Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
Mostafazadeh, Ali
2014-01-01
arXiv:1401.4315v3 [quant-ph] 27 Feb 2014 Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility Ali Mostafazadeh∗ Department of Mathematics, Ko¸c University, 34450 Sarıyer, Istanbul, Turkey Abstract The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the S-matrix of a two-level time-dependent non-Hermitian Hamiltonian H( ). We show that the application of the adiabatic approximation ...
The adiabatic approximation in multichannel scattering
Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)
Bond selective chemistry beyond the adiabatic approximation
Butler, L.J. [Univ. of Chicago, IL (United States)
1993-12-01
One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
Adiabatic approximation, semiclassical scattering, and unidirectional invisibility
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the S-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(τ). We show that the application of the adiabatic approximation to H(τ) corresponds to the semiclassical description of the original scattering problem. In particular, the geometric part of the phase of the evolving eigenvectors of H(τ) gives the pre-exponential factor of the WKB wave functions. We use these observations to give an explicit semiclassical expression for the transfer matrix. This allows for a detailed study of the semiclassical unidirectional reflectionlessness and invisibility. We examine concrete realizations of the latter in the realm of optics. (paper)
Examination of the adiabatic approximation in open systems
We examine the notion of the adiabatic approximation in open systems by applying it to closed systems. Our results shows that the notion is equivalent to the standard adiabatic approximation if the systems are initially in eigenstates, and it leads to a more general expression if the systems are in mixed states
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
A note on the geometric phase in adiabatic approximation
Tong, D M; Kwek, L C; Oh, C H
2004-01-01
It is widely held that the Berry phase of a quantum system is the geometric phase in adiabatic approximation. However, Pati and Rajagopal recently claimed that the Berry phase vanishes under strict adiabatic evolution. In this note, we reexamine and address this issue. In particular, we show that the use of the adiabatic theorem does not lead to this inconsistency. We also examine the difference between the Berry phase and the exact geometric phase. Here we find that the Berry phase may differ appreciably from the exact geometric phase if the evolution time is large enough.
Power spectra in the eikonal approximation with adiabatic and non-adiabatic modes
Bernardeau, Francis; Vernizzi, Filippo
2012-01-01
We use the so-called eikonal approximation, recently introduced in the context of cosmological perturbation theory, to compute power spectra for multi-component fluids. We demonstrate that, at any given order in standard perturbation theory, multi-point power spectra do not depend on the large-scale adiabatic modes. Moreover, we employ perturbation theories to decipher how non-adiabatic modes, such as a relative velocity between two different components, damp the small-scale matter power spectrum, a mechanism recently described in the literature. In particular, we do an explicit calculation at 1-loop order of this effect. While the 1-loop result eventually breaks down, we show how the damping effect can be fully captured by the help of the eikonal approximation. A relative velocity not only induces mode damping but also creates large-scale anisotropic modulations of the matter power spectrum amplitude. We illustrate this for the Local Group environment.
On the rotating wave approximation in the adiabatic limit
I revisit a longstanding question in quantum optics; when is the rotating wave approximation justified? In terms of the Jaynes–Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system parameters. This is explicitly shown by comparing Berry phases of the two models, where it is found that this geometrical phase is strictly zero in the Rabi model contrary to the non-trivial Berry phase of the Jaynes–Cummings model. The source of this surprising result is traced back to different topologies in the two models. (paper)
Olsen, Thomas; Thygesen, Kristian S.
2012-01-01
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...
Applications of Adiabatic Approximation to One- and Two-electron Phenomena in Strong Laser Fields
Bondar, Denys
2010-01-01
The adiabatic approximation is a natural approach for the description of phenomena induced by low frequency laser radiation because the ratio of the laser frequency to the characteristic frequency of an atom or a molecule is a small parameter. Since the main aim of this work is the study of ionization phenomena, the version of the adiabatic approximation that can account for the transition from a bound state to the continuum must be employed. Despite much work in this topic, a universally accepted adiabatic approach of bound-free transitions is lacking. Hence, based on Savichev's modified adiabatic approximation [Sov. Phys. JETP 73, 803 (1991)], we first of all derive the most convenient form of the adiabatic approximation for the problems at hand. Connections of the obtained result with the quasiclassical approximation and other previous investigations are discussed. Then, such an adiabatic approximation is applied to single-electron ionization and non-sequential double ionization of atoms in a strong low fr...
Calculational schemes enabling to go beyond crude Condon approximation in non-adiabatic electron transfer reactions are discussed with the use of continuum approximation for the solvent polarization. An algorithm for the self-consistent introduction of an effective reaction coordinate in the adiabatic transition is suggested. Effects due to deviations from the Born-Oppenheimer approximation in bridge-assisted electron transfer reactions are discussed. Interpolation formulae covering limits of coherent and sequential electron transfer in bridge-assisted processes are presented. Simple equations determining a parametric dependence of the transition probability on the reaction free energy in crude Condon approximation are included. (author)
The adiabatic versus the diabatic approximation in the decoupling of electron and nuclear motion
There are two limiting approximations that are used as starting points for the analysis of a system of interacting electrons and nuclei. The more widely used is the adiabatic approximation in which one assumes that the electrons adjust adiabatically to the instantaneous configuration of the nuclei. This yields an effective internuclear potential. In treating the nuclear motion, this potential can legitimately be expanded to fourth order in nuclear displacements from equilibrium. The difficulties of extending this expansion further are discussed. In situations where two adiabatic potentials approach each other the so-called diabatic approximation has to be used. A novel application to non-radioactive processes in solids is discussed. (author)
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
Muonic molecules as three-body Coulomb problem in adiabatic approximation
The three-body Coulomb problem is treated within the framework of the hyperspherical adiabatic approach. The surface functions are expanded into Faddeev-type components in order to ensure the equivalent representation of all possible two-body contributions. It is shown that this decomposition reduces the numerical effort considerably. The remaining radial equations are solved both in the extreme and the uncoupled adiabatic approximation to determine the binding energies of the systems (dtμ) and (d3Heμ). Whereas the ground state is described very well in the uncoupled adiabatic approximation, the excited states should be treated within the coupled adiabatic approximation to obtain good agreement with variational calculations. (orig.)
Xu, Y. J.; Khandelwal, G. S.; Wilson, John W.
1989-01-01
A simple formula for the transition probability for electron exchange between unlike ions and atoms is established within the adiabatic approximation by employing the Linear Combination of Atomic Orbitals (LCAO) method. The formula also involves an adiabatic parameter, introduced by Massey, and thus the difficulties arising from the internal energy defect and the adiabatic approximation are avoided. Specific reactions Li(+++) + H to Li(++) + H(+) and Be(4+) + H to Be(3+) + H(+) are considered as examples. The calculated capture cross section results of the present work are compared with the experimental data and with the calculation of other authors over the velocity range of 10(7) cm/sec to 10(8) cm/sec.
The effective adiabatic approximation of three-body problem with short-range potentials
The effective adiabatic approximation (EAA) of three-body problem on a line with short-range attractive δ-potentials is constructed. The EAA lower bound for the energy with an absolute accuracy of order 10-6 is obtained. It is shown that EAA provides a true asymptotics of solutions and a correct behaviour of the elastic scattering phase with an absolute accuracy of 10-3 in the interval 2 · 10-3 m < π / 6 of the relative momentum below the three-body threshold for (3 to 3) scattering. The convergence of adiabatic expansion in the framework of EAA is demonstrated
The neutron noise, induced by a rod manoeuvring experiment in a pressurized water reactor, has been calculated by the incore fuel management code SIMULATE. The space- and frequency-dependent noise in the thermal group was calculated through the adiabatic approximation in three dimensions and two-group theory, with the spatial resolution of the nodal model underlying the SIMULATE algorithm. The calculated spatial noise profiles were interpreted on physical terms. They were also compared with model calculations in a 2-D one-group model, where various approximations as well as the full space-dependent response could be calculated. The adiabatic results obtained with SIMULATE can be regarded as reliable for sub-plateau frequencies (below 0.1 Hz). (orig.)
Zhu, Xiaolei; Yarkony, David R.
2016-01-01
We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, Hd, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of Hd individually provides a starting point (seed) from which convergence of the full Hd construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,41A states of phenol and the 1,21A states of NH3, states which are coupled by conical intersections.
Rotation-vibrational states of H3+ and the adiabatic approximation.
Alijah, Alexander; Hinze, Juergen
2006-11-15
We discuss recent progress in the calculation and identification of rotation-vibrational states of H3+ at intermediate energies up to 13,000 cm(-1). Our calculations are based on the potential energy surface of Cencek et al. which is of sub-microhartree accuracy. As this surface includes diagonal adiabatic and relativistic corrections to the fixed nuclei electronic energies, the remaining discrepancies between our calculated and experimental data should be due to the neglect of non-adiabatic coupling to excited electronic states in the calculations. To account for this, our calculated energy values were adjusted empirically by a simple correction formula. Based on our understanding of the adiabatic approximation, we suggest two new approaches to account for the off-diagonal adiabatic correction, which should work; however, they have not been tested yet for H3+. Theoretical predictions made for the above-barrier energy region of recent experimental interest are accurate to 0.35 cm(-1) or better. PMID:17015396
P-wave phaseshifts for positron-hydrogen elastic scattering are calculated using a new adiabatic approximation in which the length of the radius vector from the proton to the positron is fixed but its direction is allowed to vary. This adiabatic approximation makes possible the full inclusion in the calculation of virtual states in which angular momentum is transferred to the target H atom. The results obtained agree qualitatively with the highly accurate results of Bhatia and co-workers (Phys. Rev.; A9:219 (1974)) and are much closer to them than the results obtained using the usual adiabatic approximation in which the radius vector from the proton to the positron is fixed. (author)
Formulas which are needed to calculate transmission coefficients for the adiabatic coupled-channel approximation method are described. In terms of these coefficients, nuclear absorption cross sections may be obtained. First, derivations are given of various cross sections for a system of coupled inelastic channels in terms of the S matrix. The adiabatic approximation method is discussed for a rotational band, and the dynamical nuclear S matrix is obtained from the S matrix for scattering from a static rotor. The formulas are valid for a spheroidal rotor, with or without an extra-core particle, which does not interact with the projectile but does provide angular momentum to the target
Tunneling splittings in formic acid dimer: An adiabatic approximation to the Herring formula
Small symmetric molecules and low-dimensional model Hamiltonians are excellent systems for benchmarking theories to compute tunneling splittings. In this work, we investigate a three dimensional model Hamiltonian coupled to a harmonic bath that describes concerted proton transfer in the formic acid dimer. The three modes include the symmetric proton stretch, the symmetric dimer rock, and the dimer stretch. These modes provide a paradigm for the symmetric and anti-symmetric coupled tunneling pathways, these being recognized in the literature as two of the more important classes of coupling. The effects of selective vibrational excitation and coupling to a bath on the tunneling splittings are presented. The splittings for highly excited states are computed using a novel method that makes an adiabatic approximation to the Herring estimate. Results, which are in excellent agreement with the exact splittings, are compared with those obtained using the Makri-Miller approach. This latter method has been shown to provide quality results for tunneling splittings including highly excited vibrational states
Andrade, Tomás; Kelly, William R.; Marolf, Donald
2015-10-01
The gravitational Dirichlet problem—in which the induced metric is fixed on boundaries at finite distance from the bulk—is related to simple notions of UV cutoffs in gauge/gravity duality and appears in discussions relating the low-energy behavior of gravity to fluid dynamics. We study the Einstein-Maxwell version of this problem, in which the induced Maxwell potential on the wall is also fixed. For flat walls in otherwise asymptotically flat spacetimes, we identify a moduli space of Majumdar-Papapetrou-like static solutions parametrized by the location of an extreme black hole relative to the wall. Such solutions may be described as balancing gravitational repulsion from a negative-mass image source against electrostatic attraction to an oppositely signed image charge. Standard techniques for handling divergences yield a moduli space metric with an eigenvalue that becomes negative near the wall, indicating a region of negative kinetic energy and suggesting that the Hamiltonian may be unbounded below. One may also surround the black hole with an additional (roughly spherical) Dirichlet wall to impose a regulator whose physics is more clear. Negative kinetic energies remain, though new terms do appear in the moduli space metric. The regulator dependence indicates that the adiabatic approximation may be ill-defined for classical extreme black holes with Dirichlet walls.
We consider the application of the method of adiabatic waveguide modes for calculating the propagation of electromagnetic radiation in three-dimensional (3D) irregular integrated optical waveguides. The method of adiabatic modes takes into account a three-dimensional distribution of quasi-waveguide modes and explicit ('inclined') tangential boundary conditions. The possibilities of the method are demonstrated on the example of numerical research of two major elements of integrated optics: a waveguide of 'horn' type and a thin-film generalised waveguide Luneburg lens by the methods of adiabatic modes and comparative waveguides. (integral optical waveguides)
Barban C.
2013-03-01
Full Text Available CoRoT and Kepler measurements reveal us that the amplitudes of solar-like oscillations detected in red giant stars scale from stars to stars in a characteristic way. This observed scaling relation is not yet fully understood but constitutes potentially a powerful diagnostic about mode physics. Quasi-adiabatic theoretical scaling relations in terms of mode amplitudes result in systematic and large differences with the measurements performed for red giant stars. The use of a non-adiabatic intensity-velocity relation derived from a non-adiabatic pulsation code significantly reduces the discrepancy with the CoRoT measurements. The origin of the remaining difference is still unknown. Departure from adiabatic eigenfunction is a very likely explanation that is investigated in the present work using a 3D hydrodynamical model of the surface layers of a representative red giant star.
Graphical abstract: We solve a 1D N-electron system, with N small, by mapping it onto an N-dimensional one-electron problem. We compare the exact solutions to the results from adiabatic density and density matrix functionals for different physical situations. Highlights: ► Static and dynamical correlations. ► Memory dependence of exchange-correlation functionals in TDDFT. ► Linear and non-linear response. ► Laser-induced population control. - Abstract: To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N-electron problem onto an N-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories.
Buchel, Alex; Noronha, Jorge
2016-01-01
We use holography for the ab-initio determination of the non-equilibrium behavior of matter in a Friedmann-Lemaitre-Robertson-Walker Universe. We focus on matter without scale invariance and develop an expansion for the corresponding entropy production in terms of the derivatives of the cosmological scale factor. We show that the resulting series is asymptotic and we discuss its resurgent properties. Finally, we compute the resummed entropy production rate in de Sitter Universe at late times and show that the leading order approximation given by bulk viscosity effects can strongly overestimate/underestimate the rate depending on the microscopic parameters.
Graphical abstract: The time-dependent electron density is mapped via inversion of the ground-state Kohn–Sham formalism on two spin-densities, and thus an accurate adiabatic correlation potential is obtained. Research highlights: ► An adiabatic approximation for time-dependent density functional theory is proposed. ► Inverting static spin-density functional theory yields accurate correlation potentials. ► The derivative discontinuity is reproduced. ► Tested for strong-field ionization and molecules at large internuclear distance. - Abstract: It has recently been shown by Thiele et al. [M. Thiele, E. K. U. Gross, S. Kümmel, Phys. Rev. Lett. 100 (2008) 153004] that the exact adiabatic approximation in time-dependent density functional theory gives a good description of non-sequential double ionization in the one-dimensional helium atom. In this paper, we propose an adiabatic approximation based on the inversion of ground-state spin-density functional theory and apply it to several model systems. We demonstrate that our approach reproduces the derivative discontinuity and yields correlation potentials close to the exact correlation potentials for a strong-field ionization process as well as for the 1D H2 and LiH molecules at large internuclear distance.
The program for calculation of the cross sections of neutron interaction with deformed nuclei by the strongly coupled channel method in the adiabatic approximation is described. The results of test calculations of cross sections of elastic and inelastic neutron scattering with initial energy of 0.1; 0.6; 2.0; 2.5 MeV on the sup(238)U nucleus are presented
Lu, Deyu
The adiabatic-connection fluctuation-dissipation theorem (ACFDT) is a formal theoretical framework to treat van der Waals (vdW) dispersion interactions. Under the random phase approximation (RPA), it yields the correct asymptotic behavior at large distances, but the short-range correlation is overestimated. It has been demonstrated that non-local exchange-correlation kernels can systematically correct the errors of RPA for homogenous electron gas. However, direct extension of non-local kernels derived from the electron gas model to inhomogeneous systems raises several issues. In addition to the high computational expense, the non-local kernels worsen the rare gas dimer binding curve as compared to RPA. In this study, we propose a quasi-local approximation of the non-local kernel in order to address these issues. This research used resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704.
Engel, D.; Klews, M.; Wunner, G.
2009-02-01
We have developed a new method for the fast computation of wavelengths and oscillator strengths for medium-Z atoms and ions, up to iron, at neutron star magnetic field strengths. The method is a parallelized Hartree-Fock approach in adiabatic approximation based on finite-element and B-spline techniques. It turns out that typically 15-20 finite elements are sufficient to calculate energies to within a relative accuracy of 10-5 in 4 or 5 iteration steps using B-splines of 6th order, with parallelization speed-ups of 20 on a 26-processor machine. Results have been obtained for the energies of the ground states and excited levels and for the transition strengths of astrophysically relevant atoms and ions in the range Z=2…26 in different ionization stages. Catalogue identifier: AECC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3845 No. of bytes in distributed program, including test data, etc.: 27 989 Distribution format: tar.gz Programming language: MPI/Fortran 95 and Python Computer: Cluster of 1-26 HP Compaq dc5750 Operating system: Fedora 7 Has the code been vectorised or parallelized?: Yes RAM: 1 GByte Classification: 2.1 External routines: MPI/GFortran, LAPACK, PyLab/Matplotlib Nature of problem: Calculations of synthetic spectra [1] of strongly magnetized neutron stars are bedevilled by the lack of data for atoms in intense magnetic fields. While the behaviour of hydrogen and helium has been investigated in detail (see, e.g., [2]), complete and reliable data for heavier elements, in particular iron, are still missing. Since neutron stars are formed by the collapse of the iron cores of massive stars, it may be assumed that their atmospheres contain an iron plasma. Our objective is to fill the gap
J. D. Biamonte
2011-06-01
Full Text Available In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.
Quantum adiabatic machine learning
Pudenz, Kristen L.; Lidar, Daniel A.
2011-01-01
We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. We apply and illustrate this app...
Adiabatic Invariance of Oscillons/I-balls
Kawasaki, Masahiro; Takeda, Naoyuki
2015-01-01
Real scalar fields are known to fragment into spatially localized and long-lived solitons called oscillons or $I$-balls. We prove the adiabatic invariance of the oscillons/$I$-balls for a potential that allows periodic motion even in the presence of non-negligible spatial gradient energy. We show that such potential is uniquely determined to be the quadratic one with a logarithmic correction, for which the oscillons/$I$-balls are absolutely stable. For slightly different forms of the scalar potential dominated by the quadratic one, the oscillons/$I$-balls are only quasi-stable, because the adiabatic charge is only approximately conserved. We check the conservation of the adiabatic charge of the $I$-balls in numerical simulation by slowly varying the coefficient of logarithmic corrections. This unambiguously shows that the longevity of oscillons/$I$-balls is due to the adiabatic invariance.
Quantum adiabatic machine learning
Pudenz, Kristen L
2011-01-01
We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. We apply and illustrate this approach in detail to the problem of software verification and validation.
Oreshkov, Ognyan
2010-01-01
We propose a theory of adiabaticity in quantum Markovian dynamics based on a structural decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of Markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the underlying Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As an application of our theory, we propose a framework for decoherence-assisted computation in noiseless codes under general Markovian noise. We also formulate a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by non-dissipative means.
Semi adiabatic theory of seasonal Markov processes
Talkner, P. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1999-08-01
The dynamics of many natural and technical systems are essentially influenced by a periodic forcing. Analytic solutions of the equations of motion for periodically driven systems are generally not known. Simulations, numerical solutions or in some limiting cases approximate analytic solutions represent the known approaches to study the dynamics of such systems. Besides the regime of weak periodic forces where linear response theory works, the limit of a slow driving force can often be treated analytically using an adiabatic approximation. For this approximation to hold all intrinsic processes must be fast on the time-scale of a period of the external driving force. We developed a perturbation theory for periodically driven Markovian systems that covers the adiabatic regime but also works if the system has a single slow mode that may even be slower than the driving force. We call it the semi adiabatic approximation. Some results of this approximation for a system exhibiting stochastic resonance which usually takes place within the semi adiabatic regime are indicated. (author) 1 fig., 8 refs.
Wireless adiabatic power transfer
Research highlights: → Efficient and robust mid-range wireless energy transfer between two coils. → The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. → Wireless energy transfer is insensitive to any resonant constraints. → Wireless energy transfer is insensitive to noise in the neighborhood of the coils. - Abstract: We propose a technique for efficient mid-range wireless power transfer between two coils, by adapting the process of adiabatic passage for a coherently driven two-state quantum system to the realm of wireless energy transfer. The proposed technique is shown to be robust to noise, resonant constraints, and other interferences that exist in the neighborhood of the coils.
Adiabatically implementing quantum gates
We show that, through the approach of quantum adiabatic evolution, all of the usual quantum gates can be implemented efficiently, yielding running time of order O(1). This may be considered as a useful alternative to the standard quantum computing approach, which involves quantum gates transforming quantum states during the computing process
Wireless adiabatic power transfer
Rangelov, A. A.; Suchowski, H.; Silberberg, Y.; Vitanov, N. V.
2010-01-01
We propose a technique for efficient mid-range wireless power transfer between two coils, by adapting the process of adiabatic passage for a coherently driven two-state quantum system to the realm of wireless energy transfer. The proposed technique is shown to be robust to noise, resonant constraints, and other interferences that exist in the neighborhood of the coils.
Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust
Roberto CasadioDipartimento di Fisica, Universita' di Bologna and INFN, Bologna; Fabio Finelli(Dipartimento di Fisica, Universita' di Bologna and INFN, Bologna); Giovanni Venturi(Department of Physics, University of Bologna, and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Italy)
2015-01-01
The semiclassical collapse of a sphere of quantized dust is studied. A Born-Oppenheimer decomposition is performed for the wave function of the system and the semiclassical limit is considered for the gravitational part. The method of adiabatic invariants for time dependent Hamiltonians is then employed to find (approximate) solutions to the quantum dust equations of motions. This allows us to obtain corrections to the adiabatic approximation of the dust states associated with the time evolut...
Time Development of Exponentially Small Non-Adiabatic Transitions
Hagedorn, George A.; Joye, Alain
2003-01-01
Optimal truncations of asymptotic expansions are known to yield approximations to adiabatic quantum evolutions that are accurate up to exponentially small errors. In this paper, we rigorously determine the leading order non--adiabatic corrections to these approximations for a particular family of two--level analytic Hamiltonian functions. Our results capture the time development of the exponentially small transition that takes place between optimal states by means of a particular switching fu...
Amendt, Peter; Bellei, Claudio; Wilks, Scott
2012-01-01
The plasma analog of an adiabatic lapse rate (or temperature variation with height) in atmospheric physics is obtained. A new source of plasma temperature gradient in a binary ion species mixture is found that is proportional to the concentration gradient and difference in average ionization states . Application to inertial-confinement-fusion implosions indicates a potentially strong effect in plastic (CH) ablators that is not modeled with mainline (single-fluid) simulations. An associated pl...
Nonresonance adiabatic photon trap
Popov, S S; Burdakov, A V; Ushkova, M Yu
2016-01-01
Concept of high efficiency photon storage based on adiabatic confinement between concave mirrors is presented and experimentally investigated. The approach is insensitive to typical for Fabri-Perot cells requirements on quality of accumulated radiation, tolerance of resonator elements and their stability. Experiments have been carried out with the trap, which consists from opposed concave cylindrical mirrors and conjugated with them spherical mirrors. In result, high efficiency for accumulation of radiation with large angular spread and spectrum width has been confirmed. As radiation source a commercial fiber laser has been used.
Adiabatic boiling of two-phase coolant in upward flow
A mathematical model of the process of adiabatic boiling (self-condensation) of a two-phase coolant in upward (downward) flow is developed. The model takes account of changes in phase properties with static pressure decrease. The process is investigated numerically. Approximate analytical formulas for design calculations are obtained. It is shown that effects of adiabatic boiling (self-condensation) should be taken into account when calculating two-phase coolant flow in stretched vertical channels
Is the sech/tanh Adiabatic Pulse Really Adiabatic?
Rosenfeld, Daniel; Zur, Yuval
1998-05-01
Adiabatic pulses are most conveniently studied in the frequency frame which is a frame of reference rotating at the instantaneous frequency of the pulse. In this frame the adiabatic condition ‖γBeff‖ ≫ |θ≳| sets an upper limit on the sweep rate θ≳ of the Beffvector. This, in turn, places a lower bound on the pulse duration. Adiabatic behavior is studied at the threshold duration and two pulses are examined: (i) a pulse with a constant sweep rate (CAPpulse) and (ii) a conventional sech/tanh adiabatic pulse. It is shown that the sech/tanh pulse performs robust magnetization inversion although it seems to violate the adiabatic condition. This puzzling phenomenon is solved by switching into a second-order rotating frame of reference (SORF) where it is shown that the adiabatic condition is fulfilled. This frame coincides with the frequency frame at the beginning of the pulse. Assuming an RF field along thex-axis of the frequency frame, the SORF then rotates about the commony-axis during the pulse with thez-axis of the new frame aligned with the Beffvector. It is shown that adiabatic motion may be performed in the SORF, in which the sweep rate is increased indefinitely; the adiabatic condition is violated by this motion in the frequency frame but is fulfilled in the SORF. The lower bound on the sweep rate in the frequency frame is thereby lifted.
Adiabatic and non-adiabatic processes in strong Coulomb fields
Adiabatic and non-adiabatic behaviour of relativistic electrons in external Coulomb fields of time-dependent strength is studied within the framework of a model for the description of a shell electron's behaviour during a heavy-ion collision. A classification scheme for types of non-adiabatic behaviour is suggested; its relevance for the analysis of pair production processes in strong Coulomb fields is discussed (K-Shell Ionization). An ansatz for the vacuum polarization potential is introduced and employed to demonstrate the special role of vacuum polarization for adiabatic and non-adiabatic behaviour in very strong Coulomb fields (Zα > 1). The implications of the underlaying specific features of the vacuum polarization charge density in very strong fields for pair production mechanisms are considered. (orig.)
Beyond the random phase approximation
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Classical nuclear motion coupled to electronic non-adiabatic transitions
Agostini, Federica; Gross, E K U
2014-01-01
We present a detailed derivation and numerical tests of a new mixed quantum-classical scheme to deal with non-adiabatic processes. The method is presented as the zero-th order approximation to the exact coupled dynamics of electrons and nuclei offered by the factorization of the electron-nuclear wave function [A. Abedi, N. T. Maitra and E. K. U. Gross, Phys. Rev. Lett., 105 (2010)]. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Non-adiabatic primordial fluctuations
Noller, J
2009-01-01
We consider general non-adiabatic single fluid cosmological perturbations. We derive the second-order action and its curvature variables assuming only the (linearized) Einstein equations for a perfect fluid stress-energy tensor. The derivation is therefore carried out at the same level of generality that has been achieved before for adiabatic modes. We also allow for arbitrary "speed of sound" profiles in our derivation. As a result we find a new conserved super-horizon quantity and relate it to the adiabatically conserved curvature perturbation. We then use the formalism to investigate a family of non-adiabatic hydrodynamical primordial matter models and the power spectra they produce. This yields a new scale-invariant solution that can resolve the horizon problem if implemented in a contracting phase.
What lies between a free adiabatic expansion and a quasi-static one?
Miranda, E. N.
2012-01-01
An expression is found that relates the initial and final volumes and temperatures for any adiabatic process. It is given in terms of a parameter r that smoothly interpolates between a free adiabatic expansion (r = 0) and a quasi-static one (r = 1). The parameter has to be evaluated numerically, but an approximate expression is given.
Classical nuclear motion coupled to electronic non-adiabatic transitions
Agostini, Federica; Abedi, Ali; Gross, E. K. U.
2014-12-01
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Classical nuclear motion coupled to electronic non-adiabatic transitions
Agostini, Federica; Abedi, Ali; Gross, E. K. U. [Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle (Germany)
2014-12-07
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Classical nuclear motion coupled to electronic non-adiabatic transitions
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations
The split of a generalised Chaplygin gas with an equation of state p=−A/ρα into an interacting mixture of pressureless matter and a dark-energy component with equation of state pΛ=−ρΛ implies the existence of non-adiabatic pressure perturbations. We demonstrate that the square of the effective (non-adiabatic) sound speed cs of the medium is proportional to the ratio of the perturbations of the dark energy to those of the dark matter. Since, as demonstrated explicitly for the particular case α=−1/2, dark-energy perturbations are negligible compared with dark-matter perturbations on scales that are relevant for structure formation, we find |cs2|≪1. Consequently, there are no oscillations or instabilities which have plagued previous adiabatic Chaplygin-gas models
Optimizing adiabaticity in quantum mechanics
MacKenzie, R; Renaud-Desjardins, L
2011-01-01
A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution operator related to it. Since the latter depends in a complicated way on the Hamiltonian, it is not yet clear how the condition can be used to extract useful information about the optimal Hamiltonian. The condition is tested on an exactly-soluble time-dependent problem (a spin in a magnetic field), where perfectly adiabatic evolution can be easily identified.
Optimization of Adiabatic Selective Pulses
Rosenfeld, Daniel; Panfil, Shimon L.; Zur, Yuval
1997-06-01
Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theBeffvector and the rate of motion upon it. In this paper, a method is described for optimizing adiabatic inversion pulses to achieve a frequency-selective magnetization inversion over a given bandwidth in a shorter time and to improve slice profile. An efficient adiabatic pulse is used as an initial condition. This pulse allows for flexibility in choosing its parameters; in particular, the transition sharpness may be traded off against the inverted bandwidth. The considerations for selecting the parameters of the pulse according to the requirements of the design are discussed. The optimization process then improves the slice profile by optimizing the rate of motion along the trajectory of the pulse while preserving the trajectory itself. The adiabatic behavior of the optimized pulses is fully preserved over a twofold range of variation in the RF amplitude which is sufficient for imaging applications in commercial high-field MRI machines. Design examples demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse.
A Many Particle Adiabatic Invariant
Hjorth, Poul G.
For a system of N charged particles moving in a homogeneous, sufficiently strong magnetic field, a many-particle adiabatic invariant constrains the collisional exchange of energy between the degrees of freedom perpendicular to and parallel to the magnetic field. A description of the phenomenon in...
Studies in Chaotic adiabatic dynamics
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)
Post-Newtonian expansions of the binding energy and gravitational wave flux truncated at the same relative post-Newtonian order form the basis of the standard adiabatic approximation to the phasing of gravitational waves from inspiralling compact binaries. Viewed in terms of the dynamics of the binary, the standard approximation is equivalent to neglecting certain conservative post-Newtonian terms in the acceleration. In an earlier work, we had proposed a new complete adiabatic approximant constructed from the energy and flux functions. At the leading order, it employs the 2PN energy function rather than the 0PN one in the standard approximation, so that, effectively, the approximation corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration. In this paper, we compare the overlaps of the standard and complete adiabatic templates with the exact waveform in the adiabatic approximation of a test-mass motion in the Schwarzschild spacetime, for the VIRGO and the advanced LIGO noise spectra. It is found that the complete adiabatic approximants lead to a remarkable improvement in the effectualness at lower PN (<3PN) orders, while standard approximants of order ≥3PN provide a good lower bound to the complete approximants for the construction of effectual templates. Faithfulness of complete approximants is better than that of standard approximants except for a few post-Newtonian orders. Standard and complete approximants beyond the adiabatic approximation are also studied using the Lagrangian templates of Buonanno, Chen and Vallisneri
Digital Waveguide Adiabatic Passage Part 1: Theory
Vaitkus, Jesse A; Greentree, Andrew D
2016-01-01
Spatial adiabatic passage represents a new way to design integrated photonic devices. In conventional adiabatic passage designs require smoothly varying waveguide separations. Here we show modelling of adiabatic passage devices where the waveguide separation is varied digitally. Despite digitisation, our designs show robustness against variations in the input wavelength and refractive index contrast of the waveguides relative to the cladding. This approach to spatial adiabatic passage opens new design strategies and hence the potential for new photonics devices.
Adiabatic Mass Loss Model in Binary Stars
Ge, H. W.
2012-07-01
Rapid mass transfer process in the interacting binary systems is very complicated. It relates to two basic problems in the binary star evolution, i.e., the dynamically unstable Roche-lobe overflow and the common envelope evolution. Both of the problems are very important and difficult to be modeled. In this PhD thesis, we focus on the rapid mass loss process of the donor in interacting binary systems. The application to the criterion of dynamically unstable mass transfer and the common envelope evolution are also included. Our results based on the adiabatic mass loss model could be used to improve the binary evolution theory, the binary population synthetic method, and other related aspects. We build up the adiabatic mass loss model. In this model, two approximations are included. The first one is that the energy generation and heat flow through the stellar interior can be neglected, hence the restructuring is adiabatic. The second one is that he stellar interior remains in hydrostatic equilibrium. We model this response by constructing model sequences, beginning with a donor star filling its Roche lobe at an arbitrary point in its evolution, holding its specific entropy and composition profiles fixed. These approximations are validated by the comparison with the time-dependent binary mass transfer calculations and the polytropic model for low mass zero-age main-sequence stars. In the dynamical time scale mass transfer, the adiabatic response of the donor star drives it to expand beyond its Roche lobe, leading to runaway mass transfer and the formation of a common envelope with its companion star. For donor stars with surface convection zones of any significant depth, this runaway condition is encountered early in mass transfer, if at all; but for main sequence stars with radiative envelopes, it may be encountered after a prolonged phase of thermal time scale mass transfer, so-called delayed dynamical instability. We identify the critical binary mass ratio for the
Design of Selective Adiabatic Inversion Pulses Using the Adiabatic Condition
Rosenfeld, Daniel; Panfil, Shimon L.; Zur, Yuval
1997-12-01
Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in the presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theBeffvector and the rate of motion along it. In this paper, we describe a method by which optimized modulation functions can be constructed to render insensitivity toB1inhomogeneity over a predeterminedB1range and over a wide band of frequencies. This is accomplished by requiring that the optimized pulse fulfill the adiabatic condition over this range ofB1inhomogeneity and over the desired frequency band for the complete duration of the pulse. A trajectory similar to the well-known sech/tanh adiabatic pulse, i.e., a half-ellipse, is used. The optimization process improves the slice profile by optimizing the rate of motion along this trajectory. The optimized pulse can be tailored to the specific design requirements; in particular, the transition sharpness may be traded off against the inverted bandwidth. Two design examples, including experimental results, demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse: in the first example, a large frequency band is to be inverted using a weak RF amplitude in a short time. In the second example, a pulse with a very sharp transition is required.
Analysis of double hybrid density-functionals along the adiabatic connection
Cornaton, Yann; Teale, Andrew M; Fromager, Emmanuel
2013-01-01
We present a graphical analysis of the adiabatic connections underlying double-hybrid density-functional methods that employ second-order perturbation theory. Approximate adiabatic connection formulae relevant to the construction of these functionals are derived and compared directly with those calculated using accurate ab initio methods. The discontinuous nature of the approximate adiabatic integrands is emphasized, the discontinuities occurring at interaction strengths which mark the transitions between regions that are: (i) described predominantly by second- order perturbation theory (ii) described by a mixture of density-functional and second-order perturbation theory contributions and (iii) described purely by density-functional theory. Numerical examples are presented for a selection of small molecular systems and van der Waals dimers. The impacts of commonly used approximations in each of the three sections of the adiabatic connection are discussed along with possible routes for the development of impr...
Entropy in adiabatic regions of convection simulations
Tanner, Joel D; Demarque, Pierre
2016-01-01
One of the largest sources of uncertainty in stellar models is caused by the treatment of convection in stellar envelopes. One dimensional stellar models often make use of the mixing length or equivalent approximations to describe convection, all of which depend on various free parameters. There have been attempts to rectify this by using 3D radiative-hydrodynamic simulations of stellar convection, and in trying to extract an equivalent mixing length from the simulations. In this paper we show that the entropy of the deeper, adiabatic layers in these simulations can be expressed as a simple function of og g and log T_{eff} which holds potential for calibrating stellar models in a simple and more general manner.
Entropy in Adiabatic Regions of Convection Simulations
Tanner, Joel D.; Basu, Sarbani; Demarque, Pierre
2016-05-01
One of the largest sources of uncertainty in stellar models is caused by the treatment of convection in stellar envelopes. One-dimensional stellar models often make use of the mixing length or equivalent approximations to describe convection, all of which depend on various free parameters. There have been attempts to rectify this by using 3D radiative-hydrodynamic simulations of stellar convection, and in trying to extract an equivalent mixing length from the simulations. In this Letter, we show that the entropy of the deeper, adiabatic layers in these simulations can be expressed as a simple function of {log}g and {log}{T}{{eff}}, which holds potential for calibrating stellar models in a simple and more general manner.
Adiabatic pumping through quantum dots
A finite charge can be pumped through a mesoscopic system in the absence of an applied bias voltage by changing periodically in time some parameters of the system. If these parameters change slowly with respect to all internal time scales of the system, pumping is adiabatic. The scope of this work is to investigate adiabatic pumping through a quantum dot, in particular the influence of Coulomb interaction between electrons in the dot on the pumped charge. On one hand we develop a formalism based on Green's functions, in order to calculate the pumped charge from the weak-tunnel-coupling regime down to the Kondo regime. We extend our calculations to a system with a superconducting contact. On the other hand we use a systematic perturbation expansion for the calculation of the pumped charge, giving us the possibility to analyze processes which contribute to charge pumping and to highlight the important role of interaction-induced level renormalization. (orig.)
Adiabatic theory for the bipolaron
A translation-invariant adiabatic theory is constructed for the bipolaron. It is shown that motions in the bipolaron are divided: the relative electron coordinates describe fast electron oscillations in the induced polarization well and the center of mass coordinates represent slow electron movement followed by polarization. Nonlinear differential bipolaron equations are derived which are asymptotically exact in the adiabatic limit. Particlelike solutions of these equations correspond to the bipolaron bound state. The exact solution yields the value of the ion critical parameter η=0.31 for which the bipolaron state is stable, where η=ε∞/ε0 and ε∞,ε0 are high-frequency and static dielectric permittivities. The energy, the total energy, the effective mass, the radius, and the critical values of the electron-phonon coupling constants are calculated for the bipolaron. The results obtained are generalized to the case of two-dimensional bipolarons
Molecular Scattering and Born-Oppenheimer Approximation
Vania, Sordoni
2008-01-01
In this paper, we study the scattering wave operators for a diatomic molecules by using the Born-Oppenheimer approximation. Assuming that the ratio h^2 between the electronic and nuclear masses is small, we construct adiabatic wave operators that, under some non trapping conditions, approximate the two-cluster wave operators up to any powers of the parameter h
Assessment of Several Moist Adiabatic Processes Associated with Convective Energy Calculation
李耀东; 高守亭; 刘健文
2004-01-01
Several methods dealing with the moist adiabatic process are described in this paper. They are based on static energy conservation, pseudo-equivalent potential temperature conservation, the strict pseudoadiabatic equation, and the reversible moist adiabatic process, respectively. Convective energy parameters, which are closely related to the moist adiabatic process and which reflect the gravitational effects of condensed liquid water, are reintroduced or defined, including MCAPE [Modified-CAPE (convective available potential energy)], DCAPE (Downdraft-CAPE), and MDCAPE (Modified-Downdraft-CAPE). Two real case analyses with special attention given to condensed liquid water show that the selection of moist adiabatic process does affect the calculated results of CAPE and the gravitational effects of condensed liquid water are not negligible in severe storms. Intercomparisons of these methods show that static energy conservation is consistent with pseudo-equivalent potential temperature conservation not only in physical properties but also in calculated results, and both are good approximations to the strict pseudo-adiabatic equation. The lapse rate linked with the reversible moist adiabatic process is relatively smaller than that linked with other moist adiabatic processes, especially when considering solidification of liquid water in the reversible adiabatic process.
Highly stripped ions on hydrogen atoms: the adiabatic approach
The simple Lorentzian form for the adiabatic radial matrix elements which dominate low-energy charge transfer in highly stripped systems is exploited to derive the S matrix for the Asub(Z)sup(Z+) + H(1s) → Asub(Z)sup(Z-1)+ + H+ scattering process. The approximations used are discussed and the results of the theory are compared with measured He2+ + H(1s) → He+ + H+ cross sections. Agreement is satisfactory for low velocities. (author)
Adiabatic processes in monatomic gases
A kinetic model is used to predict the temperature evolution of a monatomic ideal gas undergoing an adiabatic expansion or compression at a constant finite rate, and it is then generalized to treat real gases. The effects of interatomic forces are considered, using as examples the gas with the square-well potential and the van der Waals gas. The model is integrated into a Carnot cycle operating at a finite rate to compare the efficiency's rate-dependent behavior with the reversible result. Limitations of the model, rate penalties, and their importance are discussed
Additional adiabatic heating of plasma
A theoretical possibility of a plasma additional adiabatic heating up to temperatures needed for the begin of D-T thermonuclear fusion reaction, has been found on the base of the polyenergetic conjugation expression, developed in the Thermodynamics of Accumulation Processes. TAP is a branch of the non-equilibrium thermodynamics. The thermodynamics of irreversible processes is another branch of the entire non-equilibrium thermodynamics. TAP deals with the phenomena associated with the introduction, conversion and accumulation of mass or energy or both in the affected, open or closed systems. (author) 2 refs
Adiabatic and non-adiabatic charge pumping in a single-level molecular motor
We propose a design for realizing quantum charge pump based on a recent proposal for a molecular motor (Seldenthuis J S et al 2010 ACS Nano 4 6681). Our design is based on the presence of a moiety with a permanent dipole moment which can rotate, thereby modulating the couplings to metallic contacts at both ends of the molecule. Using the non-equilibrium Keldysh Green’s function formalism (NEGF), we show that our design indeed generates a pump current. In the non-interacting pump, the variation of frequency from adiabatic to non-adiabatic regime, can be used to control the direction as well as the amplitude of the average current. The effect of Coulomb interaction is considered within the first- and the second- order perturbation. The numerical implementation of the scheme is quite demanding, and we develop an analytical approximation to obtain a speed-up giving results within a reasonable time. We find that the amplitude of the average pumped current can be controlled by both the driving frequency and the Coulomb interaction. The direction of of pumped current is shown to be determined by the phase difference between left and right anchoring groups. (paper)
A New Approach to the Quantum Adiabatic Condition
The quantum adiabatic theorem is the basis of adiabatic quantum computation. However, the exact necessary and sufficient conditions for adiabatic evolution are still under debate. We discuss the adiabatic condition of a system undergoing a special evolution route, and obtain an explicit formula that is necessary and sufficient for the adiabatic evolution in this route. Based on this formula, we find that the traditional adiabatic condition is neither sufficient nor necessary. Finally, we show that no adiabatic process can occur even the evolution speed goes to 0 in some examples, which is surprising since the adiabatic theorem states that if the evolution of a system is slow enough, the adiabatic process could occur
Stellar oscillations. II The non-adiabatic case
Samadi, R; Sonoi, T
2015-01-01
A leap forward has been performed due to the space-borne missions, MOST, CoRoT and Kepler. They provided a wealth of observational data, and more precisely oscillation spectra, which have been (and are still) exploited to infer the internal structure of stars. While an adiabatic approach is often sufficient to get information on the stellar equilibrium structures it is not sufficient to get a full understanding of the physics of the oscillation. Indeed, it does not permit one to answer some fundamental questions about the oscillations, such as: What are the physical mechanisms responsible for the pulsations inside stars? What determines the amplitudes? To what extent the adiabatic approximation is valid? All these questions can only be addressed by considering the energy exchanges between the oscillations and the surrounding medium. This lecture therefore aims at considering the energetical aspects of stellar pulsations with particular emphasis on the driving and damping mechanisms. To this end, the full non-...
Adiabatic compression of elongated field-reversed configurations
The simplest model of plasma dynamics is the adiabatic model. In this model the plasma is assumed to be in MHD equilibrium at each instant of time. The equilibria are connected by the requirement that they all have the same entropy per unit flux, i.e., the equilibria form a sequence generated by adiabatic changes. The standard way of computing such a sequence of equilibria was developed by Grad, but its practical use requires a fairly complicated code. It would be helpful if approximately the same results could be gotten either with a much simpler code or by analytical techniques. A one-dimensional equilibrium code is described and its results are checked against a two-dimensional equilibrium. An even simpler analytic calculation is then presented
Influence of viscosity and the adiabatic index on planetary migration
Bitsch, B; Kley, W
2013-01-01
The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state, where the internal dissipation is balanced by radiative transport, and the migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. In this paper we investigate the influence of different viscosity prescriptions (alpha-type and constant) and adiabatic indices on disk structures and how this affects the migration rate of planets embedded in such disks. We perform 3D numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20Earthmass planets is studied. Low-viscosity disks...
Complete Adiabatic Quantum Search in Unsorted Databases
Xu, Nanyang; Peng, Xinhua; Shi, Mingjun; Du, Jiangfeng
2008-01-01
We propose a new adiabatic algorithm for the unsorted database search problem. This algorithm saves two thirds of qubits than Grover's algorithm in realizations. Meanwhile, we analyze the time complexity of the algorithm by both perturbative method and numerical simulation. The results show it provides a better speedup than the previous adiabatic search algorithm.
Shortcut to adiabatic gate teleportation
Santos, Alan C.; Silva, Raphael D.; Sarandy, Marcelo S.
2016-01-01
We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able to implement teleportation as a universal computational primitive. In this scenario, we provide the counterdiabatic driving for arbitrary n -qubit gates, which allows to achieve universality through a variety of gate sets. Remarkably, our approach maps the superadiabatic Hamiltonian HSA for an arbitrary n -qubit gate teleportation into the implementation of a rotated superadiabatic dynamics of an n -qubit state teleportation. This result is rather general, with the speed of the evolution only dictated by the quantum speed limit. In particular, we analyze the energetic cost for different Hamiltonian interpolations in the context of the energy-time complementarity.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-04-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.
Quantum gates with controlled adiabatic evolutions
Hen, Itay
2015-02-01
We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building blocks in the construction of arbitrary "adiabatic circuits," analogously to the manner in which gates are used in the circuit model. One implication of the above construction is that arbitrary classical boolean circuits as well as gate model circuits may be directly translated to adiabatic algorithms with no additional resources or complexities. We show that while these adiabatic algorithms fail to exhibit certain aspects of the inherent fault tolerance of traditional quantum adiabatic algorithms, they may have certain other experimental advantages acting as quantum gates.
On the statistical mechanics of an adiabatic ensemble
S.N.Andreev
2004-01-01
Full Text Available Different descriptions of an adiabatic process based on statistical thermodynamics and statistical mechanics are discussed. Equality of the so-called adiabatic and isolated susceptibilities and its generalization as well as adiabatic invariants are essentially used to describe adiabatic processes in the framework of quantum and classical statistical mechanics. It is shown that distribution function in adiabatic ensemble differs from a quasi-equilibrium canonical form provided the heat capacity of the system is not constant in adiabatic process.
Partial evolution based local adiabatic quantum search
Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one. Later, they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database. In the present paper, following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original “global” one, this “new” algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M = 1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed. (general)
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems
Digital Waveguide Adiabatic Passage Part 2: Experiment
Ng, Vincent; Chaboyer, Zachary J; Nguyen, Thach; Dawes, Judith M; Withford, Michael J; Greentree, Andrew D; Steel, M J
2016-01-01
Using a femtosecond laser writing technique, we fabricate and characterise three-waveguide digital adiabatic passage devices, with the central waveguide digitised into five discrete waveguidelets. Strongly asymmetric behaviour was observed, devices operated with high fidelity in the counter-intuitive scheme while strongly suppressing transmission in the intuitive. The low differential loss of the digital adiabatic passage designs potentially offers additional functionality for adiabatic passage based devices. These devices operate with a high contrast ($>\\!90\\%$) over a 60~nm bandwidth, centered at $\\sim 823$~nm.
Adiabatic Compression of Oxygen: Real Fluid Temperatures
Barragan, Michelle; Wilson, D. Bruce; Stoltzfus, Joel M.
2000-01-01
The adiabatic compression of oxygen has been identified as an ignition source for systems operating in enriched oxygen atmospheres. Current practice is to evaluate the temperature rise on compression by treating oxygen as an ideal gas with constant heat capacity. This paper establishes the appropriate thermodynamic analysis for the common occurrence of adiabatic compression of oxygen and in the process defines a satisfactory equation of state (EOS) for oxygen. It uses that EOS to model adiabatic compression as isentropic compression and calculates final temperatures for this system using current approaches for comparison.
Thermoelectric Effects under Adiabatic Conditions
George Levy
2013-10-01
Full Text Available This paper investigates not fully explained voltage offsets observed by several researchers during the measurement of the Seebeck coefficient of high Z materials. These offsets, traditionally attributed to faulty laboratory procedures, have proven to have an irreducible component that cannot be fully eliminated in spite of careful laboratory procedures. In fact, these offsets are commonly observed and routinely subtracted out of commercially available Seebeck measurement systems. This paper offers a possible explanation based on the spontaneous formation of an adiabatic temperature gradient in the presence of a force field. The diffusion-diffusion heat transport mechanism is formulated and applied to predict two new thermoelectric effects. The first is the existence of a temperature gradient across a potential barrier in a semiconductor and the second is the Onsager reciprocal of the first, that is, the presence of a measureable voltage that arises across a junction when the temperature gradient is forced to zero by a thermal clamp. Suggested future research includes strategies for utilizing the new thermoelectric effects.
Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem
Pan, Yu; James, Matthew R. [Australian National University, Research School of Engineering, Canberra (Australia); Miao, Zibo [The University of Melbourne, Department of Electrical and Electronic Engineering, Melbourne (Australia); Amini, Nina H. [CNRS, Laboratoire des Signaux et Systemes (L2S) Supelec, Gif-Sur-Yvette (France); Ugrinovskii, Valery [University of New South Wales at ADFA, School of Engineering and Information Technology, Canberra (Australia)
2015-12-15
Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)
Niven, Ivan
2008-01-01
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discuss
Adiabatic hydrodynamics: The eightfold way to dissipation
Haehl, Felix M; Rangamani, Mukund
2015-01-01
We provide a complete solution to hydrodynamic transport at all orders in the gradient expansion compatible with the second law constraint. The key new ingredient we introduce is the notion of adiabaticity, which allows us to take hydrodynamics off-shell. Adiabatic fluids are such that off-shell dynamics of the fluid compensates for entropy production. The space of adiabatic fluids is quite rich, and admits a decomposition into seven distinct classes. Together with the dissipative class this establishes the eightfold way of hydrodynamic transport. Furthermore, recent results guarantee that dissipative terms beyond leading order in the gradient expansion are agnostic of the second law. While this completes a transport taxonomy, we go on to argue for a new symmetry principle, an Abelian gauge invariance that guarantees adiabaticity in hydrodynamics. We suggest that this symmetry is the macroscopic manifestation of the microscopic KMS invariance. We demonstrate its utility by explicitly constructing effective ac...
Nonlinear effects generation in non-adiabatically tapered fibres
Palací, Jesús; Mas, Sara; Monzón-Hernández, David; Martí, Javier
2015-12-01
Nonlinear effects are observed in a non-adiabatically tapered optical fibre. The designed structure allows for the introduction of self-phase modulation, which is observed through pulse breaking and spectral broadening, in approximately a centimetre of propagation using a commercial telecom laser. These devices are simple to fabricate and suitable to generate and control a variety of nonlinear effects in practical applications because they do not experience short-term degradation as previously reported approaches. Experimental and theoretical results are obtained, showing a good agreement.
Adiabatic collapse and explosion of small mass iron nuclei
Adiabatic collapse of iron nuclei with 1.5 and 1.7 Msun masses is investigated using the equation of state and electron capture rate in the Fermi-gas approximation, derived at the Illinois University. Reduction of lepton number in the collapse process leads to the fact that under quite different presupernova nucleus parameters the calculated mass of homologie nucleus is only about 1 Msun. Therefore the mass of the above lying layers through which the shock wave should pass, becomes quite high loosing the energy for dissociation, which hampers any sufficient mass and kinetic energy losses. 17 refs.; 8 figs.; 2 tabs
Relativistic blast waves in two dimensions. I - The adiabatic case
Shapiro, P. R.
1979-01-01
Approximate solutions are presented for the dynamical evolution of strong adiabatic relativistic blast waves which result from a point explosion in an ambient gas in which the density varies both with distance from the explosion center and with polar angle in axisymmetry. Solutions are analytical or quasi-analytical for the extreme relativistic case and numerical for the arbitrarily relativistic case. Some general properties of nonplanar relativistic shocks are also discussed, including the incoherence of spherical ultrarelativistic blast-wave fronts on angular scales greater than the reciprocal of the shock Lorentz factor, as well as the conditions for producing blast-wave acceleration.
Adiabatic Connection for Strictly-Correlated Electrons
Liu, Zhenfei; Burke, Kieron
2009-01-01
Modern density functional theory (DFT) calculations employ the Kohn-Sham (KS) system of non-interacting electrons as a reference, with all complications buried in the exchange-correlation energy (Exc). The adiabatic connection formula gives an exact expression for Exc. We consider DFT calculations that instead employ a reference of strictly-correlated electrons. We define a "decorrelation energy" that relates this reference to the real system, and derive the corresponding adiabatic connection...
On adiabatic invariant in generalized Galileon theories
Ema, Yohei; Jinno, Ryusuke; Mukaida, Kyohei; Nakayama, Kazunori
2015-01-01
We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is us...
Quantum and classical dynamics in adiabatic computation
Crowley, P. J. D.; Duric, T.; Vinci, W.; Warburton, P. A.; Green, A. G.
2014-01-01
Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations th...
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher; Russell, Alexander
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities i...
An Integrated Programming and Development Environment for Adiabatic Quantum Optimization
Humble, Travis S.; McCaskey, Alex J.; Bennink, Ryan S.; Billings, Jay J.; D'Azevedo, Ed F.; Sullivan, Blair D.; Klymko, Christine F.; Seddiqi, Hadayat
2013-01-01
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware has raised challenging questions about how to evaluate adiabatic quantum optimization programs. Processor behavior depends on multiple steps to synthesize an adiabatic quantum program, which are each highly tunable. We present an integrated programming and development environment for adiabatic quantum optimization called JADE tha...
On criterion of modal adiabaticity
WANG; Ning(
2001-01-01
［1］Pierce, A. D., Extension of the method of normal modes to sound propagation in an almost-stratified medium, J. Acoust.Soc. Am., 1965, 37: 19－27.［2］Wang, D. Z. , Shang, E. C., Underwater Acoustics (in Chinese), Beijing: Science Press, 1981.［3］Zhang Renhe, Li Fenghua, Beam-displacement rya-mode theory of sound propagation in shallow water, Science in China, Ser.A, 1999, 42(7): 739－749.［4］Zhou Jixun, Zhang Xuezhen, Rogers P., Resonance interaction of sound waves with internal solitons in coastal zone, J.Acoust. Soc. Am., 1991, 90: 2042－2054.［5］Shang, E. C., Wang, Y. Y., The impact of mesoscale oceanic structure on global-scale acoustic propagation, in Theoretical and Computational Acoustics (ed. Ding Lee et al. ), Singapore: World Scientific Publishing Co. , 1996, 409－431.［6］Milder, D. M., Ray and wave invariants for SOFAR channel propagation, J. Acoust. Soc. Am., 1969, 46: 1259－1263.［7］Nag l, A., Milder, D. M., Adiabatic mode theory of underwater sound propagation in a range-dependent environment, J.Acoust. Soc. Am., 1978, 63: 739－749.［8］Brekhovskikh, L. M., Waves in Layered Media, 2nd ed., New York: Academic Press Inc., 1973.［9］Brekhovskikh, L. M., Lysanov, Yu., Fundamental of Ocean Acoustics, Ch. 7, Sec. 7.2, Berlin: Springer-Verlag, 1982.［10］Evans, R. B., A coupled mode solution for acoustic propagation in a wave-guide with stepwise depth variations of a penerable bottom, J. Acoust. Soc. A.m., 1983, 74: 188－195.［11］Jensen, F. B., Kuperman, W. A., Porter, M. B. et al., Computational Ocean Acoustics, New York: Springer-Verlag,1992.［12］Wang Ning, Inverse scattering problem for the coupled second order ODE, Journal of The Physical Society of Japan, 1995, 64(12): 4907－4915.
Invariant Hermitian Operator and Density Operator for the Adiabatically Time-Dependent System
YAN Feng-Li; YANG Lin-Guang
2001-01-01
The density operator is approximately expressed as a function of the invariant Hermitian operator for the adiabatically time-dependent system. Using this method, the calculation of the density operator for the Heisenberg spin system in a weakly time-dependent magnetic field is exemplified. By virtue of the density operator, we obtain equilibrium.``
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Benabbas, Abdelkrim; Salna, Bridget; Sage, J. Timothy; Champion, Paul M.
2015-03-01
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical "gating" distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working near
Benabbas, Abdelkrim; Salna, Bridget; Sage, J. Timothy; Champion, Paul M., E-mail: champ@neu.edu [Department of Physics and Center for Interdisciplinary Research on Complex Systems,Northeastern University, Boston, Massachusetts 02115 (United States)
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical “gating” distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working
Exploring adiabatic quantum trajectories via optimal control
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring the properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time. (paper)
Adiabatic cooling of a single trapped ion
Poulsen, Gregers
2012-01-01
We present experimental results on adiabatic cooling of a single 40Ca+ ion in a linear radiofrequency trap. After a period of laser cooling, the secular frequency along the rf-field-free axis is adiabatically lowered by nearly a factor of eight from 583 kHz to 75 kHz. For an ion originally Doppler laser cooled to a temperature of 0.65 +/- 0.03 mK, a temperature of 87 +/- 7 \\mu K is measured after the adiabatic expansion. Applying the same adiabatic cooling procedure to a single sideband cooled ion in the ground state (P0 = 0.978 +/- 0.002) resulted in a final ground state occupation of 0.947 +/- 0.005. Both results are in excellent agreement with an essentially fully adiabatic behavior. The results have a wide range of perspectives within such diverse fields as ion based quantum information science, high resolution molecular ion spectroscopy and ion chemistry at ultra-low temperatures.
Symmetry-Protected Quantum Adiabatic Transistors
Williamson, Dominic J.; Bartlett, Stephen D.
2014-03-01
An essential development in the history of computing was the invention of the transistor as it allowed logic circuits to be implemented in a robust and modular way. The physical characteristics of semiconductor materials were the key to building these devices. We aim to present an analogous development for quantum computing by showing that quantum adiabatic transistors (as defined by Flammia et al.) are built upon the essential qualities of symmetry-protected (SP) quantum ordered phases in one dimension. Flammia et al. and Renes et al. have demonstrated schemes for universal adiabatic quantum computation using quantum adiabatic transistors described by interacting spin chain models with specifically chosen Hamiltonian terms. We show that these models can be understood as specific examples of the generic situation in which all SP phases lead to quantum computation on encoded edge degrees of freedom by adiabatically traversing a symmetric phase transition into a trivial symmetric phase. This point of view is advantageous as it allows us to readily see that the computational properties of a quantum adiabatic transistor arise from a phase of matter rather than due to carefully tuned interactions.
Accurate adiabatic correction in the hydrogen molecule
Pachucki, Krzysztof, E-mail: krp@fuw.edu.pl [Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw (Poland); Komasa, Jacek, E-mail: komasa@man.poznan.pl [Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań (Poland)
2014-12-14
A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10{sup −12} at an arbitrary internuclear distance. Such calculations have been performed for 88 internuclear distances in the range of 0 < R ⩽ 12 bohrs to construct the adiabatic correction potential and to solve the nuclear Schrödinger equation. Finally, the adiabatic correction to the dissociation energies of all rovibrational levels in H{sub 2}, HD, HT, D{sub 2}, DT, and T{sub 2} has been determined. For the ground state of H{sub 2} the estimated precision is 3 × 10{sup −7} cm{sup −1}, which is almost three orders of magnitude higher than that of the best previous result. The achieved accuracy removes the adiabatic contribution from the overall error budget of the present day theoretical predictions for the rovibrational levels.
Adiabatic process reversibility: microscopic and macroscopic views
The reversibility of adiabatic processes was recently addressed by two publications. In the first (Miranda 2008 Eur. J. Phys. 29 937-43), an equation was derived relating the initial and final volumes and temperatures for adiabatic expansions of an ideal gas, using a microscopic approach. In that relation the parameter r accounts for the process reversibility, ranging between 0 and 1, which corresponds to the free and reversible expansion, respectively. In the second (Anacleto and Pereira 2009 Eur. J. Phys. 30 177-83), the authors have shown that thermodynamics can effectively and efficiently be used to obtain the general law for adiabatic processes carried out by an ideal gas, including compressions, for which r≥1. The present work integrates and extends the aforementioned studies, providing thus further insights into the analysis of the adiabatic process. It is shown that Miranda's work is wholly valid for compressions. In addition, it is demonstrated that the adiabatic reversibility coefficient given in terms of the piston velocity and the root mean square velocity of the gas particles is equivalent to the macroscopic description, given just by the quotient between surroundings and system pressure values. (letters and comments)
Adiabatic change of state of photon gas
The authors introduced and justified the k problem as a thermodynamical contradiction of photon gas. In thermodynamics of photon gas the main contradiction is called the k problem: the piezotropic-autobarotropic equation of state P = u/3 is adiabatic if k = 1 exclusively, while the adiabatic connection PV4/3 = const (or rather the Poisson equation Pρ-4/3 = const, ρ = u/c2) requires that k = 4/3. The present paper shows that the equations of state PV4/3 = const, TV1/3 = const, T-4/3P1/3 = const and P = u/3 cannot be valid for the adiabatic change of state of photon gas, simultaneously. Furthermore, the Planck's distribution -- and so the Wien's law and the Rayleigh-Jeans connection as well -- cannot be invariant in case of adiabatic change of state of photon gas. Namely, in case of adiabatic change of state of photon gas, a new type of ultraviolet catastrophe appears. These results possess a fundamental important in case of arbitrary deformation of electromagnetic radiation fields or quantum plasmas
Inertial parameters in the interacting boson fermion approximation
The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors)
Reconstructing the adiabatic exchange-correlation kernel of time-dependent density-functional theory
The interacting and the Kohn-Sham static density-density response functions for different one-dimensional two-electron singlet systems are reconstructed numerically. From their inverse we obtain the exact static exchange-correlation kernel. This quantity represents the adiabatically exact approximation of the frequency-dependent exchange-correlation kernel that is crucial for time-dependent linear density-response theory. We investigate its performance for nonlocal perturbations and analyze its sum rule properties. We also compute the adiabatically exact transition energies that follow from the static kernel within linear-response theory.
Nonadiabatic exchange dynamics during adiabatic frequency sweeps
Barbara, Thomas M.
2016-04-01
A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging.
Energy efficiency of adiabatic superconductor logic
Adiabatic superconductor logic (ASL), including adiabatic quantum-flux-parametron (AQFP) logic, exhibits high energy efficiency because its bit energy can be decreased below the thermal energy through adiabatic switching operations. In the present paper, we present the general scaling laws of ASL and compare the energy efficiency of ASL with those of other energy-efficient logics. Also, we discuss the minimum energy-delay product (EDP) of ASL at finite temperature. Our study shows that there is a maximum temperature at which the EDP can reach the quantum limit given by ħ/2, which is dependent on the superconductor material and the Josephson junction quality, and that it is reasonable to operate ASL at cryogenic temperatures in order to achieve an EDP that approaches ħ/2. (paper)
Experimental study on the adiabatic shear bands
Four martensitic steels (Z50CDV5 steel, 28CND8 steel, 35NCDV16 steel and 4340 steel) with different hardness between 190 and 600 Hsub(B) (Brinell hardness), have been studied by means of dynamic compressive tests on split Hopkinson pressure bar. Microscopic observations show that the fracture are associated to the development of adiabatic shear bands (except 4340 steel with 190 Hsub(B) hardness). By means of tests for which the deformation is stopped at predetermined levels, the measurement of shear and hardness inside the band and the matrix indicates the chronology of this phenomenon: first the localization of shear, followed by the formation of adiabatic shear band and ultimatly crack initiation and propagation. These results correlated with few simulations by finite elements have permitted to suggest two mecanisms of deformation leading to the formation of adiabatic shear bands in this specific test
Staying adiabatic with unknown energy gap
Nehrkorn, J; Ekert, A; Smerzi, A; Fazio, R; Calarco, T
2011-01-01
We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total evolution time. We test the algorithm on the Landau-Zener transition and then apply it on the quantum adiabatic computation of 3-SAT: The result is compatible with an exponential speed-up for up to twenty qubits with respect to classical algorithms. We finally study a possible algorithm improvement by combining it with the quantum Zeno effect.
Ramsey numbers and adiabatic quantum computing
Gaitan, Frank; Clark, Lane
2011-01-01
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\\geq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers $R(m,n)$. We show how the computation of $R(m,n)$ can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctl...
Superconducting system for adiabatic quantum computing
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results
On black hole spectroscopy via adiabatic invariance
Jiang Qingquan, E-mail: qqjiangphys@yeah.net [College of Physics and Electronic Information, China West Normal University, Nanchong, Sichuan 637002 (China); Han Yan [College of Mathematic and Information, China West Normal University, Nanchong, Sichuan 637002 (China)
2012-12-05
In this Letter, we obtain the black hole spectroscopy by combining the black hole property of adiabaticity and the oscillating velocity of the black hole horizon. This velocity is obtained in the tunneling framework. In particular, we declare, if requiring canonical invariance, the adiabatic invariant quantity should be of the covariant form I{sub adia}= Contour-Integral p{sub i}dq{sub i}. Using it, the horizon area of a Schwarzschild black hole is quantized independently of the choice of coordinates, with an equally spaced spectroscopy always given by {Delta}A=8{pi}l{sub p}{sup 2} in the Schwarzschild and Painleve coordinates.
Complexity of the Quantum Adiabatic Algorithm
Hen, Itay
2013-01-01
The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.
Adiabatic Flame Temperature for Combustion of Methane
Rebeca Pupo
2011-01-01
Full Text Available This project calculated the adiabatic flame temperature of a combustion reaction of pure methane and oxygen, assuming that all of the heat liberated by the combustion reaction goes into heating the resulting mixture. Mole fractions of methane to oxygen were computed from 0.05 to 0.95, in increments of 0.05, and then an integral was computed was computed with respect to temperature using the moles of product produced or leftover moles of reactants from the starting mole fraction times the specific heat of each respective gas. The highest adiabatic flame temperature evaluated, occurred at a mole fraction of 0.35.
Influence of viscosity and the adiabatic index on planetary migration
Bitsch, B.; Boley, A.; Kley, W.
2013-02-01
Context. The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state. It has been shown that in active disks, where the internal dissipation is balanced by radiative transport, migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. Aims: In this paper we investigate the influence of different viscosity prescriptions (α-type and constant) and adiabatic indices on disk structures. We then determine how this affects the migration rate of planets embedded in such disks. Methods: We perform three-dimensional numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20 MEarth planets is studied. Results: Low-viscosity disks have cooler temperatures and the migration rates of embedded planets tend toward the isothermal limit. Hence, in these disks, planets migrate inwards even in the fully radiative case. The effect of outward migration can only be sustained if the viscosity in the disk is large. Overall, the differences between the treatments for the equation of state seem to play a more important role in disks with higher viscosity. A change in the adiabatic index and in the viscosity changes the zero-torque radius that separates inward from outward migration. Conclusions: For larger viscosities, temperatures in the disk become higher and the zero-torque radius moves to larger radii, allowing outward migration of a 20-MEarth planet to persist over an extended radial range. In combination with large disk masses, this may allow for an extended period of the outward migration of growing
New Theory on Fully Nonlinear Adiabatic TWM in Terms of Elliptic Functions
Qian, Shunrong
2016-01-01
I'm presenting a new elegant formulation of the theory of fully nonlinear adiabatic TWM (FNA-TWM) in terms of elliptic function here. Note that the linear case of SFG and DFG in the undepleted pump approximation described by the FVH representation has been exploited several years ago. For the sake of completeness, I present the pseudo-FVH representation to describe OPA. Moreover, I'm trying to display an overview of TWM processes and show that both the linear cases, the linear adiabatic SFG(DFG) and the linear OPA, are only the special cases of my theory. Finally I also point out that the geometric image of the so-called adiabatic basis acts as the geodesic line of the generalized Bloch sphere.
The adiabatic limit of the exact factorization of the electron-nuclear wave function
Eich, Florian G
2016-01-01
We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model proton- coupled electron transfer in different non-adiabatic regimes.
The adiabatic limit of the exact factorization of the electron-nuclear wave function
Eich, F. G.; Agostini, Federica
2016-08-01
We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes.
Adiabatic transition probability for a tangential crossing
Watanabe, Takuya
2006-01-01
We consider a time-dependent Schrödinger equation whose Hamiltonian is a $2\\times 2$ real symmetric matrix. We study, using an exact WKB method, the adiabatic limit of the transition probability in the case where several complex eigenvalue crossing points accumulate to one real point.
On the double adiabatic continuous spectrum
In earlier work it has been found that the Alfven and cusp (or slow) continuous spectra can become unstable in toroidal geometry, as judged from the linearized double adiabatic equations. In this paper the validity of fluid approaches to the present problem is investigated. The physical implications of the stability conditions are discussed. (Author)
Pulsed adiabatic structure and complete population transfer
Population can be transferred between atomic or molecular energy states in a variety of ways. The basic idea of adiabatic transfer, discussed in many textbooks, is as follows. One begins with an atom that is in some single energy state (an eigenstate of an initial Hamiltonian). This energy state is one of many possible states, known variously as the unperturbed states or basis states or diabatic states. Next one begins to change the Hamiltonian very slowly. The changes may occur in either the diagonal elements (the basis state energies) or in the off-diagonal elements (interactions between basis states). If there are off-diagonal elements then the Hamiltonian will no longer commute with the original one. Because the Hamiltonian is no longer the one that was used to define the original basis states, it will cause these states to become mixed. However, if the change is sufficiently slow, the system can remain in a single eigenstate of the changing Hamiltonian -- an adiabatic state, composed of a combination of basis states. Finally, at some later time, one examines the system once again in the original basis. One finds that the population has undergone a change, and now resides in a different unperturbed state. One has produced population transfer. There are many illustrative examples of adiabatic passage, both theory and experiment. The author mentions briefly two common examples, inelastic collisions between atoms, and the static Stark effect in Rydberg atoms, before continuing with the main objective, a discussion of adiabatic passage induced by laser pulses
Adiabatic reversible compression: a molecular view
The adiabatic compression (or expansion) of an ideal gas has been analysed. Using the kinetic theory of gases the usual relation between temperature and volume is obtained, while textbooks follow a thermodynamic approach. In this way we show, once again, the agreement between a macroscopic view (thermodynamics) and a microscopic one (kinetic theory). (author)
Recent adiabaticity results from orbit calculations
There has been much activity recently in an attempt to find a straightforward method of predicting the limits of adiabatic behavior in high-beta magnetic-mirror configurations. The particle-orbit code TIBRO was used to obtain numerical results on nonadiabatic behavior with which the predictions of theoretical expressions can be compared. These results are summarized. (MOW)
Adiabatic Excitation of Longitudinal Bunch Shape Oscillations
By modulating the rf voltage at near twice the synchrotrons frequency we are able to modulate the longitudinal bunch shape. We show experimentally that this can be done while preserving the longitudinal emittance when the rf voltage modulation is turned on adiabatically. Experimental measurements will be presented along with theoretical predictions
Wigner phase space distribution via classical adiabatic switching
Bose, Amartya [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Makri, Nancy [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801 (United States)
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
Wigner phase space distribution via classical adiabatic switching
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations
Primeval adiabatic perturbations: constraints from the mass distribution
The autocorrelation function of the mass distribution after decoupling of matter and radiation is computed under the assumption of linear primeval adiabatic perturbations using a new numerical method, and the results are compared to what is inferred from the present galaxy distribution. The computations are based on a Friedmann-Lemaitre model with Λ = 0 containing radiation, zero-mass neutrinos, hydrogen, and helium. The primeval power spectrum of density fluctuations is taken to approximate a power law k/sup v/. If the density parameter is Ω0 = 2q0< or approx. =0.1; or, if ν< or approx. =2, then the coherence length of the residual mass distribution is too large: when the amplitude is adjusted to make the first generation of objects form at z< or approx. =2, there are unacceptably large fluctuations in the mass distribution now on scales approx.12 to 40 Mpc. If ν = 3 to 4, this problem is avoided, but to prevent diverging curvature fluctuations the power law k/sup v/ must be truncated at a rather large comoving wavelength, lambda/sub x/approx.1 Mpc. The parameters thus are tightly limited, but it appears that one still can find a consistent scenario for the development of galaxies out of linear primeval adiabatic perturbations
Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics
Albert, Julian; Kaiser, Dustin; Engel, Volker
2016-05-01
Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.
The dynamic instability of adiabatic blast waves
Ryu, Dongsu; Vishniac, Ethan T.
1991-01-01
Adiabatic blastwaves, which have a total energy injected from the center E varies as t(sup q) and propagate through a preshock medium with a density rho(sub E) varies as r(sup -omega) are described by a family of similarity solutions. Previous work has shown that adiabatic blastwaves with increasing or constant postshock entropy behind the shock front are susceptible to an oscillatory instability, caused by the difference between the nature of the forces on the two sides of the dense shell behind the shock front. This instability sets in if the dense postshock layer is sufficiently thin. The stability of adiabatic blastwaves with a decreasing postshock entropy is considered. Such blastwaves, if they are decelerating, always have a region behind the shock front which is subject to convection. Some accelerating blastwaves also have such region, depending on the values of q, omega, and gamma where gamma is the adiabatic index. However, since the shock interface stabilizes dynamically induced perturbations, blastwaves become convectively unstable only if the convective zone is localized around the origin or a contact discontinuity far from the shock front. On the other hand, the contact discontinuity of accelerating blastwaves is subject to a strong Rayleigh-Taylor instability. The frequency spectra of the nonradial, normal modes of adiabatic blastwaves have been calculated. The results have been applied to the shocks propagating through supernovae envelopes. It is shown that the metal/He and He/H interfaces are strongly unstable against the Rayleigh-Taylor instability. This instability will induce mixing in supernovae envelopes. In addition the implications of this work for the evolution of planetary nebulae is discussed.
Inverse engineering rigorous adiabatic Hamiltonian for non-Hermitian system
Wu, Qi-Cheng; Chen, Ye-Hong; Huang, Bi-Hua; Xia, Yan; Song, Jie
2016-01-01
We generalize the quantum adiabatic theorem to the non-Hermitian system and build a rigorous adiabaticity condition with respect to the adiabatic phase. The non-Hermitian Hamiltonian inverse engineering method is proposed for the purpose to adiabatically drive a artificial quantum state. For the sake of clearness, we take a concrete two-level system as an example to show the usefulness of the inverse engineering method. The numerical simulation result shows that our scheme can work well even ...
ADIABATIC MASS LOSS IN BINARY STARS. I. COMPUTATIONAL METHOD
The asymptotic response of donor stars in interacting binary systems to very rapid mass loss is characterized by adiabatic expansion throughout their interiors. In this limit, energy generation and heat flow through the stellar interior can be neglected. We model this response by constructing model sequences, beginning with a donor star filling its Roche lobe at an arbitrary point in its evolution, holding its specific entropy and composition profiles fixed as mass is removed from the surface. The stellar interior remains in hydrostatic equilibrium. Luminosity profiles in these adiabatic models of mass-losing stars can be reconstructed from the specific entropy profiles and their gradients. These approximations are validated by comparison with time-dependent binary mass transfer calculations. We describe how adiabatic mass-loss sequences can be used to quantify threshold conditions for dynamical timescale mass transfer, and to establish the range of post-common envelope binaries that are allowed energetically. In dynamical timescale mass transfer, the adiabatic response of the donor star drives it to expand beyond its Roche lobe, leading to runaway mass transfer and the formation of a common envelope with its companion star. For donor stars with surface convection zones of any significant depth, this runaway condition is encountered early in mass transfer, if at all; but for main-sequence stars with radiative envelopes, it may be encountered after a prolonged phase of thermal timescale mass transfer, a so-called delayed dynamical instability. We identify the critical binary mass ratio for the onset of dynamical timescale mass transfer as that ratio for which the adiabatic response of the donor star radius to mass loss matches that of its Roche lobe at some point during mass transfer; if the ratio of donor to accretor masses exceeds this critical value, dynamical timescale mass transfer ensues. In common envelope evolution, the dissipation of orbital energy of the
Exchange-correlation functionals via local interpolation along the adiabatic connection
Vuckovic, Stefan; Savin, Andreas; Teale, Andrew M; Gori-Giorgi, Paola
2016-01-01
The construction of density-functional approximations is explored by modeling the adiabatic connection em locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of range of local interpolation models against accurate exchange-correlation energy densities. The importance of the strictly-correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approache...
Perturbation to Mei symmetry and adiabatic invariants for Hamilton systems
Ding Ning; Fang Jian-Hui
2008-01-01
Based on the concept of adiabatic invariant,this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems.The exact invaxiants of Mei symmetry for the system without perturbation are given.The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T.; Gross, E. K. U.
2015-03-01
The Born-Oppenheimer (BO) approximation allows to visualize the coupled electron-nuclear dynamics in molecular systems as a set of nuclei moving on a single potential energy surface representing the effect of the electrons in a given eigenstate. Many interesting phenomena, however, such as vision or charge separation in organic photovoltaic materials, take place in conditions beyond its range of validity. Nevertheless, the basic construct of the adiabatic treatment, the BO potential energy surfaces, is employed to describe non-adiabatic processes and the full problem is represented in terms of adiabatic states and transitions among them in regions of strong non-adiabatic coupling. But the concept of single potential energy is lost. The alternative point of view arising in the framework of the exact factorization of the electron-nuclear wave function will be presented. A single, time-dependent, potential energy provides the force driving the nuclear motion and is adopted as starting point for the development of quantum-classical approximations to the full quantum mechanical problem.
Hydrodynamic stability of inverted annular flow in an adiabatic simulation
In experiments, inverted annular flow was simulated adiabatically with turbulent water jets, issuing downward from long aspect nozzles, enclosed in gas annuli. Velocities, diameters, and gas species were varied, and core jet length, shape, break-up mode, and dispersed-core droplet sizes were recorded at approximately 750 data points. Inverted annular flow was observed to develop into inverted slug flow at low relative velocities, and into dispersed droplet flow at high relative velocities. For both of the above transitions from inverted annular flow, a correlation for core jet length was developed by extending work done on free liquid jets to include this new, coaxial, jet disintegration phenomenon. The result, showing length dependence upon diameter, jet Reynolds number, jet Weber number, void fraction, and gas Weber number, correlates the data well, especially at moderate-to-large relative velocities
Differential geometric treewidth estimation in adiabatic quantum computation
Wang, Chi; Jonckheere, Edmond; Brun, Todd
2016-07-01
The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.
Dynamics of adiabatic blast waves in media of finite mass
A basic formulation is developed to describe the mass motion for nonrelativistic, spherically symmetric blast waves. The formulation is quite general in the sense that it applies to blast waves generated by either a strong explosion or a continuous energy injection, and in that it applies to an arbitrary density distribution. A simple method is developed to describe the motion of the shock by modifying the Kompaneets approximation. The formulation is applied to blast waves in specific density distributions, including an exponential medium, a Gaussian medium, and a medium with density distribution which asymptotically approaches a power law. Comparisons with numerical results for spherically symmetric blast waves are made. The one-dimensional formulation is generalized to nonspherically symmetric blast waves by making the assumption that the blast wave expands radially. Comparisons are made with numerical results for an adiabatic supershell in a plane-parallel medium. 32 refs
On the power of coherently controlled quantum adiabatic evolutions
We provide a new approach to adiabatic state preparation that uses coherent control and measurement to average different adiabatic evolutions in ways that cause their diabatic errors to cancel, allowing highly accurate state preparations using less time than conventional approaches. We show that this new model for adiabatic state preparation is polynomially equivalent to conventional adiabatic quantum computation by providing upper bounds on the cost of simulating such evolutions on a circuit-based quantum computer. Finally, we show that this approach is robust to small errors in the quantum control register and that the system remains protected against noise on the adiabatic register by the spectral gap. (paper)
Weinberg Soft Theorems from Weinberg Adiabatic Modes
Mirbabayi, Mehrdad
2016-01-01
Soft theorems for the scattering of low energy photons and gravitons and cosmological consistency conditions on the squeezed-limit correlation functions are both understood to be consequences of invariance under large gauge transformations. We apply the same method used in cosmology -- based on the identification of an infinite set of "adiabatic modes" and the corresponding conserved currents -- to derive flat space soft theorems for electrodynamics and gravity. We discuss how the recent derivations based on the asymptotic symmetry groups (BMS) can be continued to a finite size sphere surrounding the scattering event, when the soft photon or graviton has a finite momentum. We give a finite distance derivation of the antipodal matching condition previously imposed between future and past null infinities, and explain why all but one radiative degrees of freedom decouple in the soft limit. In contrast to earlier works on BMS, we work with adiabatic modes which correspond to large gauge transformations that are $...
Quantum adiabatic evolution with energy degeneracy levels
Zhang, Qi
2016-01-01
A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert space and the aggregate of degenerate eigenstates become the classical-kind phase space and a high-dimensional subspace in the phase space, respectively. Compared with the previous analogous study by a different method, the current result is qualitatively different in that the first-order deviation derived here is always perpendicular to the degeneracy subspace. A tripod-scheme Hamiltonian with two degenerate dark states is employed to illustrate the adiabatic deviation with degeneracy levels.
Adiabatic Quantum Optimization for Associative Memory Recall
Hadayat eSeddiqi
2014-12-01
Full Text Available Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO. Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.
Adiabatic Quantum Simulation of Quantum Chemistry
Babbush, Ryan; Love, Peter J.; Aspuru-Guzik, Alán
2014-10-01
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
Robust Classification with Adiabatic Quantum Optimization
Denchev, Vasil S.; Ding, Nan; Vishwanathan, S. V. N.; Neven, Hartmut
2012-01-01
We propose a non-convex training objective for robust binary classification of data sets in which label noise is present. The design is guided by the intention of solving the resulting problem by adiabatic quantum optimization. Two requirements are imposed by the engineering constraints of existing quantum hardware: training problems are formulated as quadratic unconstrained binary optimization; and model parameters are represented as binary expansions of low bit-depth. In the present work we...
Exchange-Correlation Functionals via Local Interpolation along the Adiabatic Connection.
Vuckovic, Stefan; Irons, Tom J P; Savin, Andreas; Teale, Andrew M; Gori-Giorgi, Paola
2016-06-14
The construction of density-functional approximations is explored by modeling the adiabatic connection locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of a range of local interpolation models against accurate exchange-correlation energy densities. The importance of the strictly correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approaches based on global models, and prospects for future approximations based on the local adiabatic connection are discussed. PMID:27116427
Adiabatic graph-state quantum computation
Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any MBQC on a graph state with generalized flow (gflow) can be converted into an adiabatically driven holonomic computation, which we call adiabatic graph-state quantum computation (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of H-dot as well as the degree of H, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated. (paper)
Adiabatic electronic flux density: a Born-Oppenheimer Broken Symmetry ansatz
Pohl, Vincent
2016-01-01
The Born-Oppenheimer approximation leads to the counterintuitive result of a vanishing electronic flux density upon vibrational dynamics in the electronic ground state. To circumvent this long known issue, we propose using pairwise anti-symmetrically translated vibronic densities to generate a symmetric electronic density that can be forced to satisfy the continuity equation approximately. The so-called Born-Oppenheimer broken symmetry ansatz yields all components of the flux density simultaneously while requiring only knowledge about the nuclear quantum dynamics on the electronic adiabatic ground state potential energy surface. The underlying minimization procedure is transparent and computationally inexpensive, and the solution can be computed from the standard output of any quantum chemistry program. Taylor series expansion reveals that the implicit electron dynamics originates from non-adiabatic coupling to the explicit Born-Oppenheimer nuclear dynamics. The new approach is applied to the ${\\rm H}_2^+$ mo...
Salom, Igor; Dmitrašinović, V.
2016-05-01
We construct the three-body permutation symmetric O (6) hyperspherical harmonics and use them to solve the non-relativistic three-body Schrödinger equation in three spatial dimensions. We label the states with eigenvalues of the U (1) ⊗ SO(3)rot ⊂ U (3) ⊂ O (6) chain of algebras, and we present the K ≤ 4 harmonics and tables of their matrix elements. That leads to closed algebraic form of low-K energy spectra in the adiabatic approximation for factorizable potentials with square-integrable hyper-angular parts. This includes homogeneous pairwise potentials of degree α ≥ - 1. More generally, a simplification is achieved in numerical calculations of non-adiabatic approximations to non-factorizable potentials by using our harmonics.
Joye, Alain; Pfister, Charles-Edouard
1993-01-01
The Schriidinger equation in the adiabatic limit when the Hamiltonian depends analytically on time and possesses for any fixed time two nondegenerate eigen-values e,(t) and e,(f) bounded away from the rest of the spectrum is considered herein. An approximation of the evolution called superadiabatic evolution is constructed and studied. Then a solution of the equation which is asymptotically an eigenfunction of energy e,(t) when t- ,-co is considered. Using superadiabatic evolution, an explici...
Adiabatic transport of Bose-Einstein condensate in double-well trap
Nesterenko, V. O.; A.N. Novikov; Cherny, A. Yu.; Cruz, F. F. de Souza; Suraud, E.
2009-01-01
A complete irreversible adiabatic transport of Bose-Einstein condensate (BEC) in a double-well trap is investigated within the mean field approximation. The transfer is driven by time-dependent (Gaussian) coupling between the wells and their relative detuning. The protocol successfully works in a wide range of both repulsive and attractive BEC interaction. The nonlinear effects caused by the interaction can be turned from detrimental into favorable for the transport. The results are compared ...
Effects of finite-β on the adiabatic invariant J in axisymmetric magnetic confinement configurations
An expression for the second adiabatic invariant J is derived including the effects of plasma diamagnetism and displaced magnetic surfaces. It is shown that for values of β approximately little than epsilon, where β is the ratio of kinetic to magnetic pressure and epsilon is the inverse aspect ratio of the torus, J becomes a decreasing function of PSI, the flux function, in the outer region of the plasma column. (author)
An approximation of nonlinear theory of relativistic gyrotrons with variable magnetic fields is formulated. It is assumed that, for a single electron being decelerated by a high-frequency field, the condition of cyclotron resonance is satisfied identically over the entire interaction space. Other electrons captured by the wave, which undergo small oscillations, are decelerated with the resonant electron. Using the method of adiabatic invariants, a longitudinal amplitude distribution is determined for the high-frequency field that prevents escape of any electrons
Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit
M Ávila
2014-07-01
The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the nonadiabatic corrections to an adiabatic quantum computer are merely theoretical considerations. By the above reason, we consider the particular case of a quantum-dot-confined electron spin qubit working adiabatically in the nanoscale regime (e.g., in the MeV range of energies) and include nonadiabatic corrections in it. If the decoherence times of a quantum dot computer are ∼100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be > 1010. However, if the quantum-dot-confined electron spin qubit is very excited (i.e., the semiclassical limit) the number of operations of such a computer would be approximately the same as that of a classical computer. Our results suggest that for an adiabatic quantum computer to operate successfully within the decoherence times, it is necessary to take into account nonadiabatic corrections.
Phase relations and adiabats in boiling seafloor geothermal systems
Bischoff, James L.; Pitzer, Kenneth S.
1985-11-01
Observations of large salinity variations and vent temperatures in the range of 380-400°C suggest that boiling or two-phase separation may be occurring in some seafloor geothermal systems. Consideration of flow rates and the relatively small differences in density between vapors and liquids at the supercritical pressures at depth in these systems suggests that boiling is occurring under closed-system conditions. Salinity and temperature of boiling vents can be used to estimate the pressure-temperature point in the subsurface at which liquid seawater first reached the two-phase boundary. Data are reviewed to construct phase diagrams of coexisting brines and vapors in the two-phase region at pressures corresponding to those of the seafloor geothermal systems. A method is developed for calculating the enthalpy and entropy of the coexisting mixtures, and results are used to construct adiabats from the seafloor to the P-T two-phase boundary. Results for seafloor vents discharging at 2300 m below sea level indicate that a 385°C vent is composed of a brine (7% NaCl equivalent) in equilibrium with a vapor (0.1% NaCl). Brine constitutes 45% by weight of the mixture, and the fluid first boiled at approximately 1 km below the seafloor at 415°C, 330 bar. A 400°C vent is primarily vapor (88 wt.%, 0.044% NaCl) with a small amount of brine (26% NaCl) and first boiled at 2.9 km below the seafloor at 500°C, 520 bar. These results show that adiabatic decompression in the two-phase region results in dramatic cooling of the fluid mixture when there is a large fraction of vapor.
Accuracy vs run time in adiabatic quantum search
Rezakhani, A T; Lidar, D A
2010-01-01
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm, and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: the error decreases exponentially for short times, then decreases polynomially for longer times. We show that the well known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.
Hypergraph Ramsey Numbers and Adiabatic Quantum Algorithm
Qu, Ri; Bao, Yan-ru
2012-01-01
Gaitan and Clark [Phys. Rev. Lett. 108, 010501 (2012)] have recently presented a quantum algorithm for the computation of the Ramsey numbers R(m, n) using adiabatic quantum evolution. We consider that the two-color Ramsey numbers R(m, n; r) for r-uniform hypergraphs can be computed by using the similar ways in [Phys. Rev. Lett. 108, 010501 (2012)]. In this comment, we show how the computation of R(m, n; r) can be mapped to a combinatorial optimization problem whose solution be found using adi...
Adiabatic quantum algorithm for search engine ranking
Garnerone, Silvano; Lidar, Daniel A
2011-01-01
We propose an adiabatic quantum algorithm to evaluate the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this quantum algorithm outputs any component of the PageRank vector-and thus the ranking of the corresponding webpage-in a time which scales polylogarithmically in the number of webpages. This would constitute an exponential speed-up with respect to all known classical algorithms designed to evaluate the PageRank.
Adiabatic chaos in the spin orbit problem
Benettin, Giancarlo; Guzzo, Massimiliano; Marini, Valerio
2008-05-01
We provide evidences that the angular momentum of a symmetric rigid body in a spin orbit resonance can perform large scale chaotic motions on time scales which increase polynomially with the inverse of the oblateness of the body. This kind of irregular precession appears as soon as the orbit of the center of mass is non-circular and the angular momentum of the body is far from the principal directions with minimum (maximum) moment of inertia. We also provide a quantitative explanation of these facts by using the theory of adiabatic invariants, and we provide numerical applications to the cases of the 1:1 and 1:2 spin orbit resonances.
Adiabatic fission barriers in superheavy nuclei
Jachimowicz, P.; Kowal, M; Skalski, J.
2016-01-01
Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy we calculated static fission barriers $B_{f}$ for 1305 heavy and superheavy nuclei $98\\leq Z \\leq 126$, including even - even, odd - even, even - odd and odd - odd systems. For odd and odd-odd nuclei, adiabatic potential energy surfaces were calculated by a minimization over configurations with one blocked neutron or/and proton on a level from ...
Brane World Dynamics and Adiabatic Matter creation
Gopakumar, P
2006-01-01
We have treated the adiabatic matter creation process in various three-brane models by applying thermodynamics of open systems. The matter creation rate is found to affect the evolution of scale factor and energy density of the universe. We find modification at early stages of cosmic dynamics. In GB and RS brane worlds, by chosing appropriate parameters we obtain standard scenario, while the warped DGP model has different Friedmann equations. During later stages, since the matter creation is negligible the evolution reduces to FRW expansion, in RS and GB models.
Dark Energy and Dark Matter from an additional adiabatic fluid
Dunsby, Peter K. S.; Luongo, Orlando; Reverberi, Lorenzo
2016-01-01
The Dark Sector is described by an additional barotropic fluid which evolves adiabatically during the universe's history and whose adiabatic exponent $\\gamma$ is derived from the standard definitions of specific heats. Although in general $\\gamma$ is a function of the redshift, the Hubble parameter and its derivatives, we find that our assumptions lead necessarily to solutions with $\\gamma = $ constant in a FLRW universe. The adiabatic fluid acts effectively as the sum of two distinct compone...
Adiabatic Flame Temperature and Specific Heat of Combustion Gases
Torii, Shuichi; Yano, Toshiaki; Tsunoda, Yukio; トリイ, シュウイチ; ヤノ, トシアキ; ツノダ, ユキオ; 鳥居, 修一; 矢野, 利明; 角田, 幸男
1992-01-01
The aim of the present work is to examine adiabatic flame temperature and the specific heat of combustion gases for both hydrocarbon-air and alcohol-air mixtures by means of a method of chemical equilibrium calculation. Emphasis is placed on the elucidation of simplified correlation equations capable of predicting (i) adiabatic flame temperature at any equivalence ratio and (ii) the specific heat of combustion gases when the adiabatic flame temperature, the gas temperature and the equivalence...
Adiabatic renormalization in theories with modified dispersion relations
Nacir, D. Lopez; Mazzitelli, F. D.; Simeone, C.
2007-01-01
We generalize the adiabatic renormalization to theories with dispersion relations modified at energies higher than a new scale $M_C$. We obtain explicit expressions for the mean value of the stress tensor in the adiabatic vacuum, up to the second adiabatic order. We show that for any dispersion relation the divergences can be absorbed into the bare gravitational constants of the theory. We also point out that, depending on the renormalization prescription, the renormalized stress tensor may c...
Symmetry of the adiabatic condition in the piston problem
This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be compatible with the invariance of total entropy under a system-surroundings interchange. This paper also strengthens some recently published ideas concerning the concepts of heat and dissipative work, and is primarily intended for teachers and graduate students, as well as for all who are interested in this fascinating problem.
Magnesium Diboride Superconducting Coils for Adiabatic Demagnetization Refrigerators (ADR's) Project
National Aeronautics and Space Administration — For Adiabatic Demagnetization Refrigerators (ADRs) in space applications, it is desirable to have very light weight, small diameter, high current density...
A quantum search algorithm based on partial adiabatic evolution
Zhang Ying-Yu; Hu He-Ping; Lu Song-Feng
2011-01-01
This paper presents and implements a specified partial adiabatic search algorithm on a quantum circuit. It studies the minimum energy gap between the first excited state and the ground state of the system Hamiltonian and it finds that, in the case of M=1, the algorithm has the same performance as the local adiabatic algorithm. However, the algorithm evolves globally only within a small interval, which implies that it keeps the advantages of global adiabatic algorithms without losing the speedup of the local adiabatic search algorithm.
A quantum search algorithm based on partial adiabatic evolution
This paper presents and implements a specified partial adiabatic search algorithm on a quantum circuit. It studies the minimum energy gap between the first excited state and the ground state of the system Hamiltonian and it finds that, in the case of M = 1, the algorithm has the same performance as the local adiabatic algorithm. However, the algorithm evolves globally only within a small interval, which implies that it keeps the advantages of global adiabatic algorithms without losing the speedup of the local adiabatic search algorithm. (general)
Adiabatic calorimetry (RSST and VSP) tests with sodium acetate
Kirch, N.W.
1993-09-01
As requested in the subject reference, adiabatic calorimetry (RSST and VSP) tests have been performed with sodium acetate covering TOC concentrations from 3 to 7% with the following results: Exothermic activity noted around 200{degrees}C. Propagating reaction initiated at about 300{degrees}C. Required TOC concentration for propagation estimated at about 6 w% (dry mixture) or about 20 w% sodium acetate. Heat of reaction estimated to be 3.7 MJ per kg of sodium acetate (based on VSP test with 3 w% TOC and using a dry mixture specific heat of 1000 J kg{sup {minus}1} K{sup {minus}1}). Based upon the above results we estimate that a moisture content in excess of 14 w% would prevent a propagating reaction of a stoichiometric mixture of fuel and oxidizer ({approximately} 38 w% sodium acetate and {approximately}62 w% sodium nitrate). Assuming that the fuel can be treated as sodium acetate equivalent, and considering that the moisture content in the organic containing waste generally is believed to be in excess of 14 w%, it follows that the possibility of propagating reactions in the Hanford waste tanks can be ruled out.
Nickel Bubble Expansion in Type Ia Supernovae: Adiabatic Solutions
Wang, C Y
2006-01-01
We examine the expansion properties of the Nickel bubble in SNe Ia due to the radioactive heating from the 56Ni->56Co->56Fe decay sequence, under adiabatic, spherically symmetric approximation. We consider an exponentially -declining medium for the ejecta substrate, allowing for the density gradient as expected in a Type Ia supernova. The heating gives rise to an inflated Ni bubble, which induces a forward shock that compresses the outer ambient gas into a shell. As the heating saturates, the flow tends toward a freely-expanding state with the structure frozen into the ejecta. The thickness of the shell takes up ~ 100 in a narrow region limited by numerical resolution. The structure of the shell can be approximately described by a self-similar solution determined by its expansion rate and ambient density gradient. Compared to the case using a uniform-density medium, the density contrast of the inferred ejecta clumps is enhanced, while the interaction of the clumps with the remnant is deferred to a more advanc...
Adiabatic collapse of rotating gas clouds
The gravitational, axisymmetric and adiabatic collapse of rotating gas clouds with various initial conditions has been calculated numerically by means of Fluid-In-Cell method. We have assumed that the gas is ideal and its change is adiabatic except for heat production by shock waves and that, initially, a cloud has no motion in a meridional plane and has spherical and polytropic distributions of mass and temperature. The results of calculations show that a cloud which has initially larger rotational energy bounced more easily, i.e., bounces at lower central density. The bounce occurs first in the direction of the rotation axis and next in direction perpendicular to it. A shock wave generated by the bounce is strong especially in the vicinity of the rotation axis. At first the shock front is nearly parallel to the equatorial plane but it becomes gradually spherical as it propagates outwards. Calculations have been performed until the mass enclosed inside the shock front becomes as large as 95 percent of the total mass. At this final stage either a rotating spheroidal core or a rotating ring is left in the central region; a ring is formed if initially a cloud is rotating more rapidly, less centrally condensed and at lower temperature. (auth.)
Adiabatic cooling of solar wind electrons
Sandbaek, Ornulf; Leer, Egil
1992-01-01
In thermally driven winds emanating from regions in the solar corona with base electron densities of n0 not less than 10 exp 8/cu cm, a substantial fraction of the heat conductive flux from the base is transfered into flow energy by the pressure gradient force. The adiabatic cooling of the electrons causes the electron temperature profile to fall off more rapidly than in heat conduction dominated flows. Alfven waves of solar origin, accelerating the basically thermally driven solar wind, lead to an increased mass flux and enhanced adiabatic cooling. The reduction in electron temperature may be significant also in the subsonic region of the flow and lead to a moderate increase of solar wind mass flux with increasing Alfven wave amplitude. In the solar wind model presented here the Alfven wave energy flux per unit mass is larger than that in models where the temperature in the subsonic flow is not reduced by the wave, and consequently the asymptotic flow speed is higher.
Adiabatic model of (d, p) reactions with explicitly energy-dependent nonlocal potentials
Johnson, RC; Timofeyuk, NK
2014-01-01
We have developed an approximate way of dealing with explicit energy-dependence of non-local nucleon optical potentials as used to predict the $(d,p)$ cross sections within the adiabatic theory. Within this approximation, the non-local optical potentials have to be evaluated at an energy shifted from half the incident deuteron energy by the $n-p$ kinetic energy averaged over the range of the $n-p$ interaction and then treated as an energy-independent non-local potential. Thus the evaluation o...
One and two-particle systems in toroidal quantum nanorings under adiabatic approximation
Rincón Fulla, Marlon
2011-01-01
En este trabajo se presenta un estudio teórico de varios sistemas bi-particulares, como es el caso de un sistema electrón-electrón y electrón-hueco (asumiendo masas efectivas iguales para ambas partículas) restringidos a moverse en anillos cuánticos semiconductores dentro de un régimen de confinamiento infinito. El estudio de estos sistemas nano-estructurados fue hecho bajo la aproximación de masa efectiva y se centró en el cálculo e interpretación del espectro energético del sistema. Con el ...
Rovibrational cross sections from reactance matrices calculated in adiabatic nuclei approximation
Body frame reactance matrices obtained from elastic scattering calculations at fixed internuclear separations are transformed into laboratory frame matrices to compute differential and integral cross sections for simultaneous rotational and vibrational excitation of a molecule. Transformation for vibrational excitation is obtained by integrating the real and imaginary parts of the body-frame t-matrices over internuclear separation. Vibrational wave functions are assumed to be given. The rotational transformation involves an eight-fold sum over angular momenta. The summands involve Asub(lambda)-coefficients and Legendre polynomials, which are each evaluated by separate subprograms. Differential, integral, and momentum transfer cross sections are computed from the transformed t-matrices. (Auth.)
Collective motion of two-electron atom in hyperspherical adiabatic approximation
Mohamed, A. S., E-mail: asalah@ksu.edu.sa [King Saud University, Riyadh, 11491 (Saudi Arabia); Al-Azhar University, Cairo, Nasr City (Egypt); Nikitin, S. I., E-mail: dept.kpme@unecon.ru [St. Petersburg State University of economics, St. Petersburg, 191023 (Russian Federation)
2015-03-30
This work is devoted to calculate bound states in the two-electron atoms. The separation of variables has carried out in hyper spherical coordinate system (R, θ, α). Assuming collective motion of the electrons, where the hper angle (α∼π/4) and (θ∼π). The separation of the rotational variables leads to system of differential equations with more simple form as compared with non restricted motion. Energy of doubly excited P{sup e} and D{sup 0} states are calculated semi classically by using quantization condition of Bohr -Somerfield. The results compared with previously published data.
Andrade, Tomas; Marolf, Donald
2015-01-01
The gravitational Dirichlet problem -- in which the induced metric is fixed on boundaries at finite distance from the bulk -- is related to simple notions of UV cutoffs in gauge/gravity duality and appears in discussions relating the low-energy behavior of gravity to fluid dynamics. We study the Einstein-Maxwell version of this problem, in which the induced Maxwell potential on the wall is also fixed. For flat walls in otherwise-asymptotically-flat spacetimes, we identify a moduli space of Majumdar-Papapetrou-like static solutions parametrized by the location of an extreme black hole relative to the wall. Such solutions may be described as balancing gravitational repulsion from a negative-mass image-source against electrostatic attraction to an oppositely-signed image charge. Standard techniques for handling divergences yield a moduli space metric with an eigenvalue that becomes negative near the wall, indicating a region of negative kinetic energy and suggesting that the Hamiltonian may be unbounded below. O...
Tichauer, Kenneth M.; Osswald, Christian R.; Dosmar, Emily; Guthrie, Micah J.; Hones, Logan; Sinha, Lagnojita; Xu, Xiaochun; Mieler, William F.; St. Lawrence, Keith; Kang-Mieler, Jennifer J.
2015-06-01
Clinical symptoms of diabetic retinopathy are not detectable until damage to the retina reaches an irreversible stage, at least by today's treatment standards. As a result, there is a push to develop new, "sub-clinical" methods of predicting the onset of diabetic retinopathy before the onset of irreversible damage. With diabetic retinopathy being associated with the accumulation of long-term mild damage to the retinal vasculature, retinal blood vessel permeability has been proposed as a key parameter for detecting preclinical stages of retinopathy. In this study, a kinetic modeling approach used to quantify vascular permeability in dynamic contrast-enhanced medical imaging was evaluated in noise simulations and then applied to retinal videoangiography data in a diabetic rat for the first time to determine the potential for this approach to be employed clinically as an early indicator of diabetic retinopathy. Experimental levels of noise were found to introduce errors of less than 15% in estimates of blood flow and extraction fraction (a marker of vascular permeability), and fitting of rat retinal fluorescein angiography data provided stable maps of both parameters.
Rotational excitation of H2O by para-H2 from an adiabatically reduced dimensional potential
Scribano, Yohann; Faure, Alexandre; Lauvergnat, David
2012-03-01
Cross sections and rate coefficients for low lying rotational transitions in H2O colliding with para-hydrogen pH2 are computed using an adiabatic approximation which reduces the dimensional dynamics from a 5D to a 3D problem. Calculations have been performed at the close-coupling level using the recent potential of Valiron et al. [J. Chem. Phys. 129, 134306 (2008), 10.1063/1.2988314]. A good agreement is found between the reduced adiabatic calculations and the 5D exact calculations, with an impressive time saving and memory gain. This adiabatic reduction of dimensionality seems very promising for scattering studies involving the excitation of a heavy target molecule by a light molecular projectile.
We study the adiabatic tunneling of Bose—Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram. (general)
Diophantine approximation and badly approximable sets
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Fully quantum non-adiabatic dynamics in electronic-nuclear coherent state basis
Humeniuk, Alexander
2016-01-01
Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of the potential energy surfaces between wavepackets therefore usually have to be approximated. It is shown, that if a modified form of valence bond theory is used instead of the usual MO-based theories, the matrix elements can be obtained exactly. This is so because the molecular Hamiltonian only contains the Coulomb potential, for which matrix elements between different basis functions (consisting of Gaussian nuclear and electronic orbitals) are all well-known. In valence bond theory the self-consistent field calculation can be avoided so that the matrix elements are analytical functions of the nuclear coordinates. A method for simulating non-adiabatic quantum dynamics is sketched, where coherent state trajectories are propagated "on the fly" on adiabatic potential energy surf...
Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes
Agostini, Federica; Min, Seung Kyu; Gross, E. K. U.
2015-10-01
In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schroedinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics.
Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes
Agostini, Federica; Gross, E K U
2015-01-01
In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schroedinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics.
In radiation damage cascade displacement spikes ions and electrons can reach very high temperatures and be out of thermal equilibrium. Correct modelling of cascades with molecular dynamics should allow for the non-adiabatic exchange of energy between ions and electrons using a consistent model for the electronic stopping, electronic temperature rise, and thermal conduction by the electrons. We present a scheme for correcting embedded atom potentials for these non-adiabatic properties at the level of the second-moment approximation, and parameterize for the bcc transition metals above the Debye temperature. We use here the Finnis–Sinclair and Derlet–Nguyen–Manh–Dudarev potentials as models for the bonding, but the corrections derived from them can be applied to any suitable empirical potential. We show with two-temperature MD simulations that computing the electronic thermal conductivity during the cascade evolution has a significant impact on the heat exchange between ions and electrons. (paper)
Lu, Jianfeng
2016-01-01
In the spirit of the fewest switches surface hopping, the frozen Gaussian approximation with surface hopping (FGA-SH) method samples a path integral representation of the non-adiabatic dynamics in the semiclassical regime. An improved sampling scheme is developed in this work for FGA-SH based on birth and death branching processes. The algorithm is validated for the standard test examples of non-adiabatic dynamics.
Plasmas in particle accelerators: adiabatic theories for bunched beams
Three different formalisms for discussing Vlasov's equation for bunched beam problems with anharmonic space charge forces are outlined. These correspond to the use of a drift kinetic equation averaged over random betatron motions; a fluidkinetic adiabatic regime analogous to the theory of Chew, Goldberger, and Low; and an adiabatic hydrodynamic theory
Teleportation of an Unknown Atomic State via Adiabatic Passage
无
2007-01-01
We propose a scheme for teleporting an unknown atomic state via adiabatic passage. Taking advantage of adiabatic passage, the atom has no probability of being excited and thus the atomic spontaneous emission is suppressed.We also show that the fidelity can reach 1 under certain condition.
Adiabat-shaping in indirect drive inertial confinement fusion
Adiabat-shaping techniques were investigated in indirect drive inertial confinement fusion experiments on the National Ignition Facility as a means to improve implosion stability, while still maintaining a low adiabat in the fuel. Adiabat-shaping was accomplished in these indirect drive experiments by altering the ratio of the picket and trough energies in the laser pulse shape, thus driving a decaying first shock in the ablator. This decaying first shock is designed to place the ablation front on a high adiabat while keeping the fuel on a low adiabat. These experiments were conducted using the keyhole experimental platform for both three and four shock laser pulses. This platform enabled direct measurement of the shock velocities driven in the glow-discharge polymer capsule and in the liquid deuterium, the surrogate fuel for a DT ignition target. The measured shock velocities and radiation drive histories are compared to previous three and four shock laser pulses. This comparison indicates that in the case of adiabat shaping the ablation front initially drives a high shock velocity, and therefore, a high shock pressure and adiabat. The shock then decays as it travels through the ablator to pressures similar to the original low-adiabat pulses when it reaches the fuel. This approach takes advantage of initial high ablation velocity, which favors stability, and high-compression, which favors high stagnation pressures
High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
Quiroz, Gregory
2012-01-01
We introduce high-order dynamical decoupling strategies for open system adiabatic quantum computation. Our numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupling, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.
Quantum adiabatic algorithm for factorization and its experimental implementation.
Peng, Xinhua; Liao, Zeyang; Xu, Nanyang; Qin, Gan; Zhou, Xianyi; Suter, Dieter; Du, Jiangfeng
2008-11-28
We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in a NMR quantum information processor and experimentally factorize the number 21. In the range that our classical computer could simulate, the quantum adiabatic algorithm works well, providing evidence that the running time of this algorithm scales polynomially with the problem size. PMID:19113467
Robust Classification with Adiabatic Quantum Optimization
Denchev, Vasil S; Vishwanathan, S V N; Neven, Hartmut
2012-01-01
We propose a non-convex training objective for robust binary classification of data sets in which label noise is present. The design is guided by the intention of solving the resulting problem by adiabatic quantum optimization. Two requirements are imposed by the engineering constraints of existing quantum hardware: training problems are formulated as quadratic unconstrained binary optimization; and model parameters are represented as binary expansions of low bit-depth. In the present work we validate this approach by using a heuristic classical solver as a stand-in for quantum hardware. Testing on several popular data sets and comparing with a number of existing losses we find substantial advantages in robustness as measured by test error under increasing label noise. Robustness is enabled by the non-convexity of our hardware-compatible loss function, which we name q-loss.
Number Partitioning via Quantum Adiabatic Computation
Smelyanskiy, Vadim N.; Toussaint, Udo; Clancy, Daniel (Technical Monitor)
2002-01-01
We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.
Adiabatic theory for anisotropic cold molecule collisions
We developed an adiabatic theory for cold anisotropic collisions between slow atoms and cold molecules. It enables us to investigate the importance of the couplings between the projection states of the rotational motion of the atom about the molecular axis of the diatom. We tested our theory using the recent results from the Penning ionization reaction experiment 4He(1s2s 3S) + HD(1s2) → 4He(1s2) + HD+(1s) + e− [Lavert-Ofir et al., Nat. Chem. 6, 332 (2014)] and demonstrated that the couplings have strong effect on positions of shape resonances. The theory we derived provides cross sections which are in a very good agreement with the experimental findings
Adiabatic theory for anisotropic cold molecule collisions.
Pawlak, Mariusz; Shagam, Yuval; Narevicius, Edvardas; Moiseyev, Nimrod
2015-08-21
We developed an adiabatic theory for cold anisotropic collisions between slow atoms and cold molecules. It enables us to investigate the importance of the couplings between the projection states of the rotational motion of the atom about the molecular axis of the diatom. We tested our theory using the recent results from the Penning ionization reaction experiment (4)He(1s2s (3)S) + HD(1s(2)) → (4)He(1s(2)) + HD(+)(1s) + e(-) [Lavert-Ofir et al., Nat. Chem. 6, 332 (2014)] and demonstrated that the couplings have strong effect on positions of shape resonances. The theory we derived provides cross sections which are in a very good agreement with the experimental findings. PMID:26298122
Adiabatic theory for anisotropic cold molecule collisions
Pawlak, Mariusz [Schulich Faculty of Chemistry, Technion–Israel Institute of Technology, Haifa 32000 (Israel); Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń (Poland); Shagam, Yuval; Narevicius, Edvardas [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel); Moiseyev, Nimrod [Schulich Faculty of Chemistry, Technion–Israel Institute of Technology, Haifa 32000 (Israel); Faculty of Physics, Technion–Israel Institute of Technology, Haifa 32000 (Israel)
2015-08-21
We developed an adiabatic theory for cold anisotropic collisions between slow atoms and cold molecules. It enables us to investigate the importance of the couplings between the projection states of the rotational motion of the atom about the molecular axis of the diatom. We tested our theory using the recent results from the Penning ionization reaction experiment {sup 4}He(1s2s {sup 3}S) + HD(1s{sup 2}) → {sup 4}He(1s{sup 2}) + HD{sup +}(1s) + e{sup −} [Lavert-Ofir et al., Nat. Chem. 6, 332 (2014)] and demonstrated that the couplings have strong effect on positions of shape resonances. The theory we derived provides cross sections which are in a very good agreement with the experimental findings.
Adiabatic Liquid Piston Compressed Air Energy Storage
Petersen, Tage; Elmegaard, Brian; Pedersen, Allan Schrøder
This project investigates the potential of a Compressed Air Energy Storage system (CAES system). CAES systems are used to store mechanical energy in the form of compressed air. The systems use electricity to drive the compressor at times of low electricity demand with the purpose of converting the...... compensates the added investment. •When comparing ALP-CAES to an adiabatic CAES system, where compression heat is stored in thermal oil, the ALP-CAES system is found only to be competitive under a very specific set of operating/design conditions, including very high operation pressure and the use of very...... primarily due to the investment in turbine/generator, heat exchangers, and a large quantity of thermal oil. To improve the economy, it would be relevant to investigate the possibility of replacing the thermal oil by water, for example by injecting the water directly into the air flow between the different...
Parametric Erosion Investigation: Propellant Adiabatic Flame Temperature
P. J. Conroy
2002-01-01
Full Text Available The influence of quasi-independent parameters and their potential influence on erosion in guns have been investigated. Specifically, the effects of flame temperature and the effect of assuming that the Lewis number (ratio of mass-to-heat transport to the surface, Le = 1, has been examined. The adiabatic flame temperature for a propellant was reduced by the addition of a diluent from a high temperature of 3843 K (similar to that of M9 down to 3004 K, which is near the value for M30A1 propellant. Mass fractions of critical species at the surface with and without the assumption of Le = 1 are presented, demonstrating that certain species preferentially reach the surface providing varied conditions for the surface reactions. The results for gun tube bore surface regression qualitatively agree with previous studies and with current experimental data.
Index Theory and Adiabatic Limit in QFT
Wawrzycki, Jaroslaw
2011-01-01
The paper has the form of a proposal concerned with the relationship between the three mathematically rigorous approaches to quantum field theory: 1) local algebraic formulation of Haag, 2) Wightman formulation and 3) the perturbative formulation based on the microlocal renormalization method. In this project we investigate the relationship between 1) and 3) and utilize the known relationships between 1) and 2). The main goal of the proposal lies in obtaining obstructions for the existence of the adiabatic limit (confinement problem in the phenomenological standard model approach). We extend the method of deformation of D\\"utsch and Fredenhagen (in the Bordeman-Waldmann sense) and apply Fedosov construction of the formal index -- an analog of the index for deformed symplectic manifolds, generalizing the Atiyah-Singer index. We present some first steps in realization of the proposal.
Index Theory and Adiabatic Limit in QFT
Wawrzycki, Jarosław
2013-08-01
The paper has the form of a proposal concerned with the relationship between the three mathematically rigorous approaches to quantum field theory: (1) local algebraic formulation of Haag, (2) Wightman formulation and (3) the perturbative formulation based on the microlocal renormalization method. In this project we investigate the relationship between (1) and (3) and utilize the known relationships between (1) and (2). The main goal of the proposal lies in obtaining obstructions for the existence of the adiabatic limit ( confinement problem in the phenomenological standard model approach). We extend the method of deformation of Dütsch and Fredenhagen (in the Bordeman-Waldmann sense) and apply Fedosov construction of the formal index—an analog of the index for deformed symplectic manifolds, generalizing the Atiyah-Singer index. We present some first steps in realization of the proposal.
Adiabatic Rearrangement of Hollow PV Towers
Eric A Hendricks
2010-10-01
Full Text Available Diabatic heating from deep moist convection in the hurricane eyewall produces a towering annular structure of elevated potential vorticity (PV. This structure has been referred to as a hollow PV tower. The sign reversal of the radial gradient of PV satisfies the Charney-Stern necessary condition for combined barotropic-baroclinic instability. For thin enough annular structures, small perturbations grow exponentially, extract energy from the mean flow, and lead to hollow tower breakdown, with significant vortex structural and intensity change. The three-dimensional adiabatic rearrangements of two prototypical hurricane-like hollow PV towers (one thick and one thin are examined in an idealized framework. For both hollow towers, dynamic instability causes air parcels with high PV to be mixed into the eye preferentially at lower levels, where unstable PV wave growth rates are the largest. Little or no mixing is found to occur at upper levels. The mixing at lower and middle levels is most rapid for the breakdown of the thin hollow tower, consistent with previous barotropic results. For both hollow towers, this advective rearrangement of PV affects the tropical cyclone structure and intensity in a number of ways. First, the minimum central pressure and maximum azimuthal mean velocity simultaneously decrease, consistent with previous barotropic results. Secondly, isosurfaces of absolute angular momentum preferentially shift inward at low levels, implying an adiabatic mechanism by which hurricane eyewall tilt can form. Thirdly, a PV bridge, similar to that previously found in full-physics hurricane simulations, develops as a result of mixing at the isentropic levels where unstable PV waves grow most rapidly. Finally, the balanced mass field resulting from the PV rearrangement is warmer in the eye between 900 and 700 hPa. The location of this warming is consistent with observed warm anomalies in the eye, indicating that in certain instances the hurricane
Adiabatic and Isocurvature Perturbation Projections in Multi-Field Inflation
Gordon, Chris
2013-01-01
Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the adiabatic perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the adiabatic pe...
Adiabatic logic future trend and system level perspective
Teichmann, Philip
2012-01-01
Adiabatic logic is a potential successor for static CMOS circuit design when it comes to ultra-low-power energy consumption. Future development like the evolutionary shrinking of the minimum feature size as well as revolutionary novel transistor concepts will change the gate level savings gained by adiabatic logic. In addition, the impact of worsening degradation effects has to be considered in the design of adiabatic circuits. The impact of the technology trends on the figures of merit of adiabatic logic, energy saving potential and optimum operating frequency, are investigated, as well as degradation related issues. Adiabatic logic benefits from future devices, is not susceptible to Hot Carrier Injection, and shows less impact of Bias Temperature Instability than static CMOS circuits. Major interest also lies on the efficient generation of the applied power-clock signal. This oscillating power supply can be used to save energy in short idle times by disconnecting circuits. An efficient way to generate the p...
How detrimental is decoherence in adiabatic quantum computation?
Albash, Tameem
2015-01-01
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time-scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit $T_2$ time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary canc...
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
Zamstein, Noa; Tannor, David J. [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)
2012-12-14
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schroedinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schrödinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
Adiabatic self-trapped states in zigzag nanotubes
Brizhik, L S [Bogolyubov Institute for Theoretical Physics, 03680 Kyiv (Ukraine); Eremko, A A [Bogolyubov Institute for Theoretical Physics, 03680 Kyiv (Ukraine); Piette, B M A G [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom); Zakrzewski, W J [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)
2007-08-01
We study the polaron (soliton) states of a quasiparticle (electron, hole, exciton) in a quasi-one-dimensional (quasi-1D) model which describes a carbon-type zigzag nanotube structure. In the Hamiltonian of the system we include the electron-phonon interaction that arises from the dependence of both the on-site and the hopping interaction energies on the lattice deformation. We derive, in the adiabatic approximation, the equations for the self-trapped states of a quasiparticle in a zigzag nanotube. We show that the ground state of such a system depends on the strength of the electron-phonon coupling and we find polaron-type solutions with different symmetries. Namely, at a relatively weak coupling a quasiparticle is self-trapped in a quasi-1D polaron state which has an azimuthal symmetry. When the coupling constant exceeds some critical value, the azimuthal symmetry breaks down and the quasiparticle state can be described as a two-dimensional small polaron on the nanotube surface. In the crossover region between the two solutions there is a range of intermediate couplings, in which the two structures, the quasi-1D polaron and the strongly localized 2D polaron, coexist as their energies are very close together. We note that the results of this analytical study are in quantitative agreement with what has recently been observed numerically.
Bendall; Skinner
1998-10-01
To provide the most efficient conditions for spin decoupling with least RF power, master calibration curves are provided for the maximum centerband amplitude, and the minimum amplitude for the largest cycling sideband, resulting from STUD+ adiabatic decoupling applied during a single free induction decay. The principal curve is defined as a function of the four most critical experimental input parameters: the maximum amplitude of the RF field, RFmax, the length of the sech/tanh pulse, Tp, the extent of the frequency sweep, bwdth, and the coupling constant, Jo. Less critical parameters, the effective (or actual) decoupled bandwidth, bweff, and the sech/tanh truncation factor, beta, which become more important as bwdth is decreased, are calibrated in separate curves. The relative importance of nine additional factors in determining optimal decoupling performance in a single transient are considered. Specific parameters for efficient adiabatic decoupling can be determined via a set of four equations which will be most useful for 13C decoupling, covering the range of one-bond 13C1H coupling constants from 125 to 225 Hz, and decoupled bandwidths of 7 to 100 kHz, with a bandwidth of 100 kHz being the requirement for a 2 GHz spectrometer. The four equations are derived from a recent vector model of adiabatic decoupling, and experiment, supported by computer simulations. The vector model predicts an inverse linear relation between the centerband and maximum sideband amplitudes, and it predicts a simple parabolic relationship between maximum sideband amplitude and the product JoTp. The ratio bwdth/(RFmax)2 can be viewed as a characteristic time scale, tauc, affecting sideband levels, with tauc approximately Tp giving the most efficient STUD+ decoupling, as suggested by the adiabatic condition. Functional relationships between bwdth and less critical parameters, bweff and beta, for efficient decoupling can be derived from Bloch-equation calculations of the inversion profile
On the applicability of the adiabatic theory for atomic systems in strong laser fields
Martiskainen, Hanna
2014-01-01
The semi-classical three-step model (TSM) is commonly used to describe the generation of high-order harmonics. The adiabatic approximation, where time is treated as an instantaneous parameter rather than a dynamical variable, plays a key role in the derivation of the TSM. At the limit of $\\omega\\to0$, where $\\omega$ is the laser frequency, the ac-field is reduced to a dc-field and the adiabatic calculations provide the exact photo-induced dynamics. The main goal of this work is to find out for what laser parameters (i.e., field amplitude $\\epsilon_{0}$ and frequency $\\omega$) the exact photo-induced dynamics can be obtained within the framework of perturbation theory where the adiabatic Hamiltonian, as used in the first step of the TSM, serves as the zero-order Hamiltonian. We introduce a method for calculating these values of the laser parameters which avoids the need to calculate explicitly the high order terms in the perturbation series expansion of the solutions of the Schr\\"odinger equation. A simple 1D ...
New simple expressions for average number of electrons in the valence orbital of a reacting ion and the charge susceptibility are obtained that allow one to calculate adiabatic free energy surfaces (AFES) and corresponding kinetic regime diagrams (KRD) for adiabatic processes of electron transfer from the ion, located in a polar liquid, to a metal within the framework of the exactly solvable (in the limit T→0) model of the metal with the infinitely wide conduction band. This model represents one of limiting cases of the Anderson model that may be applied to s-p metals. Unlike previous studies of the adiabatic reactions in the model of the metal with the infinitely wide conduction band, the present work takes into account the electron-electron correlation effects in an exact manner. General results are illustrated with KRD which determine the regions of the physical parameters of the system corresponding to various types of electron transfer processes. AFES are calculated for some typical parameters sets. The exact AFES are compared with those calculated within the Hartree-Fock approximation. It is shown that the correlation effects are of importance and results not only in a considerable decrease of the activation free energy but also to qualitatively different shapes of AFES in some regions of the system parameters
Are the reactions of quinones on graphite adiabatic?
Outer sphere electron transfer reactions on pure metal electrodes are often adiabatic and hence independent of the electrode material. Since it is not clear, whether adiabatic electron transfer can also occur on a semi-metal like graphite, we have re-investigated experimental data presented in a recent communication by Nissim et al. [Chemical Communications 48 (2012) 3294] on the reactions of quinones on graphite. We have supplemented their work by DFT calculations and conclude, that these reactions are indeed adiabatic. This contradicts the assertion of Nissim et al. that the rates are proportional to the density of states at the Fermi level
Title: Quadrupole collective inertia in nuclear fission: cranking approximation
Baran, A; Dobaczewski, J; Nazarewicz, W
2010-01-01
Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.
Quadrupole collective inertia in nuclear fission: Cranking approximation
Baran, A.; Sheikh, J. A.; Dobaczewski, J.; Nazarewicz, W.; Staszczak, A.
2011-11-01
A collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian overlap approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.
On the persistence of adiabatic shear bands
Bassim M.N.
2012-08-01
Full Text Available It is generally agreed that the initiation and development of adiabatic shear bands (ASBs are manifestations of damage in metallic materials subjected to high strain rates and large strains as those due to impact in a Hopkinson Bar system. Models for evolution of these bands have been described in the literature. One question that has not received attention is how persistent these bands are and whether their presence and effect can be reversed or eliminated by using a process of thermal (heat treatment or thermo-mechanical treatment that would relieve the material from the high strain associated with ASBs and their role as precursors to crack initiation and subsequent failure. Since ASBs are more prevalent and more defined in BCC metals including steels, a study was conducted to investigate the best conditions of generating ASBs in a heat treatable steel, followed by determining the best conditions for heat treatment of specimens already damaged by the presence of ASBs in order to relieve the strains due to ASBs and restore the material to an apparent microstructure without the “scars” due to the previous presence of ASBs. It was found that heat treatment achieves the curing from ASBs. This presentation documents the process undertaken to achieve this objective.
Graph isomorphism and adiabatic quantum computing
Gaitan, Frank; Clark, Lane
2014-03-01
In the Graph Isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and maps G --> G'. If yes (no), then G and G' are said to be isomorphic (non-isomorphic). The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. We present a quantum algorithm that solves arbitrary instances of GI, and which provides a novel approach to determining all automorphisms of a graph. The algorithm converts a GI instance to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. Numerical simulation of the algorithm's quantum dynamics shows that it correctly distinguishes non-isomorphic graphs; recognizes isomorphic graphs; and finds the automorphism group of a graph. We also discuss the algorithm's experimental implementation and show how it can be leveraged to solve arbitrary instances of the NP-Complete Sub-Graph Isomorphism problem.
Adiabatic fission barriers in superheavy nuclei
Jachimowicz, P; Skalski, J
2016-01-01
Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy we calculated static fission barriers $B_{f}$ for 1305 heavy and superheavy nuclei $98\\leq Z \\leq 126$, including even - even, odd - even, even - odd and odd - odd systems. For odd and odd-odd nuclei, adiabatic potential energy surfaces were calculated by a minimization over configurations with one blocked neutron or/and proton on a level from the 10-th below to the 10-th above the Fermi level. The parameters of the model that have been fixed previously by a fit to masses of even-even heavy nuclei were kept unchanged. A search for saddle points has been performed by the "Imaginary Water Flow" method on a basic five-dimensional deformation grid, including triaxiality. Two auxiliary grids were used for checking the effects of the mass asymmetry and hexadecapole non-axiallity. The ground states were found by energy minimization over configurations and deformations...
Wave packet dynamics in the optimal superadiabatic approximation
Betz, Volker; Manthe, Uwe
2016-01-01
We explain the concept of superadiabatic approximations and show how in the context of the Born- Oppenheimer approximation they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic electronic energy levels near the avoided crossing is required for the computation. In particular, this means that no diabatization procedure is necessary, the adiabatic energy levels can be computed on the fly, and they only need to be computed to higher accuracy when an avoided crossing is detected. We test the quality of our method on the paradigmatic example of photo-dissociation of NaI, finding very good agreement with results of exact wave packet calculations.
General dynamical description of quasi-adiabatically encircling exceptional points
Milburn, Thomas J; Holmes, Catherine A; Portolan, Stefano; Rotter, Stefan; Rabl, Peter
2014-01-01
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process predicted for an adiabatic encircling of an exceptional point. In this work we analyze this process for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasi-stationarity interrupted by abrupt non-adiabatic transitions. Our findings explain the breakdown of the adiabatic theorem as well as the chiral behavior noticed previously in this context, and we provide a unified framework to describe quasi-adiabatic dynamical effects in non-Hermitian systems in a qualitative and quantitative way.
Adiabatic and isocurvature perturbation projections in multi-field inflation
Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry, seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the isocurvature perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the adiabatic perturbation in the flat field space limit
AN ADIABATIC APPROACH FOR LOW POWER FULL ADDER DESIGN
Prof. Dinesh Chandra
2011-09-01
Full Text Available Over the past decade, several adiabatic logic styles have been reported. This paper deals with the design of a 1-bit full adder using several adiabatic logic styles, which are derived from static CMOS logic, without a large change. The full adders are designed using 180nm technology parameters provided by predictive technology and simulated using HSPICE. The full adders designed are compared in terms of average power consumption with different values of load capacitance, temperature and input frequency. The different designs of full adder are also compared on the basis of propagation delay exhibit by them. It is found that, full adders designed with adiabatic logic styles tends to consume very low power in comparison to full adder designed with static CMOS logic. Under certain operating conditions, one of adiabatic designs of full adder achieves upto 74% power saving in comparison to the full adder designedwith static CMOS logic.
Magnesium Diboride Superconducting Coils for Adiabatic Demagnetization Refrigerators (ADR's) Project
National Aeronautics and Space Administration — For Adiabatic Demagnetization Refrigerators(ADR's) for space it is desirable to have very light weight, small diameter, high current density superconducting wires...
Application of adiabatic calorimetry to metal systems. Final report
Research on the application of adiabatic calorimetry to metal systems is described. Investigations into formation of pearlite in steels, ferromagnetic effects, cold working and annealing, solid solution alloys, pure solid metals, and pure liquid metals, are briefly described
Case Study of Indirect Adiabatic Cooling System in Historical Building
Brahmanis, A; Lešinskis, A; Krūmiņš, A
2013-01-01
The objective of the present study is to investigate the efficiency of indirect adiabatic chiller-based cooling system efficiency dependence of outdoor air humidity. The system is located in historical building, in temperate climate of Latvia.
Non-adiabatic quantum effects from a Standard Model time-dependent Higgs vev
We consider the time-dependence of the Higgs vacuum expectation value (vev) given by the dynamics of the Standard Model and study the non-adiabatic production of both bosons and fermions, which is intrinsically non-perturbative. In the Hartree approximation, we analyze the general expressions that describe the dissipative dynamics due to the back-reaction of the produced particles. In particular, we solve numerically some relevant cases for the Standard Model phenomenology in the regime of relatively small oscillations of the Higgs vev
Adiabatic instability in coupled dark energy-dark matter models
Bean, Rachel; Flanagan, Eanna E.; Trodden, Mark
2007-01-01
We consider theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe. Such theories can possess an adiabatic regime in which the quintessence field always sits at the minimum of its effective potential, which is set by the local dark matter density. We show that if the coupling strength is much larger than gravitational, then the adiabatic regime is always subject to an instability. The instability, whi...
Hybrid adiabatic potentials in the QCD string model
Kalashnikova, Yu S; Kalashnikova, Yu.S.
2003-01-01
The short- and intermediate-distance behaviour of the hybrid adiabatic potentials is calculated in the framework of the QCD string model. The calculations are performed with the inclusion of Coulomb force. Spin-dependent force and the so-called string correction term are treated as perturbation at the leading potential-type regime. Reasonably good agreement with lattice measurements takes place for adiabatic curves excited with magnetic components of field strength correlators.
Adiabatic frequency conversion of quantum optical information in atomic vapor
Vewinger, Frank; Appel, Juergen; Figueroa, Eden; Lvovsky, A. I.
2006-01-01
We experimentally demonstrate a quantum communication protocol that enables frequency conversion and routing of quantum optical information in an adiabatic and thus robust way. The protocol is based on electromagnetically-induced transparency in systems with multiple excited levels: transfer and/or distribution of optical states between different signal modes is implemented by adiabatically changing the control fields. The proof-of-principle experiment is performed using the hyperfine levels ...
Adiabatic CMB perturbations in pre-big bang string cosmology
Enqvist, Kari; Enqvist, Kari; Sloth, Martin S.
2002-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations in the axion field can give rise to a nearly flat spectrum of adiabatic perturbations with a spectral tilt $\\Delta n$ in the range $-0.1 \\lesssim \\Delta n \\lesssim 0.3$.
Realization of adiabatic Aharonov-Bohm scattering with neutrons
Sjöqvist, Erik; Almquist, Martin; Mattsson, Ken; Gürkan, Zeynep Nilhan; Hessmo, Björn
2015-11-01
The adiabatic Aharonov-Bohm (AB) effect is a manifestation of the Berry phase acquired when some slow variables take a planar spin around a loop. While the effect has been observed in molecular spectroscopy, direct measurement of the topological phase shift in a scattering experiment has been elusive in the past. Here, we demonstrate an adiabatic AB effect by explicit simulation of the dynamics of unpolarized very slow neutrons that scatter on a long straight current-carrying wire.
Dependence of adiabatic population transfer on pulse profile
S Dasgupta; T kushwaha; D Goswami
2006-06-01
Control of population transfer by rapid adiabatic passage has been an established technique wherein the exact amplitude profile of the shaped pulse is considered to be insignificant. We study the effect of ultrafast shaped pulses for two-level systems, by density-matrix approach. However, we find that adiabaticity depends simultaneously on pulse profile as well as the frequency modulation under non-resonant conditions.
Adiabatic Quantum Programming: Minor Embedding With Hard Faults
Klymko, Christine; Sullivan, Blair D.; Humble, Travis S.
2012-01-01
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells. These methods extend with fabric growth while scaling linearly in time and quadratically in footprint. We also provi...
Vacuum vessel eddy current modeling for TFTR adiabatic compression experiments
DeLucia, J.; Bell, M.; Wong, K.L.
1985-07-01
A relatively simple current filament model of the TFTR vacuum vessel is described. It is used to estimate the three-dimensional structure of magnetic field perturbations in the vicinity of the plasma that arise from vacuum vessel eddy currents induced during adiabatic compression. Eddy currents are calculated self-consistently with the plasma motion. The Shafranov formula and adiabatic scaling laws are used to model the plasma. Although the specific application is to TFTR, the present model is of generation applicability.
Vacuum vessel eddy current modeling for TFTR adiabatic compression experiments
A relatively simple current filament model of the TFTR vacuum vessel is described. It is used to estimate the three-dimensional structure of magnetic field perturbations in the vicinity of the plasma that arise from vacuum vessel eddy currents induced during adiabatic compression. Eddy currents are calculated self-consistently with the plasma motion. The Shafranov formula and adiabatic scaling laws are used to model the plasma. Although the specific application is to TFTR, the present model is of generation applicability
Non Adiabatic Centrifugal Compressor Gas Dynamic Performance Definition
Soldatova, Kristina
2014-01-01
Most centrifugal compressors operate in conditions with negligible heat transfer (adiabatic compression). Their plant tests conditions are similar or close to adiabatic conditions. Test regulations establish measures to diminish influence of a heat transfer “compressor body – atmospheric air” to an exit temperature. Therefore a temperature rise in a compressor is used to calculate a work input coefficient and efficiency. Unlike it high pressure centrifugal compressors of gas turbines and supe...
Bin Qin
2014-01-01
Relationships between fuzzy relations and fuzzy topologies are deeply researched. The concept of fuzzy approximating spaces is introduced and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained.
Stochastic approximation: invited paper
Lai, Tze Leung
2003-01-01
Stochastic approximation, introduced by Robbins and Monro in 1951, has become an important and vibrant subject in optimization, control and signal processing. This paper reviews Robbins' contributions to stochastic approximation and gives an overview of several related developments.
Rasin, A
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Dynamical fluctuations in classical adiabatic processes: General description and their implications
Zhang, Qi; Gong, Jiangbin; Oh, C. H.
2010-01-01
Dynamical fluctuations in classical adiabatic processes are not considered by the conventional classical adiabatic theorem. In this work a general result is derived to describe the intrinsic dynamical fluctuations in classical adiabatic processes. Interesting implications of our general result are discussed via two subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model with an adiabatically moving fixed-point solution, and the possible "pollution" to Hannay's angle or...
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Energy analysis of a recent approximation to the atmospheric primitive equations
Stevens, Duane E.
2011-01-01
An approximation to the thermodynamic equation was introduced by Holton which was motivated by an energy principle involving a quadratic expression in temperature deviation, which he identified as available potential energy. The approximation consists of neglecting the component of adiabatic warming/cooling due to the temporally and horizontally variable part of the specific volume on a constant pressure surface, WKT*. If the approximation is made, the system lacks a total energy principle in...
WANG Xue-bin
2008-01-01
The coexistent phenomenon of deformed and transformed adiabatic shear bands(ASBs) of ductile metal was analyzed using the JOHNSON-COOK model and gradient-dependent plasticity(GDP). The effects of melting point, density, heat capacity and work to heat conversion factor were investigated. Higher work to heat conversion factor, lower density, lower heat capacity and higher melting point lead to wider transformed ASB and higher local plastic shear deformation between deformed and transformed ASBs. Higher work to heat conversion factor, lower density, lower heat capacity and lower melting point cause higher local plastic shear deformation in the deformed ASB. Three reasons for the scatter in experimental data on the ASB width were pointed out and the advantages of the work were discussed. If the transformed ASB width is used to back-calculate the internal length parameter in the GDP, undoubtedly, the parameter will be extremely underestimated.
Zero-point energy, tunneling, and vibrational adiabaticity in the Mu + H2 reaction
Mielke, Steven L.; Garrett, Bruce C.; Fleming, Donald G.; Truhlar, Donald G.
2015-01-09
Abstract: Isotopic substitution of muonium for hydrogen provides an unparalleled opportunity to deepen our understanding of quantum mass effects on chemical reactions. A recent topical review [Aldegunde et al., Mol. Phys. 111, 3169 (2013)] of the thermal and vibrationally-stateselected reaction of Mu with H2 raises a number of issues that are addressed here. We show that some earlier quantum mechanical calculations of the Mu + H2 reaction, which are highlighted in this review and which have been used to benchmark approximate methods, are in error by as much as 19% in the low-temperature limit. We demonstrate that an approximate treatment of the Born–Oppenheimer diagonal correction that was used in some recent studies is not valid for treating the vibrationally-state-selected reaction. We also discuss why vibrationally adiabatic potentials that neglect bend zero-point energy are not a useful analytical tool for understanding reaction rates and why vibrationally nonadiabatic transitions cannot be understood by considering tunneling through vibrationally adiabatic potentials. Finally, we present calculations on a hierarchical family of potential energy surfaces to assess the sensitivity of rate constants to the quality of the potential surface.
Physics on the adiabatically changed Finslerian manifold and cosmology
Lipovka, Anton A
2016-01-01
In present paper we confirm our previous result [4] that Planck constant is adiabatic invariant of electromagnetic field propagating on the adiabatically changed Finslerian manifold. Direct calculation from cosmological parameters gives value h=6x10(-27) (erg s). We also confirm that Planck constant (and hence other fundamental constants which depend on h) is varied on time due to changing of geometry. As an example the variation of the fine structure constant is calculated. Its relative variation ((da/dt)/a) consist 1.0x10(-18) (1/s). We show that on the Finsler manifold characterized by adiabatically changed geometry, classical free electromagnetic field is quantized geometrically, from the properties of the manifold in such manner that adiabatic invariant of field is ET=6x10(-27)=h. Electrodynamic equations on the Finslerian manifold are suggested. It is stressed that quantization naturally appears from these equations and is provoked by adiabatically changed geometry of manifold. We consider in details tw...
Adiabatic condition and the quantum hitting time of Markov chains
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P' where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP' and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
Global adiabaticity and non-Gaussianity consistency condition
Romano, Antonio Enea; Sasaki, Misao
2016-01-01
In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, $R_c$, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of $R_c$ holds only after the perturbation has reached the adiabatic limit where the constant mode of $R_c$ dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, $\\delta P_{nad}\\equiv\\delta P-c_w^2\\delta\\rho$ where $c_w^2=\\dot P/\\dot\\rho$, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of $R_c$ on super-horizon scales. In this paper, we consider models that satisfies $\\d...
Interplay between electric and magnetic effect in adiabatic polaritonic systems
Alabastri, Alessandro
2013-01-01
We report on the possibility of realizing adiabatic compression of polaritonic wave on a metallic conical nano-structure through an oscillating electric potential (quasi dynamic regime). By comparing this result with an electromagnetic wave excitation, we were able to relate the classical lighting-rod effect to adiabatic compression. Furthermore, we show that while the magnetic contribution plays a marginal role in the formation of adiabatic compression, it provides a blue shift in the spectral region. In particular, magnetic permeability can be used as a free parameter for tuning the polaritonic resonances. The peculiar form of adiabatic compression is instead dictated by both the source and the metal permittivity. The analysis is performed by starting from a simple electrostatic system to end with the complete electromagnetic one through intermediate situations such as the quasi-electrostatic and quasi-dynamic regimes. Each configuration is defined by a particular set of equations which allows to clearly determine the individual role played by the electric and magnetic contribution in the generation of adiabatic compression. We notice that these findings can be applied for the realization of a THz nano-metric generator. © 2013 Optical Society of America.
YueShihong; ZhangKecun
2002-01-01
In a dot product space with the reproducing kernel (r. k. S. ) ,a fuzzy system with the estimation approximation errors is proposed ,which overcomes the defect that the existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach. The structure of the new fuzzy approximator benefits a course got by other means.
Malvina Baica
1985-01-01
The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF), and defines it as Generalized Euclidean Algorithm (abbr. GEA) to approximate irrationals.This paper deals with approximation of irrationals of degree n=2,3,5. Though approximations of these irrationals in a variety of patterns are known, the results are new and practical, since there is used an algorithmic method.
Expectation Consistent Approximate Inference
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability distributions which are made consistent on a set of moments and encode different features of the original intractable distribution. In this way we are able to use Gaussian approximations for models with ...
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Fowler-Nordheim emission modified by laser pulses in the adiabatic regime
Rokhlenko, Alexander
2016-01-01
We investigate enhanced field emission due to a continuous or pulsed oscillating field added to a constant electric field $E$ at the emitter surface. When the frequency of oscillation, field strength, and property of the emitter material satisfy the Keldysh condition $\\gamma<1/2$ one can use the adiabatic approximation for treating the oscillating field, i.e. consider the tunneling through the instantaneous Fowler-Nordheim barrier created by both fields. Due to the great sensitivity of the emission to the field strength the average tunneling current can be much larger than the current produced by only the constant field. We carry out the computations for arbitrary strong constant electric fields, beyond the commonly used Fowler-Nordheim approximation which exhibit in particular an important property of the wave function inside the potential barrier where it is found to be monotonically decreasing without oscillations.
A coupled-trajectory quantum-classical approach to decoherence in non-adiabatic processes
Min, Seung Kyu; Gross, E K U
2015-01-01
We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasi-classical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as effect of the coupling to the nuclei and correctly reproduces the expected quantum behaviour. Moreover, the splitting of the nuclear wave packet is captured as consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in the Letter is supported by numerical results that are compared to quantum mechanical calculations.
Extended adiabatic blast waves and a model of the soft X-ray background. [interstellar matter
Cox, D. P.; Anderson, P. R.
1981-01-01
An analytical approximation is generated which follows the development of an adiabatic spherical blast wave in a homogeneous ambient medium of finite pressure. An analytical approximation is also presented for the electron temperature distribution resulting from coulomb collisional heating. The dynamical, thermal, ionization, and spectral structures are calculated for blast waves of energy E sub 0 = 5 x 10 to the 50th power ergs in a hot low-density interstellar environment. A formula is presented for estimating the luminosity evolution of such explosions. The B and C bands of the soft X-ray background, it is shown, are reproduced by such a model explosion if the ambient density is about .000004 cm, the blast radius is roughly 100 pc, and the solar system is located inside the shocked region. Evolution in a pre-existing cavity with a strong density gradient may, it is suggested, remove both the M band and OVI discrepancies.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Sasaki, Misao
2015-01-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid $\\delta P_{nad}$, another is for a general matter field $\\delta P_{c,nad}$, and the last one is valid only on superhorizon scales. The first two definitions coincide if $c_s^2=c_w^2$ where $c_s$ is the propagation speed of the perturbation, while $c_w^2=\\dot P/\\dot\\rho$. Assuming the adiabaticity in the general sense, $\\delta P_{c,nad}=0$, we derive a relation between the lapse function in the comoving slicing $A_c$ and $\\delta P_{nad}$ valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as $c_s\
Integrated polarization rotator/converter by stimulated Raman adiabatic passage.
Xiong, Xiao; Zou, Chang-Ling; Ren, Xi-Feng; Guo, Guang-Can
2013-07-15
We proposed a polarization rotator inspired by stimulated Raman adiabatic passage model from quantum optics, which is composed of a signal waveguide and an ancillary waveguide. The two orthogonal modes in signal waveguide and the oblique mode in ancillary waveguide form a Λ-type three-level system. By controlling the width of signal waveguide and the gap between two waveguides, adiabatic conversion between two orthogonal modes can be realized in the signal waveguide. With such adiabatic passage, polarization conversion is completed within 150 μm length, with the efficiencies over 99% for both conversions between horizontal polarization and vertical polarization. In addition, such a polarization rotator is quite robust against fabrication error, allowing a wide range of tolerances for the rotator geometric parameters. Our work is not only significative to photonic simulations of coherent quantum phenomena with engineered photonic waveguides, but also enlightens the practical applications of these phenomena in optical device designs. PMID:23938558
Expectation Consistent Approximate Inference
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Adiabatic fluctuations from cosmic strings in a contracting universe
We show that adiabatic, super-Hubble, and almost scale invariant density fluctuations are produced by cosmic strings in a contracting universe. An essential point is that isocurvature perturbations produced by topological defects such as cosmic strings on super-Hubble scales lead to a source term which seeds the growth of curvature fluctuations on these scales. Once the symmetry has been restored at high temperatures, the isocurvature seeds disappear, and the fluctuations evolve as adiabatic ones in the expanding phase. Thus, cosmic strings may be resurrected as a mechanism for generating the primordial density fluctuations observed today
Non-adiabatic pumping through interacting quantum dots
Cavaliere, Fabio; Governale, Michele; König, Jürgen
2009-01-01
We study non-adiabatic two-parameter charge and spin pumping through a single-level quantum dot with Coulomb interaction. For the limit of weak tunnel coupling and in the regime of pumping frequencies up to the tunneling rates, $\\Omega \\lesssim \\Gamma/\\hbar$, we perform an exact resummation of contributions of all orders in the pumping frequency. As striking non-adiabatic signatures, we find frequency-dependent phase shifts in the charge and spin currents, which allow for an effective single-...
Adiabatic theory of ionization of atoms by intense laser pulses
As a first step towards the adiabatic theory of ionization of atoms by intense laser pulses, here we consider the simplest one-dimensional zero-range potential model. The asymptotic solution to the time-dependent Schroedinger equation in the adiabatic regime is obtained and the photoelectron spectrum is calculated. The factorization formula for the photoelectron spectrum in the back-rescattering region, first suggested by Morishita et al. [Phys. Rev. Lett. 100, 013903 (2008)] on the basis of ab initio calculations, is derived analytically.
Quantum Adiabatic Pumping by Modulating Tunnel Phase in Quantum Dots
Taguchi, Masahiko; Nakajima, Satoshi; Kubo, Toshihiro; Tokura, Yasuhiro
2016-08-01
In a mesoscopic system, under zero bias voltage, a finite charge is transferred by quantum adiabatic pumping by adiabatically and periodically changing two or more control parameters. We obtained expressions for the pumped charge for a ring of three quantum dots (QDs) by choosing the magnetic flux penetrating the ring as one of the control parameters. We found that the pumped charge shows a steplike behavior with respect to the variance of the flux. The value of the step heights is not universal but depends on the trajectory of the control parameters. We discuss the physical origin of this behavior on the basis of the Fano resonant condition of the ring.
Resonances and adiabatic invariance in classical and quantum scattering theory
Jain, S R
2004-01-01
We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non-relativistic and relativistic regimes. Further, a connection between statistical quantities like quantal resonance-width and classical friction has been established with a classically deterministic quantity, the stability exponent of an adiabatically perturbed periodic orbit. This relation can be employed to estimate the rate of energy dissipation in finite quantum systems.
Nanoscale resolution for fluorescence microscopy via adiabatic passage
Rubio, Juan Luis; Ahufinger, Verònica; Mompart, Jordi
2015-01-01
We propose the use of the subwavelength localization via adiabatic passage technique for fluorescence microscopy with nanoscale resolution in the far field. This technique uses a {\\Lambda}-type medium coherently coupled to two laser pulses: the pump, with a node in its spatial profile, and the Stokes. The population of the {\\Lambda} system is adiabatically transferred from one ground state to the other except at the node position, yielding a narrow population peak. This coherent localization allows fluorescence imaging with nanometer lateral resolution. We derive an analytical expression to asses the resolution and perform a comparison with the coherent population trapping and the stimulated-emission-depletion techniques.
Adiabatic and isothermal compressibility in the liquid state
The paper reviews the work carried out on the adiabatic and isothermal compressibility of liquid alkali metals. Saturated liquid states are discussed, including thermodynamic relations, adiabatic compressibility and isothermal compressibility. Results for the compressibility, and other related quantities, for the saturated liquids: lithium, potassium, rubidium, caesium and sodium, over the temperature range approx.= 300 - 18000 K, are presented. Subcooled liquid states are also examined with respect to its thermodynamic relations, and compressibility results (and other related quantities) for the same elements are given. An assessment of errors and data reliability is briefly discussed. (U.K.)
High beta lasing in micropillar cavities with adiabatic layer design
Lermer, M.; Gregersen, Niels; Lorke, M.;
2013-01-01
We report on lasing in optically pumped adiabatic micropillar cavities, based on the AlAs/GaAs material system. A detailed study of the threshold pump power and the spontaneous emission β factor in the lasing regime for different diameters dc is presented. We demonstrate a reduction of the thresh...... threshold pump power by over 2 orders of magnitude from dc = 2.25 μm down to 0.95 μm. Lasing with β factors exceeding 0.5 shows that adiabatic micropillars are operating deeply in the cavity quantum electrodynamics regime....
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Thin and superthin ion current sheets. Quasi-adiabatic and nonadiabatic models
L. M. Zelenyi
2000-01-01
Full Text Available Thin anisotropic current sheets (CSs are phenomena of the general occurrence in the magnetospheric tail. We develop an analytical theory of the self-consistent thin CSs. General solitions of the Grad-Shafranov equation are obtained in a quasi-adiabatic approximation which neglects the jumps of the sheet adiabatic invariant Iz This is possible if the anisotropy of the initial distribution function is not too strong. The resulting structure of the thin CSs is interpreted as a sum of negative dia- and positive paramagnetic currents flowing near the neutral plane. In the immediate vicinity of the magnetic field reversal region the paramagnetic current arising from the meandering motion of the ions on Speiser orbits dominates. The maximum CS thick-ness is achieved in the case of weak plasma anisotropy and is of the order of the thermal ion gyroradius outside the sheet. A unified picture of thin CS scalings includes both the quasi-adiabatic regimes of weak and strong anisotropies and the nonadiabatic limit of super-strong anisotropy of the source ion distribution. The later limit corresponds to the case of almost field-aligned initial distribution, when the ratio of the drift velocity outside the CS to the thermal ion velocity exceeds the ratio of the magnetic field outside the CS to its value in-side the CS (vD/vT> B0/Bn. In this regime the jumps of Iz, become essential, and the current sheet thickness is approaching to some small but finite value, which depends upon the parameter Bn /B0. Convective electric field increases the effective anisotropy of the source distribution and might produce the essential CS thinning which could have important implications for the sub-storm dynamics.
Franck, Odile
2013-01-01
A generalized adiabatic connection for ensembles (GACE) is presented. In contrast to the traditional adiabatic connection formulation, both ensemble weights and interaction strength can vary along a GACE path while the ensemble density is held fixed. The theory is presented for non-degenerate two-state ensembles but it can in principle be extended to any ensemble of fractionally occupied excited states. Within such a formalism an exact expression for the ensemble exchange-correlation density-functional energy, in terms of the conventional ground-state exchange-correlation energy, is obtained by integration over the ensemble weight. Stringent constraints on the functional are thus obtained when expanding the ensemble exchange-correlation energy through second order in the ensemble weight. For illustration purposes, the analytical derivation of the GACE is presented for the H2 model system in a minimal basis, leading thus to a simple density-functional approximation to the ensemble exchange-correlation energy. ...
Yarkony, David
2015-03-01
The construction of fit single state potential energy surfaces (PESs), analytic representations of ab initio electronic energies and energy gradients, is now well established. These single state PESs, which are essential for accurate quantum dynamics and have found wide application in more approximate quasi-classical treatments, have revolutionized adiabatic dynamics. The situation for nonadiabatic processes involving dissociative and large amplitude motion is less sanguine. In these cases, compared to single electronic state dynamics, both the electronic structure data and the representation are more challenging to determine. We describe the recent development and applications of algorithms that enable description of multiple adiabatic electronic potential energy surfaces coupled by conical intersections in their full dimensionality using coupled quasi-diabatic states. These representations are demonstrably quasi-diabatic, provide accurate representations of conical intersection seams and can smooth out the discontinuities in electronic structure energies due to changing active orbital spaces that routinely afflict global multistate representations.
Relativistic gravitational collapse in non-comoving coordinates: The post-quasistatic approximation
Herrera, L.; Barreto, W.; Di Prisco, A.; Santos, N. O.
2002-01-01
A general, iterative, method for the description of evolving self-gravitating relativistic spheres is presented. Modeling is achieved by the introduction of an ansatz, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post--quasistatic approximation. As examples of application of the method we discuss three models, in the adiabatic case.
Approximations to toroidal harmonics
Toroidal harmonics P/sub n-1/2/1(cosh μ) and Q/sub n-1/2/1(cosh μ) are useful in solutions to Maxwell's equations in toroidal coordinates. In order to speed their computation, a set of approximations has been developed that is valid over the range 0 -10. The simple method used to determine the approximations is described. Relative error curves are also presented, obtained by comparing approximations to the more accurate values computed by direct summation of the hypergeometric series
Static NLO susceptibilities testing approximation schemes against exact results
Del Freo, L; Painelli, A; Freo, Luca Del; Terenziani, Francesca; Painelli, Anna
2001-01-01
The reliability of the approximations commonly adopted in the calculation of static optical (hyper)polarizabilities is tested against exact results obtained for an interesting toy-model. The model accounts for the principal features of typical nonlinear organic materials with mobile electrons strongly coupled to molecular vibrations. The approximations introduced in sum over states and finite field schemes are analyzed in detail. Both the Born-Oppenheimer and the clamped nucleus approximations turn out to be safe for molecules, whereas for donor-acceptor charge transfer complexes deviations from adiabaticity are expected. In the regime of low vibrational frequency, static susceptibilities are strongly dominated by the successive derivatives of the potential energy and large vibrational contributions to hyperpolarizabilities are found. In this regime anharmonic corrections to hyperpolarizabilities are very large, and the harmonic approximation, exact for the linear polarizability, turns out totally inadequate ...
Approximations in Inspection Planning
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.; Bloch, Allan
2000-01-01
. One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found by the......Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations...... inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C.
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximation Behooves Calibration
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms
In this paper, we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state. If the overlap between the initial state and final state of the quantum system is not equal to zero, both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding “complexity. But when the initial state has a zero overlap with the solution state in the problem, the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time. However, inspired by a related reference, a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the 'intrinsic' fault of the second model — an increase in energy. Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above. These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems. (general)
Scalings for a traveling mirror adiabatic magnetic compressor
Bellan, P. M.
1982-01-01
Detailed practical scaling relations for a traveling mirror adiabatic magnetic compressor are derived, and an example is given of how this technique could be used to translate, compress, and heat the Los Alamos FRX-C reversed field theta pinch plasma.
Adiabatic waves along interfacial layers near the critical point
Gouin, Henri
2008-01-01
Near the critical point, isothermal interfacial zones are investigated starting from a non-local density of energy. From the equations of motion of thermocapillary fluids, we point out a new kind of adiabatic waves propagating along the interfacial layers. The waves are associated with the second derivatives of densities and propagate with a celerity depending on the proximity of the critical point.
When an Adiabatic Irreversible Expansion or Compression Becomes Reversible
Anacleto, Joaquim; Ferreira, J. M.; Soares, A. A.
2009-01-01
This paper aims to contribute to a better understanding of the concepts of a "reversible process" and "entropy". For this purpose, an adiabatic irreversible expansion or compression is analysed, by considering that an ideal gas is expanded (compressed), from an initial pressure P[subscript i] to a final pressure P[subscript f], by being placed in…
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable. PMID:27279216
Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition
QIAN Shang-Wu; GU Zhi-Yu
2005-01-01
There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the generaltime-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.
Adiabatic CMB perturbations in pre-big bang string cosmology
Enqvist, Kari; Sloth, Martin Snoager
2001-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations in...
Digitized adiabatic quantum computing with a superconducting circuit
Barends, R.; Shabani, A.; Lamata, L.; Kelly, J.; Mezzacapo, A.; Heras, U. Las; Babbush, R.; Fowler, A. G.; Campbell, B.; Chen, Yu; Chen, Z.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; O’Malley, P. J. J.; Quintana, C.; Roushan, P.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Solano, E.; Neven, H.; Martinis, John M.
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition
There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the general time-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.
Adiabatic single scan two-dimensional NMR spectrocopy.
Pelupessy, Philippe
2003-10-01
New excitation schemes, based on the use adiabatic pulses, for single scan two-dimensional NMR experiments (Frydman et al., Proc. Nat. Acad. Sci. 2002, 99, 15 858-15 862) are introduced. The advantages are discussed. Applications in homo- and heteronuclear experiments are presented. PMID:14519020
A Quantum Adiabatic Algorithm for Factorization and Its Experimental Implementation
Peng, Xinhua; Liao, Zeyang; Xu, Nanyang; Qin, Gan; Zhou, Xianyi; Suter, Dieter; Du, Jiangfeng
2008-01-01
We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical simulations indicate that the running time grows only quadratically with the number of qubits.
Adiabatic and diabatic aerosol transport to the Jungfraujoch
Lugauer, M.; Baltensperger, U.; Furger, M.; Jost, D.T.; Schwikowski, M.; Gaeggeler, H.W. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-09-01
Synoptic scale vertical motion, here detected by the geopotential height of the 500 hPa surface, mainly accounts for the aerosol transport to the Jungfraujoch in winter. In summer, diabatic convection provides the dominant vertical transport mechanism. Nevertheless, synoptic scale adiabatic motion still determines whether diabatic convection can develop. (author) 2 figs., 2 refs.
Dark Energy and Dark Matter from an additional adiabatic fluid
Dunsby, Peter K S; Reverberi, Lorenzo
2016-01-01
The Dark Sector is described by an additional barotropic fluid which evolves adiabatically during the universe's history and whose adiabatic exponent $\\gamma$ is derived from the standard definitions of specific heats. Although in general $\\gamma$ is a function of the redshift, the Hubble parameter and its derivatives, we find that our assumptions lead necessarily to solutions with $\\gamma = $ constant in a FLRW universe. The adiabatic fluid acts effectively as the sum of two distinct components, one evolving like non-relativistic matter and the other depending on the value of the adiabatic index. This makes the model particularly interesting as a way of simultaneously explaining the nature of both Dark Energy and Dark Matter, at least at the level of the background cosmology. The $\\Lambda$CDM model is included in this family of theories when $\\gamma = 0$. We fit our model to SNIa, $H(z)$ and BAO data, discussing the model selection criteria. The implications for the early-universe and the growth of small per...
On the hydrogen-air adiabatic isochoric complete combustion pressure
A simple and fast method for calculating the AICC state (adiabatic Isochoric Complete Combustion) for the hydrogen-air reaction is presented. By comparison with more detailed algorithms it is shown that the proposed method produces satisfactory results, and is thus a viable alternative in situations where the use of detailed algorithms or of tables is too time-consuming. (orig.)
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
Kutzelnigg, Werner; Jaquet, Ralph
2006-11-15
After a short historical account of the theory of the H3+ ion, two ab initio methods are reviewed that allow the computation of the ground-state potential energy surface (PES) of H3+ in the Born-Oppenheimer (BO) approximation, with microhartree or even sub-microhartree accuracy, namely the R12 method and the method of explicitly correlated Gaussians. The BO-PES is improved by the inclusion of relativistic effects and adiabatic corrections. It is discussed how non-adiabatic effects on rotation and vibration can be simulated by corrections to the moving nuclear masses. The importance of the appropriate analytic fit to the computed points of the PES for the subsequent computation of the rovibronic spectrum is addressed. Some recent extensions of the computed PES in the energy region above the barrier to linearity are reviewed. This involves a large set of input geometries and the correct treatment of the dissociation asymptotics, including the coupling with the first excited singlet state. Some comments on this state as well as on the lowest triplet state of H3+ are made. The paper ends with a few remarks on the ion H5+. PMID:17015373
Coherent Dynamics in Dressed Optical Lattices Beyond the Born-Oppenheimer Approximation
Reeves, Jeremy; Krinner, Ludwig; Stewart, Mike; Pazmino, Arturo; Schneble, Dominik
2015-05-01
Usual treatments of matter-wave diffraction assume that the zero-point energy in the diffracting potential is much smaller than the gap between the dressed levels. However, in near-resonant weak-driving scenarios, zero-point motion can mix the adiabatic dressed states, making the diffracting potentials highly non-adiabatic, such that the usual Born-Oppenheimer approximation for the external and internal degrees of freedom no longer applies. We model the dynamics of a matter wave in a microwave-coupled state-dependent lattice in this regime, and quantify the importance of these effects on recent experiments. Supported by NSF grant PHY-1205894.
Ingersoll, Andrew P.
2005-01-01
Expressions are derived for the potential energy of a fluid whose density depends on three variables: temperature, pressure, and salinity. The thermal expansion coefficient is a function of depth, and the application is to thermobaric convection in the oceans. Energy conservation, with conversion between kinetic and potential energies during adiabatic, inviscid motion, exists for the Boussinesq and anelastic approximations but not for all approximate systems of equations. In the Boussinesq/an...
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Accuracy of Approximate Eigenstates
Lucha, Wolfgang; Lucha, Wolfgang
2000-01-01
Besides perturbation theory, which requires, of course, the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum theory. For a reasonable choice of the employed trial subspace of the domain of H, the lowest eigenvalues of H usually can be located with acceptable precision whereas the trial-subspace vectors corresponding to these eigenvalues approximate, in general, the exact eigenstates of H with much less accuracy. Accordingly, various measures for the accuracy of the approximate eigenstates derived by variational techniques are scrutinized. In particular, the matrix elements of the commutator of the operator H and (suitably chosen) different operators, with respect to degenerate approximate eigenstates of H obtained by some variational method, are proposed here as new criteria for the accuracy of variational eigenstates. These considerations are applied to that Hamiltonian the eig...
Synthesis of approximation errors
Bareiss, E.H.; Michel, P.
1977-07-01
A method is developed for the synthesis of the error in approximations in the large of regular and irregular functions. The synthesis uses a small class of dimensionless elementary error functions which are weighted by the coefficients of the expansion of the regular part of the function. The question is answered whether a computer can determine the analytical nature of a solution by numerical methods. It is shown that continuous least-squares approximations of irregular functions can be replaced by discrete least-squares approximation and how to select the discrete points. The elementary error functions are used to show how the classical convergence criterions can be markedly improved. There are eight numerical examples included, 30 figures and 74 tables.
White, Martin
2014-01-01
This year marks the 100th anniversary of the birth of Yakov Zel'dovich. Amongst his many legacies is the Zel'dovich approximation for the growth of large-scale structure, which remains one of the most successful and insightful analytic models of structure formation. We use the Zel'dovich approximation to compute the two-point function of the matter and biased tracers, and compare to the results of N-body simulations and other Lagrangian perturbation theories. We show that Lagrangian perturbation theories converge well and that the Zel'dovich approximation provides a good fit to the N-body results except for the quadrupole moment of the halo correlation function. We extend the calculation of halo bias to 3rd order and also consider non-local biasing schemes, none of which remove the discrepancy. We argue that a part of the discrepancy owes to an incorrect prediction of inter-halo velocity correlations. We use the Zel'dovich approximation to compute the ingredients of the Gaussian streaming model and show that ...
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM that...
Discrete Bose-Einstein systems in a box with low adiabatic invariant
The Bose-Einstein energy spectrum of a quantum gas, confined in a (cubic) box, is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, Aat and the adiabatic invariant, TV2/3, i.e. on γ=AatTV2/3. Even within the approximation of noninteracting particles in the gas, the calculation of the thermodynamic properties of Bose-Einstein systems turns out to be a difficult mathematical problem. It is solved in the textbooks and most papers by approximating the sums by integrals. The present study compares the total number of particles and the total energy obtained by summing up the exact contributions of the eigenvalues and their weights, for defined values of γ, to the results of the approximate integrals. Then, the passage from sums to integrals is done in a more rigorous manner and better analytical approximations are found. The corrected thermodynamic functions depend on γ. The critical temperature is corrected also in order to describe more accurately the discrete Bose-Einstein systems and their onset of the phase transition. (author)
Comments on "MSE minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel"
Marquet, Pascal
2015-01-01
In a recent paper, Romps (JAS, vol.72, p.3639-3646, 2015, hereafter R15) argues that the moist-air static energy (MSE) is only approximately conserved for an adiabatically lifted parcel, and that the quantity "MSE - CAPE" could be used as a true conserved variable, where CAPE is the convective available energy. However, the thermodynamic equations are written in R15 by making several assumptions, not all of which are explicitly mentioned. This comment aims to clarify the hypotheses made in R15. It will show that these assumptions call into question the validity of the moist-air internal energy, enthalpy and entropy functions in R15, meaning that several of the conclusions in the paper should be revisited. It also demonstrates that it is possible to obtain more precise and general formulations for moist-air energy, enthalpy and entropy functions, in particular by using the third law of thermodynamics.
Adiabatic hydrodynamic modes in dielectric environment in a random electric field
Stupka, Anton
2016-01-01
Dielectric is considered in the electric field that has equal to zero the first moment and different from zero the second moment of strength in an equilibrium. The equations of ideal hydrodynamics are obtained in such a field for the case of the neglect of dissipative effects. A new variable - the second moment of electric field strength is included in the Euler equation. A temporal equation for this variable is obtained on the basis of Maxwell equations in the hydrodynamic approximation. Adiabatic one-dimensional waves of small amplitude are studied in this system. Proceeding from the theoretical estimation of the intracrystalline field in an ionic crystal the good consent of the obtained numerical values of transversal velocity of this wave with transversal velocity of sound for isotropic crystals of alkali halides is found.
Fermi-Dirac gas of atoms in a box with low adiabatic invariant
Quantum degenerate Fermi-Dirac gas of atoms, confined in a cubic box, shows an energy spectrum, which is discrete and strongly dependent on the atomic mass number, Aat, box geometry and temperature, for low product of Aat and the adiabatic invariant, TV1/3, i.e. on γ = AatTV1/3. The present study compares the total number of particles and the total energy obtained by summing up the contributions of a finite number of states, defined by the values of γ, to the widespread approximations of the corresponding integrals. The sums show simple calculation algorithms and more precise results for a large interval of values of γ. A new accurate analytic formula for the chemical potential of the Fermi-Dirac quantum gas is also given. (author)
Critical stability of almost adiabatic convection in a rapidly rotating thick spherical shell
In this work, the convection equations in the almost adiabatic approximation is studied for which the choice of physical parameters is primarily based on possible applications to the hydrodynamics of the deep interiors of the Earth and planets and moons of the terrestrial group. The initial system of partial differential equations (PDEs) was simplified to a single second-order ordinary differential equation for the pressure or vertical velocity component to investigate the linear stability of convection. The critical frequencies, modified Rayleigh numbers, and distributions of convection are obtained at various possible Prandtl numbers and in different thick fluid shells. An analytical WKB-type solution was obtained for the case when the inner radius of the shell is much smaller than the outer radius and convective sources are concentrated along the inner boundary.
Extended adiabatic blast waves and a model of the soft x-ray background
An analytical approximation is generated which follows the development of an adiabatic spherical blast wave in a homogeneous ambient medium of finite pressure. At early times when the external pressure is negligible, the structure is that of the usual self-similar solution. At later times, the structure evolves smoothly as the shock weakens, the postshock compression declines, and the gradients in pressure and density become less severe within the shocked region. The complete structure should be reliable down to a postshock compression of about 2, with conditions close inside the shock remaining well described somewhat longer. An analytical approximation is also presented for the electron-temperature distribution resulting from Coulomb collisional heating. It is shown that thermal conduction, limited by saturation at early times, fades in importance just as Coulomb collisional heating becomes significant. An estimate is made of the nonequilibrium cooling coefficient and the degree of ionization equilibrium expected by the time significant cooling sets in. From the estimates of the end point of the adiabatic era, based on the collisional equilibrium emissivity, are shown to be reasonably accurate. The dynamical, thermal, ionization, and spectral structures are calculated for blast waves of energy E0 = 5 x 1050 ergs in a hot, low-density interstellar environment. A formulais presented for estimating the luminosity evolution of such explosions, including the effects of nonequilibrium ionization. It is shown that the B and C bands of the soft x-ray background are reproduced by such a model explosion if the ambient density is about 0.004 cm(sup -3), the blast radius is roughly 100 pc, and the solar system is located inside the shocked region. The age of such an explosion is roughly 10(sup 5) years. This result is almost independent of whether there is apprecialy non-Coulomb heating of the electrons
Non-adiabatic dynamics of molecules in optical cavities
Kowalewski, Markus, E-mail: mkowalew@uci.edu; Bennett, Kochise; Mukamel, Shaul, E-mail: smukamel@uci.edu [Department of Chemistry, University of California, Irvine, California 92697-2025 (United States)
2016-02-07
Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces thereby opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use quantities readily accessible from quantum chemistry codes like the adiabatic potential energy surfaces and dipole moments to carry out wave packet simulations in the dressed basis. The implications for photochemistry are demonstrated for a set of model systems representing typical situations found in molecules.
On some issues of gravitationally induced adiabatic particle productions
Pan, Supriya; Pramanik, Souvik
2016-01-01
In this work, we investigate the current accelerating universe driven by the gravitationally induced adiabatic matter creation process. To elaborate the underlying cognitive content, here we consider three models of adiabatic particle creation and constrain the model parameters by fitting the models with the Union 2.1 data set using $\\chi^2$ minimization technique. The models are analyzed by two geometrical and model independent tests, viz., cosmography and $Om$-diagnostic, which are widely used to distinguish the cosmological models from $\\Lambda$CDM. We also compared present values of those model independent parameters with that of the flat $\\Lambda$CDM model. Finally, the validity of the generalized second law of thermodynamics and the condition of thermodynamic equilibrium for the particle production models have been tested.
Adiabatic far-field sub-diffraction imaging
Cang, Hu; Salandrino, Alessandro; Wang, Yuan; Zhang, Xiang
2015-08-01
The limited resolution of a conventional optical imaging system stems from the fact that the fine feature information of an object is carried by evanescent waves, which exponentially decays in space and thus cannot reach the imaging plane. We introduce here an adiabatic lens, which utilizes a geometrically conformal surface to mediate the interference of slowly decompressed electromagnetic waves at far field to form images. The decompression is satisfying an adiabatic condition, and by bridging the gap between far field and near field, it allows far-field optical systems to project an image of the near-field features directly. Using these designs, we demonstrated the magnification can be up to 20 times and it is possible to achieve sub-50 nm imaging resolution in visible. Our approach provides a means to extend the domain of geometrical optics to a deep sub-wavelength scale.
Improved Refrigerant Characteristics Flow Predictions in Adiabatic Capillary Tube
Shodiya Sulaimon
2012-07-01
Full Text Available This study presents improved refrigerant characteristics flow predictions using homogenous flow model in adiabatic capillary tube, used in small vapor compression refrigeration system. The model is based on fundamental equations of mass, momentum and energy. In order to improve the flow predictions, the inception of vaporization in the capillary tube is determined by evaluating initial vapor quality using enthalpy equation of refrigerant at saturation point and the inlet entrance effect of the capillary tube is also accounted for. Comparing this model with experimental data from open literature showed a reasonable agreement. Further comparison of this new model with earlier model of Bansal showed that the present model could be use to improve the performance predictions of refrigerant flow in adiabatic capillary tube.
Non-adiabatic theoretical observables in Delta Scuti stars
Moya, A; Dupret, M A
2004-01-01
Phase differences and amplitude ratios at different colour photometric bands are currently being used to discriminate pulsation modes in order to facilitate mode identification of kappa-driven non-radial pulsating stars. In addition to physical inputs (e.g., mass, T_eff, etc.), these quantities depend on the non-adiabatic treatment of the atmosphere. This paper presents theoretical results concerning Delta Scuti pulsating stars. The envelope of each of these stellar structures possesses a convection zone whose development is determined by various factors. An interacting pulsation-atmosphere physical treatment is introduced which supplies two basic non-adiabatic physical quantities: the relative effective temperature variation and the phase lag phi^T, defined as the angle between effective temperature variations and radial displacement. These quantities can be used to derive the phase differences and amplitude ratios. Numerical values for these quantities depend critically on the alpha MLT parameter used to ca...
The adiabatic motion of charged dust grains in rotating magnetospheres
Northrop, T. G.; Hill, J. R.
1983-01-01
Adiabatic equations of motion are derived for the micrometer-sized dust grains detected in the Jovian and Saturn magnetospheres by the Pioneer 10 and 11 spacecraft. The adiabatic theory of charged particle motion is extended to the case of variable grain charge. Attention is focused on the innermost and outermost limits to the grain orbit evolution, with all orbits tending to become circular with time. The parameters such as the center equation of motion, the drift velocity, and the parallel equation of motion are obtained for grains in a rotating magnetosphere. Consideration is given to the effects of periodic grain charge-discharge, which are affected by the ambient plasma properties and the grain plasma velocity. The charge-discharge process at the gyrofrequency is determined to eliminate the invariance of the magnetic moment and cause the grain to exhibit radial movement. The magnetic moment increases or decreases as a function of the gyrophase of the charge variation.
Crack propagation of Ti alloy via adiabatic shear bands
This study was focused on the characterization of the origin and mechanism of crack propagation as a result of hot induction bending of Ti alloy. Plates of Ti–6Al–4V alloy with 12.5 mm of thickness were submitted to hot induction bending below the beta transus temperature. Optical and scanning electron microscopy analysis showed crack formation in the tensile zone. Microstructural evidence showed that cracks propagate through the adiabatic shear bands by Dimple-Void mechanism. However, voids formation before shear banding also occurred. In both mechanisms adiabatic shear bands are formed via dynamic recrystallization where the alpha–beta interphase works as stress concentrator promoting the formation of dimples and voids
Excitation energies along a range-separated adiabatic connection
Rebolini, Elisa; Teale, Andrew M; Helgaker, Trygve; Savin, Andreas
2014-01-01
We present a study of the variation of total energies and excitationenergies along a range-separated adiabatic connection. This connectionlinks the non-interacting Kohn-Sham electronic system to the physicalinteracting system by progressively switching on theelectron-electron interactions whilst simultaneously adjusting aone-electron effective potential so as to keep the ground-statedensity constant. The interactions are introduced in arange-dependent manner, first introducing predominantly long-range,and then all-range, interactions as the physical system is approached,as opposed to the conventional adiabatic connection where theinteractions are introduced by globally scaling the standard Coulomb interaction.Reference data are reported for the He and Be atoms and the H2molecule, obtained by calculating the short-range effective potentialat the full configuration-interaction level using Lieb'sLegendre-transform approach. As the strength of the electron-electroninteractions increases, the excitation energies, ...
Crack propagation of Ti alloy via adiabatic shear bands
Mendoza, I., E-mail: ivanmendozabravo@gmail.com [Instituto Tecnológico de Veracruz (Mexico); Villalobos, D. [Instituto Tecnológico de Veracruz (Mexico); Alexandrov, B.T. [The Ohio State University (United States)
2015-10-01
This study was focused on the characterization of the origin and mechanism of crack propagation as a result of hot induction bending of Ti alloy. Plates of Ti–6Al–4V alloy with 12.5 mm of thickness were submitted to hot induction bending below the beta transus temperature. Optical and scanning electron microscopy analysis showed crack formation in the tensile zone. Microstructural evidence showed that cracks propagate through the adiabatic shear bands by Dimple-Void mechanism. However, voids formation before shear banding also occurred. In both mechanisms adiabatic shear bands are formed via dynamic recrystallization where the alpha–beta interphase works as stress concentrator promoting the formation of dimples and voids.
Non-adiabatic dynamics of molecules in optical cavities
Kowalewski, Markus; Mukamel, Shaul
2016-01-01
Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use quantities readily accessible from quantum chemistry codes like the adiabatic potential energy surfaces and dipole moments to carry out wave packet simulations in the dressed basis. The implications for photochemistry are demonstrated for a set of model systems representing typical situations found in molecules.
Adiabatic theorem for the time-dependent wave operator
The application of time-dependent wave operator theory to the development of a quantum adiabatic perturbation theory is treated both theoretically and numerically, with emphasis on the description of field-matter interactions which involve short laser pulses. It is first shown that the adiabatic limit of the time-dependent wave operator corresponds to a succession of instantaneous static Bloch wave operators. Wave operator theory is then shown to be compatible with the two-time Floquet theory of light-matter interaction, thus allowing the application of Floquet theory to cases which require the use of a degenerate active space. A numerical study of some problems shows that the perturbation strength associated with nonadiabatic processes can be reduced by using multidimensional active spaces and illustrates the capacity of the wave operator approach to produce a quasiadiabatic treatment of a nominally nonadiabatic Floquet dynamical system
Microscopic expression for heat in the adiabatic basis.
Polkovnikov, Anatoli
2008-11-28
We derive a microscopic expression for the instantaneous diagonal elements of the density matrix rho(nn)(t) in the adiabatic basis for an arbitrary time-dependent process in a closed Hamiltonian system. If the initial density matrix is stationary (diagonal) then this expression contains only squares of absolute values of matrix elements of the evolution operator, which can be interpreted as transition probabilities. We then derive the microscopic expression for the heat defined as the energy generated due to transitions between instantaneous energy levels. If the initial density matrix is passive [diagonal with rho(nn)(0) monotonically decreasing with energy] then the heat is non-negative in agreement with basic expectations of thermodynamics. Our findings also can be used for systematic expansion of various observables around the adiabatic limit. PMID:19113464
DESIGN OF TERNARY COUNTER BASED ON ADIABATIC DOMINO CIRCUIT
Yang Qiankun; Wang Pengjun; Zheng Xuesong
2013-01-01
By researching the ternary counter and low power circuit design method,a novel design of low power ternary Domino counter on switch-level is proposed.Firstly,the switch-level structure expression of ternary loop operation circuit with enable pin is derived according to the switch-signal theory,and the one bit ternary counter is obtained combining the ternary adiabatic Domino literal operation circuit and buffer.Then the switch-level structure expression of enable signal circuit is derived,and the four bits ternary counter is obtained by cascade connection.Finally,the circuit is simulated by Spice tool and the output waveforms transform in proper order indicating that the logic function is correct.The energy consumption of the four bits ternary adiabatic Domino counter is 63％ less than the conventional Domino counterpart.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
The Adiabatic Piston and the Second Law of Thermodynamics
Crosignani, B; Conti, C
2002-01-01
A detailed analysis of the adiabatic-piston problem reveals peculiar dynamical features that challenge the general belief that isolated systems necessarily reach a static equilibrium state. In particular, the fact that the piston behaves like a perpetuum mobile, i.e., it never stops but keeps wandering, undergoing sizable oscillations, around the position corresponding to maximum entropy, has remarkable implications on the entropy variations of the system and on the validity of the second law when dealing with systems of mesoscopic dimensions.
Single-parameter adiabatic charge pumping in carbon nanotube resonators
Perroni, C. A.; Nocera, A.; Cataudella, V.
2013-01-01
Single-parameter adiabatic charge pumping, induced by a nearby radio-frequency antenna, is achieved in suspended carbon nanotubes close to the mechanical resonance. The charge pumping is due to an important dynamic adjustment of the oscillating motion to the antenna signal and it is different from the mechanism active in the two-parameter pumping. Finally, the second harmonic oscillator response shows an interesting relationship with the first harmonic that should be experimentally observed.
Quantum pumping with adiabatically modulated barriers in graphene
Zhu, Rui; Chen, Huiming
2009-01-01
We study the adiabatic quantum pumping characteristics in the graphene modulated by two oscillating gate potentials out of phase. The angular and energy dependence of the pumped current is presented. The direction of the pumped current can be reversed when a high barrier demonstrates stronger transparency than a low one, which results from the Klein paradox. The underlying physics of the pumping process is illuminated.
Geometry of adiabatic Hamiltonians for two-level quantum systems
We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve corresponding to the Hamiltonian of the system for which the geometrical quantities have a simple physical interpretation. In particular, the curvature of the curve has the role of the nonadiabatic coupling. (paper)
High-Fidelity Entangled Bell States via Shortcuts to Adiabaticity
Paul, Koushik
2016-01-01
We present a couple of protocols based on shortcut to adiabaticity techniques for rapid generation of robust entangled Bell states in a system of two two-state systems. Our protocols rely on the so-called transitionless quantum driving (TQD) algorithm and Lewis-Riesenfeld invariant (LRI) method. Both TQD and LRI methods result in high fidelity in population transfer.Our study shows that it is possible to prepare an entangled state in infinitely short time without losing robustness and efficiency.
Adiabatic Hyperspherical Approach to the Problems of Muon Catalyzed Fusion
The adiabatic hyperspherical approach (AHSA) is applied for the numerical investigation of the scattering processes and resonances in Coulomb three-body mesic atomic systems. The results of the calculations of elastic and inelastic cross sections in low-energy collisions aμ + b (a, b = p, d, t), energies, lifetimes and local characteristics of resonant states of mesic molecular ions nHeaμ+ (n = 3, 4) are presented.
Linear response of galactic halos to adiabatic gravitational perturbations
Murali, Chigurupati; Tremaine, Scott
1997-01-01
We determine the response of a self-similar isothermal stellar system to small adiabatic gravitational perturbations. For odd spherical harmonics, the response is identical to the response of the analogous isothermal fluid system. For even spherical harmonics, the response can be regarded as an infinite series of wavetrains in $\\log r$, implying alternating compression and rarefaction in equal logarithmic radius intervals. Partly because of the oscillatory nature of the solutions, tidal field...
The Adiabatic Piston and the Second Law of Thermodynamics
Crosignani, B.; Di Porto, P.; de Conti, C.
2002-01-01
A detailed analysis of the adiabatic-piston problem reveals peculiar dynamical features that challenge the general belief that isolated systems necessarily reach a static equilibrium state. In particular, the fact that the piston behaves like a perpetuum mobile, i.e., it never stops but keeps wandering, undergoing sizable oscillations, around the position corresponding to maximum entropy, has remarkable implications on the entropy variations of the system and on the validity of the second law...
Richtárik, Peter
2008-01-01
In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising as a level set of the model. We show that by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical ...
Approximate Bayesian recursive estimation
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111. ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Local approximate inference algorithms
Jung, Kyomin; Shah, Devavrat
2006-01-01
We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say $G$. Our algorithm is based on decomposition of $G$ into {\\em appropriately} chosen small components; then computing estimates locally in each of these components and then producing a {\\em good} global solution. We show that if the underlying graph $G$ either excl...
Fragments of approximate counting
Buss, S.R.; Kolodziejczyk, L.. A.; Thapen, Neil
2014-01-01
Roč. 79, č. 2 (2014), s. 496-525. ISSN 0022-4812 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : approximate counting * bounded arithmetic * ordering principle Subject RIV: BA - General Mathematics Impact factor: 0.541, year: 2014 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9287274&fileId=S0022481213000376
Highlights: • Development of optimization rules for S2 quadrature sets. • Studying the dependency of optimized S2 quadratures on composition and geometry. • Demonstrating S2 procedures preserving the features of higher approximations. - Abstract: Discrete ordinates method relies on approximating the integral term of the transport equation with the aid of quadrature summation rules. These quadratures are usually based on certain assumptions which assure specific symmetry rules and transport/diffusion limits. Generally, these assumptions are not problem-dependent which results in inaccuracies in some instances. Here, various methods have been developed for more accurate estimation of the independent angle in S2 approximation, as it is tightly related to valid estimation of the diffusion coefficient/length. We proposed and examined a method to reduce a complicated problem that usually is consisting many energy groups and discrete directions (SN) to an equivalent one-group S2 problem while it mostly preserves general features of the original model. Some numerical results are demonstrated to show the accuracy of proposed method
NMR implementation of adiabatic SAT algorithm using strongly modulated pulses.
Mitra, Avik; Mahesh, T S; Kumar, Anil
2008-03-28
NMR implementation of adiabatic algorithms face severe problems in homonuclear spin systems since the qubit selective pulses are long and during this period, evolution under the Hamiltonian and decoherence cause errors. The decoherence destroys the answer as it causes the final state to evolve to mixed state and in homonuclear systems, evolution under the internal Hamiltonian causes phase errors preventing the initial state to converge to the solution state. The resolution of these issues is necessary before one can proceed to implement an adiabatic algorithm in a large system where homonuclear coupled spins will become a necessity. In the present work, we demonstrate that by using "strongly modulated pulses" (SMPs) for the creation of interpolating Hamiltonian, one can circumvent both the problems and successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. This work also demonstrates that the SMPs tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence, and will be the modality in future implementation of quantum information processing by NMR. PMID:18376911
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Non-adiabatic energy dissipation in metal homoepitaxy
Hagemann, Ulrich; Huba, Kornelia; Krix, David; Nienhaus, Hermann [Experimental Physics, University of Duisburg-Essen (Germany)
2009-07-01
The growth of metal films releases energies of typically a few eV per metal atom. By now, the energy is believed to be dissipated adiabatically by direct excitation of phonons. We present data which give strong evidence for the creation of electron-hole pairs during Mg homoepitaxy, i.e., for a non-adiabatic dissipation channel. To detect the generated hot charge carriers, large-area ultrathin metal film Mg/p-Si(001) Schottky diodes were fabricated. The homogeneous Schottky barrier height was determined as 0.52 eV and the reverse current could be reduced to below 1 nA at low temperatures. During exposure of the diodes to a thermal Mg atom beam internal currents in the 100 pA range are observed. The currents can be attributed to two mechanisms: first the internal exoemission process (chemicurrent effect) due to non-adiabatic energy dissipation and second the photocurrent due to the infrared radiation of the evaporator. By varying the evaporator temperature and the Mg film thickness the two current contributions can be distinguished. The chemicurrent during Mg homoepitaxy depends exponentially on the evaporation temperature yielding the Mg evaporation enthalpy of 1.3 eV. The strong exponential attenuation of the chemicurrent with increasing Mg film thickness further supports the concept of generation of ballistic charge carriers by the metal formation process.
Analysis of adiabatic transfer in cavity quantum electrodynamics
Joyee Ghosh; R Ghosh; Deepak Kumar
2011-10-01
A three-level atom in a conﬁguration trapped in an optical cavity forms a basic unit in a number of proposed protocols for quantum information processing. This system allows for efﬁcient storage of cavity photons into long-lived atomic excitations, and their retrieval with high ﬁdelity, in an adiabatic transfer process through the ‘dark state’ by a slow variation of the control laser intensity. We study the full quantum mechanics of this transfer process with a view to examine the non-adiabatic effects arising from inevitable excitations of the system to states involving the upper level of , which is radiative. We ﬁnd that the ﬁdelity of storage is better, the stronger the control ﬁeld and the slower the rate of its switching off. On the contrary, unlike the adiabatic notion, retrieval is better with faster rates of switching on of an optimal control ﬁeld. Also, for retrieval, the behaviour with dissipation is non-monotonic. These results lend themselves to experimental tests. Our exact computations, when applied to slow variations of the control intensity for strong atom–photon couplings, are in very good agreement with Berry’s superadiabatic transfer results without dissipation.
Adiabatic Shear Mechanisms for the Hard Cutting Process
YUE Caixu; WANG Bo; LIU Xianli; FENG Huize; CAI Chunbin
2015-01-01
The most important consequence of adiabatic shear phenomenon is formation of sawtooth chip. Lots of scholars focused on the formation mechanism of sawtooth, and the research often depended on experimental approach. For the present, the mechanism of sawtooth chip formation still remalns some ambiguous aspects. This study develops a combined numerical and experimental approach to get deeper understanding of sawtooth chip formation mechanism for Polycrystalline Cubic Boron Nitride (PCBN) tools orthogonal cutting hard steel GCr15. By adopting the Johnson-Cook material constitutive equations, the FEM simulation model established in this research effectively overcomes serious element distortions and cell singularity in high straln domaln caused by large material deformation, and the adiabatic shear phenomenon is simulated successfully. Both the formation mechanism and process of sawtooth are simulated. Also, the change features regarding the cutting force as well as its effects on temperature are studied. More specifically, the contact of sawtooth formation frequency with cutting force fluctuation frequency is established. The cutting force and effect of cutting temperature on mechanism of adiabatic shear are investigated. Furthermore, the effects of the cutting condition on sawtooth chip formation are researched. The researching results show that cutting feed has the most important effect on sawtooth chip formation compared with cutting depth and speed. This research contributes a better understanding of mechanism, feature of chip formation in hard turning process, and supplies theoretical basis for the optimization of hard cutting process parameters.
Irreconcilable difference between quantum walks and adiabatic quantum computing
Wong, Thomas G.; Meyer, David A.
2016-06-01
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.
Adiabatic shear mechanisms for the hard cutting process
Yue, Caixu; Wang, Bo; Liu, Xianli; Feng, Huize; Cai, Chunbin
2015-05-01
The most important consequence of adiabatic shear phenomenon is formation of sawtooth chip. Lots of scholars focused on the formation mechanism of sawtooth, and the research often depended on experimental approach. For the present, the mechanism of sawtooth chip formation still remains some ambiguous aspects. This study develops a combined numerical and experimental approach to get deeper understanding of sawtooth chip formation mechanism for Polycrystalline Cubic Boron Nitride (PCBN) tools orthogonal cutting hard steel GCr15. By adopting the Johnson-Cook material constitutive equations, the FEM simulation model established in this research effectively overcomes serious element distortions and cell singularity in high strain domain caused by large material deformation, and the adiabatic shear phenomenon is simulated successfully. Both the formation mechanism and process of sawtooth are simulated. Also, the change features regarding the cutting force as well as its effects on temperature are studied. More specifically, the contact of sawtooth formation frequency with cutting force fluctuation frequency is established. The cutting force and effect of cutting temperature on mechanism of adiabatic shear are investigated. Furthermore, the effects of the cutting condition on sawtooth chip formation are researched. The researching results show that cutting feed has the most important effect on sawtooth chip formation compared with cutting depth and speed. This research contributes a better understanding of mechanism, feature of chip formation in hard turning process, and supplies theoretical basis for the optimization of hard cutting process parameters.
White, Alexander; Mozyrsky, Dmitry
2016-01-01
Accurate simulation of the non-adiabatic dynamics of molecules in excited electronic states is key to understanding molecular photo-physical processes. Here we present a novel method, based on a semiclassical approximation, that is as efficient as the commonly used mean field Ehrenfest or ad hoc Surface Hopping methods and properly accounts for interference and decoherence effects. This novel method is an extension of Hellers Thawed Gaussian wavepacket dynamics that includes coupling between potential energy surfaces. The accuracy of the method can be systematically improved.
Bernard, R; Goutte, H; Gogny, D; Dubray, N; Lacroix, D
2009-11-24
Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in {sup 238}U. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn't seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in {sup 238}U and {sup 239}U for an excitation energy of 2.3 MeV above the barrier. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.
Lacroix D.
2010-03-01
Full Text Available Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in 238U [1]. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn’t seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in 238U and 239U for an excitation energy of 2.3 MeV above the barrier [2–4]. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.
Piezoelectric control of the mobility of a domain wall driven by adiabatic and non-adiabatic torques
de Ranieri, E.; Roy, P. E.; Fang, D.; Vehsthedt, E. K.; Irvine, A. C.; Heiss, D.; Casiraghi, A.; Campion, R. P.; Gallagher, B. L.; Jungwirth, T.; Wunderlich, J.
2013-09-01
The rich internal degrees of freedom of magnetic domain walls make them an attractive complement to electron charge for exploring new concepts of storage, transport and processing of information. Here we use the tunable internal structure of a domain wall in a perpendicularly magnetized GaMnAsP/GaAs ferromagnetic semiconductor and demonstrate devices in which piezoelectrically controlled magnetic anisotropy yields up to 500% mobility variations for an electrical-current-driven domain wall. We observe current-induced domain wall motion over a wide range of current-pulse amplitudes and report a direct observation and the piezoelectric control of the Walker breakdown separating two regimes with different mobilities. Our work demonstrates that in spin-orbit-coupled ferromagnets with weak extrinsic domain wall pinning, the piezoelectric control allows one to experimentally assess the upper and lower boundaries of the characteristic ratio of adiabatic and non-adiabatic spin-transfer torques in the current-driven domain wall motion.
Rajinder Pal
2016-01-01
Entropy generation, and hence exergy destruction, in adiabatic flow of unstable and surfactant-stabilized emulsions was investigated experimentally in different diameter pipes. Four types of emulsion systems are investigated covering a broad range of the dispersed-phase concentration: (a) unstable oil-in-water (O/W) emulsions without surfactant; (b) surfactant-stabilized O/W emulsions; (c) unstable water-in-oil (W/O) emulsions without surfactant; and (d) surfactant-stabilized W/O emulsions. T...
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)
Approximation by Cylinder Surfaces
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points in the...
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Approximations to Euler's constant
We study a problem of finding good approximations to Euler's constant γ=lim→∞ Sn, where Sn = Σk=Ln (1)/k-log(n+1), by linear forms in logarithms and harmonic numbers. In 1995, C. Elsner showed that slow convergence of the sequence Sn can be significantly improved if Sn is replaced by linear combinations of Sn with integer coefficients. In this paper, considering more general linear transformations of the sequence Sn we establish new accelerating convergence formulae for γ. Our estimates sharpen and generalize recent Elsner's, Rivoal's and author's results. (author)
Chen, Dan
2012-01-01
We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a Monte-Carlo data structure for this problem that can be constructed in O(nlog n$ time, can answer queries O((log n)^{4/3}) expected time, and answers correctly with high probability.
The Compact Approximation Property does not imply the Approximation Property
Willis, George A.
1992-01-01
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
The results of application of the quantum-mechanical adiabatic theory to vibrational predissociation (VPD) of water dimers, (H2O)2 and (D2O)2, are presented. We consider the VPD processes including the totally symmetric OH mode of the dimer and the bending mode of the fragment. The VPD in the adiabatic representation is induced by breakdown of the vibrational adiabatic approximation, and two types of nonadiabatic coupling matrix elements are involved: one provides the VPD induced by the low-frequency dissociation mode and the other provides the VPD through channel interactions induced by the low-frequency modes. The VPD rate constants were calculated using the Fermi golden rule expression. A closed form for the nonadiabatic transition matrix element between the discrete and continuum states was derived in the Morse potential model. All of the parameters used were obtained from the potential surfaces of the water dimers, which were calculated by the density functional theory procedures. The VPD rate constants for the two processes were calculated in the non-Condon scheme beyond the so-called Condon approximation. The channel interactions in and between the initial and final states were taken into account, and those are found to increase the VPD rates by 3(1) orders of magnitude for the VPD processes in (H2O)2 ((D2O)2). The fraction of the bending-excited donor fragments is larger than that of the bending-excited acceptor fragments. The results obtained by quantum-mechanical approach are compared with both experimental and quasi-classical trajectory calculation results
Mineo, H.; Kuo, J. L. [Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan (China); Niu, Y. L. [Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190 (China); Lin, S. H. [Department of Applied Chemistry, Institute of Molecular Science and Center for Interdisciplinary Molecular Science, National Chiao-Tung University, Shin-Chu 300, Taiwan (China); Fujimura, Y. [Department of Applied Chemistry, Institute of Molecular Science and Center for Interdisciplinary Molecular Science, National Chiao-Tung University, Shin-Chu 300, Taiwan (China); Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578 (Japan)
2015-08-28
The results of application of the quantum-mechanical adiabatic theory to vibrational predissociation (VPD) of water dimers, (H{sub 2}O){sub 2} and (D{sub 2}O){sub 2}, are presented. We consider the VPD processes including the totally symmetric OH mode of the dimer and the bending mode of the fragment. The VPD in the adiabatic representation is induced by breakdown of the vibrational adiabatic approximation, and two types of nonadiabatic coupling matrix elements are involved: one provides the VPD induced by the low-frequency dissociation mode and the other provides the VPD through channel interactions induced by the low-frequency modes. The VPD rate constants were calculated using the Fermi golden rule expression. A closed form for the nonadiabatic transition matrix element between the discrete and continuum states was derived in the Morse potential model. All of the parameters used were obtained from the potential surfaces of the water dimers, which were calculated by the density functional theory procedures. The VPD rate constants for the two processes were calculated in the non-Condon scheme beyond the so-called Condon approximation. The channel interactions in and between the initial and final states were taken into account, and those are found to increase the VPD rates by 3(1) orders of magnitude for the VPD processes in (H{sub 2}O){sub 2} ((D{sub 2}O){sub 2}). The fraction of the bending-excited donor fragments is larger than that of the bending-excited acceptor fragments. The results obtained by quantum-mechanical approach are compared with both experimental and quasi-classical trajectory calculation results.
Presented are calculated dependences for adiabatic compressibility, isoentropy coefficient and thermodynamic sound velocity of a two-phase media with homogeneous disperse structure being in a state of equilibrium. The character of the change of the values mentioned for vapor water media at the change of vapor mass composition in the mixture from zero to 1 is shown. Comparison of the calculated data as to dependences obtained with the experimental ones for critical regimes of vapor-water flow outflow through short and long cylindrical channels with sharp entrance rims. The calculation error does not exceed approximately 12%. Analysis of the results obtained showed that at outflow through short channels of metastable vapor liquid flow the main characteristics, like at outflow through long channels, are determined by the pressure in the exit cross section, mass vapor content and specific volume of the mixture, which are calculated with account for real overheating of the liquid to the exit cross section. At critical regime of outflow through the very long channels, when one can not neglect hydraulic resistance in the channel and the process is not isoentropic, the pressure and mass vapor content in the exit cross section also unambiguously determine the value of adiabatic compressibility of two-phase media, sound velocity and isoentropy coefficient in the cross section. Conclusion is made that the dependences obtained can be used with sufficient for practical purposes accuracy when solving different engineering problems, as well as for the calculations of the mixture consumption at flow of the reactor contours NAI with WWR
Shortcuts to Adiabaticity by Counterdiabatic Driving in Trapped-ion Transport
An, Shuoming; del Campo, Adolfo; Kim, Kihwan
2016-01-01
Adiabatic dynamics plays an essential role in quantum technologies. By driving a quantum system slowly, the quantum evolution can be engineered with suppressed excitation. Yet, environmentally-induced decoherence limits the implementation of adiabatic protocols. Shortcuts to adiabaticity (STA) have the potential to revolutionize quantum technologies by speeding up the time evolution while mimicking adiabatic dynamics. These nonadiabatic protocols can be engineered by means an auxiliary control field is used to tailor excitations. Here we present the first experimental realization of counterdiabatic driving in a continuous variable system, implementing a shortcut to the adiabatic transport of a trapped ion, in which nonadiabatic transitions are suppressed during all stages of the process. The resulting dynamics is equivalent to a "fast-motion video" of the adiabatic trajectory. We experimentally demonstrate the enhanced robustness of the protocol with respect to alternative approaches based on classical local ...
Non-adiabatic study of the Kepler subgiant KIC 6442183
Grosjean M.
2015-01-01
Full Text Available Thanks to the precision of Kepler observations, [3] were able to measure the linewidth and amplitude of individual modes (including mixed modes in several subgiant power spectra. We perform a forward modelling of a Kepler subgiant based on surface properties and observed frequencies. Non-adiabatic computations including a time- dependent treatment of convection give the lifetimes of radial and non-radial modes. Next, combining the lifetimes and inertias with a stochastic excitation model gives the amplitudes of the modes. We can now directly compare theoretical and observed linewidths and amplitudes of mixed-modes to obtain new constraints on our theoretical models.
Landau-Zener Transitions in an Adiabatic Quantum Computer
Johansson, J; Amin, M. H. S.; Berkley, A. J.; Bunyk, P.; Choi, V.; Harris, R.; Johnson, M. W.; Lanting, T. M.; Lloyd, Seth; ROSE, G
2008-01-01
We report an experimental measurement of Landau-Zener transitions on an individual flux qubit within a multi-qubit superconducting chip designed for adiabatic quantum computation. The method used isolates a single qubit, tunes its tunneling amplitude Delta into the limit where Delta is much less than both the temperature T and the decoherence-induced energy level broadening, and forces it to undergo a Landau-Zener transition. We find that the behavior of the qubit agrees to a high degree of a...
Modeling of the Adiabatic and Isothermal Methanation Process
Porubova, Jekaterina; Bazbauers, Gatis; Markova, Darja
2011-01-01
Increased use of biomass offers one of the ways to reduce anthropogenic impact on the environment. Using various biomass conversion processes, it is possible to obtain different types of fuels: • solid, e.g. bio-carbon; • liquid, e.g. biodiesel and ethanol; • gaseous, e.g. biomethane. Biomethane can be used in the transport and energy sector, and the total methane production efficiency can reach 65%. By modeling adiabatic and isothermal methanation processes, the most effective one from the methane production point of view is defined. Influence of the process parameters on the overall efficiency of the methane production is determined.
Adiabatic transport of qubits around a black hole
Viennot, David
2016-01-01
We consider localized qubits evolving around a black hole following a quantum adiabatic dynamics. We develop a geometric structure (based on fibre bundles) permitting to describe the quantum states of a qubit and the spacetime geometry in a single framework. The quantum decoherence induced by the black hole on the qubit is analysed in this framework (the role of the dynamical and geometric phases in this decoherence is treated), especially for the quantum teleportation protocol when one qubit falls to the event horizon. A simple formula to compute the fidelity of the teleportation is derived. The case of a Schwarzschild black hole is analysed.
Numerical studies of optical forces from adiabatic rapid passage
Stack, Daniel; Elgin, John; Metcalf, Harold [Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800 (United States); Anisimov, Petr M. [Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)
2011-07-15
We present a numerical study of the properties of optical forces on moving atoms derived from purely stimulated processes produced by multiple adiabatic rapid-passage sequences. The optical Bloch equations are solved for a carefully timed sequence of frequency-swept pulses that can produce a force much larger than the ordinary radiative force. We describe the effects of the sweep range, peak intensity, sweep direction, number of pulses, atomic velocity, and spontaneous emission. Since the momentum of thermal atoms is much larger than that transferred by a single absorption-stimulated emission cycle, multiple repetitions are needed to make a significant velocity change.
Adiabatic quantum computation and quantum annealing theory and practice
McGeoch, Catherine C
2014-01-01
Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov
Adiabatic regularisation of power spectra in nonminimally coupled chaotic inflation
Alinea, Allan L
2016-01-01
We investigate the effect of adiabatic regularisation on both the tensor- and scalar-perturbation power spectra in \\textit{nonminimally} coupled chaotic inflation. Similar to that of the \\textit{minimally} coupled general single-field inflation, we find that the subtraction term is suppressed by an exponentially decaying factor involving the number of $ e $-folds. By following the subtraction term long enough beyond horizon crossing, the regularised power spectrum tends to the "bare" power spectrum. This study justifies the use of the unregularised ("bare") power spectrum in standard calculations.
Plasma heating via adiabatic magnetic compression-expansion cycle
Avinash, K.; Sengupta, M.; Ganesh, R.
2016-06-01
Heating of collisionless plasmas in closed adiabatic magnetic cycle comprising of a quasi static compression followed by a non quasi static constrained expansion against a constant external pressure is proposed. Thermodynamic constraints are derived to show that the plasma always gains heat in cycles having at least one non quasi static process. The turbulent relaxation of the plasma to the equilibrium state at the end of the non quasi static expansion is discussed and verified via 1D Particle in Cell (PIC) simulations. Applications of this scheme to heating plasmas in open configurations (mirror machines) and closed configurations (tokamak, reverse field pinche) are discussed.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Interacting boson approximation
Lectures notes on the Interacting Boson Approximation are given. Topics include: angular momentum tensors; properties of T/sub i//sup (n)/ matrices; T/sub i//sup (n)/ matrices as Clebsch-Gordan coefficients; construction of higher rank tensors; normalization: trace of products of two s-rank tensors; completeness relation; algebra of U(N); eigenvalue of the quadratic Casimir operator for U(3); general result for U(N); angular momentum content of U(3) representation; p-Boson model; Hamiltonian; quadrupole transitions; S,P Boson model; expectation value of dipole operator; S-D model: U(6); quadratic Casimir operator; an O(5) subgroup; an O(6) subgroup; properties of O(5) representations; quadratic Casimir operator; quadratic Casimir operator for U(6); decomposition via SU(5) chain; a special O(3) decomposition of SU(3); useful identities; a useful property of D/sub αβγ/(α,β,γ = 4-8) as coupling coefficients; explicit construction of T/sub x//sup (2)/ and d/sub αβγ/; D-coefficients; eigenstates of T3; and summary of T = 2 states
Quantum pumping in closed systems, adiabatic transport, and the Kubo formula
Cohen, Doron
2003-01-01
Quantum pumping in closed systems is considered. We explain that the Kubo formula contains all the physically relevant ingredients for the calculation of the pumped charge ($Q$) within the framework of linear response theory. The relation to the common formulations of adiabatic transport and ``geometric magnetism" is clarified. We distinguish between adiabatic and dissipative contributions to $Q$. On the one hand we observe that adiabatic pumping does not have to be quantized. On the other ha...
Adiabatic heavy-ion fusion potentials for fusion at deep sub-barrier energies
S V S Sastry; S Kailas; A K Mohanty; A Saxena
2005-01-01
The recently reported unusual behaviour of fusion cross-sections at extreme sub-barrier energies has been examined. The adiabatic limit of fusion barriers has been determined from experimental data using the barrier penetration model. These adiabatic barriers are consistent with the adiabatic fusion barriers derived from the modified Wilzynska–Wilzynski prescription. The fusion barrier systematics has been obtained for a wide range of heavy-ion systems.
Wójcik, P.; Zegrodnik, M.; Rzeszotarski, B.; Adamowski, J.
2016-09-01
The tunneling conductance through the half-metal/conical magnet/superconductor (HM/CM/SC) junctions is investigated with the use of the Bogoliubov-de Gennes equations in the framework of Blonder-Tinkham-Klapwijk formalism. Due to the spin band separation in the HM, the conductance in the subgap region is mainly determined by the anomalous Andreev reflection, the probability of which strongly depends on the spin transmission in the CM layer. We show that the spins of electrons injected from the HM can be transmitted through the CM to the SC either adiabatically or non-adiabatically depending on the period of the spatial modulation of the exchange field. We find that the conductance in the subgap region oscillates as a function of the CM layer thickness wherein the oscillations transform from the irregular pattern in the non-adiabatic regime to the regular one in the adiabatic regime. For both adiabatic and non-adiabatic transport regimes the conductance is studied over a broad range of parameters determining the spiral magnetization in the CM. We find that in the non-adiabatic regime, the decrease of the exchange field amplitude in the CM leads to the emergence of the conductance peak for the particular CM thickness in agreement with recent experiments.
Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems
Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants, i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results. (general)
Adiabatic regularization and particle creation for scalar and spin one-half fields
Landete, Aitor; Torrenti, Francisco
2013-01-01
The extension of the adiabatic regularization method to spin-$1/2$ fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-$1/2$ fields. We also provide a general overview of the adiabatic method to analyze particle creation and perform renormalization of relevant expectation values. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.
Adiabatic invariants in stellar dynamics, 3: Application to globular cluster evolution
Weinberg, Martin D.
1994-01-01
The previous two companion papers demonstrate that slowly varying perturbations may not result in adiabatic cutoffs and provide a formalism for computing the long-term effects of time-dependent perturbations on stellar systems. Here, the theory is implemented in a Fokker-Planck code and a suite of runs illustrating the effects of shock heating on globular cluster evolution are described. Shock heating alone results in considerable mass loss for clusters with R(sub g) less than or approximately 8 kpc: a concentration c = 1.5 cluster with R(sub g) kpc loses up to 95% of its initial mass in 15 Gyr. Only those with concentration c greater than or approximately 1.3 survive disk shocks inside of this radius. Other effects, such as mass loss by stellar evolution, will decrease this survival bound. Loss of the initial halo together with mass segregation leads to mass spectral indices, x, which may be considerably larger than their initial values.
Schedule path optimization for adiabatic quantum computing and optimization
Zeng, Lishan; Zhang, Jun; Sarovar, Mohan
2016-04-01
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are probabilistic in nature and the minimum gap between the ground state and first excited state of the system during evolution is a major factor in determining the success probability. In this work we investigate a strategy for increasing the minimum gap and success probability by introducing intermediate Hamiltonians that modify the evolution path between initial and final Hamiltonians. We focus on an optimization problem relevant to recent hardware implementations and present numerical evidence for the existence of a purely local intermediate Hamiltonian that achieve the optimum performance in terms of pushing the minimum gap to one of the end points of the evolution. As a part of this study we develop a convex optimization formulation of the search for optimal adiabatic schedules that makes this computation more tractable, and which may be of independent interest. We further study the effectiveness of random intermediate Hamiltonians on the minimum gap and success probability, and empirically find that random Hamiltonians have a significant probability of increasing the success probability, but only by a modest amount.
Stimulated Raman Adiabatic Passage (STIRAP) Among Degenerate-Level Manifolds
Kis, Z; Shore, B W; Vitanov, N V; Kis, Zsolt; Karpati, Attila; Shore, Bruce W.; Vitanov, Nikolay V.
2004-01-01
We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (g, e and f) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction (g - e) and to the Stokes-pulse interaction (e-f). We show that in general a sufficient condition for complete population removal from the g set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence g, e and f. We show that when this condition holds it is possible to achieve the degenerate counterpart of conventional STIRAP, whereby adiabatic passage produces complete population transfer. Indeed, the system is equivalent to a set of independent three-state systems, in each of which a STIRAP procedure can be implemented. We describe a scheme of unitary transformations that produces this result. We also examine the cases when this degeneracy constraint does not hold, and show what can be accomplished in those cases. For example, fo...
Adiabatic creation of coherent superposition states via multiple intermediate states
Karpati, A
2003-01-01
We consider an adiabatic population transfer process that resembles the well established stimulated Raman adiabatic passage (STIRAP). In our system, the states have nonzero angular momentums $J$, therefore, the coupling laser fields induce transitions among the magnetic sublevels of the states. In particular, we discuss the possibility of creating coherent superposition states in a system with coupling pattern $J=0\\Leftrightarrow J=1$ and $J=1\\Leftrightarrow J=2$. Initially, the system is in the J=0 state. We show that by two delayed, overlapping laser pulses it is possible to create any final superposition state of the magnetic sublevels $|2,-2>$, $|2,0>$, $|2,+2>$. Moreover, we find that the relative phases of the applied pulses influence not only the phases of the final superposition state but the probability amplitudes as well. We show that if we fix the shape and the time-delay between the pulses, the final state space can be entirely covered by varying the polarizations and relative phases of the two pu...
Optimization using quantum mechanics: quantum annealing through adiabatic evolution
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable time-dependent Hamiltonian, where 'ℎ' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toy-models-double-well potentials and other one-dimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schroedinger's evolutions, for the toy models, or path-integral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated non-trivial Landau-Zener tunnelling phenomena is discussed and emphasized. (topical review)
Observational tests of non-adiabatic Chaplygin gas
Carneiro, S
2014-01-01
In a previous paper it was shown that any dark sector model can be mapped into a non-adiabatic fluid formed by two interacting components, one with zero pressure and the other with equation-of-state parameter $\\omega = -1$. It was also shown that the latter does not cluster and, hence, the former is identified as the observed clustering matter. This guarantees that the dark matter power spectrum does not suffer from oscillations or instabilities. It applies in particular to the generalised Chaplygin gas, which was shown to be equivalent to interacting models at both background and perturbation levels. In the present paper we test the non-adiabatic Chaplygin gas against the Hubble diagram of type Ia supernovae, the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background and the linear power spectrum of large scale structures. We consider two different compilations of SNe Ia, namely the Constitution and SDSS samples, both calibrated with the MLCS2k2 fitter, and for the ...
The 0.1K bolometers cooled by adiabatic demagnetization
Roellig, T.; Lesyna, L.; Kittel, P.; Werner, M.
1983-01-01
The most straightforward way of reducing the noise equivalent power of bolometers is to lower their operating temperature. We have been exploring the possibility of using conventionally constructed bolometers at ultra-low temperatures to achieve NEP's suitable to the background environment of cooled space telescopes. We have chosen the technique of adiabatic demagnetization of a paramagnetic salt as a gravity independent, compact, and low power way to achieve temperatures below pumped He-3 (0.3 K). The demagnetization cryostat we used was capable of reaching temperatures below 0.08 K using Chromium Potassium Alum as a salt from a starting temperature of 1.5 K and a starting magnetic field of 30,000 gauss. Computer control of the magnetic field decay allowed a temperature of 0.2 K to be maintained to within 0.5 mK over a time period exceeding 14 hours. The refrigerator duty cycle was over 90 percent at this temperature. The success of these tests has motivated us to construct a more compact portable adiabatic demagnetization cryostat capable of bolometer optical tests and use at the 5m Hale telescope at 1mm wavelengths.
AB INITIO SIMULATIONS FOR MATERIAL PROPERTIES ALONG THE JUPITER ADIABAT
We determine basic thermodynamic and transport properties of hydrogen-helium-water mixtures for the extreme conditions along Jupiter's adiabat via ab initio simulations, which are compiled in an accurate and consistent data set. In particular, we calculate the electrical and thermal conductivity, the shear and longitudinal viscosity, and diffusion coefficients of the nuclei. We present results for associated quantities like the magnetic and thermal diffusivity and the kinematic shear viscosity along an adiabat that is taken from a state-of-the-art interior structure model. Furthermore, the heat capacities, the thermal expansion coefficient, the isothermal compressibility, the Grüneisen parameter, and the speed of sound are calculated. We find that the onset of dissociation and ionization of hydrogen at about 0.9 Jupiter radii marks a region where the material properties change drastically. In the deep interior, where the electrons are degenerate, many of the material properties remain relatively constant. Our ab initio data will serve as a robust foundation for applications that require accurate knowledge of the material properties in Jupiter's interior, e.g., models for the dynamo generation.
General background conditions for K-bounce and adiabaticity
Romano, Antonio Enea
2016-01-01
We study the background conditions for a bounce in a single scalar field model with a generalized kinetic term $K(X)$. At the background level we impose the existence of two turning points where the derivative of the Hubble parameter $H$ changes sign and of a bounce point where the Hubble parameter vanishes. We find the conditions for $K(X)$ and the potential which ensure the above requirements. We then give the examples of two models constructed according to these conditions. One is based on a quadratic $K$, and the other on a $K$ which is avoiding divergences of the second time derivative of the scalar field, which may otherwise occur. An appropriate choice of the initial conditions can lead to a sequence of consecutive bounces. In models where the bounce occurs when the potential is not constant, large non adiabatic perturbations are produced, which can in turn source the growth of anisotropies. In the region where these models have a constant potential they became adiabatic on any scale and because of thi...
On the Time Dependence of Adiabatic Particle Number
Dabrowski, Robert
2016-01-01
We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation. Naively, this is not a well-defined notion for such a non-equilibrium process, as the particle number at intermediate times depends on a basis choice of reference states with respect to which particles and anti-particles are defined, even though the final late-time particle number is independent of this basis choice. The basis choice is associated with a particular truncation of the adiabatic expansion. The adiabatic expansion is divergent, and we show that if this divergent expansion is truncated at its optimal order, a universal time dependence is obtained, confirming a general result of Dingle and Berry. This optimally truncated particle number provides a clear picture of quantum interference effects for perturbations with non-trivial temporal sub-structure. We illustrate the...
Schedule path optimization for adiabatic quantum computing and optimization
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are probabilistic in nature and the minimum gap between the ground state and first excited state of the system during evolution is a major factor in determining the success probability. In this work we investigate a strategy for increasing the minimum gap and success probability by introducing intermediate Hamiltonians that modify the evolution path between initial and final Hamiltonians. We focus on an optimization problem relevant to recent hardware implementations and present numerical evidence for the existence of a purely local intermediate Hamiltonian that achieve the optimum performance in terms of pushing the minimum gap to one of the end points of the evolution. As a part of this study we develop a convex optimization formulation of the search for optimal adiabatic schedules that makes this computation more tractable, and which may be of independent interest. We further study the effectiveness of random intermediate Hamiltonians on the minimum gap and success probability, and empirically find that random Hamiltonians have a significant probability of increasing the success probability, but only by a modest amount. (paper)
FRW-type cosmologies with adiabatic matter creation
Some properties of cosmological models with matter creation are investigated in the framework of the Friedmann-Robertson-Walker line element. For adiabatic matter creation, as developed by Prigogine and co-workers, we derive a simple expression relating the particle number density n and energy density ρ which holds regardless of the matter creation rate. The conditions to generate inflation are discussed and by considering the natural phenomenological matter creation rate ψ=3βnH, where β is a pure number of the order of unity and H is the Hubble parameter, a minimally modified hot big-bang model is proposed. The dynamic properties of such models can be deduced from the standard ones simply by replacing the adiabatic index γ of the equation of state by an effective parameter γ*=γ(1-β). The thermodynamic behavior is determined and it is also shown that ages large enough to agree with observations are obtained even given the high values of H suggested by recent measurements. copyright 1996 The American Physical Society
Graphical abstract: Two trajectories for the collision of a proton with the Lithium tetramer. On the left, the proton is scattered away, and a Li2 molecule plus two isolated Lithium atoms result. On the right, the proton is captured and a LiH molecule is created. Highlights: ► Scattering of a proton with Lithium clusters described from first principles. ► Description based on non-adiabatic molecular dynamics. ► The electronic structure is described with time-dependent density-functional theory. ► The method allows to discern reaction channels depending on initial parameters. - Abstract: We have employed non-adiabatic molecular dynamics based on time-dependent density-functional theory to characterize the scattering behavior of a proton with the Li4 cluster. This technique assumes a classical approximation for the nuclei, effectively coupled to the quantum electronic system. This time-dependent theoretical framework accounts, by construction, for possible charge transfer and ionization processes, as well as electronic excitations, which may play a role in the non-adiabatic regime. We have varied the incidence angles in order to analyze the possible reaction patterns. The initial proton kinetic energy of 10 eV is sufficiently high to induce non-adiabatic effects. For all the incidence angles considered the proton is scattered away, except in one interesting case in which one of the Lithium atoms captures it, forming a LiH molecule. This theoretical formalism proves to be a powerful, effective and predictive tool for the analysis of non-adiabatic processes at the nanoscale.
Dynamics of the 12C-12C system in the static molecular mean field approximation
The interaction between two 12C ions at low energy is investigated in the mean field (Hartree-Fock) approximation. The authors assume adiabaticity for the molecular motion and calculate the interaction energy by the constrained Hartree-Fock method, using the inderdistance d separating the two ions as the constrained quantity. This energy is calculated by using the Skyrme SIII force, without spin-orbit. (orig./AH)
Operators of Approximations and Approximate Power Set Spaces
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
Fuks, Johanna I
2014-01-01
We explore an asymmetric two-fermion Hubbard dimer to test the accuracy of the adiabatic approximation of time-dependent density functional theory in modelling time-resolved charge transfer. We show that the model shares essential features of a ground state long-range molecule in real-space, and by applying a resonant field we show that the model also reproduces essential traits of the CT dynamics. The simplicity of the model allows us to propagate with an "adiabatically-exact" approximation, i.e. one that uses the exact ground-state exchange-correlation functional, and compare with the exact propagation. This allows us to study the impact of the time-dependent charge-transfer step feature in the exact correlation potential of real molecules on the resulting dynamics. Tuning the parameters of the dimer allows a study both of charge-transfer between open-shell fragments and between closed-shell fragments. We find that the adiabatically-exact functional is unable to properly transfer charge, even in situations ...
Approximation algorithms and hardness of approximation for knapsack problems
Buhrman, H.; Loff, B.; Torenvliet, L.
2012-01-01
We show various hardness of approximation algorithms for knapsack and related problems; in particular we will show that unless the Exponential-Time Hypothesis is false, then subset-sum cannot be approximated any better than with an FPTAS. We also give a simple new algorithm for approximating knapsac
Approximate nonlinear self-adjointness and approximate conservation laws
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness. (paper)
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K2O2 is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period
Krix, David; Nienhaus, Hermann
2014-08-01
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K2O2 is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period.
Krix, David; Nienhaus, Hermann, E-mail: hermann.nienhaus@uni-due.de [Faculty of Physics, University of Duisburg-Essen and Center of Nanointegration Duisburg-Essen (CENIDE), Lotharstr. 1, D-47048 Duisburg (Germany)
2014-08-21
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K{sub 2}O{sub 2} is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period.
On the adiabatic stability of solitons and the matching of conservation laws
Lochak, Pierre
1984-08-01
We derive a series of identities which generalize and simplify the results obtained for adiabatically modulated solitons in the case of perturbed specific integrable equations. It stresses the importance of the variational properties of the solitons, which make an adiabatic theorem plausible. A precise conjecture is made and its validity discussed from different points of view.
A note on the non-adiabatic geometric phase and quantum computation
Blais, A
2003-01-01
We consider the non-adiabatic, or Aharonov-Anandan, geometric phase as a tool for intrinsically fault-tolerant quantum computation. While this phase seems to answer many of the issues related to the adiabatic version of the geometric gate, we show that it is not straightforward to implement and that it is sensitive to small errors.
$\\sigma $ -Approximately Contractible Banach Algebras
Momeni, M; Yazdanpanah, T.; Mardanbeigi, M. R.
2012-01-01
We investigate $\\sigma $ -approximate contractibility and $\\sigma $ -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where $\\sigma $ is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.
Reversibility and Adiabatic Computation Trading Time and Space for Energy
Li, Maozhen; Li, Ming; Vitanyi, Paul
1996-01-01
Future miniaturization and mobilization of computing devices requires energy parsimonious `adiabatic' computation. This is contingent on logical reversibility of computation. An example is the idea of quantum computations which are reversible except for the irreversible observation steps. We propose to study quantitatively the exchange of computational resources like time and space for irreversibility in computations. Reversible simulations of irreversible computations are memory intensive. Such (polynomial time) simulations are analysed here in terms of `reversible' pebble games. We show that Bennett's pebbling strategy uses least additional space for the greatest number of simulated steps. We derive a trade-off for storage space versus irreversible erasure. Next we consider reversible computation itself. An alternative proof is provided for the precise expression of the ultimate irreversibility cost of an otherwise reversible computation without restrictions on time and space use. A time-irreversibility tra...
Influence of coherent adiabatic excitation on femtosecond transient signals
Conde, A Peralta; Longarte, A
2016-01-01
The transient signals derived from femtosecond pump-probe experiments are analyzed in terms of the coherent evolution of the energy levels perturbed by the excitation pulse. The model system is treated as the sum of independent two-level subsystems that evolve adiabatically or are permanently excited, depending on the detuning from the central wavelength of the excitation laser. This approach will allow us to explain numerically and analytically the convergence between the coherent and incoherent (rate equations) treatments for complex multi-level systems. It will be also shown that the parameter that determines the validity of the incoherent treatment is the distribution of states outside and inside the laser bandwidth, rather than the density of states as it is commonly accepted.
Non-adiabatic perturbations in decaying vacuum cosmology
We investigate a spatially flat Friedmann-Lemaître-Robertson-Walker cosmology in which a decaying vacuum term causes matter production at late times. Assuming a decay proportional to the Hubble rate, the ratio of the background energy densities of dark matter and dark energy changes with the cosmic scale factor as a−3/2. The intrinsically non-adiabatic two-component perturbation dynamics of this model is reduced to a single second-order equation. Perturbations of the vacuum term are shown to be negligible on scales that are relevant for structure formation. On larger scales, dark-energy perturbations give a somewhat higher contribution but remain always smaller than the dark-matter perturbations
Adiabatic quantum-flux-parametron cell library adopting minimalist design
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits
Adiabatic quantum-flux-parametron cell library adopting minimalist design
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-05-01
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits.
Controlled Rapid Adiabatic Passage in a V-Type System
Song, Yunheung; Lee, Han-Gyeol; Jo, Hanlae; Ahn, Jaewook
2016-05-01
In chirped rapid adiabatic passage (RAP), chirp sign determines the final state to which the complete population transfer (CPT) occurs in a three-level V-type system. In this study, we show that laser intensity can be alternatively used as a control means in RAP, when the laser pulse is chirped and of a spectral hole resonant to one of the excited states. We verified such excitation selectivity in the experiment performed as-shaped femtosecond laser pulses interacting with the lowest three levels (5S, 5 P1/2, and 5 P3/2) of atomic rubidium. The successful demonstration implies that this intensity-dependent RAP in conjunction with laser beam profile programming may allow excitation selectivity for atoms or ions arranged in space.
Adiabatic quantum-flux-parametron cell library adopting minimalist design
Takeuchi, Naoki, E-mail: takeuchi-naoki-kx@ynu.jp [Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501 (Japan); Yamanashi, Yuki; Yoshikawa, Nobuyuki [Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501 (Japan); Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501 (Japan)
2015-05-07
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits.
Adiabatic Floquet model for the optical response in femtosecond filaments
Hofmann, Michael
2016-01-01
The standard model of femtosecond filamentation is based on phenomenological assumptions which suggest that the ionization-induced carriers can be treated as free according to the Drude model, while the nonlinear response of the bound carriers follows the all-optical Kerr effect. Here, we demonstrate that the additional plasma generated at a multiphoton resonance dominates the saturation of the nonlinear refractive index. Since resonances are not captured by the standard model, we propose a modification of the latter in which ionization enhancements can be accounted for by an ionization rate obtained from non-Hermitian Floquet theory. In the adiabatic regime of long pulse envelopes, this augmented standard model is in excellent agreement with direct quantum mechanical simulations. Since our proposal maintains the structure of the standard model, it can be easily incorporated into existing codes of filament simulation.
Properties of a two stage adiabatic demagnetization refrigerator
Fukuda, H.; Ueda, S.; Arai, R.; Li, J.; Saito, A. T.; Nakagome, H.; Numazawa, T.
2015-12-01
Currently, many space missions using cryogenic temperatures are being planned. In particular, high resolution sensors such as Transition Edge Sensors need very low temperatures, below 100 mK. It is well known that the adiabatic demagnetization refrigerator (ADR) is one of most useful tools for producing ultra-low temperatures in space because it is gravity independent. We studied a continuous ADR system consisting of 4 stages and demonstrated it could provide continuous temperatures around 100 mK. However, there was some heat leakage from the power leads which resulted in reduced cooling power. Our efforts to upgrade our ADR system are presented. We show the effect of using the HTS power leads and discuss a cascaded Carnot cycle consisting of 2 ADR units.
Adiabatic quantum pump in a zigzag graphene nanoribbon junction
张林
2015-01-01
The adiabatic electron transport is theoretically studied in a zigzag graphene nanoribbon (ZGNR) junction with two time-dependent pumping electric fields. By modeling a ZGNR p–n junction and applying the Keldysh Green’s function method, we find that a pumped charge current is flowing in the device at a zero external bias, which mainly comes from the photon-assisted tunneling process and the valley selection rule in an even-chain ZGNR junction. The pumped charge current and its ON and OFF states can be efficiently modulated by changing the system parameters such as the pumping frequency, the pumping phase difference, and the Fermi level. A ferromagnetic ZGNR device is also studied to generate a pure spin current and a fully polarized spin current due to the combined spin pump effect and the valley valve effect. Our finding might pave the way to manipulate the degree of freedom of electrons in a graphene-based electronic device.
Nucleon-deuteron scattering using the adiabatic projection method
Elhatisari, Serdar; Meißner, Ulf-G; Rupak, Gautam
2016-01-01
In this paper we discuss the adiabatic projection method, a general framework for scattering and reaction calculations on the lattice. We also introduce several new techniques developed to study nucleus-nucleus scattering and reactions on the lattice. We present technical details of the methods for large-scale problems. To estimate the systematic errors of the calculations we consider simple two-particle scattering on the lattice. Then we benchmark the accuracy and efficiency of the numerical methods by applying these to calculate fermion-dimer scattering in lattice effective field theory with and without a long-range Coulomb potential. The fermion-dimer calculations correspond to neutron-deuteron and proton-deuteron scattering in the spin-quartet channel at leading order in pionless effective field theory.
Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics
Hoover, W.G.
1980-05-28
Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility.
Cosmological consequences of an adiabatic matter creation process
Nunes, Rafael C
2016-01-01
In this paper we investigate the cosmological consequences of a continuous matter creation associated with the production of particles by the gravitational field acting on the quantum vacuum. To illustrate this, three phenomenological models are considered. An equivalent scalar field description is presented for each models. The effects on the cosmic microwave background power spectrum are analyzed for the first time in the context of adiabatic matter creation cosmology. Further, we introduce a model independent treatment, $Om$, which depends only on the Hubble expansion rate and the cosmological redshift to distinguish any cosmological model from $\\Lambda$CDM by providing a null test for the cosmological constant, meaning that, for any two redshifts $z_1$, $z_2$, $Om (z)$ is same, i.e. $Om (z_1)- Om (z_2)= 0$. Also, this diagnostic can differentiate between several cosmological models by indicating their quintessential/ phantom behavior without knowing the accurate value of the matter density, and the presen...
Optical waveguide device with an adiabatically-varying width
Watts; Michael R. , Nielson; Gregory N.
2011-05-10
Optical waveguide devices are disclosed which utilize an optical waveguide having a waveguide bend therein with a width that varies adiabatically between a minimum value and a maximum value of the width. One or more connecting members can be attached to the waveguide bend near the maximum value of the width thereof to support the waveguide bend or to supply electrical power to an impurity-doped region located within the waveguide bend near the maximum value of the width. The impurity-doped region can form an electrical heater or a semiconductor junction which can be activated with a voltage to provide a variable optical path length in the optical waveguide. The optical waveguide devices can be used to form a tunable interferometer (e.g. a Mach-Zehnder interferometer) which can be used for optical modulation or switching. The optical waveguide devices can also be used to form an optical delay line.
Some properties of adiabatic blast waves in preexisting cavities
Cox, D. P.; Franco, J.
1981-01-01
Cox and Anderson (1982) have conducted an investigation regarding an adiabatic blast wave in a region of uniform density and finite external pressure. In connection with an application of the results of the investigation to a study of interstellar blast waves in the very hot, low-density matrix, it was found that it would be desirable to examine situations with a positive radial density gradient in the ambient medium. Information concerning such situations is needed to learn about the behavior of blast waves occurring within preexisting, presumably supernova-induced cavities in the interstellar mass distribution. The present investigation is concerned with the first steps of a study conducted to obtain the required information. A review is conducted of Sedov's (1959) similarity solutions for the dynamical structure of any explosion in a medium with negligible pressure and power law density dependence on radius.
Adiabatic principles in atom-diatom collisional energy transfer
This work describes the application of numerical methods to the solution of the time dependent Schroedinger equation for non-reactive atom-diatom collisions in which only one of the degrees of freedom has been removed. The basic method involves expanding the wave function in a basis set in two of the diatomic coordinates in a body-fixed frame (with respect to the triatomic complex) and defining the coefficients in that expansion as functions on a grid in the collision coordinate. The wave function is then propagated in time using a split operator method. The bulk of this work is devoted to the application of this formalism to the study of internal rotational predissociation in NeHF, in which quasibound states of the triatom predissociate through the transfer of energy from rotation of the diatom into translational energy in the atom-diatom separation coordinate. The author analyzes the computed time dependent wave functions to calculate the lifetimes for several quasibound states; these are in agreement with time independent quantum calculations using the same potential. Moreover, the time dependent behavior of the wave functions themselves sheds light on the dynamics of the predissociation processes. Finally, the partial cross sections of the products in those processes is determined with multiple exit channels. These show strong selectivity in the orbital angular momentum of the outgoing fragments, which the author explains with an adiabatic channel interpretation of the wave function's dynamics. The author also suggests that the same formalism might profitably be used to investigate the quantum dynamics of open-quotes quasiresonant vibration-rotation transferclose quotes, in which remarkably strong propensity rules in certain inelastic atom-diatom collision arise from classical adiabatic invariance theory
Observational tests of non-adiabatic Chaplygin gas
Carneiro, S.; Pigozzo, C.
2014-10-01
In a previous paper [1] it was shown that any dark sector model can be mapped into a non-adiabatic fluid formed by two interacting components, one with zero pressure and the other with equation-of-state parameter ω = -1. It was also shown that the latter does not cluster and, hence, the former is identified as the observed clustering matter. This guarantees that the dark matter power spectrum does not suffer from oscillations or instabilities. It applies in particular to the generalised Chaplygin gas, which was shown to be equivalent to interacting models at both background and perturbation levels. In the present paper we test the non-adiabatic Chaplygin gas against the Hubble diagram of type Ia supernovae, the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background and the linear power spectrum of large scale structures. We consider two different compilations of SNe Ia, namely the Constitution and SDSS samples, both calibrated with the MLCS2k2 fitter, and for the power spectrum we use the 2dFGRS catalogue. The model parameters to be adjusted are the present Hubble parameter, the present matter density and the Chaplygin gas parameter α. The joint analysis best fit gives α ≈ - 0.5, which corresponds to a constant-rate energy flux from dark energy to dark matter, with the dark energy density decaying linearly with the Hubble parameter. The ΛCDM model, equivalent to α = 0, stands outside the 3σ confidence interval.
Observational tests of non-adiabatic Chaplygin gas
In a previous paper [1] it was shown that any dark sector model can be mapped into a non-adiabatic fluid formed by two interacting components, one with zero pressure and the other with equation-of-state parameter ω = -1. It was also shown that the latter does not cluster and, hence, the former is identified as the observed clustering matter. This guarantees that the dark matter power spectrum does not suffer from oscillations or instabilities. It applies in particular to the generalised Chaplygin gas, which was shown to be equivalent to interacting models at both background and perturbation levels. In the present paper we test the non-adiabatic Chaplygin gas against the Hubble diagram of type Ia supernovae, the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background and the linear power spectrum of large scale structures. We consider two different compilations of SNe Ia, namely the Constitution and SDSS samples, both calibrated with the MLCS2k2 fitter, and for the power spectrum we use the 2dFGRS catalogue. The model parameters to be adjusted are the present Hubble parameter, the present matter density and the Chaplygin gas parameter α. The joint analysis best fit gives α ≈ - 0.5, which corresponds to a constant-rate energy flux from dark energy to dark matter, with the dark energy density decaying linearly with the Hubble parameter. The ΛCDM model, equivalent to α = 0, stands outside the 3σ confidence interval
Adiabatic motion of charged dust grains in rotating magnetospheres
Dust grains in the ring systems and rapidly rotating magnetospheres of the outer planets such as Jupiter and Saturn may be sufficiently charged that the magnetic and electric forces on them are comparable with the gravitational force. The adiabatic theory of charged particle motion has previously been applied to electrons and atomic size particles. But it is also applicable to these charged dust grains in the micrometer and smaller size range. We derive here the guiding center equation of motion, drift velocity, and parallel equation of motion for these grains in a rotating magnetosphere. The effects of periodic grain charge-discharge have not been treated previously and have been included in this analysis. Grain charge is affected by the surrounding plasma properties and by the grain plasma velocity (among other factors), both of which may vary over the gyrocircle. The resulting charge-discharge process at the gyrofrequency destroys the invariance of the magnetic moment and causes a grain to move radially. The magnetic moment may increase or decrease, depending on the gyrophase of the charge variation. If it decreases, the motion is always toward synchronous radius for an equatorial grain. But the orbit becomes circular before the grain reaches synchronous radius, a conclusion that follows from an exact constant of the motion. This circularization can be viewed as a consequence of the gradual reduction in the magnetic moment. This circularization also suggests that dust grains leaving Io could not reach the region of the Jovian ring, but several effects could change that conclusion. Excellent qualitative and quantitative agreement is obtained between adiabatic theory and detailed numerical orbit integrations
Observational tests of non-adiabatic Chaplygin gas
Carneiro, S.; Pigozzo, C., E-mail: saulo.carneiro@pq.cnpq.br, E-mail: cpigozzo@ufba.br [Instituto de Física, Universidade Federal da Bahia, Campus de Ondina, Salvador, BA 40210-340 (Brazil)
2014-10-01
In a previous paper [1] it was shown that any dark sector model can be mapped into a non-adiabatic fluid formed by two interacting components, one with zero pressure and the other with equation-of-state parameter ω = -1. It was also shown that the latter does not cluster and, hence, the former is identified as the observed clustering matter. This guarantees that the dark matter power spectrum does not suffer from oscillations or instabilities. It applies in particular to the generalised Chaplygin gas, which was shown to be equivalent to interacting models at both background and perturbation levels. In the present paper we test the non-adiabatic Chaplygin gas against the Hubble diagram of type Ia supernovae, the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background and the linear power spectrum of large scale structures. We consider two different compilations of SNe Ia, namely the Constitution and SDSS samples, both calibrated with the MLCS2k2 fitter, and for the power spectrum we use the 2dFGRS catalogue. The model parameters to be adjusted are the present Hubble parameter, the present matter density and the Chaplygin gas parameter α. The joint analysis best fit gives α ≈ - 0.5, which corresponds to a constant-rate energy flux from dark energy to dark matter, with the dark energy density decaying linearly with the Hubble parameter. The ΛCDM model, equivalent to α = 0, stands outside the 3σ confidence interval.
Thermodynamic study of ibuprofen by adiabatic calorimetry and thermal analysis
Molar heat capacities of ibuprofen were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 80 to 400 K. The polynomial functions of Cp,m (J K-1 mol-1) versus T were established on the heat capacity measurements by means of the least fitting square method. The functions are as follows: for solid ibuprofen, at the temperature range of 79.105 K≤T≤333.297 K, Cp,m=144.27+77.046X+3.5171X2+10.925X3+11.224X4, where X=(T-206.201)/127.096; for liquid ibuprofen, at the temperature range of 353.406 K≤T≤378.785 K, Cp,m=325.79+8.9696X-1.6073X2-1.5145X3, where X=(T-366.095)/12.690. A fusion transition at T=348.02 K was found from the Cp-T curve. The molar enthalpy and entropy of the fusion transition were determined to be 26.65 kJ mol-1 and 76.58 J mol-1 K-1, respectively. The thermodynamic functions on the base of the reference temperature of 298.15 K, (HT-H298.15) and (ST-S298.15), were derived. Thermal characteristic of ibuprofen was studied by thermo-gravimetric analysis (TG-DTG) and differential scanning calorimeter (DSC). The temperature of fusion, the molar enthalpy and entropy of fusion obtained by DSC were well consistent with those obtained by adiabatic calorimeter. The evaporation process of ibuprofen was investigated further by TG and DTG, and the activation energy of the evaporation process was determined to be 80.3±1.4 kJ mol-1
Correlated adiabatic and isocurvature CMB fluctuations in the wake of WMAP
Valiviita, J; Valiviita, Jussi; Muhonen, Vesa
2003-01-01
In the general correlated models, in addition to the usual adiabatic component with a spectral index n_ad1 there is another adiabatic component with a spectral index n_ad2 generated by the entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature CMB fluctuations of the WMAP group, who set the two adiabatic spectral indices equal. Allowing n_ad1 and n_ad2 to vary independently we find that the WMAP data favor models where the two adiabatic components have opposite spectral tilts. Using the WMAP data only, the 2-sigma upper bound for the isocurvature fraction f_iso of the initial power spectrum at k_0=0.05 Mpc^{-1} increases somewhat, e.g., from 0.76 of n_ad2 = n_ad1 models to 0.84 with a prior n_iso < 1.84 for the isocurvature spectral index.
On the observability and asymmetry of adiabatic state flips generated by exceptional points
Uzdin, Raam; Moiseyev, Nimrod [Physics Department and Minerva Center for Nonlinear Physics of Complex Systems, Technion-Israel Institute of Technology (Israel); Mailybaev, Alexei, E-mail: raam@technion.ac.il [Institute of Mechanics, Lomonosov Moscow State University (Russian Federation)
2011-10-28
In open quantum systems where the effective Hamiltonian is not Hermitian, it is known that the adiabatic (or instantaneous) basis can be multivalued: by adiabatically transporting an eigenstate along a closed loop in the parameter space of the Hamiltonian, it is possible to end up in an eigenstate different from the initial eigenstate. This 'adiabatic flip' effect is an outcome of the appearance of a degeneracy known as an 'exceptional point' inside the loop. We show that contrary to what is expected of the transport properties of the eigenstate basis, the interplay between gain/loss and non-adiabatic couplings imposes fundamental limitations on the observability of this adiabatic flip effect. (paper)
Stimulated Raman adiabatic passage in a three-level superconducting circuit
Kumar, K. S.; Vepsäläinen, A.; Danilin, S.; Paraoanu, G. S.
2016-02-01
The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering--enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic-adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level.
Approximation by planar elastic curves
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2015-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Approximate sine-Gordon solitons
Stratopoulos, G.N. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom)); Zakrzewski, W.J. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom))
1993-08-01
We look at the recently proposed scheme of approximating a sine-Gordon soliton by an expression derived from two dimensional instantons. We point out that the scheme of Sutcliffe in which he uses two dimensional instantons can be generalised to higher dimensions and that these generalisations produce even better approximations than the original approximation. We also comment on generalisations to other models. (orig.)
Frimurer, Thomas M.; Günther, Peter H.; Sørensen, Morten Dahl;
1999-01-01
adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)......adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)...
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Buchachenko, A. A.; Stolyarov, A. V.; Szczȩśniak, M. M.; Chałasiński, G.
2012-09-01
The coefficients at the lowest-order electrostatic, induction, and dispersion terms of the anisotropic long-range potential between the two KRb(1Σ+) molecules are evaluated through the static and dynamic molecular properties using the ab initio coupled cluster techniques. Adiabatic channel potentials for the ground-state molecules are obtained and used for the numerical quantum capture probability calculations in the spirit of the statistical adiabatic channel models. Capture rate coefficients for indistinguishable (polarized) and distinguishable (unpolarized) molecules at temperatures below 10 μK agree well with those computed with the simple isotropic dispersion R-6 potential, but underestimate the measured ones [Ospelkaus et al., Science 327, 853 (2010), 10.1126/science.1184121] up to a factor of 3. Preliminary assessment of the effects of higher-order long-range terms, retardation of dispersion forces, and magnetic dipole-dipole interaction does not offer any clear perspectives for drastic improvement of the capture approximation for the reactions studied.
Bellan, Paul; Wongwaitayakornkul, Pakorn; Chai, Kil-Byoung; Greig, Amelia; Li, Hui
2015-11-01
Magnetized inertial fusion (MIF) is based on having an imploding liner adiabatically compress a magnetized plasma to the density and temperature required for thermonuclear fusion. The goal of the Caltech research program is to determine the scaling of the temperature and density increase when an actual experimental plasma is adiabatically compressed. The plasma parameters will be more modest than a fusion-grade configuration, but in compensation, the shot repetition rate will be much higher and the experiments will be non-destructive. The non-destructive feature results from having a high-speed magnetized plasma jet impact a localized heavy gas. From the point of view of an observer in the frame of the magnetized plasma jet, it will look as if the heavy gas is impacting and compressing the magnetized plasma and so, except for some geometrical differences, the configuration is equivalent to a liner impacting and compressing a stationary magnetized plasma. The experiment will be modeled by 3D numerical MHD and PIC codes. (as of approximately September 15).
Theory of magnetohydrodynamic waves: The WKB approximation revisited
Past treatments of the eikonal or WKB theory of the propagation of magnetohydrodynamics waves have assumed a strictly isentropic background. IF in fact there is a gradient in the background entropy, then in second order in the WKB ordering, adiabatic fluctuations (in the Lagrangian sense) are not strictly isentropic in the Eulerian sense. This means that in the second order of the WKB expansion, which determines the variation of wave amplitude along rays, the violation of isentropy must be accounted for. The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments
Bond charge approximation for valence electron density in elemental semiconductors
The spatial valence electron distribution in silicon and diamond is calculated in adiabatic bond charge approximation at zero temperature when bond charges have the Gaussian shape and their tensor character is taken into account. An agreement between theory and experiment has been achieved. For this purpose Xia's ionic pseudopotentials and Schulze-Unger's dielectric function are used. By two additional parameters Asub(B) and Zsub(B)sup(') we describe the spatial extent of the bond charge and local-field corrections, respectively. The parameter Zsub(B)sup(') accounts for the ratio between the Coulomb and exchange correlation interactions of the valence electrons and its silicon and diamond values have different signs. (author)
Systematic investigations of deep sub-barrier fusion reactions using an adiabatic approach
Ichikawa, Takatoshi
2015-01-01
To describe fusion hindrance observed in fusion reactions at extremely low incident energies, I propose a novel extension of the standard CC model by introducing a damping factor that describes a smooth transition from sudden to adiabatic processes. I demonstrate the performance of this model by systematically investigating various deep sub-barrier fusion reactions. I extend the standard CC model by introducing a damping factor into the coupling matrix elements in the standard CC model. I adopt the Yukawa-plus-exponential (YPE) model as a basic heavy ion-ion potential, which is advantageous for a unified description of the one- and two-body potentials. For the purpose of these systematic investigations, I approximate the one-body potential with a third-order polynomial function based on the YPE model. Calculated fusion cross sections for the medium-heavy mass systems of $^{64}$Ni + $^{64}$Ni, $^{58}$Ni + $^{58}$Ni, and $^{58}$Ni + $^{54}$Fe, the medium-light mass systems of $^{40}$Ca + $^{40}$Ca, $^{48}$Ca + ...
Extended adiabatic blast waves and a model of the soft X-ray background
Cox, D. P.; Anderson, P. R.
1982-01-01
The suggestion has been made that much of the soft X-ray background observed in X-ray astronomy might arise from being inside a very large supernova blast wave propagating in the hot, low-density component of the interstellar (ISM) medium. An investigation is conducted to study this possibility. An analytic approximation is presented for the nonsimilar time evolution of the dynamic structure of an adiabatic blast wave generated by a point explosion in a homogeneous ambient medium. A scheme is provided for evaluating the electron-temperature distribution for the evolving structure, and a procedure is presented for following the state of a given fluid element through the evolving dynamical and thermal structures. The results of the investigation show that, if the solar system were located within a blast wave, the Wisconsin soft X-ray rocket payload would measure the B and C band count rates that it does measure, provided conditions correspond to the values calculated in the investigation.
Approximate solutions for the skyrmion
Ponciano, J A; Fanchiotti, H; Canal-Garcia, C A
2001-01-01
We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate analytical solutions. We show that Pade approximants are well suited to continue analytically the asymptotic representation obtained in terms of a power series expansion near the origin, obtaining explicit approximate solutions for the Skyrme equations. We improve the approximations by applying the 2-point Pade approximant procedure whereby the exact behaviour at spatial infinity is incorporated. An even better convergence to the exact solution is obtained by introducing a modified form for the approximants. The new representations share the same analytical properties with the exact solution at both small and large values of the radial variable r.
The Smoothed Approximate Linear Program
Desai, V V; Moallemi, C C
2009-01-01
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program--the `smoothed approximate linear program'--is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate substantially superior bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. Second, experiments with our approach on a challenging problem (the game of Tetris) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several AD...
Energy-Efficient and Secure S-Box circuit using Symmetric Pass Gate Adiabatic Logic
Kumar, Dinesh [University of Kentucky, Lexington; Mohammad, Azhar [University of Kentucky, Lexington; Singh, Vijay [University of Kentucky, Lexington; Perumalla, Kalyan S [ORNL
2016-01-01
Differential Power Analysis (DPA) attack is considered to be a main threat while designing cryptographic processors. In cryptographic algorithms like DES and AES, S-Box is used to indeterminate the relationship between the keys and the cipher texts. However, S-box is prone to DPA attack due to its high power consumption. In this paper, we are implementing an energy-efficient 8-bit S-Box circuit using our proposed Symmetric Pass Gate Adiabatic Logic (SPGAL). SPGAL is energy-efficient as compared to the existing DPAresistant adiabatic and non-adiabatic logic families. SPGAL is energy-efficient due to reduction of non-adiabatic loss during the evaluate phase of the outputs. Further, the S-Box circuit implemented using SPGAL is resistant to DPA attacks. The results are verified through SPICE simulations in 180nm technology. SPICE simulations show that the SPGAL based S-Box circuit saves upto 92% and 67% of energy as compared to the conventional CMOS and Secured Quasi-Adiabatic Logic (SQAL) based S-Box circuit. From the simulation results, it is evident that the SPGAL based circuits are energy-efficient as compared to the existing DPAresistant adiabatic and non-adiabatic logic families. In nutshell, SPGAL based gates can be used to build secure hardware for lowpower portable electronic devices and Internet-of-Things (IoT) based electronic devices.
Song, Chuan-Jing; Zhang, Yi
2015-08-01
For El-Nabulsi's fractional Birkhoff system, Mei symmetry perturbation, the corresponding Mei-type adiabatic invariants and Noether-type adiabatic invariants are investigated in this paper. Firstly, based on El-Nabulsi-Birkhoff fractional equations, Mei symmetry and the corresponding Mei conserved quantity, Noether conserved quantity deduced indirectly by Mei symmetry are studied. Secondly, Mei-type exact invariants and Noether-type exact invariants are given on the basis of the definition of adiabatic invatiant. Thirdly, Mei symmetry perturbation, Mei-type adiabatic invariants and Noether-type adiabatic invariants for the disturbed El-Nabulsi's fractional Birkhoff system are studied. Finally, two examples, Hojman-Urrutia problem for Mei-type adiabatic invariants and another for the Noether-type adiabatic invariants, are given to illustrate the application of the results. Supported by the National Natural Science Foundation of China under Grant Nos. 10972151 and 11272227, and the Innovation Program for Scientific Research of Nanjing University of Science and Technology
The growth of dry convection in the conditionally stable troposphere: Non-adiabatic effects
Kherani, E A; Sobral, J H A
2014-01-01
In this work, we study the growth characteristics of the convective instability (CI) in the dry troposphere by relaxing the adiabatic compressibility condition of Oberbeck-Boussinesq (OB) approach. We derive a new non-adiabatic-Boussinesq (NAB) expression for the modified Brunt-Vaisala frequency $(\\omega_b)$, without considering the adiabatic compressibility condition of OB approach. This NAB expression reduces to the known Oberbeck-Boussinesq (OB) expression under adiabatic compressibility condition. The NAB expression of $\\omega_b$ is found to be modified from its OB counterpart such that the stabilizing adiabatic lapse rate in OB expression is replaced by a modified non-adiabatic lapse rate given as $\\left(\\eta - 1 \\right)$ times the auto-convective lapse rate. Here $\\eta$ is the ratio of hydrostatic density to the total density. We perform numerical experiments of CI for the conditionally stable troposphere i.e for the troposphere that has the environmental lapse rate negative but smaller than the adiabat...
Approximate Grammar for Information Extraction
Sriram, V; Reddy, B. Ravi Sekar; Sangal, R.
2003-01-01
In this paper, we present the concept of Approximate grammar and how it can be used to extract information from a documemt. As the structure of informational strings cannot be defined well in a document, we cannot use the conventional grammar rules to represent the information. Hence, the need arises to design an approximate grammar that can be used effectively to accomplish the task of Information extraction. Approximate grammars are a novel step in this direction. The rules of an approximat...
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
Stottmeister, Alexander
2015-01-01
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework, and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g. spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article, and its companion, affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).
Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
Stottmeister, Alexander; Thiemann, Thomas
2016-06-01
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).
Ahmadi, H; Maghari, A
2016-01-01
The underlying physics behind the molecular harmonic emission in relatively long sin$^2$-like laser pulses is investigated. We numerically solved the full-dimensional electronic time-dependent Schr\\"{o}dinger equation beyond the Born-Oppenheimer approximation for simple molecular ion H$_2^+$. The occurrence and the effect of electron localization, non-adiabatic redshift and spatially asymmetric emission are evaluated to understand better complex patterns appearing in the high-order harmonic generation (HHG) spectrum. Results show that the complex patterns in the HHG spectrum originate mainly from a non-adiabatic response of the molecule to the rapidly changing laser field and also from a spatially asymmetric emission along the polarization direction. The effect of electron localization on the HHG spectrum was not observed as opposed to what is reported in the literature.
Thermodynamic study of ibuprofen by adiabatic calorimetry and thermal analysis
Xu Fen; Sun Lixian; Tan Zhicheng; Liang Jianguo; Li Ruilian
2004-03-23
Molar heat capacities of ibuprofen were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 80 to 400 K. The polynomial functions of C{sub p,m} (J K{sup -1} mol{sup -1}) versus T were established on the heat capacity measurements by means of the least fitting square method. The functions are as follows: for solid ibuprofen, at the temperature range of 79.105 K{<=}T{<=}333.297 K, C{sub p,m}=144.27+77.046X+3.5171X{sup 2}+10.925X{sup 3}+11.224X{sup 4}, where X=(T-206.201)/127.096; for liquid ibuprofen, at the temperature range of 353.406 K{<=}T{<=}378.785 K, C{sub p,m}=325.79+8.9696X-1.6073X{sup 2}-1.5145X{sup 3}, where X=(T-366.095)/12.690. A fusion transition at T=348.02 K was found from the C{sub p}-T curve. The molar enthalpy and entropy of the fusion transition were determined to be 26.65 kJ mol{sup -1} and 76.58 J mol{sup -1} K{sup -1}, respectively. The thermodynamic functions on the base of the reference temperature of 298.15 K, (H{sub T}-H{sub 298.15}) and (S{sub T}-S{sub 298.15}), were derived. Thermal characteristic of ibuprofen was studied by thermo-gravimetric analysis (TG-DTG) and differential scanning calorimeter (DSC). The temperature of fusion, the molar enthalpy and entropy of fusion obtained by DSC were well consistent with those obtained by adiabatic calorimeter. The evaporation process of ibuprofen was investigated further by TG and DTG, and the activation energy of the evaporation process was determined to be 80.3{+-}1.4 kJ mol{sup -1}.
Milovich, J. L.; Robey, H. F.; Clark, D. S.; Baker, K. L.; Casey, D. T.; Cerjan, C.; Field, J.; MacPhee, A. G.; Pak, A.; Patel, P. K.; Peterson, J. L.; Smalyuk, V. A.; Weber, C. R.
2015-12-01
Experimental results from indirectly driven ignition implosions during the National Ignition Campaign (NIC) [M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013)] achieved a record compression of the central deuterium-tritium fuel layer with measured areal densities up to 1.2 g/cm2, but with significantly lower total neutron yields (between 1.5 × 1014 and 5.5 × 1014) than predicted, approximately 10% of the 2D simulated yield. An order of magnitude improvement in the neutron yield was subsequently obtained in the "high-foot" experiments [O. A. Hurricane et al., Nature 506, 343 (2014)]. However, this yield was obtained at the expense of fuel compression due to deliberately higher fuel adiabat. In this paper, the design of an adiabat-shaped implosion is presented, in which the laser pulse is tailored to achieve similar resistance to ablation-front instability growth, but with a low fuel adiabat to achieve high compression. Comparison with measured performance shows a factor of 3-10× improvement in the neutron yield (>40% of predicted simulated yield) over similar NIC implosions, while maintaining a reasonable fuel compression of >1 g/cm2. Extension of these designs to higher laser power and energy is discussed to further explore the trade-off between increased implosion velocity and the deleterious effects of hydrodynamic instabilities.
Agostini, Federica; Suzuki, Yasumitsu; Gross, E K U
2013-01-01
The exact nuclear time-dependent potential energy surface arises from the exact decomposition of electronic and nuclear motion, recently presented in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Such time-dependent potential drives nuclear motion and fully accounts for the coupling to the electronic subsystem. We investigate the features of the potential in the context of electronic non-adiabatic processes and employ it to study the performance of the classical approximation on nuclear dynamics. We observe that the potential, after the nuclear wave-packet splits at an avoided crossing, develops dynamical steps connecting different regions, along the nuclear coordinate, in which it has the same slope as one or the other adiabatic surface. A detailed analysis of these steps is presented for systems with different non-adiabatic coupling strength. The exact factorization of the electron-nuclear wave-function is at the basis of the decomposition. In particular, the nuclear par...
Milovich, J. L., E-mail: milovich1@llnl.gov; Robey, H. F.; Clark, D. S.; Baker, K. L.; Casey, D. T.; Cerjan, C.; Field, J.; MacPhee, A. G.; Pak, A.; Patel, P. K.; Peterson, J. L.; Smalyuk, V. A.; Weber, C. R. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
2015-12-15
Experimental results from indirectly driven ignition implosions during the National Ignition Campaign (NIC) [M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013)] achieved a record compression of the central deuterium-tritium fuel layer with measured areal densities up to 1.2 g/cm{sup 2}, but with significantly lower total neutron yields (between 1.5 × 10{sup 14} and 5.5 × 10{sup 14}) than predicted, approximately 10% of the 2D simulated yield. An order of magnitude improvement in the neutron yield was subsequently obtained in the “high-foot” experiments [O. A. Hurricane et al., Nature 506, 343 (2014)]. However, this yield was obtained at the expense of fuel compression due to deliberately higher fuel adiabat. In this paper, the design of an adiabat-shaped implosion is presented, in which the laser pulse is tailored to achieve similar resistance to ablation-front instability growth, but with a low fuel adiabat to achieve high compression. Comparison with measured performance shows a factor of 3–10× improvement in the neutron yield (>40% of predicted simulated yield) over similar NIC implosions, while maintaining a reasonable fuel compression of >1 g/cm{sup 2}. Extension of these designs to higher laser power and energy is discussed to further explore the trade-off between increased implosion velocity and the deleterious effects of hydrodynamic instabilities.
Berman, G P; Tsifrinovich, V I
2004-01-01
We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schrodinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.
Intrinsic Heating and Cooling in Adiabatic Processes for Bosons in Optical Lattices
We show that by raising the lattice ''adiabatically'' as in many current optical lattice experiments on bosons, even though the temperature may decrease initially, it will eventually rise linearly with lattice height, taking the system farther away from quantum degeneracy. This increase has nothing to do with the entropy of the bulk Mott phase and is caused by the adiabatic compression of the mobile atoms between Mott layers. Our studies show that one can reverse the temperature rise to reach quantum degeneracy by adiabatic expansion, which can be achieved by a variety of methods
Avron, Joseph
2016-01-01
We derive the relativistically exact Eikonal equation for ring interferometers undergoing adiabatic deformations. The leading term in the adiabatic expansion of the phase shift is independent of the refraction index $n$ and is given by a line integral generalizing results going back to Sagnac to all orders in $\\beta$. The next term in the adiabaticity is of lower order in $\\beta$ and may be as important as the first in nonrelativistic cases. This term is proportional to $n^2$ and has the form of a double integral. It generalizes previous results to fibers with chromatic dispersion and puts Sagnac and Fizeau interferometers under a single umbrella.
Regnier, D; Schunck, N; Verriere, M
2016-01-01
Accurate knowledge of fission fragment yields is an essential ingredient of numerous applications ranging from the formation of elements in the r-process to fuel cycle optimization for nuclear energy. The need for a predictive theory applicable where no data is available is an incentive to develop a fully microscopic approach to fission dynamics. In this work, we calculate the pre-neutron emission charge and mass distributions of the fission fragments formed in the neutron-induced fission of 239Pu using a microscopic method based on nuclear energy density functional (EDF) method, where large amplitude collective motion is treated adiabatically using the time dependent generator coordinate method (TDGCM) under the Gaussian overlap approximation (GOA). Fission fragment distributions are extracted from the flux of the collective wave packet through the scission line. We find that the main characteristics of the fission charge and mass distributions can be well reproduced by existing energy functionals even in tw...
Ting, M; Rugar, D; Yip, C Y; Fessler, J A
2003-01-01
Magnetic Resonance Force Microscopy (MRFM) is an emergent technology for measuring spin-induced attonewton forces using a micromachined cantilever. In the interrupted Oscillating Cantilever-driven Adiabatic Reversal (iOSCAR) method, small ensembles of electron spins are manipulated by an external radio frequency (RF) magnetic field to produce small periodic deviations in the resonant frequency of the cantilever. These deviations can be detected by frequency demodulation, followed by conventional amplitude or energy detection. In this paper, we develop optimal detectors for several signal models that have been hypothesized for measurements induced by iOSCAR spin manipulation. We show that two simple variants of the energy detector--the filtered energy detector and a hybrid filtered energy/amplitude/energy detector--are approximately asymptotically optimal for the Discrete-Time (D-T) random telegraph signal model assuming White Gaussian Noise (WGN). For the D-T random walk signal model, the filtered energy dete...
Matrix-Free Approximate Equilibration
Bradley, Andrew M.; Murray, Walter
2011-01-01
The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be approximate. We develop approximate equilibration algorithms for nonsymmetric and symmetric matrices having signed elements that access a matrix only by matrix-vector products.
Development of a semi-adiabatic isoperibol solution calorimeter
Venkata Krishnan, R.; Jogeswararao, G.; Parthasarathy, R.; Premalatha, S.; Prabhakar Rao, J.; Gunasekaran, G.; Ananthasivan, K., E-mail: asivan@igcar.gov.in [Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu (India)
2014-12-15
A semi-adiabatic isoperibol solution calorimeter has been indigenously developed. The measurement system comprises modules for sensitive temperature measurement probe, signal processing, data collection, and joule calibration. The sensitivity of the temperature measurement module was enhanced by using a sensitive thermistor coupled with a lock-in amplifier based signal processor. A microcontroller coordinates the operation and control of these modules. The latter in turn is controlled through personal computer (PC) based custom made software developed with LabView. An innovative summing amplifier concept was used to cancel out the base resistance of the thermistor. The latter was placed in the dewar. The temperature calibration was carried out with a standard platinum resistance (PT100) sensor coupled with an 8½ digit multimeter. The water equivalent of this calorimeter was determined by using electrical calibration with the joule calibrator. The experimentally measured values of the quantum of heat were validated by measuring heats of dissolution of pure KCl (for endotherm) and tris (hydroxyl methyl) amino-methane (for exotherm). The uncertainity in the measurements was found to be within ±3%.
Cosmological consequences of an adiabatic matter creation process
Nunes, Rafael C.; Pan, Supriya
2016-06-01
In this paper, we investigate the cosmological consequences of a continuous matter creation associated with the production of particles by the gravitational field acting on the quantum vacuum. To illustrate this, three phenomenological models are considered. An equivalent scalar field description is presented for each models. The effects on the cosmic microwave background power spectrum are analysed for the first time in the context of adiabatic matter creation cosmology. Further, we introduce a model independent treatment, Om, which depends only on the Hubble expansion rate and the cosmological redshift to distinguish any cosmological model from Λ cold dark matter by providing a null test for the cosmological constant, meaning that, for any two redshifts z1, z2, Om(z) is same, i.e. Om(z1) - Om(z2) = 0. Also, this diagnostic can differentiate between several cosmological models by indicating their quintessential/phantom behaviour without knowing the accurate value of the matter density, and the present value of the Hubble parameter. For our models, we find that particle production rate is inversely proportional to Om. Finally, the validity of the generalized second law of thermodynamics bounded by the apparent horizon has been examined.
Adiabatic photo-steering theory in topological insulators
Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane–Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed. (focus issue review)
Development of a semi-adiabatic isoperibol solution calorimeter
A semi-adiabatic isoperibol solution calorimeter has been indigenously developed. The measurement system comprises modules for sensitive temperature measurement probe, signal processing, data collection, and joule calibration. The sensitivity of the temperature measurement module was enhanced by using a sensitive thermistor coupled with a lock-in amplifier based signal processor. A microcontroller coordinates the operation and control of these modules. The latter in turn is controlled through personal computer (PC) based custom made software developed with LabView. An innovative summing amplifier concept was used to cancel out the base resistance of the thermistor. The latter was placed in the dewar. The temperature calibration was carried out with a standard platinum resistance (PT100) sensor coupled with an 8½ digit multimeter. The water equivalent of this calorimeter was determined by using electrical calibration with the joule calibrator. The experimentally measured values of the quantum of heat were validated by measuring heats of dissolution of pure KCl (for endotherm) and tris (hydroxyl methyl) amino-methane (for exotherm). The uncertainity in the measurements was found to be within ±3%
Adiabatic quantum pump in a zigzag graphene nanoribbon junction
Zhang, Lin
2015-11-01
The adiabatic electron transport is theoretically studied in a zigzag graphene nanoribbon (ZGNR) junction with two time-dependent pumping electric fields. By modeling a ZGNR p-n junction and applying the Keldysh Green’s function method, we find that a pumped charge current is flowing in the device at a zero external bias, which mainly comes from the photon-assisted tunneling process and the valley selection rule in an even-chain ZGNR junction. The pumped charge current and its ON and OFF states can be efficiently modulated by changing the system parameters such as the pumping frequency, the pumping phase difference, and the Fermi level. A ferromagnetic ZGNR device is also studied to generate a pure spin current and a fully polarized spin current due to the combined spin pump effect and the valley valve effect. Our finding might pave the way to manipulate the degree of freedom of electrons in a graphene-based electronic device. Project supported by the National Natural Science Foundation of China (Grant No. 110704033), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010416), and the Natural Science Foundation for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140005).
When an adiabatic irreversible expansion or compression becomes reversible
This paper aims to contribute to a better understanding of the concepts of a reversible process and entropy. For this purpose, an adiabatic irreversible expansion or compression is analysed, by considering that an ideal gas is expanded (compressed), from an initial pressure Pi to a final pressure Pf, by being placed in contact with a set of N work reservoirs with pressures decreasing (increasing) in a geometric or arithmetic progression. The gas entropy change ΔS is evaluated and it is clearly shown that ΔS > 0 for any finite N, but as the number of work reservoirs goes to infinity the entropy change goes to zero, i.e. the process becomes reversible. Additionally, this work draws attention to the work reservoir concept, which is virtually ignored in the literature, and to its analogy with the commonly used heat reservoir concept. Finally, it complements and reinforces an earlier study dealing with irreversible cooling or heating so that the synergy created by the two studies is important from both theoretical and educational standpoints
Hamiltonian formalism for general-relativistic adiabatic fluids
We derive the Hamiltonian structures of three theories: non-relativistic, special-relativistic, and general-relativistic adiabatic fluids, each in the Eulerian representation in Riemannian space (or Lorentzian spacetime), all by the same procedure using standard variational principles. The evolution in each case is generated by a Hamiltonian that is equivalent to that obtained from a canonical analysis. For the gravitational variables, the Poisson bracket has the usual canonical symplectic structure. However, for the fluid variables, the three theories all share the same Lie-Poisson bracket, when expressed in the appropriate spaces of physical variables constructed here. This shared Lie-Poisson bracket is associated to the dual of the semidirect-product Lie algebra of vector fields acting on differential forms. An immediate consequence of this shared structure is that each of these theories possesses an infinite family of conservation laws: the so-called ''Casimirs'' that belong to the kernel of the Lie-Poisson bracket. The role of these Casimirs in the study of Lyapunov stability (or dynamic stability) for fluid equilibria is discussed. The relationship of this approach to other approaches in the literature is also discussed. (orig.)
A quantized adiabatic time dependent mean field theory
Usually collective motion of the nucleus is essentially governed by a few dynamical parameters q like e.g. elongation necking etc. in case of fission. Microscopic approaches often aim to calculate, outgoing from the motion of the single nucleons, the Hamiltonian for the collective motion. To this end they use as a basic ingredient the collective path which is a set of Slater-determinants or BCS states, representing the various shapes of the system during the collective motion. In practice, the choice bears much arbitrariness in guessing the evolution of the collective deformation. It is therefore highly desirable to have a theory which extracts the collective path from a proper equation of motion rather than imposing it on the system. Such equations for the optimal collective path are derived by requiring slow motion and by defining collective coordinates by means of minimizing the coupling term. Assuming the collective path to consist out of Slater determinants this amounts to an adiabatic expansion of the TDHF equations and finally leads to a differential equation for the path. (orig./AH)
Hot-electron nanoscopy using adiabatic compression of surface plasmons
Giugni, Andrea
2013-10-20
Surface plasmon polaritons are a central concept in nanoplasmonics and have been exploited to develop ultrasensitive chemical detection platforms, as well as imaging and spectroscopic techniques at the nanoscale. Surface plasmons can decay to form highly energetic (or hot) electrons in a process that is usually thought to be parasitic for applications, because it limits the lifetime and propagation length of surface plasmons and therefore has an adverse influence on the functionality of nanoplasmonic devices. Recently, however, it has been shown that hot electrons produced by surface plasmon decay can be harnessed to produce useful work in photodetection, catalysis and solar energy conversion. Nevertheless, the surface-plasmon-to-hot-electron conversion efficiency has been below 1% in all cases. Here we show that adiabatic focusing of surface plasmons on a Schottky diode-terminated tapered tip of nanoscale dimensions allows for a plasmon-to-hot-electron conversion efficiency of ∼30%. We further demonstrate that, with such high efficiency, hot electrons can be used for a new nanoscopy technique based on an atomic force microscopy set-up. We show that this hot-electron nanoscopy preserves the chemical sensitivity of the scanned surface and has a spatial resolution below 50 nm, with margins for improvement.
Oscillating adiabatic temperature change of 2D diamagnetic materials
Studies on magnetocaloric effect generally concern ferromagnetic materials, due to their high magnetocaloric potential near phase transitions. Recently, this effect on diamagnetic materials was explored and oscillations on the entropy change observed as a consequence of the crossing of the Landau levels through the Fermi energy. The present paper explores the adiabatic temperature change in graphenes and thin films of non-relativistic diamagnetic materials and then compares the results with those from 3D diamagnets. Applying 10 T of magnetic field, the temperature change of a gold thin film reaches 1 K, while for bulk gold the temperature change is smaller than 6 mK. For graphenes, the temperature change reaches 4 K with a field of ∼1 T. - Highlights: • We studied magnetocaloric properties of 2D diamagnetic materials. • Temperature change of low-dimensional materials exhibits an oscillating behavior. • The effect of scattering from impurity in graphene strongly reduces the temperature change. • We propose an application involving field sensors
Mass Modeling of Disk Galaxies: Constraints and Adiabatic Contraction
Dutton, A A; Carignan, C; De Jong, R; Dutton, Aaron A.; Courteau, Stephane; Carignan, Claude; Jong, Roelof de
2003-01-01
We present a comprehensive mass modeling technique for disk galaxies with resolved rotation curves. Our models allow for a stellar disk of variable thickness and mass-to-light ratio, a gaseous disk, halo profiles with a range of inner density profile slopes (-ALPHA), oblate halos, adiabatic contraction of the halo, and fixed minimum rotation curve error values. We test our technique with data from the literature consisting of high quality HI and Halpha rotation curves for galaxies with available photometry. These galaxies consist of dwarf, low surface brightness (LSB), and high surface brightness (HSB) galaxies. We apply constraints on the disk, and halo parameters in an attempt to break the degeneracies that exist between the disk and halo and between the halo parameters themselves. With our full set of constraints we find that ALPHA=0 halos provide the best fits for 6 out of 7 galaxies; in agreement with the literature; the exception, NGC 2403 an HSB galaxy, is best fit with ALPHA~1, though ALPHA=0 still pr...
Adiabatic nonlinear waves with trapped particles. III. Wave dynamics
Dodin, I. Y.; Fisch, N. J. [Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544 (United States)
2012-01-15
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter S, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At S < 1/2, a wave is stable and exhibits group velocity splitting. At S > 1/2, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schroedinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.
Adiabatic-demagnetization-cooled bolometer system for millimeter continuum astronomy
An adiabatic-demagnetization-cooled bolometer system was constructed for the detection of astronomical one-millimeter wavelength continuum radiation. By employing chromium potassium sulfate as a refrigeration agent, bolometers were cooled to temperatures below 0.1 K. The bolometers were composed of a gallium-doped germanium thermistor epoxied to a sapphire substrate coated with a bismuth absorbing film. The most-sensitive detector tested had a measured electrical noise equivalent power (NEP) of 7 x 10-17 watts per root-hertz at a chopping frequency of 20 hertz. This value of the NEP is the lowest yet recorded for a bolometer, and represents a major gain in sensitivity. The theory of both the refrigerator and detector operation is presented and is shown to strongly constrain a useful detector system. In the laboratory, a cryogenic hold time of greater than eight hours has been achieved, with temperatures regulation of 0.1 K to within 14 microK. Such regulation is shown necessary to keep the variations in responsivity of the bolometer within 1%. The measured performance of the refrigerator and bolometer are both found to be in good agreement with theoretical predictions. Spacecraft adaptation of this system is briefly discussed. One-millimeter continuum observations of Cygnus A made with a pumped 3He refrigerator detector system are presented
Thermodynamics analysis of refinery sludge gasification in adiabatic updraft gasifier.
Ahmed, Reem; Sinnathambi, Chandra M; Eldmerdash, Usama; Subbarao, Duvvuri
2014-01-01
Limited information is available about the thermodynamic evaluation for biomass gasification process using updraft gasifier. Therefore, to minimize errors, the gasification of dry refinery sludge (DRS) is carried out in adiabatic system at atmospheric pressure under ambient air conditions. The objectives of this paper are to investigate the physical and chemical energy and exergy of product gas at different equivalent ratios (ER). It will also be used to determine whether the cold gas, exergy, and energy efficiencies of gases may be maximized by using secondary air injected to gasification zone under various ratios (0, 0.5, 1, and 1.5) at optimum ER of 0.195. From the results obtained, it is indicated that the chemical energy and exergy of producer gas are magnified by 5 and 10 times higher than their corresponding physical values, respectively. The cold gas, energy, and exergy efficiencies of DRS gasification are in the ranges of 22.9-55.5%, 43.7-72.4%, and 42.5-50.4%, respectively. Initially, all 3 efficiencies increase until they reach a maximum at the optimum ER of 0.195; thereafter, they decline with further increase in ER values. The injection of secondary air to gasification zone is also found to increase the cold gas, energy, and exergy efficiencies. A ratio of secondary air to primary air of 0.5 is found to be the optimum ratio for all 3 efficiencies to reach the maximum values. PMID:24672368
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
N-variable rational approximants
''Desirable properties'' of a two-variable generalization of Pade approximants are laid down. The ''Chisholm approximants'' are defined and are shown to obey nearly all of these properties; the alternative ways of completing a unique definition are discussed, and the ''prong structure'' of the defining equations is elucidated. Several generalizations and variants of Chisholm approximants are described: N-variable diagonal, 2-variable simple off-diagonal, N-variable simple and general off-diagonal, and rotationally covariant 2-variable approximants. All of the 2-variable approximants are capable of representing singularities of functions of two variables, and of analytically continuing beyond the polycylinder of convergence of the double series. 8 figures
Chebyshev polynomial approximation to approximate partial differential equations
Caporale, Guglielmo Maria; Cerrato, Mario
2008-01-01
This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions t...
WANG Peng
2011-01-01
Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First, Noether theorem of a system is presented. Secondly, the criterion of perturbation to Noether symmetry of the system is given. Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained. Finally, An example is given to support these results.%@@ Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First, Noether theorem of a system is presented.Secondly , the criterion of perturbation to Noether symmetry of the system is given.Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained .Finally, An example is given to support these results.
DESIGN OF TWO-PHASE SINUSOIDAL POWER CLOCK AND CLOCKED TRANSMISSION GATE ADIABATIC LOGIC CIRCUIT
Wang Pengjun; Yu Junjun
2007-01-01
First the research is conducted on the design of the two-phase sinusoidal power clock generator in this paper. Then the design of the new adiabatic logic circuit adopting the two-phase sinusoidal power clocks-Clocked Transmission Gate Adiabatic Logic (CTGAL) circuit is presented. This circuit makes use of the clocked transmission gates to sample the input signals, then the output loads are charged and discharged in a fully adiabatic manner by using bootstrapped N-Channel Metal Oxide Semiconductor (NMOS) and Complementary Metal Oxide Semiconductor (CMOS) latch structure.Finally, with the parameters of Taiwan Semiconductor Manufacturing Company (TSMC) 0.25 μm CMOS device, the transient energy consumption of CTGAL, Bootstrap Charge-Recovery Logic (BCRL)and Pass-transistor Adiabatic Logic (PAL) including their clock generators is simulated. The simulation result indicates that CTGAL circuit has the characteristic of remarkably low energy consumption.
The efficiency of Flory approximation
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
Approximate Reanalysis in Topology Optimization
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures is...... investigated. The nested optimization problem is re-formulated to accommodate the use of an approximate displacement vector and the design sensitivities are derived accordingly. It is shown that relatively rough approximations are acceptable since the errors are taken into account in the sensitivity analysis...
Area and entropy spectra of black holes via an adiabatic invariant
Liu Cheng-Zhou
2012-01-01
By considering and using an adiabatic invariant for black holes,the area and entropy spectra of static sphericallysymmetric black holes are investigated.Without using quasi-normal modes of black holes,equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant.The spectra for non-charged and charged black holes are calculated,respectively.All these results are consistent with the original Bekenstein spectra.
On the Quantitative Evaluation of Adiabatic Shear Banding Sensitivity of Various Titanium Alloys
Mazeau, C.; Beylat, L.; Longère, P.; Louvigné, P.
1997-01-01
Titanium alloys exhibit attractive ballistic performances due to their low density and their high mechanical properties. They are unfortunately very sensitive to adiabatic shear localization. This study aims to determine an empirical parameter which allows to characterise the sensitivity to the adiabatic shear banding of different grades of titanium alloys. Dynamic punching tests by split Hopkinson pressure bar are performed on disc shaped specimen to obtain shear bands. This article deals wi...
Adiabatic Low-Pass J Filters for Artifact Suppression in Heteronuclear NMR
Meier, Sebastian; Benie, Andrew J; Duus, Jens Øllgaard;
2009-01-01
NMR artifact purging: Modern NMR experiments depend on efficient coherence transfer pathways for their sensitivity and on suppression of undesired pathways leading to artifacts for their spectral clarity. A novel robust adiabatic element suppresses hard-to-get-at artifacts.......NMR artifact purging: Modern NMR experiments depend on efficient coherence transfer pathways for their sensitivity and on suppression of undesired pathways leading to artifacts for their spectral clarity. A novel robust adiabatic element suppresses hard-to-get-at artifacts....
Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field
Littlejohn, Robert; Weigert, S.
1993-01-01
The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter....
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Approximate maximizers of intricacy functionals
Buzzi, Jerome
2009-01-01
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These approximate maximizers work simultaneously for all intricacies. We also establish some properties of arbitrary approximate maximizers, in particular the existence of a threshold in the size of subsystems of approximate maximizers: most smaller subsystems are almost equidistributed, most larger subsystems determine the full system. The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size. ...
Metrical Diophantine approximation for quaternions
Dodson, Maurice
2011-01-01
The metrical theory of Diophantine approximation for quaternions is developed using recent results in the general theory. In particular, Quaternionic analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch are established.
Metrical Diophantine approximation for quaternions
Dodson, Maurice; Everitt, Brent
2014-11-01
Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.
We analyze the energy performance of a complete adiabatic circuit/system including the Power Clock Generator (PCG) at the 90 nm CMOS technology node. The energy performance in terms of the conversion efficiency of the PCG is extensively carried out under the variations of supply voltage, process corner and the driver transistor's width. We propose an energy-efficient singe cycle control circuit based on the two-stage comparator for the synchronous charge recovery sinusoidal power clock generator (PCG). The proposed PCG is used to drive the 4-bit adiabatic Ripple Carry Adder (RCA) and their simulation results are compared with the adiabatic RCA driven by the reported PCG. We have also simulated the logically equivalent static CMOS RCA circuit to compare the energy saving of adiabatic and non-adiabatic logic circuits. In the clock frequency range from 25 MHz to 1GHz, the proposed PCG gives a maximum conversion efficiency of 56.48%. This research work shows how the design of an efficient PCG increases the energy saving of adiabatic logic. (semiconductor integrated circuits)
Adiabatic Coherence Transfer in Magnetic Resonance of Homonuclear Scalar-Coupled Systems
Kurur, N. D.; Bodenhausen, G.
By analogy to heteronuclear systems, it is shown that coherence can be transferred adiabatically in the rotating frame between two selected spins I and S belonging to a homonuclear network of scalar-coupled spins. In contrast to cross polarization with constant radiofrequency field amplitudes, the transfer function obtained with adiabatic methods depends in a monotonic, nonoscillatory manner on the duration of the transfer interval. The efficiency of the transfer does not depend on the magnitude of the scalar coupling constant JIS, although it can be affected by relaxation and by couplings JIR and JSR to further spins R. Three methods are investigated: (i) adiabatic demagnetization of spin I in the rotating frame followed by observation of the resulting J-ordered state, (ii) adiabatic demagnetization of spin I in the rotating frame followed by adiabatic remagnetization of spin S, and (iii) adiabatic transfer where spins I and S are subjected simultaneously to time-dependent spin-locking fields. In all three cases, the optimum shape of the time dependence of the radiofrequency field amplitudes is discussed, with the help of a geometric interpretation of cross polarization.
An Efficient Adiabatic CMOS Circuit Design Approach for Low Power Applications
Ashish Raghuwanshi
2013-09-01
Full Text Available One of the key issues in CMOS circuit design is the large amount of power being dissipated in the circuits. Energy recovering circuitry based on adiabatic principles is a relatively new technique used to implement low power dissipating circuits. By recycling the charge at capacitive nodes in the circuit, adiabatic logic families can achieve very low power dissipation. In this paper we had design and simulate the Inverter, Two-Input Nand gate, Two-Input Nor gate, Two-Input Xor gate, 2:1 Multiplexer on the basis of CMOS Logic and Adiabatic Switching logic using 180nm CMOS technology in Cadence design environment. Two adiabatic families are used in this work, Oneis the Positive Feedback Adiabatic Logic (PFAL and the other is the Efﬁcient Charge Recovery Logic (ECRL Finally, the analysis of the average dynamic power dissipation with respect to the frequency and the load capacitance was done to show the amount of power dissipated by the CMOS, PFAL and ECRL family. The results shows that power saving of adiabatic circuit can reach more than 90% as compare to conventional static CMOS logic
Reinforcement Learning via AIXI Approximation
Veness, Joel; Ng, Kee Siong; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To deve...
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption is taken into account within Gibbsian approximation. Binary clusters are treated by means of statistical-mechanical considerations: tracing out the molecular degrees of freedom of the more volatil...
Approximate factorization with source terms
Shih, T. I.-P.; Chyu, W. J.
1991-01-01
A comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error. While two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized, the third method used generates the lowest approximate factorization error. This method may be preferred when the norms of source terms are large, and transient solutions are of interest.
Chebyshev approximation for multivariate functions
Sukhorukova, Nadezda; Ugon, Julien; Yost, David
2015-01-01
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion of alternance (maximal deviation points with alternating deviation signs). It is not very straightforward, however, how to extend the notion of alternance to the case of multivariate functions. There have been several attempts to extend the theory of Cheby...
Analytic Approximations for Spread Options
Carol Alexander; Aanand Venkatramanan
2007-01-01
Even in the simple case that two price processes follow correlated geometric Brownian motions with constant volatility no analytic formula for the price of a standard European spread option has been derived, except when the strike is zero in which case the option becomes an exchange option. This paper expresses the price of a spread option as the price of a compound exchange option and hence derives a new analytic approximation for its price and hedge ratios. This approximation has several ad...