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Supermartingales are here defined on a non-probabilistic setting and can be interpreted solely in terms of superhedging operations. The classical expectation operator is replaced by a pair of subadditive operators one of them providing a class of null sets and the other one acting as an outer integral. These operators are motivated by a financial theory of no-arbitrage pricing. Such a setting extends the classical stochastic framework by replacing the path space of the process by a trajectory set, while also providing a financial/gambling interpretation based on the notion of superhedging. The paper proves analogues of the following classical results: Doob's supermartingale decomposition and Doob's pointwise convergence theorem for nonnegative supermartingales. The approach shows how linearity of the expectation operator can be circumvented and how integrability properties in the proposed setting lead to the special case of (hedging) martingales while no integrability conditions are required for the general supermartingale case.

Relativistic PT-symmetric fermionic interacting systems are studied in 1+1 and 3+1 dimensions. The objective is to include non-Hermitian PT-symmetric interaction terms that give {\it real} spectra. Such interacting systems could describe new physics. The simplest non-Hermitian Lagrangian density is $L=L_0+L_{int}=\bar\psi(i\not\partial-m)\psi-g\bar\psi\gamma^5\psi$. The associated relativistic Dirac equation is PT invariant in 1+1 dimensions and the associated Hamiltonian commutes with PT. However, the dispersion relation $p^2=m^2-g^2$ shows that the PT symmetry is broken in the chiral limit $m\to0$. For interactions $L_{int}=-g(\bar\psi\gamma^5\psi)^N$ with N=2,3, if the associated Dirac equation is PT invariant, the dispersion relation gives complex energies as $m\to0$. Other models are studied in which x-dependent PT-symmetric potentials such as $ix^3$, $-x^4$, $i\kappa/x$, Hulth\'en, or periodic potentials are coupled to $\psi$ and the classical trajectories plane are examined. Some combinations of these potentials give a real spectrum. In 3+1 dimensions, the simplest system $L=L_0+L_{int}=\bar\psi(i\not\partial-m)\psi-g\bar\psi\gamma^5\psi$ resembles the 1+1-dimensional case but the Dirac equation is not PT invariant because $T^2=-1$. This explains the appearance of complex eigenvalues as $m\to0$. Other Lorentz-invariant 2-point and 4-point interactions give non-Hermitian PT-symmetric terms in the Dirac equation. Only the axial vector and tensor Lagrangian interactions $L_{int}=-i\bar\psi\tilde B_\mu\gamma^5\gamma^\mu\psi$ and $L_{int}=-i\bar\psi T_{\mu\nu}\sigma^{\mu\nu}\psi$ fulfil both requirements of PT invariance of the associated Dirac equation and non-Hermiticity. Both models give complex spectra as $m\to0$. The effect on the spectrum of the additional constraint of selfadjointness of the Hamiltonian with respect to the PT inner product is investigated., Comment: 16 pages, 16 figures

APOGEE-2 is a high-resolution, near-infrared spectroscopic survey observing roughly 300,000 stars across the entire sky. It is the successor to APOGEE and is part of the Sloan Digital Sky Survey IV (SDSS-IV). APOGEE-2 is expanding upon APOGEE's goals of addressing critical questions of stellar astrophysics, stellar populations, and Galactic chemodynamical evolution using (1) an enhanced set of target types and (2) a second spectrograph at Las Campanas Observatory in Chile. APOGEE-2 is targeting red giant branch (RGB) and red clump (RC) stars, RR Lyrae, low-mass dwarf stars, young stellar objects, and numerous other Milky Way and Local Group sources across the entire sky from both hemispheres. In this paper, we describe the APOGEE-2 observational design, target selection catalogs and algorithms, and the targeting-related documentation included in the SDSS data releases., Comment: 19 pages, 6 figures. Accepted to AJ

Controlling and reversing the effects of loss are major challenges in optical systems. For lasers losses need to be overcome by a sufficient amount of gain to reach the lasing threshold. We show how to turn losses into gain by steering the parameters of a system to the vicinity of an exceptional point (EP), which occurs when the eigenvalues and the corresponding eigenstates of a system coalesce. In our system of coupled microresonators, EPs are manifested as the loss-induced suppression and revival of lasing. Below a critical value, adding loss annihilates an existing Raman laser. Beyond this critical threshold, lasing recovers despite the increasing loss, in stark contrast to what would be expected from conventional laser theory. Our results exemplify the counterintuitive features of EPs and present an innovative method for reversing the effect of loss., Comment: 44 pages (12 pages Main Text, 32 pages Supplementary Material), 20 figures (4 figures Main Text, 16 figures Supplementary Material), 34 references (30 references Main Text + 4 references Supplementary Material)

We are carrying out a large ancillary program with the SDSS-III, using the fiber-fed multi-object NIR APOGEE spectrograph, to obtain high-resolution H-band spectra of more than 1200 M dwarfs. These observations are used to measure spectroscopic rotational velocities, radial velocities, physical stellar parameters, and variability of the target stars. Here, we describe the target selection for this survey and results from the first year of scientific observations based on spectra that is publicly available in the SDSS-III DR10 data release. As part of this paper we present RVs and vsini of over 200 M dwarfs, with a vsini precision of ~2 km/s and a measurement floor at vsini = 4 km/s. This survey significantly increases the number of M dwarfs studied for vsini and RV variability (at ~100-200 m/s), and will advance the target selection for planned RV and photometric searches for low mass exoplanets around M dwarfs, such as HPF, CARMENES, and TESS. Multiple epochs of radial velocity observations enable us to identify short period binaries, and AO imaging of a subset of stars enables the detection of possible stellar companions at larger separations. The high-resolution H-band APOGEE spectra provide the opportunity to measure physical stellar parameters such as effective temperatures and metallicities for many of these stars. At the culmination of this survey, we will have obtained multi-epoch spectra and RVs for over 1400 stars spanning spectral types of M0-L0, providing the largest set of NIR M dwarf spectra at high resolution, and more than doubling the number of known spectroscopic vsini values for M dwarfs. Furthermore, by modeling telluric lines to correct for small instrumental radial velocity shifts, we hope to achieve a relative velocity precision floor of 50 m/s for bright M dwarfs. We present preliminary results of this telluric modeling technique in this paper., Comment: Submitted to Astronomical Journal

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric., Comment: 4 pages, 3 figures

We have observed a large sample of spectroscopic binary stars in the Hyades Cluster, using high resolution infrared spectroscopy to detect low mass companions. We combine our double-lined infrared measurements with well constrained orbital parameters from visible light single-lined observations to derive dynamical mass ratios. Using these results, along with photometry and theoretical mass-luminosity relationships, we estimate the masses of the individual components in our binaries. In this paper we present double-lined solutions for 25 binaries in our sample, with mass ratios from ~0.1-0.8. This corresponds to secondary masses as small as ~0.15 Msun. We include here our preliminary detection of the companion to vB 142, with a very small mass ratio of q=0.06+-0.04; this indicates that the companion may be a brown dwarf. This paper is an initial step in a program to produce distributions of mass ratio and secondary mass for Hyades cluster binaries with a wide range of periods, in order to better understand binary star formation. As such, our emphasis is on measuring these distributions, not on measuring precise orbital parameters for individual binaries., Comment: 36 pages, 8 figures, accepted for publication in The Astrophysical Journal

In this brief comment we attempt to clarify the apparent discrepancy between the papers [1] and [2] on the quantum brachistochrone, namely whether it is possible to use a judicious mixture of Hermitian and non-Hermitian quantum mechanics to evade the standard lower limit on the time taken for evolution by a Hermitian Hamiltonian with given energy dispersion between two given states.

We report the results of high spectral and angular resolution infrared observations of the multiple system GL 569 A and B that were intended to measure the dynamical masses of the brown dwarf binary believed to comprise GL 569 B. Our analysis did not yield this result but, instead, revealed two surprises. First, at age ~100 Myr, the system is younger than had been reported earlier. Second, our spectroscopic and photometric results provide support for earlier indications that GL 569 B is actually a hierarchical brown dwarf triple rather than a binary. Our results suggest that the three components of GL 569 B have roughly equal mass, ~0.04 Msun., Comment: 29 pages, 10 figures, accepted for publication in the Astrophysical Journal; minor corrections to Section 5.1; changed typo in 6.D

We use high resolution infrared spectroscopy to investigate the 2001 report by Gatewood and colleagues that rho CrB's candidate extrasolar planet companion is really a low-mass star with mass 0.14+-0.05 Msun. We do not detect evidence of such a companion; the upper bounds on the (companion/primary) flux ratio at 1.6 microns are less than 0.0024 and 0.005 at the 90 and 99% confidence levels, respectively. Using the H-band mass-luminosity relationship calculated by Baraffe and colleagues, the corresponding upper limits on the companion mass are 0.11 and 0.15 Msun. Our results indicate that the infrared spectroscopic technique can detect companions in binaries with flux ratios as low as 0.01 to 0.02., Comment: 22 pages, 10 figures, accepted for publication in the Astronomical Journal

Results of a ground-based optical monitoring campaign on NGC5548 in June 1998 are presented. The broad-band fluxes (U,B,V), and the spectrophotometric optical continuum flux F_lambda(5100 A) monotonically decreased in flux while the broad-band R and I fluxes and the integrated emission-line fluxes of Halpha and Hbeta remained constant to within 5%. On June 22, a short continuum flare was detected in the broad band fluxes. It had an amplitude of about ~18% and it lasted only ~90 min. The broad band fluxes and the optical continuum F_lambda(5100 A) appear to vary simultaneously with the EUV variations. No reliable delay was detected for the broad optical emission lines in response to the EUVE variations. Narrow Hbeta emission features predicted as a signature of an accretion disk were not detected during this campaign. However, there is marginal evidence for a faint feature at lambda = 4962 A with FWHM=~6 A redshifted by Delta v = 1100 km/s with respect to Hbeta_narrow., Comment: 12 pages, 7 figures, accepted for publishing in A&A

It is possible to extract work from a quantum-mechanical system whose dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in place of the heat bath used to run a conventional classical thermodynamic heat engine. The effect of the energy bath is to maintain the expectation value of the system Hamiltonian during an isoenergetic expansion. It is shown that the existence of such a bath leads to equilibrium quantum states that maximise the von Neumann entropy. Quantum analogues of certain thermodynamic relations are obtained that allow one to define the temperature of the energy bath., Comment: 4 pages, 1 figure

Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling perturbation series for the ground-state energy of the $\mathcal{PT}$-symmetric Hamiltonian $H=p^2+{1/4}x^2+i\lambda x^3$ recently studied by Bender and Dunne. For this purpose the first 193 (nonzero) coefficients of the Rayleigh-Schr\"odinger perturbation series in powers of $\lambda^2$ for the ground-state energy were calculated. Pad\'e-summation and Pad\'e-prediction techniques recently described by Weniger are applied to this perturbation series. The qualitative features of the results obtained in this way are indistinguishable from those obtained in the case of the perturbation series for the quartic anharmonic oscillator, which is known to be a Stieltjes series., Comment: 20 pages, 0 figures

A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes., Comment: 10 pages

The zeros of the eigenfunctions of self-adjoint Sturm-Liouville eigenvalue problems interlace. For these problems interlacing is crucial for completeness. For the complex Sturm-Liouville problem associated with the Schrodinger equation for a non-Hermitian PT-symmetric Hamiltonian, completeness and interlacing of zeros have never been examined. This paper reports a numerical study of the Sturm-Liouville problems for three complex potentials, the large-N limit of a -(ix)^N potential, a quasi-exactly-solvable -x^4 potential, and an ix^3 potential. In all cases the complex zeros of the eigenfunctions exhibit a similar pattern of interlacing and it is conjectured that this pattern is universal. Understanding this pattern could provide insight into whether the eigenfunctions of complex Sturm-Liouville problems form a complete set., Comment: 13 pages, RevTex, 6 figures, for related papers, see http://www.physics.emory.edu/faculty/boettcher/#PT

Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that are central to quasi-exact solvability. These two properties define a new class of semiclassically quasi-exactly solvable potentials., Comment: 12 pages, ReVTeX

A previous paper (hep-lat/9311011) proposed a new kind of random walk on a spherically-symmetric lattice in arbitrary noninteger dimension $D$. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension. This paper examines the nature of spherically-symmetric random walks in detail. We perform a large-time asymptotic analysis of these random walks and use the results to determine the Hausdorff dimension of the process. We obtain exact results in terms of Hurwitz functions (incomplete zeta functions) for the probability of a walker going from one region of the spherical lattice to another. Finally, we show that the probability that the paths of $K$ independent random walkers will intersect vanishes in the continuum limit if $D> {{2K}\over{K-1}}$., Comment: 40 pages, 4 figures, plain tex, tared and uuencoded, WU-HEP 94

A difficult and long-standing problem in mathematical physics concerns the determination of the value of $f(\infty)$ from the asymptotic series for $f(x)$ about $x\!=\!0$. In the past the approach has been to convert the asymptotic series to a sequence of Pad\'e approximants $\{P^n_n(x)\}$ and then to evaluate these approximants at $x\!=\!\infty$. Unfortunately, for most physical applications the sequence $\{P^n_n(\infty)\}$ is slowly converging and does not usually give very accurate results. In this paper we report the results of extensive numerical studies for a large class of functions $f(x)$ associated with strong-coupling lattice approximations. We conjecture that for large $n$, $P^n_n(\infty)\!\sim\!f(\infty)+B/\ln n $. A numerical fit to this asymptotic behavior gives an accurate extrapolation to the value of $f(\infty )$., Comment: plain TEX, 7 pages, 7 figures included, WASH-U-HEP-93

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, $N$-dependent, choice of an optimizing parameter $\l$, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of $\l$ the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$., Comment: 20 pages, LaTeX, Imperial/TP/92-93/55