Abstract: The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state, which tends to the solution. We apply this time-dependent Hamiltonian approach to Grover's problem, i.e., searching a marked item in an unstructured database. We find that by adjusting the evolution rate of the Hamiltonian so as to keep the evolution adiabatic on each infinitesimal time interval, the total running time is of order $\sqrt{N},$ where N is the number of items in the database. We thus recover the advantage of Grover's standard algorithm as compared to a classical search, scaling as N. This is in contrast with the constant-rate adiabatic approach of Farhi et al. (e-print quant-ph/0001106), where the requirement of adiabaticity is expressed only globally, resulting in a time of order N.

Abstract: In Pre-Big-Bang and in Ekpyrotic Cosmology, perturbations on cosmological scales today are generated from quantum vacuum fluctuations during a phase when the Universe is contracting (viewed in the Einstein frame). The backgrounds studied to date do not yield a scale invariant spectrum of adiabatic fluctuations. Here, we present a new contracting background model (neither of Pre-Big-Bang nor of the Ekpyrotic form) involving a single scalar field coupled to gravity in which a scale-invariant spectrum of curvature fluctuations and gravitational waves results. The equation of state of this scalar field corresponds to cold matter. We demonstrate that if this contracting phase can be matched via a nonsingular bounce to an expanding Friedmann cosmology, the scale-invariance of the curvature fluctuations is maintained. We also find new background solutions for Pre-Big-Bang and for Ekpyrotic cosmology, which involve two scalar fields with exponential potentials with background values which are evolving in time. We comment on the difficulty of obtaining a scale-invariant spectrum of adiabatic fluctuations with background solutions which have been studied in the past.

Abstract: We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur, however, if the operating mode is propagating (nonevanescent) and guided at every point in the taper. Moreover, we demonstrate how straightforward taper designs in photonic crystals can violate these conditions, but that adiabaticity is restored by simple design principles involving only the independent band structures of the intermediate gratings. For these and other analyses, we develop a generalization of the standard coupled-mode theory to handle arbitrary nonuniform gratings via an instantaneous Bloch-mode basis, yielding a continuous set of differential equations for the basis coefficients. We show how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings. Unlike other numerical methods, our technique becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory. We also include numerical examples comparing to a well-established scattering-matrix method in two dimensions.

Abstract: We calculate the scalar gravitational and matter perturbations in the context of slow-roll inflation with multiple scalar fields, that take values on a (curved) manifold, to first order in slow roll. For this purpose a basis for these perturbations determined by the background dynamics is introduced and multiple-field slow-roll functions are defined. To obtain analytical solutions to first order, the scalar perturbation modes have to be treated in three different regimes. Matching is performed by identifying leading order asymptotic expansions analytically in different regions. The possible sources for multiple-field effects in the gravitational potential are the particular solution caused by the coupling to the field perturbation perpendicular to the field velocity, and the rotation of the basis. The former can contribute even to leading order if the corresponding multiple-field slow-roll function is sizable during the last 60 e-folds. Making some simplifying assumptions, the evolution of adiabatic and isocurvature perturbations after inflation is discussed. The analytical results are illustrated and checked numerically with the example of a quadratic potential.

Abstract: We analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'.

Abstract: A new molecular dynamics method for calculating free energy profiles for rare events is presented. The new method is based on the creation of an adiabatic separation between a reaction coordinate subspace and the remaining degrees of freedom within a molecular dynamics run. This is achieved by associating with the reaction coordinate(s) a high temperature and large mass, thereby allowing the activated process to occur while permitting the remaining degrees of freedom to respond adiabatically. In this limit, by applying a formal multiple time scale Liouville operator factorization, it can be rigorously shown that the free energy profile is obtained directly from the probability distribution of the reaction coordinate subspace and, therefore, no unbiasing of the configuration space or postprocessing of the output data is required. The new method is applied to a variety of model problems including a two-dimensional free energy surface and its performance tested against free energy calculations using the “blue moon ensemble” approach. The comparison shows that free energy profiles can be calculated with greater ease and efficiency using the new method.

Abstract: Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup and commonly addressed by laser fields. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the quantum Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation.

Abstract: We report on an investigation of student understanding of the first law of thermodynamics. The students involved were drawn from first-year university physics courses and a second-year thermal physics course. The emphasis was on the ability of the students to relate the first law to the adiabatic compression of an ideal gas. Although they had studied the first law, few students recognized its relevance. Fewer still were able to apply the concept of work to account for a change in temperature in an adiabatic process. Instead most of the students based their predictions and explanations on a misinterpretation of the ideal gas law. Even when ideas of energy and work were suggested, many students were unable to give a correct analysis. They frequently failed to differentiate the concepts of heat, temperature, work, and internal energy. Some of the difficulties that students had in applying the concept of work in a thermal process seemed to be related to difficulties with mechanics. Our findings also suggest that a misinterpretation of simple microscopic models may interfere with student ability to understand macroscopic phenomena. Implications for instruction in thermal physics and in mechanics are discussed.

Abstract: We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function depends only on the Hamming weight of the n bits. We also give two examples, closely related to these, where the similarity breaks down in that the quantum adiabatic algorithm succeeds in polynomial time whereas simulated annealing requires exponential time.

Abstract: Adiabatic vacuum states are a well-known class of physical states for linear quantum fields on Robertson-Walker spacetimes. We extend the definition of adiabatic vacua to general spacetime manifolds by using the notion of the Sobolev wavefront set. This definition is also applicable to interacting field theories. Hadamard states form a special subclass of the adiabatic vacua. We analyze physical properties of adiabatic vacuum representations of the Klein-Gordon field on globally hyperbolic spacetime manifolds (factoriality, quasiequivalence, local definiteness, Haag duality) and construct them explicitly, if the manifold has a compact Cauchy surface.

Abstract: We present a new 3D SPH code which solves the general relativistic field+hydrodynamics equations in the conformally flat approximation. Several test cases are considered to test different aspects of the code. We finally apply then the code to the coalescence of a neutron star binary system. The neutron stars are modeled by a polytropic equation of state (EoS) with adiabatic indices = 2 .0, = 2 .6 and = 3 .0. We calculate the gravitational wave signals, luminosities and frequency spectra by employing the quadrupole approximation for emission and back reaction in the slow motion limit. In addition, we consider the amount of ejected mass.

Abstract: Classical thermodynamics is concerned primarily with the interdependence of certain well-defined macroscopic concepts (temperature, pressure, entropy, energy, composition, etc.) possessed by a closed assembly. The usual thermodynamic equations are valid only for assemblies at equilibrium and for reversible transitions among such equilibrated assemblies. When thermodynamic considerations are applied to irreversible (i.e. “natural”) processes, the equations become inequalities, and are much less useful. For example, the principle of increase in entropy during an adiabatic irreversible process provides information only about the direction of the change. The theory of transformations is a description of a particular class of irreversible processes. This type of theory is the main concern of this chapter and may appropriately be described as kinetic. The connection between the microscopic properties of the systems of the assembly and the macroscopic (measurable) properties is made by statistical mechanics. The thermodynamics of irreversible processes has also been applied to chemical reactions, though only in the limiting case of very close approach to equilibrium.

Abstract: Adiabatic film cooling effectiveness on a flat plate surface downstream of a row of cylindrical holes is investigated. Highly resolved two dimensional surface data were measured by means of infrared thermography and carefully corrected for local conduction and radiation effects [1]. These locally acquired data are laterally averaged to give the streamwise distributions of the effectiveness. An independent variation of the flow parameters blowing rate, density ratio, and turbulence intensity as well as the geometrical parameters streamwise ejection angle and hole spacing is examined. The influences of these parameters on the laterally effectiveness is discussed and interpreted with the help of surface distributions of effectiveness and heat transfer coefficients presented in earlier publications [1, 2]. Besides the known jet in cross-flow behavior of coolant ejected from discrete holes, these data demonstrate the effect of adjacent jet interaction and its impact on jet lift-off and adiabatic effectiveness. In utilizing this large matrix of measurements the effect of single parameters and their interactions are correlated. The important scaling parameters of the effectiveness are shaped out during the correlation process and are discussed. The resulting new correlation is designed to yield the quantitatively correct effectiveness as a result of the interplay of the jet in crossflow behavior and the adjacent jet interaction. It is built modularly to allow for future inclusion of additional parameters. The new correlation is valid without any exception within the full region of interest, reaching from the point of the ejection to far downstream, for all combinations of flow and geometry parameters.Copyright © 2002 by ASME

Abstract: We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.

Abstract: We propose a mechanism by which an open quantum dot driven by two ac (radio frequency) gate voltages in the presence of a moderate in-plane magnetic field generates a spin-polarized, phase-coherent dc current. The idea combines adiabatic, nonquantized (but coherent) pumping through periodically modulated external parameters and the strong fluctuations of the electron wave function existent in chaotic cavities. We estimate that the spin polarization of the current can be observed for temperatures and Zeeman splitting energies of the order of the single-particle mean level spacing.

Abstract: Nitromethane is a prototypical example for a molecule that can bind an extra electron in two fundamentally different ways forming dipole-bound as well as valence anions. The classification of the electronic states as dipole-bound or valence does in fact suggest a diabatic viewpoint, and we investigate the coupling between these two electronic states of the nitromethane anion. The coupling element W is extracted from a cut through the two lowest adiabatic potential energy surfaces by fitting of a simple avoided crossing model potential, that is, W is effectively approximated as half the smallest splitting. High level ab initio calculations are performed to compute the two states along the cut. We discuss in particular how a balance between the two very different electronic states can be achieved, and how the temporary nature of the valence anion in a large region of the relevant nuclear coordinate space can be taken into account. The autodetachment lifetime following vertical electron attachment to the neutral is computed, but the calculation of the temporary anion state turns out to be too expensive for a study of the two adiabatic surfaces, and consequently, the second adiabatic state is only included at geometries where it lies below the neutral potential energy surfaces. We find a coupling matrix element of 30 meV. On the one hand, this value is much smaller than the vertical excitation energies underlining the need for a diabatic picture. On the other hand, this value suggests rapid transitions on a mass spectrometric timescale substantiating the notion that the dipole bound state provides an efficient doorway for attachment to the valence state.

Abstract: A quadratic free energy relationship (FER) between the kinetic activation free energy ΔG⧧ and the thermodynamic reaction asymmetry ΔGRXN is derived for acid-base ionization proton-transfer reactions AH···B→ A-···HB+ in a polar environment in the proton adiabatic regime, in which the proton is treated quantum mechanically, but does not tunnel. The description differs from traditional treatments in both the proton quantization and the identification of a solvent coordinate as the reaction coordinate. The key coefficients in the FER are analyzed analytically for the simplified case, where the proton donor−acceptor distance is held fixed (a restriction removed in the following paper). In particular, the intrinsic barrier is shown to be the sum of an intrinsic solvent barrier, largely determined by solvent reorganization, and the zero point energy difference of the proton between the reactant and the transition state in a solvent coordinate. The Bronsted coefficient is related to the quantum proton-averaged so...

Abstract: Molecular reaction dynamics in the adiabatic representation is complicated by the existence of conical intersections and the associated geometric phase effect. The first-derivative coupling vector between the corresponding electronically adiabatic states can, in general, be decomposed into longitudinal (removable) and transverse (nonremovable) parts. At intersection geometries, the longitudinal part is singular, whereas the transverse part is not. In a two-electronic-state Born–Huang expansion, an adiabatic-to-diabatic transformation completely eliminates the contribution of the longitudinal part to the nuclear motion Schrodinger equation, leaving however the transverse part contribution. We report here the results of an accurate calculation of this transverse part for the 1 2A′ and 2 2A′ electronic states of H3 obtained by solving a three-dimensional Poisson equation over the entire domain U of internal nuclear configuration space Q of importance to reactive scattering. In addition to requiring a knowledge of the first-derivative coupling vector everywhere in U, the solution depends on an arbitrary choice of boundary conditions. These have been picked so as to minimize the average value over U of the magnitude of the transverse part, resulting in an optimal diabatization angle. The dynamical importance of the transverse term in the diabatic nuclear motion Schrodinger equation is discussed on the basis of its magnitude not only in the vicinity of the conical intersection, but also over all of the energetically accessible regions of the full U domain. We also present and discuss the diabatic potential energy surfaces obtained by this optimal diabatization procedure.

Abstract: The R-matrix method is used to calculate dissociative excitation cross sections for the four lowest-lying electronically excited states of H2O in the energy range 5-15 eV. For the first time calculations are performed taking into account the nuclear motion by means of an adaptation of the adiabatic nuclei approximation. Cross sections are compared with previous and new fixed-nuclei results and also experiments. Resonance positions and widths are calculated for different geometries of the water molecule.

Abstract: The ab initio molecular dynamics method is extended to treat exchange of electrons between molecules and a reservoir at fixed chemical potential. The method is based on a rigorously grand-canonical density functional approach using separate potential energy surfaces for each oxidation state. It is shown that the resulting discontinuous dependency of excess charge on chemical potential is consistent with the statistical thermodynamics of equilibrium gas-phase reactions. The method is illustrated by an application to the adiabatic redox dynamics of an aniline molecule.

Abstract: We examine the adiabatic limit of population transfer in two-level models driven by a chirped laser field. We show that the nonadiabatic correction is minimized when the adiabatic eigenenergies associated to the dynamics are parallel. In the diagram of the difference of the eigenenergy surfaces as a function of the parameters, this corresponds to an adiabatic passage along a level line. The analytical arguments are based on the Dykhne-Davis-Pechukas treatment. We illustrate this behavior with various examples.

Abstract: We present a class of exact solutions of the Einstein gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solution is represented in a closed integral form. The energy density and both radial and tangential pressure are finite and positive inside the anisotropic star. The energy density, radial pressure, pressure-density ratio and the adiabatic speed of sound are monotonically decreasing functions. Several stellar models with the anisotropy coefficient proportional to r2 are discussed, the values of the basic physical parameters of the star (radius, mass and red shift) and bound on anisotropy parameter is obtained.

Abstract: We show that two overlapping linearly polarized laser pulses of frequencies ω and its second harmonic 2ω can strongly orient linear polar molecules, by adiabatic passage along dressed states. The resulting robust orientation can be interpreted as a laser-induced localization in the effective double well potential created by the fields, which induces a preliminary molecular alignment. The direction of the orientation can be selected by the relative phase of the fields.

Abstract: The hitherto unknown low-temperature heat capacity of nickel chromite (NiCr2O4) was measured between 8 and 381 K using adiabatic calorimetry, and some thermochemical functions [CP(T), S(T), S°298, H(T)−H(0)] were derived from the results. The standard entropy (S°298=140.0 ± 0.3 J mol−1 K−1) for nickel chromite was calculated from the results. Our calorimetric measurements indicate three major anomalies in the heat-capacity curve at temperatures between 8 and 381 K. A short literature review indicates that two of these anomalies can be accounted for, whereas an anomaly peaking at 29 K has not been reported previously.

Abstract: The crossover from nonadiabatic to adiabatic electron transfer has been theoretically studied under a spin-boson model (dissipative two-state system) description. We present numerically exact data for the thermal transfer rate and the time-dependent occupation probabilities in largely unexplored regions of parameter space, using real-time path-integral Monte Carlo simulations. The dynamical sign problem is relieved by employing a variant of the recently proposed multilevel blocking algorithm. We identify the crossover regime between nonadiabatic and adiabatic electron transfer, both in the classical (high-temperature) and the quantum (low-temperature) limit. The electron transfer dynamics displays rich behaviors, including multi-exponential decay and the breakdown of a rate description due to vibrational coherence.