Abstract: We study adiabatic ~curvature! and entropy ~isocurvature! perturbations produced during a period of cosmological inflation that is driven by multiple scalar fields with an arbitrary interaction potential. A local rotation in field space is performed to separate out the adiabatic and entropy modes. The resulting field equations show explicitly how on large scales entropy perturbations can source adiabatic perturbations if the background solution follows a curved trajectory in field space, and how adiabatic perturbations cannot source entropy perturbations in the long-wavelength limit. It is the effective mass of the entropy field that determines the amplitude of entropy perturbations during inflation. We present two applications of the equations. First, we show why one in general expects the adiabatic and entropy perturbations to be correlated at the end of inflation, and calculate the cross correlation in the context of a double inflation model with two non-interacting fields. Second, we consider two-field preheating after inflation, examining conditions under which entropy perturbations can alter the large-scale curvature perturbation and showing how our new formalism has advantages in numerical stability when the background solution follows a non-trivial trajectory in field space.

Abstract: We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on the minimum energy difference between the two lowest states of the interpolating Hamiltonian. We are unable to estimate this gap in general. We give some special symmetric cases of the satisfiability problem where the symmetry allows us to estimate the gap and we show that, in these cases, our algorithm runs in polynomial time.

Abstract: The energy balance equation for elastoplastic solids includes heat source terms that govern the conversion of some of the plastic work into heat. The remainder contributes to the stored energy of cold work due to the creation of crystal defects. This paper is concerned with the fraction β of the rate of plastic work converted into heating. We examine the status of the common assumption that β is a constant with regard to the thermodynamic foundations of thermoplasticity and experiments. A general internal-variable theory is introduced and restricted to abide by the second law of thermodynamics. Experimentally motivated assumptions reduce this theory to a special model of classical thermoplasticity. The only part of the internal energy not determined from the isothermal response is the stored energy of cold work, a function only of the internal variables. We show that this function can be inferred from stress and temperature data from a single adiabatic straining experiment. Experimental data from dynamic Kolsky-bar tests at various strain rates yield a unique stored energy function. Its knowledge is crucial for the determination of the thermomechanical response in non-isothermal processes. Such a prediction agrees well with results from dynamic tests at different rates. In these experiments, β is found to depend strongly on both strain and strain rate for various engineering materials. The model is successful in predicting this dependence. Requiring β to be constant is thus an approximation of dubious validity.

Abstract: A self-interacting two-level system depending on an external parameter is investigated. The most striking feature exhibited in this system is the presence of a nonzero tunneling probability in the adiabatic limit for large enough interaction strength. Possible experimental observation of this breakdown of adiabaticity using a Bose-Einstein condensate in an optical potential is suggested.

Abstract: 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.

Abstract: We have performed a sequence of high resolution hydrodynamic simulations of structure formation in a LCDM model to study the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects. Including only adiabatic gas physics, we demonstrate that our simulations for the thermal effect are converged down to sub-arcminute scales. In this model, the angular power spectrum of CMB anisotropies induced by the thermal effect peaks at l~10^4, and reaches an amplitude just below current observational upper limits. Fluctuations due to the kinetic effect are a factor of ~30 lower in power and peak at slightly smaller angular scales. We identify individual SZ sources and compute their counts as a function of source strength and angular size. We present a preliminary investigation of the consequences of an early epoch of energy injection which tends to suppress power on small angular scales, while giving rise to additional power on largescales from the reheated IGM at high redshift.

Abstract: A new discrete variable representation (DVR) in generalized vibrational coordinates is proposed together with a new mixed diabatic/adiabatic contraction technique for the treatment of multidimensional vibrational problems up to high vibrational excitations. Formally based on the equidistant Chebyshev DVR in the grid index the new formulation is particularly suitable for multidimensional minimum energy paths. The new Z-matrix DVR proposed in this paper encompasses usual valence coordinates as well as nonlinear maps of coordinates on optimal nonequidistant grids. The pointwise numerical calculation of all kinetic energy terms avoids the algebraic derivation of specialized analytical forms of the kinetic energy adding to the flexibility of the method. With efficient truncation schemes the generalized DVR allows for a compact representation of the time-dependent wave-packet dynamics in up to six dimensions. Vibrationally adiabatic approaches to the detailed modelling of multidimensional quantum-dynamics usually are hampered by the typically large number of (avoided) crossings in dense spectra. This problem is particularly severe for discrete variable representations. A solution is provided by the new technique of diabatic rotations leading to a systematic construction of locally diabatic channels. This allows the treatment of very dense spectra where conventional truncation techniques fail. Applying the new approach to the vibrational problem of tetratomic molecules demonstrates its flexibility and efficiency. The examples of formaldehyde, ammonia, and hydrogen peroxide cover the whole range from semirigid (CH2O) to large amplitude inversion (NH3) and torsional tunnelling dynamics (H2O2). In solving the full six-dimensional vibrational eigenvalue problems for CH2O and NH3 the Z-matrix DVR shows at least comparable if not superior numerical efficiency compared with specialized techniques. In the case of H2O2 the technique of diabatic rotations and adiabatic contraction for the first time allows the treatment of the tunneling dynamics significantly above the dissociation threshold up to the fifth OH stretch overtone. The calculated decrease of the tunneling rate by about one order of magnitude agrees well with experimental observations.

Abstract: A magnetic refrigerator device based on adiabatic magnetic refrigeration is described. The magnetic material is cyclically magnetized and demagnetized by permanent magnets in an adiabatic process. A temperature difference of 1.6 K between the hot and cold regions was obtained under a low magnetic field (0.3 T). Gadolinium was the magnetic material used in experiments at room temperature. The range of working temperatures is between 70 and 300 K for a variety of active magnetic materials. The optimized experimental setup increased the device efficiency by achieving a temperature difference between hot and cold sources up to 5 K.

Abstract: A Comment on the Letter by A. Giguere et al., Phys. Rev, Lett. 83, 2262 (1999). The authors of the Letter offer a Reply.

Abstract: Models are presented for the polytropic equation of state of self-gravitating, quiescent interstellar gas clouds. A detailed analysis, including chemistry, thermal balance, and radiative transfer, is performed for the physical state of the gas as a function of density, metallicity, velocity field, and background radiation field. We find that the stiffness of the equation of state strongly depends on all of these physical parameters, and the adiabatic index varies between ~0.2-1.4. The implications for star formation, in particular at high redshift and in starburst galaxies, and the initial stellar mass function are discussed.

Abstract: (NOTE: Each chapter concludes with Problems.) 1. The Nature of Thermodynamics. What Is Thermodynamics? Definitions. The Kilomile. Limits of the Continuum. More Definitions. Units. Temperature and the Zeroth Law of Thermodynamics. Temperature Scales. 2. Equations of State. Introduction. Equation of State of an Ideal Gas. Van der Waals' Equation for a Real Gas. P-v-T Surfaces for Real Substances. Expansivity and Compressibility. An Application. 3. The First Law of Thermodynamics. Configuration Work. Dissipative Work. Adiabatic Work and Internal Energy. Heat. Units of Heat. The Mechanical Equivalent of Heat. Summary of the First Law. Some Calculations of Work. 4. Applications of the First Law. Heat Capacity. Mayer's Equation. Enthalpy and hats of Transformation. Relationships Involving Enthalpy. Comparison of u and h. Work Done in an Adiabatic Process. 5. Consequences of the First Law. The Gay-Lussac-Joule Experiment. The Joule-Thomson Experiment. Heat Engines and the Carnot Cycle. 6. The Second Law of Thermodynamics. Introduction. The Mathematical Concept of Entropy. Irreversible Processes. Carnot's Theorem. The Clausius Inequality and the Second Law. Entropy and Available Energy. Absolute Temperature. Combined First and Second Laws. 7. Applications of the Second Law. Entropy Changes in Reversible Processes. Temperature-Entropy Diagrams. Entropy Change of the Surroundings for a Reversible Process. Entropy Change for an Ideal Gas. The Tds Equations. Entropy Change in Irreversible Processes. Free Expansion of an Ideal Gas. Entropy Change for a Liquid or Solid. 8. Thermodynamic Potentials. Introduction. The Legendre Transformation. Definition of the Thermodynamic Potentials. The Maxwell Relations. The Helmholtz Function. The Gibbs Function. Application of the Gibbs Function to Phase Transitions. An Application of the Maxwell Relations. Conditions of Stable Equilibrium. 9. The Chemical Potential and Open Systems. The Chemical Potential. Phase Equilibrium. The Gibbs Phase Rule. Chemical Recessions. Mixing Processes. 10. The Third Law of Thermodynamics. Statements of the Third Law. Methods of Cooling. Equivalence of the Statements. Consequences of the Third Law. 11. The Kinetic Theory of Gases. Basic Assumptions. Molecular Flux. Gas Pressure and the Ideal Gas Law. Equipartition of Energy. Specific Heat Capacity of an Ideal Gas. Distribution of Molecular Speeds. Mean Free Path and Collision Frequency. Effusion. Transport Processes. 12. Statistical Thermodynamics. Introduction. Coin-Tossing Experiment. Assembly of Distinguishable Particles. Thermodynamic Probability and Entropy. Quantum States and Energy Levels. Density of Quantum States. 13. Classical and Quantum Statistics. Bloltzmann Statistics. The Method of Lagrange Multipliers. The Boltzmann Distribution. The Fermi-Dirac Distribution. The Bose-Einstein Distribution. Dilute Gases and the Maxwell-Boltzmann Distribution. The Connection between Classical and Statistical Thermodynamics. Comparison of the Distributions. Alternative Statistical Models. 14. The Classical Statistical Treatment of an Ideal Gas. Thermodynamic Properties from the Partition Function. Partition Function for a Gas. Properties of a Monatomic Ideal Gas. Applicability of the Maxwell-Boltzmann Distribution. Distribution of Molecular Speeds. Equipartition of Energy. Entropy Change of Mixing Revisited. Maxwell's Demon. 15. The Heat Capacity of a Diatomic Gas. Introduction. The Quantified Linear Oscillator. Vibrational Modes of Diatomic Molecules. Rotational Modes of Diatomic Molecules. Electronic Excitation. The Total Heat Capacity. 16. The Heat Capacity of a Solid. Introduction. Einstein's Theory of the Heat Capacity of a Solid. Debye's Theory of the Heat Capacity of a Solid. 17. The Thermodynamics of Magnetism. Introduction. Paramagnetism. Properties of a Spin-1/2 Paramagnet. Adiabatic Demagnetization. NegativeTemperature. Ferromagnetism. 18. Bose-Einstein Gases. Blackbody Radiation. Properties of a Photon Gas. Bose-Einstein Condensation. Properties of a Boson Gas. Application to Liquid Helium. 19. Fermi-Dirac Gases. The Fermi Energy. The Calculation of ...m(T). Free Electrons in a Metal. Properties of a Fermion Gas. Application to White Dwarf Stars. 20. Information Theory. Introduction. Uncertainty and Information. Unit of Information. Maximum Entropy. The Connection to Statistical Thermodynamics. Information Theory and the Laws of Thermodynamics. Maxwell's Demon Exorcised. Appendix A. Review of Partial Differentiation. Partial Derivatives. Exact and Inexact Differentials. Appendix B. Stirling's Approximation. Appendix C. Alternative Approach to Finding the Boltzmann Distribution. Appendix D. Various Integrals. Bibliography. Answers to Selected Problems. Index.

Abstract: A concerted electron–proton transfer reaction is discussed, in which proton tunneling occurs simultaneously with electronic transition. It is assumed that the potential in which the proton moves is formed by two electronic states, which in the absence of their interaction would cross in the region between the two minima of the proton adiabatic potential. The proton tunneling between the two wells is, therefore, coupled to a switch between the two electronic states. The later occurs only when the proton is in the tunneling region under the barrier. A simple analytical expression for the tunneling matrix element TDA is derived, which is uniformly correct for small and large values of the electronic coupling. For small electronic coupling our expression coincides with that obtained in the nonadiabatic theory of proton-coupled electron transfer reactions. For large electronic coupling the expression is reduced to that obtained in the Born–Oppenheimer approximation. The transition from nonadiabatic to adiabatic tunneling is governed by the magnitude of the Landau–Zener parameter defined for the tunneling process. The obtained result is discussed in the context of the proton tunneling time.

Abstract: The interaction of magnetized, relativistic test particles with a monochromatic electromagnetic wave is analyzed, taking into account the passage through cyclotron resonance in the spatially varying background magnetic field in slab geometry. A resonance-averaged Hamiltonian is used to delineate two distinct regimes. In both cases, termed “adiabatic” and “nonadiabatic,” the first adiabatic invariant of the particle is broken during a resonant interaction, leading to change in energy and pitch angle. The adiabatic case is characterized by a limited range of resonant phase and a well-defined value of the change of the invariant. In the nonadiabatic case the phase at resonance ranges over 0 to 2π, and only the magnitude of the change of the invariant is determined; a phase factor gives the invariant change an effectively random sign. The appropriate regime is determined by a ratio of timescales which, in turn, depends on the particle and wave properties: adiabaticity is favored by large wave amplitudes and small parallel gradients of the geomagnetic field Bo. The long-term consequences of the two regimes are explored with a Monte Carlo simulation in the form of an iterated mapping. In a particular example, while some particles pitch angle scatter into the loss cone, energy is also removed from the distribution by particles in the adiabatic regime decaying in energy owing to repeated resonant interactions with the wave. Important potential magnetospheric applications include flux levels in the inner radiation belts, observations of “pancake” pitch angle distributions, and energization of storm time “killer” electrons.

Abstract: We study the dynamics of ultracold atoms in an optical lattice under constant bias. After recapitulating the ideas underlying Bloch oscillations and Zener's formula for interband transitions, the Bloch-Zener scenario is tested by means of accurate numerical solutions to the time-dependent Schr?dinger equation. It is shown how two shortcomings of the traditional Zener formula can be removed: the common weak-binding approximation can be circumvented by combining Kohn's insight into the structure of complex energy bands with the Dykhne-Davis-Pechukas description of transitions in terms of adiabatic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against the condensate's nonlinear self-interaction. Yet, under appropriate conditions a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic signatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggested that such experimentally detectable signatures will play an important role in future high-precision experiments aiming at the exploration of many-body dynamics in periodic potentials with condensates in optical lattices.

Abstract: We derive and parametrize a local, instantaneous exchange-correlation kernel fxc for the interacting electron gas. Our kernel is "energy optimized:" that is, it is chosen so that it leads, via the fluctuation-dissipation and adiabatic connection formulas, to an accurate correlation energy in the uniform electron gas. In this respect it differs from previous simplified kernels, which are typically optimized to provide accurate linear response at long wavelength. To the extent that it embodies relatively short-ranged correlation effects beyond the random phase approximation (RPA), we expect our kernel to be transferable to the calculation of beyond-RPA correlation effects in RPA-like codes for inhomogeneous systems. We apply it to calculate the van der Waals correlation energy between a pair of jellium slabs at all separations down to intimate contact.

Abstract: SUMMARY The variation with pressure of the derivative K′≡dK/dP, where K is the bulk modulus and P is the pressure, is more sensitive to the precise form of an equation than are the variations of density, ρ, or of K. Also, it leads more directly to estimates of thermal properties via the Gruneisen parameter, γ. Recent discussions have focused on equations relating K′ to P/K to make use of the infinite pressure extrapolation 1/K′∞=(P/K)∞. The fundamental significance of K′∞ is emphasized by a thermodynamic demonstration that, for solids, it has the same value for isothermal and adiabatic moduli, their isothermal and adiabatic derivatives and as the limit for both isothermal and adiabatic equations of state. However, this proof conflicts with the assumption, used to estimate K′∞ for regions of the Earth's deep interior, that a linear relationship between μ/K and P/K, where μ is the rigidity, extrapolates to (μ/K)∞=0. The new relationship requires K′∞≥1+γ∞, where the equality is a special condition, applicable to ideal gases, but the inequality appears to be the normal condition for real materials. For solids the usual theories of γ all converge to the relationship γ∞=K′∞/2−1/6, in which case the thermodynamic inequality becomes K′∞>5/3. Most finite strain theories fail this test. It compels reassessment of K′∞ for the lower mantle of the Earth and of equations of state suitable for the deep Earth. A new empirical relationship now appears to satisfy all requirements: where B=1−K′∞/K′0=−K0K″0/K′2∞, subscripts zero indicating zero-pressure values. Its use avoids the bias introduced by theories, such as that due to Birch, that impose values of K′∞ determined by the forms of the equations and not by the fitted data. It is important also to constrain K′0 by information additional to earth model data.

Abstract: The influence of atomic interactions on time-dependent tunneling processes of Bose-Einstein condensates is investigated. In a variety of contexts the relevant condensate dynamics can be described by a Landau-Zener equation modified by the appearance of nonlinear contributions. Based on this equation it is discussed how the interactions modify the tunneling probability. In particular, it is shown that for certain parameter values, due to a nonlinear hysteresis effect, complete adiabatic population transfer is impossible however slowly the resonance is crossed. The results also indicate that the interactions can cause significant increase as well as decrease of tunneling probabilities that should be observable in currently feasible experiments.

Abstract: We calculate the L=0 ground and excited state energies for the rare gas trimers He3, Ne3, and Ar3. An adiabatic representation is adopted to solve the nuclear Schrodinger equation, in which the Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B splines. We compare results obtained in a strict adiabatic approximation with nonperturbative coupled-adiabatic-channel calculations. Structural properties such as the pair and angle distributions are monitored as functions of the hyper-radius. These structural studies pinpoint the locus of configurational changes that occur as the trimer fragments into a diatom plus an atom. Analysis of the angular channel functions and their associated radial components permits an approximate classification of the vibrational spectrum.

Abstract: We report new accurate ab initio potential energy surfaces (PESs) for the ground ( X 2 A 1 ) and first excited ( A 2 B 2 ) electronic states of NO2. The adiabatic potential energy data are calculated by the configuration-selecting multi-reference configuration-interaction method employing the cc-pVTZ basis set. We diabatize the adiabatic potential energy data and investigate the nuclear dynamics on these coupled electronic states by a time-dependent wave packet method. First, we investigate the photodetachment spectrum of NO2− for a transition to the A 2 B 2 state and compare our findings with the available experimental results. The agreement is very satisfactory. In addition, we examine the femtosecond decay of the A 2 B 2 diabatic electronic population revealing the impact of the nonadiabatic coupling on the time-dependent dynamics (internal conversion process) of NO2. The present study based on more accurate ab initio PESs enables us to confirm our earlier estimate of the vibronic coupling strength near the energetic minimum of the X 2 A 1 – A 2 B 2 crossing seam.

Abstract: An efficient numerical method for treating electrons in magnetized plasmas has been developed. The scheme, which is based on the perturbative (δf) gyrokinetic particle simulation, splits the particle electron responses into adiabatic and nonadiabatic parts. The former is incorporated into the gyrokinetic Poisson’s equation, while the latter is calculated dynamically with the aid of the charge conservation equation. The new scheme affords us the possibility of suppressing unwanted high-frequency oscillations and, in the meantime, relaxing the Courant condition for the thermal particles moving in the parallel direction. It is most useful for studying low-frequency phenomena in plasmas. As an example, one-dimensional drift wave simulation has been carried out using the scheme and the results are presented in this paper. This methodology can easily be generalized to problems in three-dimensional toroidal geometry, as well as those in unmagnetized plasmas.

Abstract: We perform molecular dynamic simulations of a system consisting of an insulating piston, which separates two gases of hard disks, each initially at equilibrium at the same pressure but at different temperatures and densities. Upon releasing the piston, we monitor how the system returns to the global thermodynamic equilibrium with equal temperature and density on both sides. The approach of the piston to its final position is well described by an exponential law, while the heat flux is, to a good approximation, found to be proportional to the temperature difference.

Abstract: We report on the initial results of experiments being developed on the Falcon laser to simulate radiative astrophysical shocks. Cylindrically diverging blast waves were produced in low-density (~1018 cm-3), high-Z gas by laser-irradiating Xe gas jets containing atomic clusters. The blast-wave trajectory was measured by Michelson interferometry. The velocity for the blast wave is slightly less than the adiabatic Sedov-Taylor prediction, and an ionization precursor is observed ahead of the shock front. This suggests energy loss through radiative cooling and reduced compression due to preheat deposited ahead of the shock, both consistent with one-dimensional radiation hydrodynamics simulations.

Abstract: This paper reviews the state-of-the-art in the prediction of multidimensional multiphase flow and heat transfer phenomena using a two-fluid model. It is shown that accurate mechanistic CFD predictions are possible for a wide variety of adiabatic and diabatic vapor/liquid and particle/liquid two-phase flows using this computational model.