of this symmetry is a group of general linear transformations of four-component Majorana spinors GL(4,M) which is isomorphic to GL(4,R) and is the covering of an extended Lorentz group in a 6D Minkowski space M(3,3) including superluminal and scaling transformations. Physical space-time is assumed to be a 4D pseudo-Riemannian manifold. To connect the extended Lorentz symmetry in the M(3,3) space with the physical space-time, a fiber bundle over the 4D manifold is introduced with M(3,3) as a typical fiber. The action is constructed which is invariant with respect to both general 4D coordinate and local GL(4,M) spinor transformations. The components of the metric on the 6D fiber are expressed in terms of the 4D pseudo-Riemannian metric and two extra complex fields: 4D vector and scalar ones. These extra fields describe in the general case massive particles interacting with an extra U(1) gauge field and weakly interacting with ordinary particles, i.e. possessing properties of invisible (dark) matter.Comment: 24 page

Shared decision making in patients with low risk chest pain: prospective randomized pragmatic trial.

OBJECTIVE: To compare the effectiveness of shared decision making with usual care in choice of admission for observation and further cardiac testing or for referral for outpatient evaluation in patients with possible acute coronary syndrome. DESIGN: Multicenter pragmatic parallel randomized controlled trial. SETTING: Six emergency departments in the United States. PARTICIPANTS: 898 adults (aged \u3e17 years) with a primary complaint of chest pain who were being considered for admission to an observation unit for cardiac testing (451 were allocated to the decision aid and 447 to usual care), and 361 emergency clinicians (emergency physicians, nurse practitioners, and physician assistants) caring for patients with chest pain. INTERVENTIONS: Patients were randomly assigned (1:1) by an electronic, web based system to shared decision making facilitated by a decision aid or to usual care. The primary outcome, selected by patient and caregiver advisers, was patient knowledge of their risk for acute coronary syndrome and options for care; secondary outcomes were involvement in the decision to be admitted, proportion of patients admitted for cardiac testing, and the 30 day rate of major adverse cardiac events. RESULTS: Compared with the usual care arm, patients in the decision aid arm had greater knowledge of their risk for acute coronary syndrome and options for care (questions correct: decision aid, 4.2 v usual care, 3.6; mean difference 0.66, 95% confidence interval 0.46 to 0.86), were more involved in the decision (observing patient involvement scores: decision aid, 18.3 v usual care, 7.9; 10.3, 9.1 to 11.5), and less frequently decided with their clinician to be admitted for cardiac testing (decision aid, 37% v usual care, 52%; absolute difference 15%; P CONCLUSIONS: Use of a decision aid in patients at low risk for acute coronary syndrome increased patient knowledge about their risk, increased engagement, and safely decreased the rate of admission to an observation unit for cardiac testing.Trial registration ClinicalTrials.gov NCT01969240

Band alignment of epitaxial ZnS/Zn_(3)P_2 heterojunctions

The energy-band alignment of epitaxial zb-ZnS(001)/α-Zn_(3)P_(2)(001) heterojunctions has been determined by measurement of shifts in the phosphorus 2p and sulfur 2p core-level binding energies for various thicknesses (0.6–2.2 nm) of ZnS grown by molecular beam epitaxy on Zn_(3)P_(2). In addition, the position of the valence-band maximum for bulk ZnS and Zn3P2 films was estimated using density functional theory calculations of the valence-band density-of-states. The heterojunction was observed to be type I, with a valence-band offset, ΔE_V, of −1.19 ± 0.07 eV, which is significantly different from the type II alignment based on electron affinities that is predicted by Anderson theory. n^(+)-ZnS/p-Zn_(3)P_(2) heterojunctions demonstrated open-circuit voltages of >750 mV, indicating passivation of the Zn_(3)P_(2) surface due to the introduction of the ZnS overlayer. Carrier transport across the heterojunction devices was inhibited by the large conduction-band offset, which resulted in short-circuit current densities of <0.1 mA cm^(−2) under 1 Sun simulated illumination. Hence, constraints on the current density will likely limit the direct application of the ZnS/Zn_(3)P_(2) heterojunction to photovoltaics, whereas metal-insulator-semiconductor structures that utilize an intrinsic ZnS insulating layer appear promising

On the resonance eigenstates of an open quantum baker map

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside an annulus in the complex plane, $|z_{min}|\leq |z|\leq |z_{max}|$. We consider semiclassical sequences of eigenstates, such that the moduli of their eigenvalues converge to a fixed radius $r$. We prove that, if the moduli converge to $r=|z_{max}|$, then the sequence of eigenstates converges to a fixed phase space measure $\rho_{max}$. The same holds for sequences with eigenvalue moduli converging to $|z_{min}|$, with a different limit measure $\rho_{min}$. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius $|z_{min}|< r < |z_{max}|$, we identify families of eigenstates with precise self-similar properties.Comment: 32 pages, 2 figure

Au-Ag template stripped pattern for scanning probe investigations of DNA arrays produced by Dip Pen Nanolithography

We report on DNA arrays produced by Dip Pen Nanolithography (DPN) on a novel Au-Ag micro patterned template stripped surface. DNA arrays have been investigated by atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) showing that the patterned template stripped substrate enables easy retrieval of the DPN-functionalized zone with a standard optical microscope permitting a multi-instrument and multi-technique local detection and analysis. Moreover the smooth surface of the Au squares (abput 5-10 angstrom roughness) allows to be sensitive to the hybridization of the oligonucleotide array with label-free target DNA. Our Au-Ag substrates, combining the retrieving capabilities of the patterned surface with the smoothness of the template stripped technique, are candidates for the investigation of DPN nanostructures and for the development of label free detection methods for DNA nanoarrays based on the use of scanning probes.Comment: Langmuir (accepted