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.
Li, Dafa
2016-05-01
The adiabatic theorem was proposed about 90 years ago and has played an important role in quantum physics. The quantitative adiabatic condition constructed from eigenstates and eigenvalues of a Hamiltonian is a traditional tool to estimate adiabaticity and has proven to be the necessary and sufficient condition for adiabaticity. However, recently the condition has become a controversial subject. In this paper, we list some expressions to estimate the validity of the adiabatic approximation. We show that the quantitative adiabatic condition is invalid for the adiabatic approximation via the Euclidean distance between the adiabatic state and the evolution state. Furthermore, we deduce general necessary and sufficient conditions for the validity of the adiabatic approximation by different definitions.
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
Appearance of gauge fields and forces beyond the adiabatic approximation
Gosselin, Pierre [Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathematiques, Universite Grenoble I, BP74, 38402 Saint Martin d' Heres, Cedex (France); Mohrbach, Herve, E-mail: mohrbach@univ-metz.f [Laboratoire de Physique Moleculaire et des Collisions, ICPMB-FR CNRS 2843, Universite Paul Verlaine-Metz, 57078 Metz Cedex 3 (France)
2010-09-03
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix-valued quantum Hamiltonians. The results are illustrated by several physical relevant examples.
Semiclassical approximations for adiabatic slow-fast systems
Teufel, Stefan
2012-01-01
In this letter we give a systematic derivation and justification of the semiclassical model for the slow degrees of freedom in adiabatic slow-fast systems first found by Littlejohn and Flynn [5]. The classical Hamiltonian obtains a correction due to the variation of the adiabatic subspaces and the symplectic form is modified by the curvature of the Berry connection. We show that this classical system can be used to approximate quantum mechanical expectations and the time-evolution of operators also in sub-leading order in the combined adiabatic and semiclassical limit. In solid state physics the corresponding semiclassical description of Bloch electrons has led to substantial progress during the recent years, see [1]. Here, as an illustration, we show how to compute the Piezo-current arising from a slow deformation of a crystal in the presence of a constant magnetic field.
Adiabatic approximation for the Rabi model with broken inversion symmetry
Shen, Li-Tuo; Yang, Zhen-Biao; Wu, Huai-Zhi
2017-01-01
We study the properties and behavior of the Rabi model with broken inversion symmetry. Using an adiabatic approximation approach, we explore the high-frequency qubit and oscillator regimes, and obtain analytical solutions for the qubit-oscillator system. We demonstrate that, due to broken inversion symmetry, the positions of two potentials and zero-point energies in the oscillators become asymmetric and have a quadratic dependence on the mean dipole moments within the high-frequency oscillator regime. Furthermore, we find that there is a critical point above which the qubit-oscillator system becomes unstable, and the position of this critical point has a quadratic dependence on the mean dipole moments within the high-frequency qubit regime. Finally, we verify this critical point based on the method of semiclassical approximation.
Breakdown of the adiabatic Born-Oppenheimer approximation in graphene
Pisana, Simone; Lazzeri, Michele; Casiraghi, Cinzia; Novoselov, Kostya S.; Geim, A. K.; Ferrari, Andrea C.; Mauri, Francesco
2007-03-01
The adiabatic Born-Oppenheimer approximation (ABO) has been the standard ansatz to describe the interaction between electrons and nuclei since the early days of quantum mechanics. ABO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground state. ABO is well justified when the energy gap between ground and excited electronic states is larger than the energy scale of the nuclear motion. In metals, the gap is zero and phenomena beyond ABO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur. The use of ABO to describe lattice motion in metals is, therefore, questionable. In spite of this, ABO has proved effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state, is a zero-bandgap semiconductor that becomes a metal if the Fermi energy is tuned applying a gate voltage, Vg. This induces a stiffening of the Raman G peak that cannot be described within ABO.
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...
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.
Adiabatic approximation of time-dependent density matrix functional response theory.
Pernal, Katarzyna; Giesbertz, Klaas; Gritsenko, Oleg; Baerends, Evert Jan
2007-12-07
Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.
The adiabatic approximation solutions of cylindrical and spherical dust ion-acoustic solitary waves
吕克璞; 豆福全; 孙建安; 段文山; 石玉仁
2005-01-01
By using the equivalent particle theory, the adiabatic approximation solutions of the Korteweg-de Vries type equation (including KdV equation, cylindrical KdV equation and spherical KdV equation) in dust ion-acoustic solitary waves were obtained. The method can be extended to other nonlinear evolution equations.
Olsen, Thomas; Thygesen, Kristian S.
2012-01-01
while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...
Dynamo magnetic field modes in thin astrophysical disks - An adiabatic computational approximation
Stepinski, T. F.; Levy, E. H.
1991-01-01
An adiabatic approximation is applied to the calculation of turbulent MHD dynamo magnetic fields in thin disks. The adiabatic method is employed to investigate conditions under which magnetic fields generated by disk dynamos permeate the entire disk or are localized to restricted regions of a disk. Two specific cases of Keplerian disks are considered. In the first, magnetic field diffusion is assumed to be dominated by turbulent mixing leading to a dynamo number independent of distance from the center of the disk. In the second, the dynamo number is allowed to vary with distance from the disk's center. Localization of dynamo magnetic field structures is found to be a general feature of disk dynamos, except in the special case of stationary modes in dynamos with constant dynamo number. The implications for the dynamical behavior of dynamo magnetized accretion disks are discussed and the results of these exploratory calculations are examined in the context of the protosolar nebula and accretion disks around compact objects.
Zhu, Xiaolei, E-mail: virtualzx@gmail.com; Yarkony, David R., E-mail: yarkony@jhu.edu [Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218 (United States)
2016-01-28
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, H{sup d}, 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 H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.
MG13 proceedings: On the validity of the adiabatic approximation in compact binary inspirals
Maselli, Andrea; Pannarale, Francesco; Ferrari, Valeria
2013-01-01
We use the post-Newtonian-Affine model to assess the validity of the adiabatic approximation in modeling tidal effects in the phase evolution of compact binary systems. We compute the dynamical evolution of the tidal tensor, which we estimate at the 2 PN order, and of the quadrupole tensor, finding that their ratio, i.e. the tidal deformability, increases in the last phases of the inspiral. We derive the gravitational wave phase corrections due to this phenomenon and quantify how they affect gravitational wave detectability.
Limitations of the adiabatic approximation to the gravitational self-force
Pound, A; Nickel, B G; Pound, Adam; Poisson, Eric; Nickel, Bernhard G.
2005-01-01
A small body moving in the field of a much larger black hole and subjected to its own gravity moves on an accelerated world line in the background spacetime of the large black hole. The acceleration is produced by the body's gravitational self-force, which is constructed from the body's retarded gravitational field. The adiabatic approximation to the gravitational self-force is obtained instead from the half-retarded minus half-advanced field; it is known to produce the same dissipative effects as the true self-force. We argue that the adiabatic approximation is limited, because it discards important conservative terms which lead to the secular evolution of some orbital elements. We argue further that this secular evolution has measurable consequences; in particular, it affects the phasing of the orbit and the phasing of the associated gravitational wave. Our argument rests on a simple toy model involving a point electric charge moving slowly in the weak gravitational field of a central mass; the charge is al...
Baeck, Kyoung Koo; An, Heesun
2017-02-01
A very simple equation, Fij A p p=[(∂2(Via-Vja ) /∂Q2 ) /(Via-Vja ) ] 1 /2/2 , giving a reliable magnitude of non-adiabatic coupling terms (NACTs, Fij's) based on adiabatic potential energies only (Via and Vja) was discovered, and its reliability was tested for several prototypes of same-symmetry interstate crossings in LiF, C2, NH3Cl, and C6H5SH molecules. Our theoretical derivation starts from the analysis of the relationship between the Lorentzian dependence of NACTs along a diabatization coordinate and the well-established linear vibronic coupling scheme. This analysis results in a very simple equation, α =2 κ /Δc , enabling the evaluation of the Lorentz function α parameter in terms of the coupling constant κ and the energy gap Δc (Δc=|Via-Vja| Q c ) between adiabatic states at the crossing point QC. Subsequently, it was shown that QC corresponds to the point where Fij A p p exhibit maximum values if we set the coupling parameter as κ =[(Via-Vja ) ṡ(∂2(Via-Vja ) /∂Q2 ) ] Qc1 /2 /2 . Finally, we conjectured that this relation could give reasonable values of NACTs not only at the crossing point but also at other geometries near QC. In this final approximation, the pre-defined crossing point QC is not required. The results of our test demonstrate that the approximation works much better than initially expected. The present new method does not depend on the selection of an ab initio method for adiabatic electronic states but is currently limited to local non-adiabatic regions where only two electronic states are dominantly involved within a nuclear degree of freedom.
On the validity of the adiabatic approximation in compact binary inspirals
Maselli, A; Pannarale, F; Ferrari, V
2012-01-01
Using a semi-analytical approach recently developed to model the tidal deformations of neutron stars in inspiralling compact binaries, we study the dynamical evolution of the tidal tensor, which we explicitly derive at second post-Newtonian order, and of the quadrupole tensor. Since we do not assume a priori that the quadrupole tensor is proportional to the tidal tensor, i.e. the so called "adiabatic approximation", our approach enables us to establish to which extent such approximation is reliable. We find that the ratio between the quadrupole and tidal tensors (i.e., the Love number) increases as the inspiral progresses, but this phenomenon only marginally affects the emitted gravitational waveform. We estimate the frequency range in which the tidal component of the gravitational signal is well described using the stationary phase approximation at next-to-leading post-Newtonian order, comparing different contributions to the tidal phase. We also derive a semi-analytical expression for the Love number, which...
All-coupling polaron optical response: Analytic approaches beyond the adiabatic approximation
Klimin, S. N.; Tempere, J.; Devreese, J. T.
2016-09-01
In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fröhlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at T =0 by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.
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.
Zlatanov, Kaloyan N.; Vitanov, Nikolay V.
2017-07-01
The common objective of the application of adiabatic techniques in the field of quantum control is to transfer a quantum system from one discrete energy state to another. These techniques feature both high efficiency and insensitivity to variations in the experimental parameters, e.g., variations in the driving field amplitude, duration, frequency, and shape, as well as fluctuations in the environment. Here we explore the potential of adiabatic techniques for creating arbitrary predefined coherent superpositions of two quantum states. We show that an equally weighted coherent superposition can be created by temporal variation of the ratio between the Rabi frequency Ω (t ) and the detuning Δ (t ) from 0 to ∞ (case 1) or vice versa (case 2), as it is readily deduced from the explicit adiabatic solution for the Bloch vector. We infer important differences between cases 1 and 2 in the composition of the created coherent superposition: The latter depends on the dynamical phase of the process in case 2, while it does not depend on this phase in case 1. Furthermore, an arbitrary coherent superposition of unequal weights can be created by using asymptotic ratios of Ω (t )/Δ (t ) different from 0 and ∞ . We supplement the general adiabatic solution with analytic solutions for three exactly soluble models: two trigonometric models and the hyperbolic Demkov-Kunike model. They allow us not only to demonstrate the general predictions in specific cases but also to derive the nonadiabatic corrections to the adiabatic solutions.
Burow, Asbjörn M; Bates, Jefferson E; Furche, Filipp; Eshuis, Henk
2014-01-14
The random phase approximation (RPA) is an increasingly popular method for computing molecular ground-state correlation energies within the adiabatic connection fluctuation-dissipation theorem framework of density functional theory. We present an efficient analytical implementation of first-order RPA molecular properties and nuclear forces using the resolution-of-the-identity (RI) approximation and imaginary frequency integration. The centerpiece of our approach is a variational RPA energy Lagrangian invariant under unitary transformations of occupied and virtual reference orbitals, respectively. Its construction requires the solution of a single coupled-perturbed Kohn-Sham equation independent of the number of perturbations. Energy gradients with respect to nuclear displacements and other first-order properties such as one-particle densities or dipole moments are obtained from partial derivatives of the Lagrangian. Our RPA energy gradient implementation exhibits the same [Formula: see text] scaling with system size N as a single-point RPA energy calculation. In typical applications, the cost for computing the entire gradient vector with respect to nuclear displacements is ∼5 times that of a single-point RPA energy calculation. Derivatives of the quadrature nodes and weights used for frequency integration are essential for RPA gradients with an accuracy consistent with RPA energies and can be included in our approach. The quality of RPA equilibrium structures is assessed by comparison to accurate theoretical and experimental data for covalent main group compounds, weakly bonded dimers, and transition metal complexes. RPA outperforms semilocal functionals as well as second-order Møller-Plesset (MP2) theory, which fails badly for the transition metal compounds. Dipole moments of polarizable molecules and weakly bound dimers show a similar trend. RPA harmonic vibrational frequencies are nearly of coupled cluster singles, doubles, and perturbative triples quality
Adiabatic approximation for a two-level atom in a light beam
Aftalion, Amandine
2011-01-01
Following the recent experimental realization of synthetic gauge magnetic forces, Jean Dalibard adressed the question whether the adiabatic ansatz could be math- ematically justified for a model of an atom in 2 internal states, shun by a quasi resonant laser beam. In this paper, we derive rigorously the asymptotic model guessed by the physicists, and show that this asymptotic analysis contains the in- formation about the presence of vortices. Surprisingly the main difficulties do not come from the nonlinear part but from the linear Hamiltonian. More precisely, the analysis of the nonlinear minimization problem and its asymptotic reduction to simpler ones, relies on an accurate partition of low and high frequencies (or mo- menta). This requires to reconsider carefully previous mathematical works about the adiabatic limit. Although the estimates are not sharp, this asymptotic analysis provides a good insight about the validity of the asymptotic picture, with respect to the size of the many parameters initially ...
Progress toward post-adiabatic EMRI waveforms using the multiscale approximation
Moxon, Jordan; Flanagan, Eanna; Hinderer, Tanja; Pound, Adam
2017-01-01
I present updates on an analytic approximation method for use in computing orbits and waveforms for Extreme Mass Ratio Inspirals (EMRIs). EMRIs are of particular interest for future space-based gravitational wave detectors, such as (e)LISA. Such gravitational wave detectors will depend on precise predictions of the waveform to take full advantage of the available data. The analytic approximation method for which I present new developments is based on second order self force methods, improved by use of the two-timescale approximation method. Once complete, this method will allow efficient computations of highly accurate EMRI waveforms.
Northrop, J.; Shockley, R. C.; Hansen, P. G.
1980-09-01
Use of the Adiabatic Invariant Approximation (AIA) for determining horizontal sound speeds in a range dependent environment was proposed. Because the method provides a great savings in computer time over conventional ray tracing techniques, it was applied to two very-long-range paths, from Perth, Australia, to Bermuda and to Fernando de Noronha (19763.0 and 14549.3 km, respectively), where measured travel times are available. Results show that the AIA method predicts effective horizontal sound speeds of 1482.3m/s and 1480.4m/s, respectively, for the two propagation paths. These results compare favorably with the measured values of 1484.7 - or - 3.7 m/s and 1480.1 + or - 0.9 m/s.
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.
Guillory, J. U.; Terry, R. E.
1984-07-01
This report describes work done under DNA Contract 001-79-C-0189 from February 1982 to June 1983, and some more recent work. Part 1 includes treatments of a simple zero-D implosion code, analytic but very approximate scaling laws for radiation, and a discussion of preliminary work on nonlinear field penetration of plasma. Part 2 contains a discussion of electrodiffusive 1D modeling of annular plasma implosions. The thermoelectrical field, its role in field penetrations, the nonlocal constraints required in field diffusion (and some arising from field diffusion), flux limits and the acceleration process for annular plasmas are discussed.
Kondo, Kenji
2016-09-01
Spin filters using spin-orbit interaction (SOI) are very important in the field of spintronics. Therefore, a theory of devices using SOI is necessary for designing the spin filters. The spin-filtering devices can be used to generate and detect spin polarized currents. Many researchers have reported on the spin-filters using linear Rashba SOI. However, the spin-filters using square and cubic Rashba SOIs are not yet reported. This is surely because the Aharonov-Casher (AC) phases acquired under square and cubic Rashba SOIs are ambiguous. In this paper, we try to derive the AC phases acquired under nth order Rashba SOIs, which we call general Rashba SOIs, using non-Abelian SU (2) gauge theory. As a result, we have successfully derived these AC phases without completing the square methods which is useless except for linear Rashba SOI. In the process of derivation of AC phases, we have also found another expression of adiabatic approximation for a pure gauge. This finding will lead to the starting point for deeply understanding the adiabatic approximation. Using the above AC phases under general Rashba SOIs, we investigate the spin filter effect in Aharonov-Bohm (AB) ring with double quantum dots (QDs) under general Rashba SOIs. The spin transport is investigated from left nanowire to right nanowire in this structure within tight binding approximation. Especially, we focus on the difference of spin filter effects among general Rashba SOIs. We have obtained the penetrating magnetic flux dependence of spin polarization for the AB ring subject to general Rashba SOIs. It is found that the perfect spin filtering is achieved for all the Rashba SOIs. This result indicates that this AB ring under general Rashba SOIs can be a promising device for spin current generation without ferromagnetic metals. Moreover, this device under different order Rashba SOI behaves in totally different ways in response to penetrating magnetic flux, which is attributed to n times rotation of
Diestler, D J
2013-06-01
Intuition suggests that a molecular system in the electronic ground state Φ0 should exhibit an electronic flux density (EFD) in response to the motion of its nuclei. If that state is described by the Born-Oppenheimer approximation (BOA), however, a straightforward calculation of the EFD yields zero, since the electrons are in a stationary state, regardless of the state of the nuclear motion. Here an alternative pathway to a nonzero EFD from a knowledge of only the BOA ground-state wave function is proposed. Via perturbation theory a complete set of approximate vibronic eigenfunctions of the whole Hamiltonian is generated. If the complete non-BOA wave function is expressed in the basis of these vibronic eigenfunctions, the ground-state contribution to the EFD is found to involve a summation over excited states. Evaluation of this sum through the so-called "average excitation energy approximation" produces a nonzero EFD. An explicit formula for the EFD for the prototypical system, namely, oriented H2+ vibrating in the electronic ground state, is derived.
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
Biamonte, J D; Whitfield, J D; Fitzsimons, J; Aspuru-Guzik, A
2010-01-01
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 error resistant, easily controllable, and built using existing technology. Moving away from gate-model and projective measurement based implementations of quantum computing may offer a less resource-intensive, and consequently a more feasible solution. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-body interaction terms, using sparse Hamiltonians with at most three-body 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...
Gritsenko, Oleg V; Baerends, Evert Jan
2009-06-14
Time-dependent density functional (response) theory (TDDF(R)T) is applied almost exclusively in its adiabatic approximation (ATDDFT), which is restricted to predominantly single electronic excitations and neglects additional roots of the TDDFT eigenvalue problem stemming from the interaction between single and double excitations. We incorporate the effect of the latter interaction into a non-adiabatic frequency-dependent and spatially non-local Hartree-exchange-correlation (Hxc) kernel fCEDAHxc (r1, r2, omega), the explicit analytical expression of which is derived for interacting single and double excitations well separated from the other excitations, within the common energy denominator approximation (CEDA) for the Kohn-Sham (KS) and interacting density response functions, chis and chi, respectively. The kernel fCEDAHxc (r1, r2, omega) obtained from the direct analytical inverse of chiCEDAs and chiCEDA is a sum of the delta-function and non-local orbital-dependent spatial terms with frequency-dependent factors, with which fCEDAHxc acquires a modulated quadratic dependence on omega. The effective incorporation in fCEDAHxc of the complete manifold of excited states (through the delta function term) represents an extension of the kernel reported by Maitra, Zhang, Cave, and Burke [J. Chem. Phys., 2004, 120, 5932]. In the TDDFT eigenvalue equations considered in the diagonal approximation, fCEDAHxc generates two excitation energies omegaq and omegaq+1, which both correspond to the same single KS excitation omegasq, thus producing the effect of the single-double excitation interaction.
Casida, Mark E; Huix-Rotllant, Miquel
2016-01-01
In their famous paper, Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays, however, the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very similar to what the local density approximation (LDA) is to conventional ground-state DFT. Although some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.
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.
Adiabatic theorems for generators of contracting evolutions
Avron, J E; Graf, G M; Grech, P
2011-01-01
We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.
Isothermal and Adiabatic Measurements.
McNairy, William W.
1996-01-01
Describes the working of the Adiabatic Gas Law Apparatus, a useful tool for measuring the pressure, temperature, and volume of a variety of gases undergoing compressions and expansions. Describes the adaptation of this apparatus to perform isothermal measurements and discusses the theory behind the adiabatic and isothermal processes. (JRH)
Adiabatic turbocompound diesel engine
Kamo, R.; Bryzik, W.
1984-02-01
The research and development of an adiabatic turbocompound engine have shown that the concept is feasible. The ability to meet the performance and sociability goals of the future power plants has been demonstrated. Low brake specific fuel consumption, low smoke and particulates, better NO /SUB x/ -BSFC trade-off, excellent multifuel capability, white smoke suppression, and potentially lower maintenance and greater reliability and durability are some of the attributes. The absence of the water cooling system adds to its attractiveness because of lower installed weight, cost, and reduction in parasitic losses. The operating environment of an adiabatic engine is shown as the basis for analysis and designing of adiabatic components. The types of material which can satisfy the needs of an adiabatic engine are presented. These materials include high temperature metals, high performance ceramics, and glass ceramics. The use of a turbocompound system to utilize the increased exhaust energy of an adiabatic engine is covered. A minimum fuel consumption of 0.285 lb/bhp-hr was achieved at 200 psi BMEP. Although the technical feasibility and viability of an adiabatic engine was demonstrated, the adiabatic diesel engine has problems which must be solved before it becomes a commercially viable product. These problem areas where more work is required are discussed.
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; Calsamiglia, John
2010-07-30
We propose a theory of adiabaticity in quantum markovian dynamics based on a 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 Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As two applications of our theory, we propose a general framework for decoherence-assisted computation in noiseless codes and a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by nondissipative means.
Lobe, Elisabeth; Stollenwerk, Tobias; Tröltzsch, Anke
2015-01-01
In the recent years, the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. These machines are suited to solve discrete optimisation problems which are typically very hard to solve on a classical computer. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. We explain the basic principles of adiabatic ...
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.
Adiabatic quantum computation along quasienergies
Tanaka, Atushi
2009-01-01
The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy is recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [Tanaka and Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of...
Fast forward to the classical adiabatic invariant
Jarzynski, Christopher; Patra, Ayoti; Subaşı, Yiğit
2016-01-01
We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of action $I_0$, we construct a "fast-forward" potential energy function $V_{\\rm FF}(q,t)$ that, when added to $H$, guides all trajectories with initial action $I_0$ to end with the same value of action. We use this result to construct a local dynamical invariant $J(q,p,t)$ whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.
Quenching in coupled adiabatic coils
Williams, J.E.C.
1985-03-01
The prediction of the effects of a quench on stress and temperature is an important aspect of the design of superconducting magnets. Of particular interest, and the exclusive topic of this study, is the prediction of the effects of quenching in coupled adiabatic coils, such as the multi-section windings of a high field NMR spectrometer magnet. The predictive methods used here are based on the measurement of the time of propagation of quench between turns. From this measurement an approximate algorithum for the propagation time is used in a code which solves the linear differential equations for the coil currents and calculates the movement of normal zone boundaries and hence the associated winding resistance.
Semiconductor adiabatic qubits
Carroll, Malcolm S.; Witzel, Wayne; Jacobson, Noah Tobias; Ganti, Anand; Landahl, Andrew J.; Lilly, Michael; Nguyen, Khoi Thi; Bishop, Nathaniel; Carr, Stephen M.; Bussmann, Ezra; Nielsen, Erik; Levy, James Ewers; Blume-Kohout, Robin J.; Rahman, Rajib
2016-12-27
A quantum computing device that includes a plurality of semiconductor adiabatic qubits is described herein. The qubits are programmed with local biases and coupling terms between qubits that represent a problem of interest. The qubits are initialized by way of a tuneable parameter, a local tunnel coupling within each qubit, such that the qubits remain in a ground energy state, and that initial state is represented by the qubits being in a superposition of |0> and |1> states. The parameter is altered over time adiabatically or such that relaxation mechanisms maintain a large fraction of ground state occupation through decreasing the tunnel coupling barrier within each qubit with the appropriate schedule. The final state when tunnel coupling is effectively zero represents the solution state to the problem represented in the |0> and |1> basis, which can be accurately read at each qubit location.
Non-adiabatic effects in near-adiabatic mixed-field orientation and alignment
Maan, Anjali; Ahlawat, Dharamvir Singh; Prasad, Vinod
2016-11-01
We present a theoretical study of the impact of a pair of moderate electric fields tilted an angle with respect to one another on a molecule. As a prototype, we consider a molecule with large rotational constant (with corresponding small rotational period) and moderate dipole moment. Within rigid-rotor approximation, the time-dependent Schrodinger equation is solved using fourth-order Runge-Kutta method. We have analysed that lower rotational states are significantly influenced by variation in pulse durations, the tilt angle between the fields and also on the electric field strengths. We also suggest a control scheme of how the rotational dynamics, orientation and alignment of a molecule can be enhanced by a combination of near-adiabatic pulses in comparision to non-adiabatic or adiabatic pulses.
Amendt, Peter; 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 plasma thermodiffusion coefficient is derived, and charge-state diffusion in a single-species plasma is also predicted.
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.
Fixed-point adiabatic quantum search
Dalzell, Alexander M.; Yoder, Theodore J.; Chuang, Isaac L.
2017-01-01
Fixed-point quantum search algorithms succeed at finding one of M target items among N total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property—the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014), 10.1103/PhysRevLett.113.210501] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002), 10.1103/PhysRevA.65.042308] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.
Adiabatic paths and pseudoholomorphic curves
Armen; G.; Sergeev
2005-01-01
We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show that the Taubes correspondence may be considered as a (2+2)-dimensional analogue of the adiabatic limit construction.
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.…
Pinski, Sebastian D
2011-01-01
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small problems were solved; although the explanations that journalists and critics received were minimal and very little was divulged in the question and answer session. This 'unconvincing' demonstration has caused physicists and computer scientists to hit back at D-Wave. The aim of this project is to give an introduction to the historic advances in classical and quantum computing and to explore the methods of AQC. Through numerical simulations an algorithm for the Max Independent Set problem is empirically obtained.
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...
Adiabatic vs. non-adiabatic determination of specific absorption rate of ferrofluids
Natividad, Eva [Instituto de Ciencia de Materiales de Aragon (CSIC-Universidad de Zaragoza), Sede Campus Rio Ebro, Maria de Luna, 3, 50018 Zaragoza (Spain); Castro, Miguel [Instituto de Ciencia de Materiales de Aragon (CSIC-Universidad de Zaragoza), Sede Campus Rio Ebro, Maria de Luna, 3, 50018 Zaragoza (Spain)], E-mail: mcastro@unizar.es; Mediano, Arturo [Grupo de Electronica de Potencia y Microelectronica (GEPM), Instituto de Investigacion en Ingenieria de Aragon (Universidad de Zaragoza), Maria de Luna, 3, 50018 Zaragoza (Spain)
2009-05-15
The measurement of temperature variations in adiabatic conditions allows the determination of the specific absorption rate of magnetic nanoparticles and ferrofluids from the correct incremental expression, SAR=(1/m{sub MNP})C({delta}T/{delta}t). However, when measurements take place in non-adiabatic conditions, one must approximate this expression by SAR{approx}C{beta}/m{sub MNP}, where {beta} is the initial slope of the temperature vs. time curve during alternating field application. The errors arising from the use of this approximation were estimated through several experiments with different isolating conditions, temperature sensors and sample-sensor contacts. It is concluded that small to appreciable errors can appear, which are difficult to infer or control.
Performance analysis of adiabatic engine
Sudhakar, V.
1984-01-01
As the development of the adiabatic diesel engine continues with a goal of 65% reduction in net in-cylinder heat transfer over a cooled engine, several uncooled engines with intermediate levels of reduced heat transfer were studied. Some aspects and results of the adiabatic diesel engine cycle simulation are discussed. Performance test data and simulation results are compared for a conventionally cooled and uncooled Cummins NH-450 turbocompound engines. Exhaust emissions were also measured and compared.
Localization of polarons: A calculation in the adiabatic approximation
Schelling, P. K. [School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 (United States); Halley, J. W. [School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
2000-08-01
We have calculated the properties of an extra charge carrier in a polar medium in using a realistic self-consistent tight-binding molecular-dynamics method at finite temperature. This approach permits a quantitative, realistic study of polaron structure at finite temperatures. Using rutile titanium dioxide, as an example, we report numerical data on the participation ratio as a function of temperature. The results are consistent for a transition from a delocalized to a localized polaron at a temperature below about 100 K. We interpret the observed localization as arising from an Anderson-like mechanism in which the disorder associated with the thermal motion of the atoms localizes the electron. We briefly discuss implications for transport. (c) 2000 The American Physical Society.
Non-adiabatic primordial fluctuations
Noller, Johannes; Magueijo, Joao, E-mail: johannes.noller08@imperial.ac.uk [Theoretical Physics Group, Imperial College, London SW7 2BZ (United Kingdom)
2011-05-21
We consider general mixtures of isocurvature and adiabatic cosmological perturbations. With a minimal assumption set consisting of the linearized Einstein equations and a primordial perfect fluid we derive the second-order action and its curvature variables. We also allow for varying equation of state and speed of sound profiles. The derivation is therefore carried out at the same level of generality that has been achieved for adiabatic modes before. As a result we find a new conserved super-horizon quantity and relate it to the adiabatically conserved curvature perturbation. Finally we demonstrate how the formalism can be applied by considering a Chaplygin gas-like primordial matter model, finding two scale-invariant solutions for structure formation.
Analysis of Adiabatic Batch Reactor
Erald Gjonaj
2016-05-01
Full Text Available A mixture of acetic anhydride is reacted with excess water in an adiabatic batch reactor to form an exothermic reaction. The concentration of acetic anhydride and the temperature inside the adiabatic batch reactor are calculated with an initial temperature of 20°C, an initial temperature of 30°C, and with a cooling jacket maintaining the temperature at a constant of 20°C. The graphs of the three different scenarios show that the highest temperatures will cause the reaction to occur faster.
Adiabatic theory for the bipolaron
Lakhno, V.D. (Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino Moscow Region, 142292 (Russian Federation))
1995-02-01
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 [eta]=0.31 for which the bipolaron state is stable, where [eta]=[epsilon][sub [infinity
Analysis and Simulation of Adiabatic Bend Transitions in Optical Fibers
YAO Lei; LOU Shu-Qin; JIAN Shui-Sheng
2009-01-01
A low-loss criterion for bend transitions in optical fibers is proposed. An optical fiber can be tightly bent with low loss to be adiabatic for the fundamental mode, provided that an approximate upper bound on the rate of change of bend curvature for a given bend curvature is satisfied. Two typical adiabatic bend transition paths, the optimum profile and linear profile, are analyzed and studied numerically. A realizable adiabatic transition with an Archimedean spiral profile is introduced for low bend loss in tightly bent optical fibers. Design of the transitions is based on modeling of the propagation and coupling characteristics of the core and cladding modes,which clearly illustrate the physical processes involved.
Non-adiabatic holonomy operators in classical and quantum completely integrable systems
Giachetta, G; Sardanashvily, G
2002-01-01
Given a completely integrable system, we associate to any connection on its invariant tori fibred over a parameter manifold the classical and quantum holonomy operator (generalized Berry's phase factor), without any adiabatic approximation.
A Many Particle Adiabatic Invariant
Hjorth, Poul G.
1999-01-01
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...
Elementary examples of adiabatic invariance
Crawford, F.S. (Physics Department, University of California, Berkeley, CA (USA) Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 (USA))
1990-04-01
Simple classical one-dimensional systems subject to adiabatic (gradual) perturbations are examined. The first examples are well known: the adiabatic invariance of the product {ital E}{tau} of energy {ital E} and period {tau} for the simple pendulum and for the simple harmonic oscillator. Next, the adiabatic invariants of the vertical bouncer are found---a ball bouncing elastically from the floor of a rising elevator having slowly varying velocity and acceleration. These examples lead to consideration of adiabatic invariance for one-dimensional systems with potentials of the form {ital V}={ital ax}{sup {ital n}}, with {ital a}={ital a}({ital t}) slowly varying in time. Then, the horizontal bouncer is considered---a mass sliding on a smooth floor, bouncing back and forth between two impenetrable walls, one of which is slowly moving. This example is generalized to a particle in a bound state of a general potential with one slowly moving turning point.'' Finally, circular motion of a charged particle in a magnetic field slowly varying in time under three different configurations is considered: (a) a free particle in a uniform field; (b) a free particle in a nonuniform betatron'' field; and (c) a particle constrained to a circular orbit in a uniform field.
Hubac, Ivan; Babinec, Peter; Polasek, Martin; Urban, Jan; Mach, Pavel; Masik, Jozef; Leszczynski, Jerzy
1998-01-01
The coupling of electronic and vibrational motion is studied by two canonical transformations namely normal coordinate transformation and momentum transformation on molecular Hamiltonian. It is shown that by these transformations we can pass from crude approximation to adiabatic approximation and then to non-adiabatic (diabatic) Hamiltonian. This leads to renormalized fermions and renormalized diabatic phonons. Simple calculations on $H_{2}$, $HD$, and $D_{2}$ systems are performed and compar...
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.
Particle creation and non-adiabatic transitions in quantum cosmology
Massar, S
1998-01-01
The aim of this paper is to compute transitions amplitudes in quantum cosmology, and in particular pair creation amplitudes and radiative transitions. To this end, we apply a double adiabatic development to the solutions of the Wheeler-DeWitt equation restricted to mini-superspace wherein gravity is described by the scale factor $a$. The first development consists in working with instantaneous eigenstates, in $a$, of the matter Hamiltonian. The second development is applied to the gravitational part of the wave function and generalizes the usual WKB approximation. We then obtain an exact equation which replaces the Wheeler-DeWitt equation and determines the evolution, i.e. the dependence in $a$, of the coefficients of this double expansion. When working in the gravitational adiabatic approximation, the simplified equation delivers the unitary evolution of transition amplitudes occurring among instantaneous eigenstates. Upon abandoning this approximation, one finds that there is an additional coupling among ma...
New Dynamical Scaling Universality for Quantum Networks Across Adiabatic Quantum Phase Transitions
Acevedo, Oscar L.; Rodriguez, Ferney J.; Quiroga, Luis; Johnson, Neil F.; Rey, Ana M.
2014-05-01
We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.
Conformal Symmetries of Adiabatic Modes in Cosmology
Hinterbichler, Kurt; Khoury, Justin
2012-01-01
We remark on the existence of non-linearly realized conformal symmetries for scalar adiabatic perturbations in cosmology. These conformal symmetries are present for any cosmological background, beyond any slow-roll or quasi-de Sitter approximation. The dilatation transformation shifts the curvature perturbation by a constant, and corresponds to the well-known symmetry under spatial rescaling. We argue that the scalar sector is also invariant under special conformal transformations, which shift the curvature perturbation by a term linear in the spatial coordinates. We discuss whether these conformal symmetries can be extended to include tensor perturbations. Tensor modes introduce their own set of non-linearly realized symmetries. We identify an infinite set of large gauge transformations which maintain the transverse, traceless gauge condition, while shifting the tensor mode non-trivially.
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.
Adiabatic invariants for the regular region of the Dicke model
Bastarrachea-Magnani, M. A.; Relaño, A.; Lerma-Hernández, S.; López-del-Carpio, B.; Chávez-Carlos, J.; Hirsch, J. G.
2017-04-01
Adiabatic invariants for the non-integrable Dicke model are introduced. They are shown to provide approximate second integrals of motion in the energy region where the system exhibits a regular dynamics. This low-energy region, present for any set of values of the Hamiltonian parameters is described both with a semiclassical and a full quantum analysis in a broad region of the parameter space. Peres lattices in this region exhibit that many observables vary smoothly with energy, along distinct lines which beg for a formal description. It is demonstrated how the adiabatic invariants provide a rationale to their presence in many cases. They are built employing the Born–Oppenheimer approximation, valid when a fast system is coupled to a much slower one. As the Dicke model has one bosonic and one fermionic degree of freedom, two versions of the approximation are used, depending on which one is the faster. In both cases a noticeably accord with exact numerical results is obtained. The employment of the adiabatic invariants provides a simple and clear theoretical framework to study the physical phenomenology associated to these regimes, far beyond the energies where a quadratic approximation around the minimal energy configuration can be used.
Adiabatic Wankel type rotary engine
Kamo, R.; Badgley, P.; Doup, D.
1988-01-01
This SBIR Phase program accomplished the objective of advancing the technology of the Wankel type rotary engine for aircraft applications through the use of adiabatic engine technology. Based on the results of this program, technology is in place to provide a rotor and side and intermediate housings with thermal barrier coatings. A detailed cycle analysis of the NASA 1007R Direct Injection Stratified Charge (DISC) rotary engine was performed which concluded that applying thermal barrier coatings to the rotor should be successful and that it was unlikely that the rotor housing could be successfully run with thermal barrier coatings as the thermal stresses were extensive.
Theory of Adiabatic Fountain Resonance
Williams, Gary A.
2017-01-01
The theory of "Adiabatic Fountain Resonance" with superfluid ^4{He} is clarified. In this geometry a film region between two silicon wafers bonded at their outer edge opens up to a central region with a free surface. We find that the resonance in this system is not a Helmholtz resonance as claimed by Gasparini et al., but in fact is a fourth sound resonance. We postulate that it occurs at relatively low frequency because the thin silicon wafers flex appreciably from the pressure oscillations of the sound wave.
On the topology of adiabatic passage
Yatsenko, L P; Jauslin, H R
2002-01-01
We examine the topology of eigenenergy surfaces characterizing the population transfer processes based on adiabatic passage. We show that this topology is the essential feature for the analysis of the population transfers and the prediction of its final result. We reinterpret diverse known processes, such as stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic passage and Stark-chirped rapid adiabatic passage (SCRAP). Moreover, using this picture, we display new related possibilities of transfer. In particular, we show that we can selectively control the level which will be populated in STIRAP process in Lambda or V systems by the choice of the peak amplitudes or the pulse sequence.
Excitation energies along a range-separated adiabatic connection
Rebolini, Elisa, E-mail: rebolini@lct.jussieu.fr; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr; Savin, Andreas, E-mail: savin@lct.jussieu.fr [Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); Teale, Andrew M. [School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom); Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway); Helgaker, Trygve [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway)
2014-07-28
We present a study of the variation of total energies and excitation energies along a range-separated adiabatic connection. This connection links the non-interacting Kohn–Sham electronic system to the physical interacting system by progressively switching on the electron–electron interactions whilst simultaneously adjusting a one-electron effective potential so as to keep the ground-state density constant. The interactions are introduced in a range-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 the interactions are introduced by globally scaling the standard Coulomb interaction. Reference data are reported for the He and Be atoms and the H{sub 2} molecule, obtained by calculating the short-range effective potential at the full configuration-interaction level using Lieb's Legendre-transform approach. As the strength of the electron–electron interactions increases, the excitation energies, calculated for the partially interacting systems along the adiabatic connection, offer increasingly accurate approximations to the exact excitation energies. Importantly, the excitation energies calculated at an intermediate point of the adiabatic connection are much better approximations to the exact excitation energies than are the corresponding Kohn–Sham excitation energies. This is particularly evident in situations involving strong static correlation effects and states with multiple excitation character, such as the dissociating H{sub 2} molecule. These results highlight the utility of long-range interacting reference systems as a starting point for the calculation of excitation energies and are of interest for developing and analyzing practical approximate range-separated density-functional methodologies.
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-...
Confinement loss in adiabatic photonic crystal fiber tapers
Kuhlmey, Boris T.; Nguyen, Hong C.; Steel, M. J.; Eggleton, Benjamin J.
2006-09-01
We numerically study confinement loss in photonic crystal fiber (PCF) tapers and compare our results with previously published experimental data. Agreement between theory and experiment requires taking into account hole shrinkage during the tapering process, which we measure by using a noninvasive technique. We show that losses are fully explained within the adiabatic approximation and that they are closely linked to the existence of a fundamental core-mode cutoff. This cutoff is equivalent to the core-mode cutoff in depressed-cladding fibers, so that losses in PCF tapers can be obtained semiquantitatively from an equivalent depressed-cladding fiber model. Finally, we discuss the definition of adiabaticity in this open boundary problem.
(Hybrid) Baryons Quantum Numbers and Adiabatic Potentials
Page, P R
1999-01-01
We construct (hybrid) baryons in the flux-tube model of Isgur and Paton. In the limit of adiabatic quark motion, we build proper eigenstates of orbital angular momentum and indicate the flavour, spin, chirality and J^P of (hybrid) baryons. The adiabatic potential is calculated as a function of the quark positions.
Cummins/Tacom advanced adiabatic engine
Kamo, R.; Bryzik, W.
1984-01-01
Cummins Engine Company, Inc. and the U.S. Army have been jointly developing an adiabatic turbocompound engine during the last nine years. Although progress in the early years was slow, recent developments in the field of advanced ceramics have made it possible to make steady progress. It is now possible to reconsider the temperature limitation imposed on current heat engines and its subsequent influence on higher engine efficiency when using an exhaust energy utilization system. This paper presents an adiabatic turbocompound diesel engine concept in which high-performance ceramics are used in its design. The adiabatic turbocompound engine will enable higher operating temperatures, reduced heat loss, and higher exhaust energy recovery, resulting in higher thermal engine efficiency. This paper indicates that the careful selection of ceramics in engine design is essential. Adiabatic engine materials requirements are defined and the possible ceramic materials which will satisfy these requirements are identified. Examples in design considerations of engine components are illustrated. In addition to these important points, the use of ceramic coatings in the design of engine components. The first generation adiabatic engine with ceramic coatings is described. The advanced adiabatic engine with minimum friction features utilizaing ceramics is also presented. The advanced ceramic turbocharger turbine rotor as well as the oilless ceramic bearing design is described. Finally, the current status of the advanced adiabatic engine program culminating in the AA750 V-8 adiabatic engine is presented.
On a Nonlinear Model in Adiabatic Evolutions
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
PIPER Continuous Adiabatic Demagnetization Refrigerator
Kimball, Mark O.; Shirron, Peter J.; Canavan, Edgar R.; James, Bryan L.; Sampson, Michael A.; Letmate, Richard V.
2017-01-01
We report upon the development and testing of a 4-stage adiabatic demagnetization refrigerator (ADR) capable of continuous cooling at 0.100 Kelvin. This cooler is being built to cool the detector array aboard NASA's Primordial Inflation Polarization Explorer (PIPER) observatory. The goal of this balloon mission is to measure the primordial gravitational waves that should exist if the theory of cosmological inflation is correct. At altitude, the ADR will hold the array of transition-edge sensors at 100 mK continuously while periodically rejecting heat to a 1.2 K pumped helium bath. During testing on ground, the array is held at the same temperature but heat is rejected to a 4.2 K helium bath indicating the flexibility in this coolers design.
Quantum Computation by Adiabatic Evolution
Farhi, E; Gutmann, S; Sipser, M; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Sipser, Michael
2000-01-01
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on the minimum energy difference between the two lowest states of the interpolating Hamiltonian. We are unable to estimate this gap in general. We give some special symmetric cases of the satisfiability problem where the symmetry allows us to estimate the gap and we show that, in these cases, our algorithm runs in polynomial time.
On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics.
Cotton, Stephen J; Liang, Ruibin; Miller, William H
2017-08-14
The Meyer-Miller (MM) classical vibronic (electronic + nuclear) Hamiltonian for electronically non-adiabatic dynamics-as used, for example, with the recently developed symmetrical quasiclassical (SQC) windowing model-can be written in either a diabatic or an adiabatic representation of the electronic degrees of freedom, the two being a canonical transformation of each other, thus giving the same dynamics. Although most recent applications of this SQC/MM approach have been carried out in the diabatic representation-because most of the benchmark model problems that have exact quantum results available for comparison are typically defined in a diabatic representation-it will typically be much more convenient to work in the adiabatic representation, e.g., when using Born-Oppenheimer potential energy surfaces (PESs) and derivative couplings that come from electronic structure calculations. The canonical equations of motion (EOMs) (i.e., Hamilton's equations) that come from the adiabatic MM Hamiltonian, however, in addition to the common first-derivative couplings, also involve second-derivative non-adiabatic coupling terms (as does the quantum Schrödinger equation), and the latter are considerably more difficult to calculate. This paper thus revisits the adiabatic version of the MM Hamiltonian and describes a modification of the classical adiabatic EOMs that are entirely equivalent to Hamilton's equations but that do not involve the second-derivative couplings. The second-derivative coupling terms have not been neglected; they simply do not appear in these modified adiabatic EOMs. This means that SQC/MM calculations can be carried out in the adiabatic representation, without approximation, needing only the PESs and the first-derivative coupling elements. The results of example SQC/MM calculations are presented, which illustrate this point, and also the fact that simply neglecting the second-derivative couplings in Hamilton's equations (and presumably also in the Schr
Design of the PIXIE Adiabatic Demagnetization Refrigerators
Shirron, Peter J.; Kimball, Mark Oliver; Fixsen, Dale J.; Kogut, Alan J.; Li, Xiaoyi; DiPirro, Michael
2012-01-01
The Primordial Inflation Explorer (PIXIE) is a proposed mission to densely map the polarization of the cosmic microwave background. It will operate in a scanning mode from a sun-synchronous orbit, using low temperature detectors (at 0.1 K) and located inside a teslescope that is cooled to approximately 2.73 K - to match the background temperature. A mechanical cryocooler operating at 4.5 K establishes a low base temperature from which two adiabatic demagnetization refrigerator (ADR) assemblies will cool the telescope and detectors. To achieve continuous scanning capability, the ADRs must operate continuously. Complicating the design are two factors: 1) the need to systematically vary the temperature of various telescope components in order to separate the small polarization signal variations from those that may arise from temperature drifts and changing gradients within the telescope, and 2) the orbital and monthly variations in lunar irradiance into the telescope barrels. These factors require the telescope ADR to reject quasi-continuous heat loads of 2-3 millwatts, while maintaining a peak heat reject rate of less than 12 milliwatts. The detector heat load at 0.1 K is comparatively small at 1-2 microwatts. This paper will describe the 3-stage and 2-stage continuous ADRs that will be used to meet the cooling power and temperature stability requirements of the PIXIE detectors and telescope.
Quasi-adiabatic transport in Mercury's magnetotail
Delcourt, Dominique; Malova, Helmi; Zelenyi, Lev
2017-04-01
MESSENGER observations have revealed that the magnetotail of Mercury is fairly dynamical, possibly subjected to series of magnetic field line dipolarization on time scales of a few seconds. Because of the sharp reversal of the magnetic field, ions may not travel adiabatically in this region of space, and their behavior can be organized according to different categories. Among these categories, quasi-adiabatic (Speiser) ions are such that they experience negligible net change of magnetic moment upon crossing of the field reversal and can thus travel back to low altitudes. We examine the robustness of this quasi-adiabatic behavior during magnetic field line dipolarization where ions are subjected to a large induced electric field. We demonstrate that, although this surging electric field possibly yields substantial nonadiabatic heating, quasi-adiabaticity is robust for ions with velocities larger than the peak ExB drift speed, a behavior that we refer to as "strong" quasi-adiabaticity (as opposed to "weak" quasi-adiabaticity that is violated during dipolarization). We show that the impulsive energization of such quasi-adiabatic ions during dipolarization events can lead to prominent energy-time dispersion structures at low altitudes.
Partial evolution based local adiabatic quantum search
Sun Jie; Lu Song-Feng; Liu Fang; Yang Li-Ping
2012-01-01
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 2002Phys.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.
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.
Energy consumption for shortcuts to adiabaticity
Torrontegui, E.; Lizuain, I.; González-Resines, S.; Tobalina, A.; Ruschhaupt, A.; Kosloff, R.; Muga, J. G.
2017-08-01
Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the "energy cost" of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking.
Non-Adiabatic Molecular Dynamics Methods for Materials Discovery
Furche, Filipp [Univ. of California, Irvine, CA (United States); Parker, Shane M. [Univ. of California, Irvine, CA (United States); Muuronen, Mikko J. [Univ. of California, Irvine, CA (United States); Roy, Saswata [Univ. of California, Irvine, CA (United States)
2017-04-04
The flow of radiative energy in light-driven materials such as photosensitizer dyes or photocatalysts is governed by non-adiabatic transitions between electronic states and cannot be described within the Born-Oppenheimer approximation commonly used in electronic structure theory. The non-adiabatic molecular dynamics (NAMD) methods based on Tully surface hopping and time-dependent density functional theory developed in this project have greatly extended the range of molecular materials that can be tackled by NAMD simulations. New algorithms to compute molecular excited state and response properties efficiently were developed. Fundamental limitations of common non-linear response methods were discovered and characterized. Methods for accurate computations of vibronic spectra of materials such as black absorbers were developed and applied. It was shown that open-shell TDDFT methods capture bond breaking in NAMD simulations, a longstanding challenge for single-reference molecular dynamics simulations. The methods developed in this project were applied to study the photodissociation of acetaldehyde and revealed that non-adiabatic effects are experimentally observable in fragment kinetic energy distributions. Finally, the project enabled the first detailed NAMD simulations of photocatalytic water oxidation by titania nanoclusters, uncovering the mechanism of this fundamentally important reaction for fuel generation and storage.
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.)
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.
Adiabatic Quantum Search in Open Systems.
Wild, Dominik S; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y; Lukin, Mikhail D
2016-10-07
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
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...
Adiabatic quantum gates and Boolean functions
Andrecut, M; Ali, M K [Department of Physics, University of Lethbridge, Lethbridge, AB, T1K 3M4 (Canada)
2004-06-25
We discuss the logical implementation of quantum gates and Boolean functions in the framework of quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language. (letter to the editor)
Adiabatic Quantum Search in Open Systems
Wild, Dominik S.; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y.; Lukin, Mikhail D.
2016-10-01
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Faster computation of adiabatic EMRIs using resonances
Grossman, Rebecca; Perez-Giz, Gabe
2011-01-01
Motivated by the prohibitive computational cost of producing adiabatic extreme mass ratio inspirals, we explain how a judicious use of resonant orbits can dramatically expedite both that calculation and the generation of snapshot gravitational waves from geodesic sources. In the course of our argument, we clarify the resolution of a lingering debate on the appropriate adiabatic averaging prescription in favor of torus averaging over time averaging.
Quantum Adiabatic Evolution Algorithms versus Simulated Annealing
Farhi, E; Gutmann, S; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function depends only on the Hamming weight of the n bits. We also give two examples, closely related to these, where the similarity breaks down in that the quantum adiabatic algorithm succeeds in polynomial time whereas simulated annealing requires exponential time.
Analysis of interference in attosecond transient absorption in adiabatic condition
Dong, Wenpu; Wang, Xiaowei; Zhao, Zengxiu
2015-01-01
We simulate the transient absorption of attosecond pulses of infrared laser-dressed atoms by considering a three-level system with the adiabatic approximation. We study the delay-dependent interference features in the transient absorption spectra of helium atoms from the perspective of the coherent interaction processes between the attosecond pulse and the quasi-harmonics, and find that many features of the interference fringes in the absorption spectra of the attosecond pulse can be attributed to the coherence phase difference. And the modulation signals of laser-induced sidebands of the dark state is found related to the dark state with population modulated by the dressing field.
Adiabatic invariants in stellar dynamics. 2: Gravitational shocking
Weinberg, Martin D.
1994-01-01
A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.
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.
Hierarchical theory of quantum adiabatic evolution
Zhang, Qi; Gong, Jiangbin; Wu, Biao
2014-12-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.
Assessment of total efficiency in adiabatic engines
Mitianiec, W.
2016-09-01
The paper presents influence of ceramic coating in all surfaces of the combustion chamber of SI four-stroke engine on working parameters mainly on heat balance and total efficiency. Three cases of engine were considered: standard without ceramic coating, fully adiabatic combustion chamber and engine with different thickness of ceramic coating. Consideration of adiabatic or semi-adiabatic engine was connected with mathematical modelling of heat transfer from the cylinder gas to the cooling medium. This model takes into account changeable convection coefficient based on the experimental formulas of Woschni, heat conductivity of multi-layer walls and also small effect of radiation in SI engines. The simulation model was elaborated with full heat transfer to the cooling medium and unsteady gas flow in the engine intake and exhaust systems. The computer program taking into account 0D model of engine processes in the cylinder and 1D model of gas flow was elaborated for determination of many basic engine thermodynamic parameters for Suzuki DR-Z400S 400 cc SI engine. The paper presents calculation results of influence of the ceramic coating thickness on indicated pressure, specific fuel consumption, cooling and exhaust heat losses. Next it were presented comparisons of effective power, heat losses in the cooling and exhaust systems, total efficiency in function of engine rotational speed and also comparison of temperature inside the cylinder for standard, semi-adiabatic and full adiabatic engine. On the basis of the achieved results it was found higher total efficiency of adiabatic engines at 2500 rpm from 27% for standard engine to 37% for full adiabatic engine.
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.``
Rapid adiabatic passage without level crossing
Rangelov, A A; Shore, B W
2009-01-01
We present a method for achieving complete population transfer in a two-state quantum system via adiabatic time evolution in which, contrary to conventional rapid adiabatic passage produced by chirped pulses, there occurs no crossing of diabatic energy curves: there is no sign change of the detuning. Instead, we use structured pulses, in which, in addition to satisfying conditions for adiabatic evolution, there occurs a sign change of the Rabi frequency when the detuning is zero. We present simulations that offer simple geometrical interpretation of the two-dimensional motion of the Bloch vector for this system, illustrating how both complete population inversion and complete population return occur for different choices of structured pulses.
Adiabatic optimization versus diffusion Monte Carlo methods
Jarret, Michael; Jordan, Stephen P.; Lackey, Brad
2016-10-01
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k -SAT at k =2 ,3 ,4 .
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
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-01-01
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.
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
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 in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
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.
Markovian quantum master equation beyond adiabatic regime
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τA(t ) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τA(t ) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Adiabatic Quantum Computation: Coherent Control Back Action
Goswami, Debabrata
2013-01-01
Though attractive from scalability aspects, optical approaches to quantum computing are highly prone to decoherence and rapid population loss due to nonradiative processes such as vibrational redistribution. We show that such effects can be reduced by adiabatic coherent control, in which quantum interference between multiple excitation pathways is used to cancel coupling to the unwanted, non-radiative channels. We focus on experimentally demonstrated adiabatic controlled population transfer experiments wherein the details on the coherence aspects are yet to be explored theoretically but are important for quantum computation. Such quantum computing schemes also form a back-action connection to coherent control developments. PMID:23788822
Adiabatic hyperspherical analysis of realistic nuclear potentials
Daily, K M; Greene, Chris H
2015-01-01
Using the hyperspherical adiabatic method with the realistic nuclear potentials Argonne V14, Argonne V18, and Argonne V18 with the Urbana IX three-body potential, we calculate the adiabatic potentials and the triton bound state energies. We find that a discrete variable representation with the slow variable discretization method along the hyperradial degree of freedom results in energies consistent with the literature. However, using a Laguerre basis results in missing energy, even when extrapolated to an infinite number of basis functions and channels. We do not include the isospin $T=3/2$ contribution in our analysis.
On adiabatic invariant in generalized Galileon theories
Ema, Yohei; 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 useful in estimating the expansion law of the universe and also the particle production rate due to the oscillation of the Hubble parameter.
Quench propagation analysis in adiabatic superconducting windings
Ishiyama, A.; Matsumura, H.; Takita, W. (Dept. of Electrical Engineering, Waseda Univ., Tokyo (JP)); Iwasa, Y (Massachusetts Inst. of Tech., Cambridge, MA (United States). Francis Bitter National Magnet Lab.)
1991-03-01
This paper reports the basic postulate of the author's quench simulation code, developed to analyze normal-zone propagation in adiabatic magnets which is the code's computation may be immensely simplified without sacrifice in accuracy by aggregating all thermal properties of the winding affecting normal-zone propagation into a single parameter of the transverse quench velocity. In order to verify this postulate, a finite element method (FEM) analysis has been applied to solve the temporal and spatial evolution of temperature within a section of an adiabatic magnet winding.
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...
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.
Adiabatic limit in Abelian Higgs model with application to Seiberg-Witten equations
Sergeev, A.
2017-03-01
In this paper we deal with the (2 + 1)-dimensional Higgs model governed by the Ginzburg-Landau Lagrangian. The static solutions of this model, called otherwise vortices, are described by the theorem of Taubes. This theorem gives, in particular, an explicit description of the moduli space of vortices (with respect to gauge transforms). However, much less is known about the moduli space of dynamical solutions. A description of slowly moving solutions may be given in terms of the adiabatic limit. In this limit the dynamical Ginzburg-Landau equations reduce to the adiabatic equation coinciding with the Euler equation for geodesics on the moduli space of vortices with respect to the Riemannian metric (called T-metric) determined by the kinetic energy of the model. A similar adiabatic limit procedure can be used to describe approximately solutions of the Seiberg-Witten equations on 4-dimensional symplectic manifolds. In this case the geodesics of T-metric are replaced by the pseudoholomorphic curves while the solutions of Seiberg-Witten equations reduce to the families of vortices defined in the normal planes to the limiting pseudoholomorphic curve. Such families should satisfy a nonlinear ∂-equation which can be considered as a complex analogue of the adiabatic equation. Respectively, the arising pseudoholomorphic curves may be considered as complex analogues of adiabatic geodesics in (2 + 1)-dimensional case. In this sense the Seiberg-Witten model may be treated as a (2 + 1)-dimensional analogue of the (2 + 1)-dimensional Abelian Higgs model2.
On Corrections to the Born-Oppenheimer Approximation
Kerley, Gerald I
2013-01-01
This report presents a new approach for treating the coupling of electrons and nuclei in quantum mechanical calculations for molecules and condensed matter. It includes the standard "Born-Oppenheimer approximation" as a special case but treats both adiabatic and non-adiabatic corrections using perturbation theory. The adiabatic corrections include all terms that do not explicitly involve the nuclear wavefunctions, so that the nuclei move on a single electronic potential surface. The non-adiabatic corrections, which allow the nuclei to move on more than one potential surface, include coupling between the electronic and nuclear wavefunctions. The method is related to an approach first proposed by Born and Huang, but it differs in the methodology and in the definition of the electronic wavefunctions and potential surfaces. A simple example is worked out to illustrate the mechanics of the technique. The report also includes a review of previous work.
Improving the positive feedback adiabatic logic familiy
J. Fischer
2004-01-01
Full Text Available Positive Feedback Adiabatic Logic (PFAL shows the lowest energy dissipation among adiabatic logic families based on cross-coupled transistors, due to the reduction of both adiabatic and non-adiabatic losses. The dissipation primarily depends on the resistance of the charging path, which consists of a single p-channel MOSFET during the recovery phase. In this paper, a new logic family called Improved PFAL (IPFAL is proposed, where all n- and pchannel devices are swapped so that the charge can be recovered through an n-channel MOSFET. This allows to decrease the resistance of the charging path up to a factor of 2, and it enables a significant reduction of the energy dissipation. Simulations based on a 0.13µm CMOS process confirm the improvements in terms of power consumption over a large frequency range. However, the same simple design rule, which enables in PFAL an additional reduction of the dissipation by optimal transistor sizing, does not apply to IPFAL. Therefore, the influence of several sources of dissipation for a generic IPFAL gate is illustrated and discussed, in order to lower the power consumption and achieve better performance.
Startup of an industrial adiabatic tubular reactor
Verwijs, J.W.; Berg, van den H.; Westerterp, K.R.
1992-01-01
The dynamic behaviour of an adiabatic tubular plant reactor during the startup is demonstrated, together with the impact of a feed-pump failure of one of the reactants. A dynamic model of the reactor system is presented, and the system response is calculated as a function of experimentally-determine
A Diffusion Equation for Quantum Adiabatic Systems
Jain, S R
1998-01-01
For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion.
Quantum Pumping and Adiabatic Transport in Nanostructures
Wakker, G.M.M.
2011-01-01
This thesis consists of a theoretical exploration of quantum transport phenomena and quantum dynamics in nanostructures. Specifically, we investigate adiabatic quantum pumping of charge in several novel types of nanostructures involving open quantum dots or graphene. For a bilayer of graphene we fin
Adiabatic limits,vanishing theorems and the noncommutative residue
无
2009-01-01
In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
Ion motion in the current sheet with sheared magnetic field – Part 1: Quasi-adiabatic theory
A. V. Artemyev
2013-02-01
Full Text Available We present a theory of trapped ion motion in the magnetotail current sheet with a constant dawn–dusk component of the magnetic field. Particle trajectories are described analytically using the quasi-adiabatic invariant corresponding to averaging of fast oscillations around the tangential component of the magnetic field. We consider particle dynamics in the quasi-adiabatic approximation and demonstrate that the principal role is played by large (so called geometrical jumps of the quasi-adiabatic invariant. These jumps appear due to the current sheet asymmetry related to the presence of the dawn–dusk magnetic field. The analytical description is compared with results of numerical integration. We show that there are four possible regimes of particle motion. Each regime is characterized by certain ranges of values of the dawn–dusk magnetic field and particle energy. We find the critical value of the dawn–dusk magnetic field, where jumps of the quasi-adiabatic invariant vanish.
Adiabatic and Non-adiabatic quenches in a Spin-1 Bose Einstein Condensate
Boguslawski, Matthew; Hebbe Madhusudhana, Bharath; Anquez, Martin; Robbins, Bryce; Barrios, Maryrose; Hoang, Thai; Chapman, Michael
2016-05-01
A quantum phase transition (QPT) is observed in a wide range of phenomena. We have studied the dynamics of a spin-1 ferromagnetic Bose-Einstein condensate for both adiabatic and non-adiabatic quenches through a QPT. At the quantum critical point (QCP), finite size effects lead to a non-zero gap, which makes an adiabatic quench possible through the QPT. We experimentally demonstrate such a quench, which is forbidden at the mean field level. For faster quenches through the QCP, the vanishing energy gap causes the reaction timescale of the system to diverge, preventing the system from adiabatically following the ground state. We measure the temporal evolution of the spin populations for different quench speeds and determine the exponents characterizing the scaling of the onset of excitations, which are in good agreement with the predictions of Kibble-Zurek mechanism.
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.
Hojman Exact Invariants and Adiabatic Invariants of Hamilton System
无
2007-01-01
The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higherorder adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of the results.
Non-adiabatic geometrical quantum gates in semiconductor quantum dots
Solinas, P; Zanghì, N; Rossi, F; Solinas, Paolo; Zanardi, Paolo; Zanghì, Nino; Rossi, Fausto
2003-01-01
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implemented
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...
Quantum-Classical Correspondence of Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2017-04-01
We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Korteweg-de Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of time-dependent parameters. We use the Hamilton-Jacobi theory to define the generalized action. The action is independent of the history of the parameters and is directly related to the adiabatic invariant. The dispersionless KdV hierarchy is obtained from the classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity. This correspondence suggests some relation between the quantum and classical adiabatic theorems.
Non-adiabatic perturbations in multi-component perfect fluids
Koshelev, N.A., E-mail: koshna71@inbox.ru [Ulyanovsk State University, Leo Tolstoy str 42, 432970 (Russian Federation)
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Diabatic and Adiabatic Collective Motion in a Model Pairing System
Nakatsukasa, T; Nakatsukasa, Takashi; Walet, Niels R.
1998-01-01
Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field theory or a direct parametrisation of the time-dependent Schrödinger equation. A modified local harmonic equation is formulated to take account of the Nambu-Goldstone mode. It turns out that in some cases the system selects a diabatic path. Requantizing the collective Hamiltonian, a reasonable agreement with an exact calculation for the low-lying levels are obtained for both weak and strong pairing force. This improves on results of the conventional Born-Oppenheimer approximation.
Effect of Poisson noise on adiabatic quantum control
Kiely, A.; Muga, J. G.; Ruschhaupt, A.
2017-01-01
We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and provide approximations for the different noise strength regimes. We show that using the eigenstates of the noise superoperator as a basis can be a useful way of expressing the master equation. Using this, we simulate various settings to illustrate different effects of Poisson noise. In particular, we show a dip in the fidelity as a function of noise strength where high fidelity can occur in the strong-noise regime for some cases. We also investigate recent claims [J. Jing et al., Phys. Rev. A 89, 032110 (2014), 10.1103/PhysRevA.89.032110] that this type of noise may improve rather than destroy adiabaticity.
Differential geometric treewidth estimation in adiabatic quantum computation
Wang, Chi; Jonckheere, Edmond; Brun, Todd
2016-10-01
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.
The best of both Reps—Diabatized Gaussians on adiabatic surfaces
Meek, Garrett A.; Levine, Benjamin G.
2016-11-01
When simulating nonadiabatic molecular dynamics, choosing an electronic representation requires consideration of well-known trade-offs. The uniqueness and spatially local couplings of the adiabatic representation come at the expense of an electronic wave function that changes discontinuously with nuclear motion and associated singularities in the nonadiabatic coupling matrix elements. The quasi-diabatic representation offers a smoothly varying wave function and finite couplings, but identification of a globally well-behaved quasi-diabatic representation is a system-specific challenge. In this work, we introduce the diabatized Gaussians on adiabatic surfaces (DGAS) approximation, a variant of the ab initio multiple spawning (AIMS) method that preserves the advantages of both electronic representations while avoiding their respective pitfalls. The DGAS wave function is expanded in a basis of vibronic functions that are continuous in both electronic and nuclear coordinates, but potentially discontinuous in time. Because the time-dependent Schrödinger equation contains only first-order derivatives with respect to time, singularities in the second-derivative nonadiabatic coupling terms (i.e., diagonal Born-Oppenheimer correction; DBOC) at conical intersections are rigorously absent, though singular time-derivative couplings remain. Interpolation of the electronic wave function allows the accurate prediction of population transfer probabilities even in the presence of the remaining singularities. We compare DGAS calculations of the dynamics of photoexcited ethene to AIMS calculations performed in the adiabatic representation, including the DBOC. The 28 fs excited state lifetime observed in DGAS simulations is considerably shorter than the 50 fs lifetime observed in the adiabatic simulations. The slower decay in the adiabatic representation is attributable to the large, repulsive DBOC in the neighborhood of conical intersections. These repulsive DBOC terms are artifacts
Adiabatic quantum simulation of quantum chemistry.
Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-10-13
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.
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 Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
Adiabatic Quantum Optimization for Associative Memory Recall
Seddiqi, Hadayat; Humble, Travis
2014-12-01
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.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥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 correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Comment on ``Adiabatic theory for the bipolaron''
Smondyrev, M. A.; Devreese, J. T.
1996-05-01
Comments are given on the application of the Bogoliubov-Tyablikov approach to the bipolaron problem in a recent paper by Lakhno [Phys. Rev. B 51, 3512 (1995)]. This author believes that his model (1) is the translation-invariant adiabatic theory of bipolarons and (2) gives asymptotically exact solutions in the adiabatic limit while the other approaches are considered as either phenomenological or variational in nature. Numerical results by Lakhno are in contradiction with all other papers published on the subject because his model leads to much lower energies. Thus, the author concludes that bipolarons ``are more stable than was considered before.'' We prove that both the analytical and the numerical results presented by Lakhno are wrong.
Limitations of some simple adiabatic quantum algorithms
Ioannou, L M; Ioannou, Lawrence M.; Mosca, Michele
2007-01-01
Let $H(t)=(1-t/T)H_0 + (t/T)H_1$, $t\\in [0,T]$, be the Hamiltonian governing an adiabatic quantum algorithm, where $H_0$ is diagonal in the Hadamard basis and $H_1$ is diagonal in the computational basis. We prove that $H_0$ and $H_1$ must each have at least two large mutually-orthogonal eigenspaces if the algorithm's running time is to be subexponential in the number of qubits. We also reproduce the optimality proof of Farhi and Gutmann's search algorithm in the context of this adiabatic scheme; because we only consider initial Hamiltonians that are diagonal in the Hadamard basis, our result is slightly stronger than the original.
Finding cliques by quantum adiabatic evolution
Childs, A M; Goldstone, J; Gutmann, S; Childs, Andrew M.; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate (n <= 18), the quantum algorithm appears to require only a quadratic run time.
Ehrenfest's adiabatic hypothesis in Bohr's quantum theory
Pérez, Enric
2015-01-01
It is widely known that Paul Ehrenfest formulated and applied his adiabatic hypothesis in the early 1910s. Niels Bohr, in his first attempt to construct a quantum theory in 1916, used it for fundamental purposes in a paper which eventually did not reach the press. He decided not to publish it after having received the new results by Sommerfeld in Munich. Two years later, Bohr published "On the quantum theory of line-spectra." There, the adiabatic hypothesis played an important role, although it appeared with another name: the principle of mechanical transformability. In the subsequent variations of his theory, Bohr never suppressed this principle completely. We discuss the role of Ehrenfest's principle in the works of Bohr, paying special attention to its relation to the correspondence principle. We will also consider how Ehrenfest faced Bohr's uses of his more celebrated contribution to quantum theory, as well as his own participation in the spreading of Bohr's ideas.
Vibrational dynamics of the bifluoride ion. II. Adiabatic separation and proton dynamics
Epa, V. C.; Thorson, W. R.
1990-01-01
Vibrational dynamics of the bifluoride ion FHF-, which exhibits strongly anharmonic and nonseparable vibrations, is studied using the extended ab initio model potential surface described in the first paper of this series. Adiabatic separation of the proton motion from the F-F (ν1) motion forms a zero-order basis for description, although strong coupling of adiabatic states by the ν1 motion is important in higher vibrational levels and must be considered to understand the spectrum. The adiabatic protonic eigenstates at F-F separations R from 3.75 to 6.40 a.u. have been determined using the self-consistent field approximation in prolate spheroidal coordinates to provide a basis set for configuration interaction expansion of the exact eigenstates. 78 SCF eigenstates (21 σg, 21 σu, 21 πu, and 15 πg) were computed by ``exact'' numerical solution of the SCF equations. The adiabatic CI eigenstates are shown to be converged in energy to better than 1.0 cm-1 for the ground state of each symmetry type and usually better than 10 cm-1 for the lowest three to five states, and pass critical tests of accuracy such as the Hellmann-Feynman theorem. The resulting CI potential energy curves closely resemble corresponding SCF energy curves and justify the concept of mode separation even in this very anharmonic system. The adiabatic CI potential energy curves explain most aspects of the dynamics relevant to the IR and Raman spectra of FHF- (e.g., in KHF2), and calculations of ν1 dynamics within the adiabatic approximation suffice to assign most of the observed IR spectrum of KHF2(s) (to about 6000 cm-1). States corresponding qualitatively to modal overtone and combination levels such as 3ν2 and (ν2+2ν3) however exhibit avoided crossings in the neighborhood of the equilibrium configuration and ``Fermi resonance'' involving interactions of two or more such adiabatic states via the ν1 motion must be treated by close-coupling to predict both frequencies and intensities in the
Nanowire Plasmon Excitation by Adiabatic Mode Transformation
Verhagen, Ewold; Spasenović, Marko; Polman, Albert; Kuipers, L. (Kobus)
2009-05-01
We show with both experiment and calculation that highly confined surface plasmon polaritons can be efficiently excited on metallic nanowires through the process of mode transformation. One specific mode in a metallic waveguide is identified that adiabatically transforms to the confined nanowire mode as the waveguide width is reduced. Phase- and polarization-sensitive near-field investigation reveals the characteristic antisymmetric polarization nature of the mode and explains the coupling mechanism.
Pulse-driven near-resonant quantum adiabatic dynamics: lifting of quasi-degeneracy
Yatsenko, L P; Jauslin, H R
2003-01-01
We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power law rising. This allows us to determine approximative formulas for the lineshape of resonant excitation by various forms of pulses such as truncated trig-pulses. We also analyze and explain the various superpositions of states that can be obtained by the Half Stark Chirped Rapid Adiabatic Passage (Half-SCRAP) process.
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...
Temperature dependent parameters of stability and protection in an adiabatic niobium titanium coil
Brown, J.N. IV. (Michelin, Greenville, SC (US)); Tahara, Y. (Mitsubishi Electric Ako Works, Ako (JP)); Williams, J.E.C.; Iwasa, Y. (Massachusetts Inst. of Tech., Cambridge, MA (United States). Francis Bitter National Magnet Lab.)
1991-03-01
Experiments were performed to determine temperature-dependent parameters of stability and protection in a small adiabatic niobium titanium test magnet. Quench propagation velocity and minimum quench energy were measured as a function of operating temperature, transport current, and magnetic field. The operating temperature was controlled in an isothermal environment between 4.2 K and {approximately} 8 K. An existing computer code was modified to accurately predict the magnet's behavior within the temperature range. The aim of the paper is to develop improved analytical models of the effect of temperature parameters on stability in order to expand the author's understanding of thermal behaviors of adiabatic magnets operating at temperatures up to {approximately} 100 K.
The adiabatic electron affinities (EAs) for the heteroatomic molecule SO 4: An MP2/CBS study
Zheng, Wenxu; Lau, Kai-Chung; Wong, Ning-Bew; Li, Wai-Kee
2009-01-01
An MP2/CBS approach has been proposed to calculate the adiabatic electron affinities (EAs) for the heteroatomic molecule SO 4. The method involves the approximation to the complete basis set (CBS) limit at the MP2 level. The zero-point vibrational energy correction, the diagonal Born-Oppenheimer correction, and the scalar relativistic effect correction have been also made in the calculations. The present MP2/CBS predictions are found to be in good accord with the available experimental values.
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.
Adiabatic Regularization for Gauge Field and the Conformal Anomaly
Chu, Chong-Sun
2016-01-01
We construct and provide the adiabatic regularization method for a $U(1)$ gauge field in a conformally flat spacetime by quantizing in the canonical formalism the gauge fixed $U(1)$ theory with mass terms for the gauge fields and the ghost fields. We show that the adiabatic expansion for the mode functions and the adiabatic vacuum can be defined in a similar way using WKB-type solutions as the scalar fields. As an application of the adiabatic method, we compute the trace of the energy momentum tensor and reproduces the known result for the conformal anomaly obtained by the other regularization methods. The availability of the adiabatic expansion scheme for gauge field allows one to study the renormalization of the de-Sitter space maximal superconformal Yang-Mills theory using the adiabatic regularization method.
On adiabatic perturbations in the ekpyrotic scenario
Linde, A.; Mukhanov, V.; Vikman, A.
2010-02-01
In a recent paper, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in Khoury are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario.
On adiabatic perturbations in the ekpyrotic scenario
Linde, A; Vikman, A
2009-01-01
In a recent paper arXiv:0910.2230, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in arXiv:0910.2230 are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario.
Shortcuts to adiabaticity for quantum annealing
Takahashi, Kazutaka
2017-01-01
We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz, and the Hamiltonian is designed by the inverse engineering. We show that the time dependence of physical quantities such as the magnetization is independent of the speed of the Hamiltonian variation in the infinite-range model. We also show that rotating transverse magnetic fields are useful to achieve the ideal time evolution.
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 Wave-Particle Interaction Revisited
Dewar, R L; 10.1585/pfr.4.001
2009-01-01
In this paper we calculate and visualize the dynamics of an ensemble of electrons trapping in an electrostatic wave of slowly increasing amplitude, illustrating that, despite disordering of particles in angle during the trapping transition as they pass close to X-points, there is still an adiabatic invariant for the great majority of particles that allows the long-time distribution function to be predicted. Possible application of this approach to recent work on the nonlinear frequency shift of a driven wave is briefly discussed.
Adiabatic geometric phases and response functions
Jain, S R; Jain, Sudhir R.; Pati, Arun K.
1998-01-01
Treating a many-body Fermi system in terms of a single particle in a deforming mean field. We relate adiabatic geometric phase to susceptibility for the noncyclic case, and to its derivative for the cyclic case. Employing the semiclassical expression of susceptibility, the expression for geometric phase for chaotic quantum system immediately follows. Exploiting the well-known association of the absorptive part of susceptibility with dissipation, our relations may provide a quantum mechanical origin of the damping of collective excitations in Fermi systems.
Adiabatic passage in the presence of noise
Noel, T; Kurz, N; Shu, G; Wright, J; Blinov, B B
2011-01-01
We report on an experimental investigation of rapid adiabatic passage (RAP) in a trapped barium ion system. RAP is implemented on the transition from the $6S_{1/2}$ ground state to the metastable $5D_{5/2}$ level by applying a laser at 1.76 $\\mu$m. We focus on the interplay of laser frequency noise and laser power in shaping the effectiveness of RAP, which is commonly assumed to be a robust tool for high efficiency population transfer. However, we note that reaching high state transfer fidelity requires a combination of small laser linewidth and large Rabi frequency.
Quantum Adiabatic Evolution Algorithms with Different Paths
Farhi, E; Gutmann, S; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes the solution of the computational problem. These algorithms have generally been studied in the case where the "straight line" path from initial to final Hamiltonian is taken. But there is no reason not to try paths involving terms that are not linear combinations of the initial and final Hamiltonians. We give several proposals for randomly generating new paths. Using one of these proposals, we convert an algorithmic failure into a success.
Adiabatic quantum computation and quantum phase transitions
Latorre, J I; Latorre, Jose Ignacio; Orus, Roman
2003-01-01
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.
Generalized Ramsey numbers through adiabatic quantum optimization
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
Relaxation versus adiabatic quantum steady-state preparation
Venuti, Lorenzo Campos; Albash, Tameem; Marvian, Milad; Lidar, Daniel; Zanardi, Paolo
2017-04-01
Adiabatic preparation of the ground states of many-body Hamiltonians in the closed-system limit is at the heart of adiabatic quantum computation, but in reality systems are always open. This motivates a natural comparison between, on the one hand, adiabatic preparation of steady states of Lindbladian generators and, on the other hand, relaxation towards the same steady states subject to the final Lindbladian of the adiabatic process. In this work we thus adopt the perspective that the goal is the most efficient possible preparation of such steady states, rather than ground states. Using known rigorous bounds for the open-system adiabatic theorem and for mixing times, we are then led to a disturbing conclusion that at first appears to doom efforts to build physical quantum annealers: relaxation seems to always converge faster than adiabatic preparation. However, by carefully estimating the adiabatic preparation time for Lindbladians describing thermalization in the low-temperature limit, we show that there is, after all, room for an adiabatic speedup over relaxation. To test the analytically derived bounds for the adiabatic preparation time and the relaxation time, we numerically study three models: a dissipative quasifree fermionic chain, a single qubit coupled to a thermal bath, and the "spike" problem of n qubits coupled to a thermal bath. Via these models we find that the answer to the "which wins" question depends for each model on the temperature and the system-bath coupling strength. In the case of the "spike" problem we find that relaxation during the adiabatic evolution plays an important role in ensuring a speedup over the final-time relaxation procedure. Thus, relaxation-assisted adiabatic preparation can be more efficient than both pure adiabatic evolution and pure relaxation.
Generating shortcuts to adiabaticity in quantum and classical dynamics
Jarzynski, Christopher
2013-01-01
Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counter-diabatic Hamiltonian to stifle non-adiabatic transitions. Here this strategy is cast in terms of a generator of adiabatic transport, leading to a classical analogue: dissipationless classical driving. For the single-particle piston, this approach yields simple and exact expressions for both the classical and quantal counter-diabatic terms. These results are further generalized to even-power-law potentials in one degree of freedom.
Exact invariants and adiabatic invariants of the singular Lagrange system
陈向炜; 李彦敏
2003-01-01
Based on the theory of symmetries and conserved quantities of the singular Lagrange system,the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed.Firstly,the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed.Then,the conditions for the existence of the exact invariants and adiabatic invariants are proved,and their forms are given.Finally,an example is presented to illustrate these results.
Correlated mixtures of adiabatic and isocurvature cosmological perturbations
Langlois, D; Langlois, David; Riazuelo, Alain
2000-01-01
We examine the consequences of the existence of correlated mixtures of adiabatic and isocurvature perturbations on the CMB and large scale structure. In particular, we consider the four types of ``elementary'' totally correlated hybrid initial conditions, where only one of the four matter species (photons, baryons, neutrinos, CDM) deviates from adiabaticity. We then study the height and position of the acoustic peaks with respect to the large angular scale plateau as a function of the isocurvature to adiabatic ratio.
Patrick, Christopher E.; Thygesen, Kristian Sommer
2015-01-01
for the homogeneous electron gas (HEG), including the recently introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence, or (c) display a 1/k2 divergence for small wavevectors. After generalizing...... whilst maintaining a high-accuracy description of structural properties....
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.
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...
Quantum Adiabatic Algorithms and Large Spin Tunnelling
Boulatov, A.; Smelyanskiy, V. N.
2003-01-01
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
The genesis of adiabatic shear bands
Landau, P.; Osovski, S.; Venkert, A.; Gärtnerová, V.; Rittel, D.
2016-11-01
Adiabatic shear banding (ASB) is a unique dynamic failure mechanism that results in an unpredicted catastrophic failure due to a concentrated shear deformation mode. It is universally considered as a material or structural instability and as such, ASB is hardly controllable or predictable to some extent. ASB is modeled on the premise of stability analyses. The leading paradigm is that a competition between strain (rate) hardening and thermal softening determines the onset of the failure. It was recently shown that microstructural softening transformations, such as dynamic recrystallization, are responsible for adiabatic shear failure. These are dictated by the stored energy of cold work, so that energy considerations can be used to macroscopically model the failure mechanism. The initial mechanisms that lead to final failure are still unknown, as well as the ASB formation mechanism(s). Most of all - is ASB an abrupt instability or rather a gradual transition as would be dictated by microstructural evolutions? This paper reports thorough microstructural characterizations that clearly show the gradual character of the phenomenon, best described as a nucleation and growth failure mechanism, and not as an abrupt instability as previously thought. These observations are coupled to a simple numerical model that illustrates them.
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 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.
1984-07-16
Plasmas," JAYCOR Report J207-81-004, January, 1981 . 6. R. PoI, D. Fisher, T. Wilcox , S. Wong, H. Sze, L. Deraad anld W. Tsai, "Experiments on, Multiple...step with this are both r 2E and r at -0.52 cm (in from -0.66 cm thisare oth / ndE 1/20 at 2.48 ns) and the velocity profile for r>0.5245 cm is
Galley, Chad R
2016-01-01
We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 \
Galley, Chad R.; Rothstein, Ira Z.
2017-05-01
We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is v5ν Ω (t -t0) where t0 is the initial time, t is the time elapsed, and Ω and v are the angular orbital frequency and initial speed, respectively. ν is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second-order corrections of the leading radiation reaction force, which involves highly nontrivial checks of the formalism (i.e., its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging, we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.
Adiabatic isometric mapping algorithm for embedding 2-surfaces in Euclidean 3-space
Ray, Shannon; Miller, Warner A.; Alsing, Paul M.; Yau, Shing-Tung
2015-12-01
Alexandrov proved that any simplicial complex homeomorphic to a sphere with strictly non-negative Gaussian curvature at each vertex can be isometrically embedded uniquely in {{{R}}}3 as a convex polyhedron. Due to the nonconstructive nature of his proof, there have yet to be any algorithms, that we know of, that realizes the Alexandrov embedding in polynomial time. Following his proof, we developed the adiabatic isometric mapping (AIM) algorithm. AIM uses a guided adiabatic pull-back procedure on a given polyhedral metric to produce an embedding that approximates the unique Alexandrov polyhedron. Tests of AIM applied to two different polyhedral metrics suggests that its run time is sub cubic with respect to the number of vertices. Although Alexandrov’s theorem specifically addresses the embedding of convex polyhedral metrics, we tested AIM on a broader class of polyhedral metrics that included regions of negative Gaussian curvature. One test was on a surface just outside the ergosphere of a Kerr black hole.
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; 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.
The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems
Ausländer, O M; Auslaender, Ophir M.; Fishman, Shmuel
1999-01-01
The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time ...
First-order derivative couplings between excited states from adiabatic TDDFT response theory.
Ou, Qi; Bellchambers, Gregory D; Furche, Filipp; Subotnik, Joseph E
2015-02-14
We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefunction ansatz. For degenerate excited states, i.e., close to a conical intersection (CI), the two approaches are identical apart from an antisymmetric overlap term. However, if the difference between two excitation energies equals another excitation energy, the couplings from response theory exhibit an unphysical divergence. This spurious behavior is a result of the adiabatic or static kernel approximation of time-dependent density functional theory leading to an incorrect analytical structure of the quadratic response function. Numerical examples for couplings close to a CI and for well-separated electronic states are given.
Adiabat-shaping in indirect drive inertial confinement fusion
Baker, K. L.; Robey, H. F.; Milovich, J. L.; Jones, O. S.; Smalyuk, V. A.; Casey, D. T.; MacPhee, A. G.; Pak, A.; Celliers, P. M.; Clark, D. S.; Landen, O. L.; Peterson, J. L.; Berzak-Hopkins, L. F.; Weber, C. R.; Haan, S. W.; Döppner, T. D.; Dixit, S.; Hamza, A. V.; Jancaitis, K. S.; Kroll, J. J. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); and others
2015-05-15
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.
Constraints on the Adiabatic Temperature Change in Magnetocaloric Materials
Nielsen, Kaspar Kirstein; Bahl, Christian Robert Haffenden; Smith, Anders
2010-01-01
The thermodynamics of the magnetocaloric effect implies constraints on the allowed variation in the adiabatic temperature change for a magnetocaloric material. An inequality for the derivative of the adiabatic temperature change with respect to temperature is derived for both first- and second...
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.
Sufficient Condition for Validity of Quantum Adiabatic Theorem
TAO Yong
2012-01-01
In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408].
Kinetic Theory Derivation of the Adiabatic Law for Ideal Gases.
Sobel, Michael I.
1980-01-01
Discusses how the adiabatic law for ideal gases can be derived from the assumption of a Maxwell-Boltzmann (or any other) distribution of velocities--in contrast to the usual derivations from thermodynamics alone, and the higher-order effect that leads to one-body viscosity. An elementary derivation of the adiabatic law is given. (Author/DS)
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.
Shortcuts to adiabaticity in cutting a spin chain
Ren, Feng-Hua; Wang, Zhao-Ming; Gu, Yong-Jian
2017-01-01
"Shortcuts to adiabaticity" represents a strategy for accelerating a quantum adiabatic process, is useful for preparing or manipulating a quantum state. In this paper, we investigate the adiabaticity in the dynamics of an XY spin chain. During the process of cutting one long chain into two short chains, a "shortcut" can be obtained by applying a sequence of external pulses. The fidelity which measures the adiabaticity can be dramatically enhanced by increasing the pulse strength or pulse duration time. This reliability can be kept for different types of pulses, such as random pulse time interval or random strength. The free choice of the pulse can be explained by the adiabatic representation of the Hamiltonian, and it shows that the control effects are determined by the integral of the control function in the time domain.
An Integrated Development Environment for Adiabatic Quantum Programming
Humble, Travis S [ORNL; McCaskey, Alex [ORNL; Bennink, Ryan S [ORNL; Billings, Jay Jay [ORNL; D' Azevedo, Eduardo [ORNL; Sullivan, Blair D [ORNL; Klymko, Christine F [ORNL; Seddiqi, Hadayat [ORNL
2014-01-01
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware raises the question of how well quantum programs perform. Benchmarking behavior is challenging since the multiple steps to synthesize an adiabatic quantum program are highly tunable. We present an adiabatic quantum programming environment called JADE that provides control over all the steps taken during program development. JADE captures the workflow needed to rigorously benchmark performance while also allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation engine that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its use for benchmarking adiabatic quantum programs.
Thermodynamic Study of Energy Dissipation in Adiabatic Superconductor Logic
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-09-01
Because of its extremely high energy efficiency, adiabatic superconductor logic is one of the most promising candidates for the realization of a practical reversible computer. In a previous study, we proposed a logically and physically reversible logic gate using adiabatic superconductor logic, and numerically demonstrated reversible computing. In the numerical calculation, we assumed that the average energy dissipation at finite temperature corresponds to that at zero temperature. However, how the phase difference of a Josephson junction in adiabatic superconductor logic behaves at finite temperature is not yet well understood, and whether thermal noise can induce a nonadiabatic state change remains unclear. In the present study, we investigate energy dissipation in adiabatic superconductor logic at finite temperature through numerical analyses using the Monte Carlo method. We investigate the average and standard deviation of the energy dissipation through both numerical calculation and analytical estimation. Finally, we discuss the minimum energy dissipation required for adiabatic switching operations.
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...
Investigating the Performance of an Adiabatic Quantum Optimization Processor
Rose, Geordie; Dickson, Neil G; Hamze, Firas; Amin, M H S; Drew-Brook, Marshall; Chudak, Fabian A; Bunyk, Paul I; Macready, William G
2010-01-01
We calculate median adiabatic times (in seconds) of a specific superconducting adiabatic quantum processor for an NP-hard Ising spin glass instance class with up to N=128 binary variables. To do so, we ran high performance Quantum Monte Carlo simulations on a large-scale Internet-based computing platform. We compare the median adiabatic times with the median running times of two classical solvers and find that, for problems with up to 128 variables, the adiabatic times for the simulated processor architecture are about 4 and 6 orders of magnitude shorter than the two classical solvers' times. This performance difference shows that, even in the potential absence of a scaling advantage, adiabatic quantum optimization may outperform classical solvers.
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...
Adiabatic/diabatic polarization beam splitter
DeRose, Christopher; Cai, Hong
2017-09-12
The various presented herein relate to an on-chip polarization beam splitter (PBS), which is adiabatic for the transverse magnetic (TM) mode and diabatic for the transverse electric (TE) mode. The PBS comprises a through waveguide and a cross waveguide, wherein an electromagnetic beam comprising TE mode and TM mode components is applied to an input port of the through waveguide. The PBS can be utilized to separate the TE mode component from the TM mode component, wherein the TE mode component exits the PBS via an output port of the through waveguide, and the TM mode component exits the PBS via an output port of the cross waveguide. The PBS has a structure that is tolerant to manufacturing variations and exhibits high polarization extinction ratios over a wide bandwidth.
Multiplicity features of adiabatic autothermal reactors
Lovo, M.; Balakotaiah, V. (Houston Univ., TX (United States). Dept. of Chemical Engineering)
1992-01-01
In this paper singularity theory, large activation energy asymptotic, and numerical methods are used to present a comprehensive study of the steady-state multiplicity features of three classical adiabatic autothermal reactor models: tubular reactor with internal heat exchange, tubular reactor with external heat exchange, and the CSTR with external heat exchange. Specifically, the authors derive the exact uniqueness-multiplicity boundary, determine typical cross-sections of the bifurcation set, and classify the different types of bifurcation diagrams of conversion vs. residence time. Asymptotic (limiting) models are used to determine analytical expressions for the uniqueness boundary and the ignition and extinction points. The analytical results are used to present simple, explicit and accurate expressions defining the boundary of the region of autothermal operation in the physical parameter space.
Reversible logic gate using adiabatic superconducting devices
Takeuchi, N.; Yamanashi, Y.; Yoshikawa, N.
2014-09-01
Reversible computing has been studied since Rolf Landauer advanced the argument that has come to be known as Landauer's principle. This principle states that there is no minimum energy dissipation for logic operations in reversible computing, because it is not accompanied by reductions in information entropy. However, until now, no practical reversible logic gates have been demonstrated. One of the problems is that reversible logic gates must be built by using extremely energy-efficient logic devices. Another difficulty is that reversible logic gates must be both logically and physically reversible. Here we propose the first practical reversible logic gate using adiabatic superconducting devices and experimentally demonstrate the logical and physical reversibility of the gate. Additionally, we estimate the energy dissipation of the gate, and discuss the minimum energy dissipation required for reversible logic operations. It is expected that the results of this study will enable reversible computing to move from the theoretical stage into practical usage.
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.
Sliding seal materials for adiabatic engines
Lankford, J.
1985-01-01
The sliding friction coefficients and wear rates of promising carbide, oxide, and nitride materials were measured under temperature, environmental, velocity, loading conditions that are representative of the adiabatic engine environment. In order to provide guidance needed to improve materials for this application, the program stressed fundamental understanding of the mechanisms involved in friction and wear. Microhardness tests were performed on the candidate materials at elevated temperatures, and in atmospheres relevant to the piston seal application, and optical and electron microscopy were used to elucidate the micromechanisms of wear following wear testing. X-ray spectroscopy was used to evaluate interface/environment interactions which seemed to be important in the friction and wear process. Electrical effects in the friction and wear processes were explored in order to evaluate the potential usefulness of such effects in modifying the friction and wear rates in service. However, this factor was found to be of negligible significance in controlling friction and wear.
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.
Adiabatic scaling relations of galaxy clusters
Ascasibar, Y; Yepes, G; Müller, V; Gottlöber, S
2006-01-01
The aim of the present work is to show that, contrary to popular belief, galaxy clusters are **not** expected to be self-similar, even when the only energy sources available are gravity and shock-wave heating. In particular, we investigate the scaling relations between mass, luminosity and temperature of galaxy groups and clusters in the absence of radiative processes. Theoretical expectations are derived from a polytropic model of the intracluster medium and compared with the results of high-resolution adiabatic gasdynamical simulations. It is shown that, in addition to the well-known relation between the mass and concentration of the dark matter halo, the effective polytropic index of the gas also varies systematically with cluster mass, and therefore neither the dark matter nor the gas profiles are exactly self-similar. It is remarkable, though, that the effects of concentration and polytropic index tend to cancel each other, leading to scaling relations whose logarithmic slopes roughly match the predictio...
Adiabatic perturbations in coupled scalar field cosmologies
Beyer, Joschka
2014-01-01
We present a comprehensive and gauge invariant treatment of perturbations around cosmological scaling solutions for two canonical scalar fields coupled through a common potential in the early universe, in the presence of neutrinos, photons and baryons, but excluding cold dark matter. This setup is relevant for analyzing cosmic perturbations in scalar field models of dark matter with a coupling to a quintessence field. We put strong restrictions on the shape of the common potential and adopt a matrix-eigensystem approach to determine the dominant perturbations modes in such models. Similar to recent results in scenarios where standard cold dark matter couples to quintessence, we show that the stability of the adiabatic perturbation mode can be an issue for this class of scalar field dark matter models, but only for specific choices of the common potential. For an exponential coupling potential, a rather common shape arising naturally in many instances, this problem can be avoided. We explicitly calculate the d...
Adiabatic density-functional perturbation theory
Gonze, Xavier
1995-08-01
The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green's function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ``parallel-transport-gauge'' and a ``diagonal-gauge'' perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.
An adiabatic demagnetization refrigerator for SIRTF
Timbie, P. T.; Bernstein, G. M.; Richards, P. L.
1989-02-01
An adiabatic demagnetization refrigerator (ADR) has been proposed to cool bolometric infrared detectors on the multiband imaging photometer of the Space Infrared Telescope Facility (SIRTF). One such refrigerator has been built which uses a ferric ammonium alum salt pill suspended by nylon threads in a 3-T solenoid. The resonant modes of this suspension are above 100 Hz. The heat leak to the salt pill is less than 0.5 microW. The system has a hold time at 0.1K of more than 12 h. The cold stage temperature is regulated with a feedback loop that controls the magnetic field. A second, similar refrigerator is being built at a SIRTF prototype to fly on a ballon-borne telescope. It will use a ferromagnetic shield. The possibility of using a high-Tc solenoid-actuated heat switch is also discussed.
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.
Hollenberg, Sebastian
2011-01-01
The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and non-adiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g. matter) potentials. Neglecting effects of ensemble decoherence for now we study the evolution of a neutrino ensemble governed by the associated Quantum Kinetic Equations, which apply to systems with finite temperature. The Quantum Kinetic Equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g. the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g. an effective oscillation length). It is understood that this method also provides a promising starting point for...
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
Thermodynamic and spectral properties of adiabatic Peierls chains
Weber, Manuel; Assaad, Fakher F.; Hohenadler, Martin
2016-10-01
We present exact numerical results for the effects of thermal fluctuations on the experimentally relevant thermodynamic and spectral properties of Peierls chains. To this end, a combination of classical Monte Carlo sampling and exact diagonalization is used to study adiabatic half-filled Holstein and Su-Schrieffer-Heeger models. The classical nature of the lattice displacements in combination with parallel tempering permit simulations on large system sizes and a direct calculation of spectral functions in the frequency domain. Most notably, the long-range order and the associated Peierls gap give rise to a distinct low-temperature peak in the specific heat. The closing of the gap and suppression of order by thermal fluctuations involves in-gap excitations in the form of soliton-antisoliton pairs and is also reflected in the dynamic density and bond structure factors as well as in the optical conductivity. We compare our data to the widely used mean-field approximation and highlight relations to symmetry-protected topological phases and disorder problems.
Adiabatically deformed ensemble: Engineering nonthermal states of matter
Kennes, D. M.
2017-07-01
We propose a route towards engineering nonthermal states of matter, which show largely unexplored physics. The main idea relies on the adiabatic passage of a thermal ensemble under slow variations of the system Hamiltonian. If the temperature of the initial thermal ensemble is either zero or infinite, the ensemble after the passage is a simple thermal one with the same vanishing or infinite temperature. However, for any finite nonzero temperature, intriguing nonthermal ensembles can be achieved. We exemplify this in (a) a single oscillator, (b) a dimerized interacting one-dimensional chain of spinless fermions, (c) a BCS-type superconductor, and (d) the topological Kitaev chain. We solve these models with a combination of methods: either exactly, numerically using the density matrix renormalization group, or within an approximate functional renormalization group scheme. The designed states show strongly nonthermal behavior in each of the considered models. For example, for the chain of spinless fermions we exemplify how long-ranged nonthermal power-law correlations can be stabilized, and for the Kitaev chain we elucidate how the nonthermal ensemble can largely alter the transition temperature separating topological and trivial phases.
On the General Class of Models of Adiabatic Evolution
Sun, Jie; Lu, Songfeng; Liu, Fang
2016-10-01
The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown [8] that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.
EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS
陈向炜; 尚玫; 梅凤翔
2001-01-01
A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.
Adiabatic control of atomic dressed states for transport and sensing
Cooper, N. R.; Rey, A. M.
2015-08-01
We describe forms of adiabatic transport that arise for dressed-state atoms in optical lattices. Focusing on the limit of weak tunnel-coupling between nearest-neighbor lattice sites, we explain how adiabatic variation of optical dressing allows control of atomic motion between lattice sites: allowing adiabatic particle transport in a direction that depends on the internal state, and force measurements via spectroscopic preparation and readout. For uniformly filled bands these systems display topologically quantized particle transport. An implementation of the dressing scheme using optical transitions in alkaline-earth atoms is discussed as well as its favorable features for precise force sensing.
Achromatic multiple beam splitting by adiabatic passage in optical waveguides
Rangelov, Andon A
2012-01-01
A novel variable achromatic optical beam splitter with one input and $N$ output waveguide channels is introduced. The physical mechanism of this multiple beam splitter is adiabatic passage of light between neighboring optical waveguides in a fashion reminiscent of the technique of stimulated Raman adiabatic passage in quantum physics. The input and output waveguides are coupled via a mediator waveguide and the ratios of the light intensities in the output channels are controlled by the couplings of the respective waveguides to the mediator waveguide. Due to its adiabatic nature the beam splitting efficiency is robust to variations in the experimental parameters.
Adiabatic quantum algorithm for search engine ranking.
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A
2012-06-08
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of 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 algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
Adiabatic Quantum Algorithm for Search Engine Ranking
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A.
2012-06-01
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of 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 algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in “q-sampling” protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
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...
Topological States and Adiabatic Pumping in Quasicrystals
Kraus, Yaakov; Lahini, Yoav; Ringel, Zohar; Verbin, Mor; Zilberberg, Oded
2012-02-01
We find a connection between quasicrystals and topological matter, namely that quasicrystals exhibit non-trivial topological phases attributed to dimensions higher than their own [1]. Quasicrystals are materials which are neither ordered nor disordered, i.e. they exhibit only long-range order [2]. This long-range order is usually expressed as a projection from a higher dimensional ordered system. Recently, the unrelated discovery of Topological Insulators [3] defined a new type of materials classified by their topology. We show theoretically and experimentally using photonic lattices, that one-dimensional quasicrystals exhibit topologically-protected boundary states equivalent to the edge states of the two-dimensional Integer Quantum Hall Effect. We harness this property to adiabatically pump light across the quasicrystal, and generalize our results to higher dimensional systems. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.[4pt] [1] Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, arXiv:1109.5983 (2011).[0pt] [2] C. Janot, Quasicrystals (Clarendon, Oxford, 1994), 2nd ed.[0pt] [3] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
Low-power adiabatic 9T static random access memory
Yasuhiro Takahashi
2014-06-01
Full Text Available In this paper, the authors propose a novel static random access memory (SRAM that employs the adiabatic logic principle. To reduce energy dissipation, the proposed adiabatic SRAM is driven by two trapezoidal-wave pulses. The cell structure of the proposed SRAM has two high-value resistors based on a p-type metal-oxide semiconductor transistor, a cross-coupled n-type metal-oxide semiconductor (NMOS pair and an NMOS switch to reduce the short-circuit current. The inclusion of a transmission-gate controlled by a write word line signal allows the proposed circuit to operate as an adiabatic SRAM during data writing. Simulation results show that the energy dissipation of the proposed SRAM is lower than that of a conventional adiabatic SRAM.
Adiabaticity and diabaticity in strong-field ionization
Karamatskou, Antonia; Santra, Robin
2013-01-01
If the photon energy is much less than the electron binding energy, ionization of an atom by a strong optical field is often described in terms of electron tunneling through the potential barrier resulting from the superposition of the atomic potential and the potential associated with the instantaneous electric component of the optical field. In the strict tunneling regime, the electron response to the optical field is said to be adiabatic, and nonadiabatic effects are assumed to be negligible. Here, we investigate to what degree this terminology is consistent with a language based on the so-called adiabatic representation. This representation is commonly used in various fields of physics. For electronically bound states, the adiabatic representation yields discrete potential energy curves that are connected by nonadiabatic transitions. When applying the adiabatic representation to optical strong-field ionization, a conceptual challenge is that the eigenstates of the instantaneous Hamiltonian form a continuu...
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...
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 rotation, quantum search, and preparation of superposition states
Siu, M. Stewart
2007-06-01
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied “straight line” adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev’s toric code state, the cluster state of the measurement-based computation model, and the history state used in the adiabatic simulation of a quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the standard adiabatic algorithm.
Adiabatic shear bands localization in materials undergoing deformations
Ryabov, P. N.; Kudryashov, N. A.; Muratov, R. V.
2017-01-01
We consider the adiabatic shear banding phenomenon in composite materials undergoing the high speed shear deformations. The mathematical model of adiabatic shear banding in thermo-visco-plastic material is given. New two step numerical algorithm which is based on the Courant-Isaacson-Rees scheme that allows one to simulate fully localized plastic flow from initial stage of localization is proposed. To test this numerical algorithm we use three benchmark problems. The testing results show the accuracy and efficiency of proposed algorithm. The features of adiabatic shear bands formation in composites are studied. The existence of characteristic depth of localization in composites is shown. Influence of initial temperature distribution on the processes of adiabatic shear bands formation in composites is considered.
Spatial non-adiabatic passage using geometric phases
Benseny, Albert; Busch, Thomas [Okinawa Institute of Science and Technology Graduate University, Quantum Systems Unit, Okinawa (Japan); Kiely, Anthony; Ruschhaupt, Andreas [University College Cork, Department of Physics, Cork (Ireland); Zhang, Yongping [Okinawa Institute of Science and Technology Graduate University, Quantum Systems Unit, Okinawa (Japan); Shanghai University, Department of Physics, Shanghai (China)
2017-12-15
Quantum technologies based on adiabatic techniques can be highly effective, but often at the cost of being very slow. Here we introduce a set of experimentally realistic, non-adiabatic protocols for spatial state preparation, which yield the same fidelity as their adiabatic counterparts, but on fast timescales. In particular, we consider a charged particle in a system of three tunnel-coupled quantum wells, where the presence of a magnetic field can induce a geometric phase during the tunnelling processes. We show that this leads to the appearance of complex tunnelling amplitudes and allows for the implementation of spatial non-adiabatic passage. We demonstrate the ability of such a system to transport a particle between two different wells and to generate a delocalised superposition between the three traps with high fidelity in short times. (orig.)
Huo, Pengfei; Coker, David F
2012-12-14
Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.
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.
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.
ENTROPY-VORTEX WAVES IN NON-ADIABATIC FLOWS
Ibáñez S, Miguel H., E-mail: mhibanez@yahoo.com [Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Autónoma del Caribe, Barranquilla (Colombia)
2016-02-20
The Ertel theorem on the vorticity along the flow of adiabatic fluids is generalized for non-adiabatic flows. Several limiting cases are analyzed and the results are applied to flows behind different hydrodynamics fronts, particularly to thermal fronts (heat and cooling fronts). An important conclusion of the present analysis is that vorticity is inherent in the condensation’s (or hot spots) formation by thermal instabilities in plasma flows. Implications for several astrophysical plasmas are outlined.
Adiabatic invariants of the extended KdV equation
Karczewska, Anna; Infeld, Eryk; Rowlands, George
2015-01-01
When the Euler equations for shallow water are taken to the next order, beyond KdV, $\\eta^2$ is no longer an invariant. (It would seem that $\\eta$ is the only one.) However, two adiabatic invariants akin to $\\eta^2$ can be found. Here we present and test them. When the KdV expansion parameters are zero, $\\eta^2$ is recovered from both adiabatic invariants.
A Solved Model to Show Insufficiency of Quantitative Adiabatic Condition
LIU Long-Jiang; LIU Yu-Zhen; TONG Dian-Min
2009-01-01
The adiabatic theorem is a useful tool in processing quantum systems slowly evolving,but its practical application depends on the quantitative condition expressed by Hamiltonian's eigenvalues and eigenstates,which is usually taken as a sufficient condition.Recently,the sumciency of the condition was questioned,and several counterex amples have been reported.Here we present a new solved model to show the insufficiency of the traditional quantitative adiabatic condition.
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 $-0.1 \\lesssim \\Delta n \\lesssim 0.3$.
Preparation of Entangled States of Three Particles by Adiabatic Passage
郭建友
2002-01-01
We propose a novel technique for the creation of entangled states of three particles, based upon an adiabatic passage induced by a suitably crafted time-dependent external field. We derive the corresponding adiabatic and bare conditions for the preparation of entangled states. We obtain the time evolutions of the energy of the system and the populations involving the initial state and target entangled state.
The adiabatic phase mixing and heating of electrons in Buneman turbulence
Che, H.; Goldstein, M. L. [Goddard Space Flight Center, NASA, Greenbelt, Maryland 20771 (United States); Drake, J. F.; Swisdak, M. [IREAP, University of Maryland, College Park, Maryland 20742 (United States)
2013-06-15
The nonlinear development of the strong Buneman instability and the associated fast electron heating in thin current layers with Ω{sub e}/ω{sub pe}<1 is explored. Phase mixing of the electrons in wave potential troughs and a rapid increase in temperature are observed during the saturation of the instability. We show that the motion of trapped electrons can be described using a Hamiltonian formalism in the adiabatic approximation. The process of separatrix crossing as electrons are trapped and de-trapped is irreversible and guarantees that the resulting electron energy gain is a true heating process.
A connection between mix and adiabat in ICF capsules
Cheng, Baolian; Kwan, Thomas; Wang, Yi-Ming; Yi, Sunghuan (Austin); Batha, Steven
2016-10-01
We study the relationship between instability induced mix, preheat and the adiabat of the deuterium-tritium (DT) fuel in fusion capsule experiments. Our studies show that hydrodynamic instability not only directly affects the implosion, hot spot shape and mix, but also affects the thermodynamics of the capsule, such as, the adiabat of the DT fuel, and, in turn, affects the energy partition between the pusher shell (cold DT) and the hot spot. It was found that the adiabat of the DT fuel is sensitive to the amount of mix caused by Richtmyer-Meshkov (RM) and Rayleigh-Taylor (RT) instabilities at the material interfaces due to its exponential dependence on the fuel entropy. An upper limit of mix allowed maintaining a low adiabat of DT fuel is derived. Additionally we demonstrated that the use of a high adiabat for the DT fuel in theoretical analysis and with the aid of 1D code simulations could explain some aspects of the 3D effects and mix in the capsule experiments. Furthermore, from the observed neutron images and our physics model, we could infer the adiabat of the DT fuel in the capsule and determine the possible amount of mix in the hot spot (LA-UR-16-24880). This work was conducted under the auspices of the U.S. Department of Energy by the Los Alamos National Laboratory under Contract No. W-7405-ENG-36.
LUO Shao-Kai
2007-01-01
For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries for a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.
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 clas......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...
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai; PANG Ting; LIN Peng
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.
Makarov, V. A.; Petnikova, V. M.
2017-02-01
For a nonintegrable system of two coupled nonlinear Schrödinger equations the adiabatic approximation is extended for long time interaction. The method enables analytical description of the modulation of a cnoidal wave by Akhmediev breather in an isotropic nonlinear gyrotropic medium with Kerr nonlinearity and second-order group-velocity dispersion. The conditions which must be fulfilled for stable propagation of the obtained solution with amplitude and frequency modulation are determined.
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
Paredes, C.; Trueba, M.
2014-07-01
The CRDA accident in BWR plants was analysed historically in situations of stop cold and stop hot with adiabatic methods, to have considered these situations the more limiting for this type of event. The proposed analysis is done with the two methodologies in order to show that this accident is effectively limiting how much lower is the power, as well as the conservatism of the adiabatic approximation. (Author)
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.
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...
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Pu, Jin [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Jiang, Qing-Quan [China West Normal University, College of Physics and Space Science, Nanchong (China)
2017-05-15
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painleve) of coordinates as well as in different gravity frames, the adiabatic invariant I{sub adia} = circular integral p{sub i}dq{sub i} introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area. (orig.)
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...
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.
LETTERS AND COMMENTS: Adiabatic process reversibility: microscopic and macroscopic views
Anacleto, Joaquim; Pereira, Mário G.
2009-05-01
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 \\ge 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.
Rašin, Andrija
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.
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
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
Hu, Yue; Hong, Wei; Shi, Yunyu; Liu, Haiyan
2012-10-09
In molecular simulations, accelerated sampling can be achieved efficiently by raising the temperature of a small number of coordinates. For collective coordinates, the temperature-accelerated molecular dynamics method or TAMD has been previously proposed, in which the system is extended by introducing virtual variables that are coupled to these coordinates and simulated at higher temperatures (Maragliano, L.; Vanden-Eijnden, E. Chem. Phys. Lett.2005, 426, 168-175). In such accelerated simulations, steady state or equilibrium distributions may exist but deviate from the canonical Boltzmann one. We show that by assuming adiabatic decoupling between the subsystems simulated at different temperatures, correct canonical distributions and ensemble averages can be obtained through reweighting. The method makes use of the low-dimensional free energy surfaces that are estimated as Gaussian mixture probability densities through maximum likelihood and expectation maximization. Previously, we proposed the amplified collective motion method or ACM. The method employs the coarse-grained elastic network model or ANM to extract collective coordinates for accelerated sampling. Here, we combine the ideas of ACM and of TAMD to develop a general technique that can achieve canonical sampling through reweighting under the adiabatic approximation. To test the validity and accuracy of adiabatic reweighting, first we consider a single n-butane molecule in a canonical stochastic heat bath. Then, we use explicitly solvated alanine dipeptide and GB1 peptide as model systems to demonstrate the proposed approaches. With alanine dipeptide, it is shown that sampling can be accelerated by more than an order of magnitude with TAMD while correct distributions and canonical ensemble averages can be recovered, necessarily through adiabatic reweighting. For the GB1 peptide, the conformational distribution sampled by ACM-TAMD, after adiabatic reweighting, suggested that a normal simulation suffered
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.
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 clas......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...
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\
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
Aharonov, D; Kempe, J; Landau, Z; Lloyd, S; Regev, O; Aharonov, Dorit; Dam, Wim van; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded
2004-01-01
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power has been unknown. We settle this question and describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum circuit model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models provides a new vantage point from which to tackle the central issues in quantum computation, namely designing new quantum algorithms and constructing fault tolerant quantum computers. In particular, by translating the main open questions in quantum algorithms to the language of spectral gaps of sparse matrices, the result makes quantum algorithmic questions accessible to a wider scientific audience, acquainted with mathematical physics, expander theory a...
Dynamics of charged particles in an adiabatic thermal beam equilibrium
Haofei Wei
2011-02-01
Full Text Available Charged-particle motion is studied in the self-electric and self-magnetic fields of a well-matched, intense charged-particle beam and an applied periodic solenoidal magnetic focusing field. The beam is assumed to be in a state of adiabatic thermal equilibrium. The phase space is analyzed and compared with that of the well-known Kapchinskij-Vladimirskij (KV-type beam equilibrium. It is found that the widths of nonlinear resonances in the adiabatic thermal beam equilibrium are narrower than those in the KV-type beam equilibrium. Numerical evidence is presented, indicating almost complete elimination of chaotic particle motion in the adiabatic thermal beam equilibrium.
Applications of chirped Raman adiabatic rapid passage to atom interferometry
Kotru, Krish; Butts, David L.; Kinast, Joseph M.; Johnson, David M. S.; Radojevic, Antonije M.; Timmons, Brian P.; Stoner, Richard E.
2012-02-01
We present robust atom optics, based on chirped Raman adiabatic rapid passage (ARP), in the context of atom interferometry. Such ARP light pulses drive coherent population transfer between two hyperfine ground states by sweeping the frequency difference of two fixed-intensity optical fields with large single photon detunings. Since adiabatic transfer is less sensitive to atom temperature and non-uniform Raman beam intensity than standard Raman pulses, this approach should improve the stability of atom interferometers operating in dynamic environments. In such applications, chirped Raman ARP may also provide advantages over the previously demonstrated stimulated Raman adiabatic passage (STIRAP) technique, which requires precise modulation of beam intensity and zeroing of the single photon detuning. We demonstrate a clock interferometer with chirped Raman ARP pulses, and compare its stability to that of a conventional Raman pulse interferometer. We also discuss potential improvements to inertially sensitive atom interferometers. Copyright 2011 by The Charles Stark Draper Laboratory, Inc. All rights reserved.
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...
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.
Global adiabaticity and non-Gaussianity consistency condition
Antonio Enea Romano
2016-10-01
Full Text Available In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, Rc, 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 Rc holds only after the perturbation has reached the adiabatic limit where the constant mode of Rc dominates over the other (usually decaying mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, δPnad≡δP−cw2δρ where cw2=P˙/ρ˙, 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 Rc on super-horizon scales. In this paper, we consider models that satisfy δPnad=0 on all scales, which we call global adiabaticity (GA, which is guaranteed if cw2=cs2, where cs is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll (USR inflation in which cw2=cs2=1. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with cw2=cs2, which allows Rc to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.
Global adiabaticity and non-Gaussianity consistency condition
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-10-01
In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, Rc, 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 Rc holds only after the perturbation has reached the adiabatic limit where the constant mode of Rc dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, δPnad ≡ δP - cw2 δρ where cw2 = P ˙ / ρ ˙ , 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 Rc on super-horizon scales. In this paper, we consider models that satisfy δPnad = 0 on all scales, which we call global adiabaticity (GA), which is guaranteed if cw2 = cs2 , where cs is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll (USR) inflation in which cw2 = cs2 = 1. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with cw2 = cs2, which allows Rc to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.
On the adiabatic theorem when eigenvalues dive into the continuum
Cornean, Decebal Horia; Jensen, Arne; Knörr, Hans Konrad
For a Wigner-Weisskopf model of an atom consisting of a quantum dot coupled to an energy reservoir described by a three-dimensional Laplacian we study the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discre...... eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit....
Microstructure evolution mechanism in adiabatic shear band in TA2
杨扬; 熊俊; 杨续跃
2004-01-01
The micro structure evolution mechanism in adiabatic shear band in commercial pure titanium (TA2) at high strain rates(γ≈105 - 106/s) were studied. The nanosized recrystallized grains (about 50 nm in diameter) within the center of adiabatic shear band (ASB) were observed by means of transmission electronic microscope (TEM). A Rotational Dynamic Recrystallization (RDR) mechanism can explain the microstructure evolution (i. e. nanosized grains were formed within 5 - 10μs) in ASB. Kinetics calculations indicate that the recrystallized small grains are formed during the deformation and don't undergo significant growth by grain boundary migration after deformation.
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 hyperspherical approach to large-scale nuclear dynamics
Suzuki, Yasuyuki
2015-01-01
We formulate a fully microscopic approach to large-scale nuclear dynamics using a hyperradius as a collective coordinate. An adiabatic potential is defined by taking account of all possible configurations at a fixed hyperradius, and its hyperradius dependence plays a key role in governing the global nuclear motion. In order to go to larger systems beyond few-body systems, we suggest basis functions of a microscopic multicluster model, propose a method for calculating matrix elements of an adiabatic Hamiltonian with use of Fourier transforms, and test its effectiveness.
Adiabatic fluctuations from cosmic strings in a contracting universe
Brandenberger, Robert H; Yamaguchi, Masahide
2008-01-01
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.
How to Make the Quantum Adiabatic Algorithm Fail
Farhi, E; Gutmann, S; Nagaj, D; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Nagaj, Daniel
2005-01-01
The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will not find the minimum if the run time grows more slowly than square root of N. These poor choices are nonlocal and wash out any structure in the cost function to be minimized and the best that can be hoped for is Grover speedup. These failures tell us what not to do when designing quantum adiabatic algorithms.
Construction techniques for adiabatic demagnetization refrigerators using ferric ammonium alum
Wilson, Grant W.; Timbie, Peter T.
1999-07-01
We describe techniques used to fabricate the cold stage of an adiabatic demagnetization refrigerator that uses the paramagnetic salt ferric ammonium alum. We discuss the design of a leak-tight housing for the salt as well as a technique for growing ferric ammonium alum crystals that results in a housing filled with >98% refrigerant. These techniques have proven to be reliable in creating robust single-stage refrigerators. Similar techniques can be used for the second stage of a dual-stage adiabatic demagnetization refrigerator.
New design of an adiabatic demagnetization cryostat for space application
Yamamoto, Junya; Sato, Akio; Sahashi, Masashi
A new adiabatic demagnetization cryostat for cooling (in the region of 0.1 K) spaceborne far-infrared detectors is described. The cryostat contains a superconducting magnetic coil indirectly cooled by liquid helium, with the liquid nitrogen and helium vessels being connected by gas-filled thermal switches; the adiabatic demagnetization cell of the cryostat is set in vacuum at the center of the coil. The magnetic field of 3 T was obtained by a current of 11.5 A. The magnetic salt (single crystals of manganese ammonium alum) was prepared by the falling temperature technique.
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.
Kimura, Jun-Ichi; Kawabata, Hiroshi
2014-06-01
numerical mass balance calculation model for the adiabatic melting of a dry to hydrous peridotite has been programmed in order to simulate the trace element compositions of basalts from mid-ocean ridges, back-arc basins, ocean islands, and large igneous provinces. The Excel spreadsheet-based calculator, Hydrous Adiabatic Mantle Melting Simulator version 1 (HAMMS1) uses (1) a thermodynamic model of fractional adiabatic melting of mantle peridotite, with (2) the parameterized experimental melting relationships of primitive to depleted mantle sources in terms of pressure, temperature, water content, and degree of partial melting. The trace element composition of the model basalt is calculated from the accumulated incremental melts within the adiabatic melting regime, with consideration for source depletion. The mineralogic mode in the primitive to depleted source mantle in adiabat is calculated using parameterized experimental results. Partition coefficients of the trace elements of mantle minerals are parameterized to melt temperature mostly from a lattice strain model and are tested using the latest compilations of experimental results. The parameters that control the composition of trace elements in the model are as follows: (1) mantle potential temperature, (2) water content in the source mantle, (3) depth of termination of adiabatic melting, and (4) source mantle depletion. HAMMS1 enables us to obtain the above controlling parameters using Monte Carlo fitting calculations and by comparing the calculated basalt compositions to primary basalt compositions. Additionally, HAMMS1 compares melting parameters with a major element model, which uses petrogenetic grids formulated from experimental results, thus providing better constraints on the source conditions.
Taioli, Simone; Garberoglio, Giovanni; Simonucci, Stefano; a Beccara, Silvio; Aversa, Lucrezia; Nardi, Marco; Verucchi, Roberto; Iannotta, Salvatore; Dapor, Maurizio; Alfè, Dario
2013-01-28
In this work, we investigate the processes leading to the room-temperature growth of silicon carbide thin films by supersonic molecular beam epitaxy technique. We present experimental data showing that the collision of fullerene on a silicon surface induces strong chemical-physical perturbations and, for sufficient velocity, disruption of molecular bonds, and cage breaking with formation of nanostructures with different stoichiometric character. We show that in these out-of-equilibrium conditions, it is necessary to go beyond the standard implementations of density functional theory, as ab initio methods based on the Born-Oppenheimer approximation fail to capture the excited-state dynamics. In particular, we analyse the Si-C(60) collision within the non-adiabatic nuclear dynamics framework, where stochastic hops occur between adiabatic surfaces calculated with time-dependent density functional theory. This theoretical description of the C(60) impact on the Si surface is in good agreement with our experimental findings.
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.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms
SUN Jie; LU Song-Feng; Samuel L.Braunstein
2013-01-01
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.
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...
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.
Reversibility and energy dissipation in adiabatic superconductor logic.
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2017-03-06
Reversible computing is considered to be a key technology to achieve an extremely high energy efficiency in future computers. In this study, we investigated the relationship between reversibility and energy dissipation in adiabatic superconductor logic. We analyzed the evolution of phase differences of Josephson junctions in the reversible quantum-flux-parametron (RQFP) gate and confirmed that the phase differences can change time reversibly, which indicates that the RQFP gate is physically, as well as logically, reversible. We calculated energy dissipation required for the RQFP gate to perform a logic operation and numerically demonstrated that the energy dissipation can fall below the thermal limit, or the Landauer bound, by lowering operation frequencies. We also investigated the 1-bit-erasure gate as a logically irreversible gate and the quasi-RQFP gate as a physically irreversible gate. We calculated the energy dissipation of these irreversible gates and showed that the energy dissipation of these gate is dominated by non-adiabatic state changes, which are induced by unwanted interactions between gates due to logical or physical irreversibility. Our results show that, in reversible computing using adiabatic superconductor logic, logical and physical reversibility are required to achieve energy dissipation smaller than the Landauer bound without non-adiabatic processes caused by gate interactions.
Dark energy and dark matter from an additional adiabatic fluid
Dunsby, Peter K. S.; Luongo, Orlando; Reverberi, Lorenzo
2016-10-01
The dark sector is described by an additional barotropic fluid which evolves adiabatically during the Universe's history and whose adiabatic exponent γ is derived from the standard definitions of specific heats. Although in general γ is a function of the redshift, the Hubble parameter and its derivatives, we find that our assumptions lead necessarily to solutions with γ =constant in a Friedmann-Lemaître-Robertson-Walker universe. The adiabatic fluid acts effectively as the sum of two distinct components, one evolving like nonrelativistic 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 Λ CDM model is included in this family of theories when γ =0 . We fit our model to supernovae Ia, H (z ) and baryonic acoustic oscillation data, discussing the model selection criteria. The implications for the early Universe and the growth of small perturbations in this model are also discussed.
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
2016-06-09
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.
Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems
Yi Zhang
2015-01-01
Full Text Available Based on El-Nabulsi dynamical model for a non-conservative system, the problem of perturbation to Noether symmetries and adiabatic invariants of a Birkhoffian system under the action of a small disturbance is proposed and studied. Firstly, the El-Nabulsi-Pfaff variational problem from extended exponentially fractional integral is presented and the El-Nabulsi-Birkhoff equations are established. Secondly, the definitions and the criterions criteria of the Noether symmetric transformations and quasisymmetric transformations of the Birkhoffian system are given, and the Noether theorems of the system are established, which reveal the inner relationship between the Noether symmetries and the conserved quantities. Thirdly, the perturbation of Noether symmetries under a small disturbance is studied, and corresponding adiabatic invariants are obtained. As special cases, the deductions in nonconservative Hamiltonian system and nonconservative Lagrangian system and standard Birkhoffian system are given. At the end of the paper, the case known as Hojman-Urrutia problem is discussed to investigate the Noether symmetries and the adiabatic invariants, the perturbation to Noether symmetries and the adiabatic invariants under El-Nabulsi dynamical model.
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.
A Kinetic Study of the Adiabatic Polymerization of Acrylamide.
Thomson, R. A. M.
1986-01-01
Discusses theory, procedures, and results for an experiment which demonstrates the application of basic physics to chemical problems. The experiment involves the adiabatic process, in which polymerization carried out in a vacuum flask is compared to the theoretical prediction of the model with the temperature-time curve obtained in practice. (JN)
Adiabatic frequency conversion with a sign flip in the coupling
Hristova, H. S.; Rangelov, A. A.; Montemezzani, G.; Vitanov, N. V.
2016-09-01
Adiabatic frequency conversion is a method recently developed in nonlinear optics [H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, Phys. Rev. A 78, 063821 (2008), 10.1103/PhysRevA.78.063821], using ideas from the technique of rapid adiabatic passage (RAP) via a level crossing in quantum physics. In this method, the coupling coefficients are constant and the phase mismatch is chirped adiabatically. In this work, we propose another method for adiabatic frequency conversion, in which the phase mismatch is constant and the coupling is a pulse-shaped function with a sign flip (i.e., a phase step of π ) at its maximum. Compared to the RAP method, our technique has comparable efficiency but it is simpler to implement for it only needs two bulk crystals with opposite χ(2 ) nonlinearity. Moreover, because our technique requires constant nonzero frequency mismatch and has zero conversion efficiency on exact frequency matching, it can be used as a frequency filter.
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.
Flat FRW Cosmologies with Adiabatic Matter Creation Kinematic tests
Lima, J A S
1999-01-01
Some observational consequences of a cosmological scenario driven by adiabatic matter creation are investigated. Exact expressions for the lookback time, age of the universe, luminosity distance, angular diameter, and galaxy number counts redshift relations are derived and their meaning discussed in detail. The expressions of the conventional FRW models are significantly modified and provide a powerful method to limit the parameters of the models.
Fast Quasi-Adiabatic Gas Cooling: An Experiment Revisited
Oss, S.; Gratton, L. M.; Calza, G.; Lopez-Arias, T.
2012-01-01
The well-known experiment of the rapid expansion and cooling of the air contained in a bottle is performed with a rapidly responsive, yet very cheap thermometer. The adiabatic, low temperature limit is approached quite closely and measured with our apparatus. A straightforward theoretical model for this process is also presented and discussed.…
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...
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...
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...
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...
Diestler, D J
2012-03-22
The Born-Oppenheimer (BO) description of electronically adiabatic molecular processes predicts a vanishing electronic flux density (j(e)), =1/2∫dR[Δ(b) (x;R) - Δ(a) (x;R)] even though the electrons certainly move in response to the movement of the nuclei. This article, the first of a pair, proposes a quantum-mechanical "coupled-channels" (CC) theory that allows the approximate extraction of j(e) from the electronically adiabatic BO wave function . The CC theory is detailed for H(2)(+), in which case j(e) can be resolved into components associated with two channels α (=a,b), each of which corresponds to the "collision" of an "internal" atom α (proton a or b plus electron) with the other nucleus β (proton b or a). The dynamical role of the electron, which accommodates itself instantaneously to the motion of the nuclei, is submerged in effective electronic probability (population) densities, Δ(α), associated with each channel (α). The Δ(α) densities are determined by the (time-independent) BO electronic energy eigenfunction, which depends parametrically on the configuration of the nuclei, the motion of which is governed by the usual BO nuclear Schrödinger equation. Intuitively appealing formal expressions for the electronic flux density are derived for H(2)(+).
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to Noether-Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.
Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems
DING Ning; FANG Jian-Hui; WANG Peng
2007-01-01
Based on the concept of adiabatic invariant,the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied.The exact invariants of the Mei symmetry for the system without perturbation are given,The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained.
Perturbation to Lie Symmetry and Lutzky Adiabatic Invariants for Lagrange Systems
REN Ji-Rong; DING Ning; LI Ran; FANG Jian-Hui; DUAN Yi-Shi; WANG Peng; ZHANG Xiao-Ni
2008-01-01
Based on the concept of adiabatic invariant, perturbation to Lie symmetry and Lutzky adiabatic invariants for Lagrange systems are studied by using different methods from those of previous works. Exact invariants induced from Lie symmetry of the system without perturbation are given. Perturbation to Lie symmetry is discussed and Lutzky adiabatic invariants of the system subject to perturbation are obtained.
Approximate calculation of integrals
Krylov, V I
2006-01-01
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t
Approximate and renormgroup symmetries
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximating Stationary Statistical Properties
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Relativistic gravitational collapse in comoving coordinates: The post-quasistatic approximation
Herrera, L
2010-01-01
A general iterative method proposed some years ago for the description of relativistic collapse, is presented here in comoving coordinates. For doing that we redefine the basic concepts required for the implementation of the method for comoving coordinates. In particular the definition of the post-quasistatic approximation in comoving coordinates is given. We write the field equations, the boundary conditions and a set of ordinary differential equations (the surface equations) which play a fundamental role in the algorithm. As an illustration of the method, we show how to build up a model inspired in the well known Schwarzschild interior solution. Both, the adiabatic and non adiabatic, cases are considered.
Malvina Baica
1985-01-01
Full Text Available 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.
Approximations in Inspection Planning
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
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....... 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 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.
Approximations in Inspection Planning
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
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....... 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 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....
Effect of relaxation on adiabatic following
Nayfeh, M.H.
1976-09-01
A solution is presented for the damped optical Bloch equations under the excitation of a smooth pulse by first deriving three independent third-order equations of the Bloch vector components. Each equation is reduced to quadratures by assuming that the logarithmic time derivative of the field amplitude is small compared to the Rabi frequency. This results in an approximate summation of the infinite-order time-dependent perturbation in the field amplitude. The relaxation-dependent induced damping of the population inversion is calculated. Also calculated are additional relaxation-dependent contributions to the intensity-dependent refractive index. The time-integrated intensity contribution tends to cause line asymmetry, which becomes, at later times, linear in ..gamma../sub 2/ when ..gamma../sub 2/ very-much-greater-than ..gamma../sub 1/ and zero when 2..gamma../sub 2/ = ..gamma../sub 1/, where ..gamma../sub 1/ and ..gamma../sub 2/ are the atomic energy and phase-changing relaxations, respectively. The dependence of the spectral broadening on pulse length, pressure, and length of the sample is discussed. (AIP)
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
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....
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
Maksim Duškin
2015-11-01
Full Text Available Approximation and supposition This article compares exponents of approximation (expressions like Russian около, примерно, приблизительно, более, свыше and the words expressing supposition (for example Russian скорее всего, наверное, возможно. These words are often confused in research, in particular researchers often mention exponents of supposition in case of exponents of approximation. Such approach arouses some objections. The author intends to demonstrate in this article a notional difference between approximation and supposition, therefore the difference between exponents of these two notions. This difference could be described by specifying different attitude of approximation and supposition to the notion of knowledge. Supposition implies speaker’s ignorance of the exact number, while approximation does not mean such ignorance. The article offers examples proving this point of view.
Trushin, Egor; Betzinger, Markus; Blügel, Stefan; Görling, Andreas
2016-08-01
An approach to calculate fundamental band gaps, ionization energies, and electron affinities of periodic electron systems is explored. Starting from total energies obtained with the help of the adiabatic-connection fluctuation-dissipation (ACFD) theorem, these physical observables are calculated according to their basic definition by differences of the total energies of the N -, (N -1 ) -, and (N +1 ) -electron system. The response functions entering the ACFD theorem are approximated here by the direct random phase approximation (dRPA). For a set of prototypical semiconductors and insulators it is shown that even with this quite drastic approximation the resulting band gaps are very close to experiment and of a similar quality to those from the computationally more involved G W approximation. By going beyond the dRPA in the future the accuracy of the calculated band gaps may be significantly improved further.
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.
Manipulation of ultracold atoms in dressed adiabatic radio-frequency potentials
Lesanovsky, Igor; Hofferberth, S.; Schmiedmayer, Jörg
2006-01-01
We explore properties of atoms whose magnetic hyperfine sublevels are coupled by an external magnetic radio frequency (rf) field. We perform a thorough theoretical analysis of this driven system and present a number of systematic approximations which eventually give rise to dressed adiabatic radio...... frequency potentials. The predictions of this analytical investigation are compared to numerically exact results obtained by a wave packet propagation. We outline the versatility and flexibility of this class of potentials and demonstrate their potential use to build atom optical elements such as double...... wells, interferometers, and ringtraps. Moreover, we perform simulations of interference experiments carried out in rf induced double-well potentials. We discuss how the nature of the atom-field coupling mechanism gives rise to a decrease of the interference contrast....
Bast, Radovan; Jensen, Hans Jørgen Aagaard; Saue, Trond
2009-01-01
We report an implementation of adiabatic time-dependent density functional theory based on the 4-component relativistic Dirac-Coulomb Hamiltonian and a closed-shell reference. The implementation includes noncollinear spin magnetization and full derivatives of functionals, including hybrid...... and time reversal symmetry on trial vectors to obtain even better reductions in terms of memory and run time, and without invoking approximations. Further reductions are obtained by exploiting point group symmetries for D2h and subgroups in a symmetry scheme where symmetry reductions translate...... into reduction of algebra from quaternion to complex or real. For hybrid GGAs with noncollinear spin magnetization we derive a new computationally advantageous equation for the full second variational derivatives of such exchange-correlation functionals. We apply our implementation to calculations on the ns2...
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.
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.
Adiabatic tapered optical fiber fabrication in two step etching
Chenari, Z.; Latifi, H.; Ghamari, S.; Hashemi, R. S.; Doroodmand, F.
2016-01-01
A two-step etching method using HF acid and Buffered HF is proposed to fabricate adiabatic biconical optical fiber tapers. Due to the fact that the etching rate in second step is almost 3 times slower than the previous droplet etching method, terminating the fabrication process is controllable enough to achieve a desirable fiber diameter. By monitoring transmitted spectrum, final diameter and adiabaticity of tapers are deduced. Tapers with losses about 0.3 dB in air and 4.2 dB in water are produced. The biconical fiber taper fabricated using this method is used to excite whispering gallery modes (WGMs) on a microsphere surface in an aquatic environment. So that they are suitable to be used in applications like WGM biosensors.
Linear response of galactic halos to adiabatic gravitational perturbations
Murali, C; 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 fields from external sources are not strongly amplified by an intervening isothermal stellar system, except at radii can even screen the external tidal field in a manner analogous to Debye screening. As Weinberg has pointed out, individual resonances in a stellar system can strongly amplify external tidal fields over a limited radial range, but we cannot address this possibility because we examine only adiabatic perturbations. We also discuss the application of our method to the halo response caused by the slow growth of an em...
Adiabatic Tip-Plasmon Focusing for Nano-Raman Spectroscopy
Berweger, Samuel; Atkin, Joanna M.; Olmon, Robert L.; Raschke, Markus Bernd
2010-12-16
True nanoscale optical spectroscopy requires the efficient delivery of light for a spatially nanoconfined excitation. We utilize adiabatic plasmon focusing to concentrate an optical field into the apex of a scanning probe tip of {approx}10 nm in radius. The conical tips with the ability for two-stage optical mode matching of the surface plasmon polariton (SPP) grating-coupling and the adiabatic propagating SPP conversion into a localized SPP at the tip apex represent a special optical antenna concept for far-field transduction into nanoscale excitation. The resulting high nanofocusing efficiency and the spatial separation of the plasmonic grating coupling element on the tip shaft from the near-field apex probe region allows for true background-free nanospectroscopy. As an application, we demonstrate tip-enhanced Raman spectroscopy (TERS) of surface molecules with enhanced contrast and its extension into the near-IR with 800 nm excitation.
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, ...
Stimulated Raman adiabatic control of a nuclear spin in diamond
Coto, Raul; Jacques, Vincent; Hétet, Gabriel; Maze, Jerónimo R.
2017-08-01
Coherent manipulation of nuclear spins is a highly desirable tool for both quantum metrology and quantum computation. However, most of the current techniques to control nuclear spins lack fast speed, impairing their robustness against decoherence. Here, based on stimulated Raman adiabatic passage, and its modification including shortcuts to adiabaticity, we present a fast protocol for the coherent manipulation of nuclear spins. Our proposed Λ scheme is implemented in the microwave domain and its excited-state relaxation can be optically controlled through an external laser excitation. These features allow for the initialization of a nuclear spin starting from a thermal state. Moreover we show how to implement Raman control for performing Ramsey spectroscopy to measure the dynamical and geometric phases acquired by nuclear spins.
Multidimensional Study of High-Adiabat OMEGA Cryogenic Experiments
Collins, T. J. B.; Betti, R.; Bose, A.; Christopherson, A. R.; Knauer, J. P.; Marozas, J. A.; Maximov, A. V.; Mora, A.; Radha, P. B.; Shang, W.; Shvydky, A.; Stoeckl, C.; Woo, K. M.; Varchas, G.
2016-10-01
Despite recent advances in modeling laser direct-drive inertial confinement fusion (ICF) experiments, there remains a predictability gap. This is particularly shown by the shortfall in hot-spot pressures inferred from OMEGA cryogenic implosions. To address this, a series of high-adiabat, cryogenic implosions were performed on OMEGA. These shots were performed with and without single-beam smoothing by spectral dispersion, at low and high drive intensities. These shots represent a regime where good agreement with simulation is expected because of the high adiabat. Multidimensional simulations of these shots will be presented with an emphasis on comparison with experimental indicators of departure from spherical symmetry (``1-D-ness''). The roles of short- and long-wavelength perturbations are considered. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
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.
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.
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.
Adiabatic theory of solitons fed by dispersive waves
Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, Shalva
2016-09-01
We consider scattering of low-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analog of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from quantum mechanics, we give a quantitative account of the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in the spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.
Some characteristics of the atmosphere during an adiabatic process
GAO Li; LI Jianping; REN Hongli
2006-01-01
Some important characteristics of the atmosphere during an adiabatic process are investigated, which include the invariability of atmospheric entropy range and local surface potential temperature, the conservation of the atmospheric mass intervened between any isentropic surface and the ground, and the isentropic surface intersecting with the ground. The analysis shows that the atmospheric reference state (ARS) for investigation on available potential energy (APE) should be defined objectively as the state which could be approached from the existing atmosphere by adiabatic adjustment, and be related to initial atmospheric state before adjustment. For the initial atmosphere state at any time, its corresponding ARS is different from the one at another time. Based on the above-mentioned conclusions,the reference state proposed by Lorenz cannot be obtained physically, so a new conception, the conditional minimum total potential energy, is put forward in order to objectively investigate atmospheric APE.
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.
Adiabatic Evolution in XXX Spin Chain is Fast
Korepin, V
2004-01-01
Adiabatic theorem of quantum mechanics was used by E. Farhi, J. Goldstone, S. Gutmann and M. Sipser to design quantum algorithms of a new kind. A quantum computer evolves slowly enough, so that it remains in its instantaneous ground state, which tells the solution. We consider XXX Heisenberg spin chain. We rotate magnetic field and change its magnitude. The ground state evolves from a ferromagnetic one into a nontrivial ground state of XXX anti-ferromagnet. This adiabatic evolution goes very gently. Because of SU(2) symmetry and integrability only one mode get exited. We prove that the time of the evolution scales as a square root of number of qubits. This is faster then other known examples.
Robust quantum logic in neutral atoms via adiabatic Rydberg dressing
Keating, Tyler; Cook, Robert L.; Hankin, Aaron M.; Jau, Yuan-Yu; Biedermann, Grant W.; Deutsch, Ivan H.
2015-01-01
We study a scheme for implementing a controlled-Z (cz) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a σ+/σ- orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces acting on doubly excited Rydberg atoms when the blockade is imperfect. For reasonable parameters, with qubits encoded into the clock states of 133Cs, we predict that our protocol could produce a cz gate in <10 μ s with error probability on the order of 10-3.
Xu, Kebiao; Xie, Tianyu; Li, Zhaokai; Xu, Xiangkun; Wang, Mengqi; Ye, Xiangyu; Kong, Fei; Geng, Jianpei; Duan, Changkui; Shi, Fazhan; Du, Jiangfeng
2017-03-31
The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian S_{z}I_{z} on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.
Monotone Boolean approximation
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
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.
A field theory characterization of interacting adiabatic particles in cosmology
Arteaga, Daniel
2008-01-01
We explore the adiabatic particle excitations of an interacting field in a cosmological background. By following the time-evolution of the quantum state corresponding to the particle excitation, we show how the basic properties characterizing the particle propagation can be recovered from the two-point propagators. As an application, we study the background-induced dissipative effects on the propagation of a two-level atom in an expanding universe.
A field theory characterization of interacting adiabatic particles in cosmology
Arteaga, Daniel [Departament de Fisica Fonamental and Institut de Ciencies del Cosmos, Facultat de Fisica, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain)], E-mail: darteaga@ub.edu
2008-08-07
We explore the adiabatic particle excitations of an interacting field in a cosmological background. By following the time evolution of the quantum state corresponding to the particle excitation, we show how the basic properties characterizing the particle propagation can be recovered from the two-point propagators. As an application, we study the background-induced dissipative effects on the propagation of a two-level atom in an expanding universe.
Adiabatic trapping in coupled kinetic Alfven-acoustic waves
Shah, H. A.; Ali, Z. [Department of Physics, G.C. University, 54000 Lahore (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Theoretical Plasma Physics Division, P. O. Nilore, Islamabad (Pakistan)
2013-03-15
In the present work, we have discussed the effects of adiabatic trapping of electrons on obliquely propagating Alfven waves in a low {beta} plasma. Using the two potential theory and employing the Sagdeev potential approach, we have investigated the existence of arbitrary amplitude coupled kinetic Alfven-acoustic solitary waves in both the sub and super Alfvenic cases. The results obtained have been analyzed and presented graphically and can be applied to regions of space where the low {beta} assumption holds true.
Mapping the region of instability for adiabatic continuation method
GUTIÉRREZHERNANDEZ, JUAN PABLO; Fontalvo Alzate, Javier; Gómez García, Miguel Ángel
2011-01-01
The pioneer schematic ideas of Kimura and Levenspiel (Ind. Eng. Chem. Proc. Des. Dev., 16 (1977) 145 – 148) have been developed to find numerically the region of instability for adiabatic packed bed reactors. Three different cases of special industrial interest and complexity are presented. The highly exothermic gas-phase reactions: ammonia synthesis, methanol production from syn-gas, and SO₂ oxidation. Equations were parameterized and solved according to a continuation homotopy numerical met...
Hypercomputability of quantum adiabatic processes: Fact versus Prejudices
Kieu, T D
2005-01-01
We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by the algorithm in its physical implementation.
Adiabaticity of the ramping process of an ac dipole
R. Tomás
2005-02-01
Full Text Available ac dipoles in accelerators are used to excite coherent betatron oscillations at a drive frequency close to the tune. If the excitation amplitude is slowly increased to the desired value and slowly decreased back to zero there is no significant emittance growth. The aim of this article is to study the adiabaticity of the ramping process of an ac dipole as a function of the different parameters involved.
Quantum state preparation in semiconductor dots by adiabatic rapid passage
Wu, Yanwen; Piper, I.M.; Ediger, M.; Brereton, P.; Schmidgall, E. R.; Hugues, M.; Hopkinson, M.; Phillips, R.T.
2010-01-01
Preparation of a specific quantum state is a required step for a variety of proposed practical uses of quantum dynamics. We report an experimental demonstration of optical quantum state preparation in a semiconductor quantum dot with electrical readout, which contrasts with earlier work based on Rabi flopping in that the method is robust with respect to variation in the optical coupling. We use adiabatic rapid passage, which is capable of inverting single dots to a specified upper level. We d...
Adiabatic pipelining: a key to ternary computing with quantum dots.
Pečar, P; Ramšak, A; Zimic, N; Mraz, M; Lebar Bajec, I
2008-12-10
The quantum-dot cellular automaton (QCA), a processing platform based on interacting quantum dots, was introduced by Lent in the mid-1990s. What followed was an exhilarating period with the development of the line, the functionally complete set of logic functions, as well as more complex processing structures, however all in the realm of binary logic. Regardless of these achievements, it has to be acknowledged that the use of binary logic is in computing systems mainly the end result of the technological limitations, which the designers had to cope with in the early days of their design. The first advancement of QCAs to multi-valued (ternary) processing was performed by Lebar Bajec et al, with the argument that processing platforms of the future should not disregard the clear advantages of multi-valued logic. Some of the elementary ternary QCAs, necessary for the construction of more complex processing entities, however, lead to a remarkable increase in size when compared to their binary counterparts. This somewhat negates the advantages gained by entering the ternary computing domain. As it turned out, even the binary QCA had its initial hiccups, which have been solved by the introduction of adiabatic switching and the application of adiabatic pipeline approaches. We present here a study that introduces adiabatic switching into the ternary QCA and employs the adiabatic pipeline approach to successfully solve the issues of elementary ternary QCAs. What is more, the ternary QCAs presented here are sizewise comparable to binary QCAs. This in our view might serve towards their faster adoption.
Adiabatic Compression Sensitivity of AF-M315E
2015-07-01
is pressurized to specific driving pressures into an accumulator tank above a rapid-opening valve. This valve is placed directly above the burst disc...this mission. Of particular interest is the sensitivity of the propellant at elevated temperatures and the resulting system peak pressures and...dynamic response characteristics. For this study, an adiabatic compression U-tube apparatus was used to determine the driving pressure threshold levels
Characterization of Adiabatic Noise in Charge-Based Coherent Nanodevices
D'Arrigo, A.; Falci, G.; Mastellone, A.; Paladino, E.
2008-10-01
Low-frequency noise, often with 1/f spectrum, has been recognized as the main mechanism of decoherence in present-day solid state coherent nanodevices. The responsible degrees of freedom are almost static during the coherent time evolution of the device leading to effects analogous to inhomogeneous broadening in NMR. Here we present a characterization of the effects of adiabatic noise exploiting the tunability of nanodevices.
Stimulated Raman adiabatic passage in physics, chemistry and beyond
Nikolay V. Vitanov; Rangelov, Andon A.; Shore, Bruce W.; Bergmann, Klaas
2016-01-01
The technique of stimulated Raman adiabatic passage (STIRAP), which allows efficient and selective population transfer between quantum states without suffering loss due to spontaneous emission, was introduced in 1990 (Gaubatz \\emph{et al.}, J. Chem. Phys. \\textbf{92}, 5363, 1990). Since then STIRAP has emerged as an enabling methodology with widespread successful applications in many fields of physics, chemistry and beyond. This article reviews the many applications of STIRAP emphasizing the ...
Adiabatic embedment of nanomechanical resonators in photonic microring cavities
Xiong, Chi; Li, Mo; Rooks, Michael; Tang, Hong X
2014-01-01
We report a circuit cavity optomechanical system in which a nanomechanical resonator is adiabatically embedded inside an optical ring resonator with ultralow transition loss. The nanomechanical device forms part of the top layer of a horizontal silicon slot ring resonator, which enables dispersive coupling to the dielectric substrate via a tapered nanogap. Our measurements show nearly uncompromised optical quality factors (Q) after the release of the mechanical beam.
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.
Thermal reservoir sizing for adiabatic compressed air energy storage
Kere, Amelie; Goetz, Vincent; Py, Xavier; Olives, Regis; Sadiki, Najim [Perpignan Univ. (France). PROMES CNRS UPR 8521; Mercier-Allart, Eric [EDF R et D, Chatou (France)
2012-07-01
Despite the operation of the two existing industrial facilities to McIntosh (Alabama), and for more than thirty years, Huntorf (Germany), electricity storage in the form of compressed air in underground cavern (CAES) has not seen the development that was expected in the 80s. The efficiency of this form of storage was with the first generation CAES, less than 50%. The evolving context technique can significantly alter this situation. The new generation so-called Adiabatic CAES (A-CAES) is to retrieve the heat produced by the compression via thermal storage, thus eliminating the necessity of gas to burn and would allow consideration efficiency overall energy of the order of 70%. To date, there is no existing installation of A-CAES. Many studies describe the principal and the general working mode of storage systems by adiabatic compression of air. So, efficiencies of different configurations of adiabatic compression process were analyzed. The aim of this paper is to simulate and analyze the performances of a thermal storage reservoir integrated in the system and adapted to the working conditions of a CAES.
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.
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.
Numerical study of polaron problem in the adiabatic limit
Marsiglio, Frank; Li, Zhou; Blois, Cindy; Baillie, Devin
2010-03-01
We study the polaron problem in a one dimensional chain and on a two dimensional square lattice. The models we have used are the Holstein model and the Su-Schrieffer-Heeger (SSH) model. By a variational procedure based on the Lanczos method, we are able to examine the polaron problem in the limit when the mass of the ion is very large, i.e. close to the adiabatic limit. It is known that for the Holstein model there is no phase transition [1] for any nonzero phonon energy. It is also known that for the one dimensional Holstein or SSH model there will be long range order [2] (e.g. dimerization) in the adiabatic limit at half-filling. It is then interesting to study the long range order on a two dimensional square lattice in and away from the adiabatic limit. Moreover, recent progress for the single polaron near an impurity (disorder) [3] make it an interesting problem for studying bond length disorder which can change the hopping energy in a specific direction in the Holstein model. Reference: [1] H. Lowen, Phys.Rev.B 37, 8661 (1988) [2] J.E.Hirsch and E. Frandkin, Phys. Rev. Lett. 49, 402 (1982) [3]A.S.Mishchenko et.al Phys.Rev.B 79(2009) 180301(R)
Non-adiabatic oscillations of compact stars in general relativity
Gualtieri, L; Miniutti, G
2004-01-01
We have developed a formalism to study non-adiabatic, non-radial oscillations of compact stars in the frequency domain including the effects of thermal diffusion in a general relativistic framework. When a general equation of state depending on temperature is used, the perturbations of the fluid result in heat flux which is coupled with the spacetime geometry through the Einstein field equations. Our results show that the frequency of the first pressure (p) and gravity (g) oscillation modes is significantly affected by thermal diffusion, while that of the fundamental (f) mode is basically unaltered due to the global nature of that oscillation. The damping time of the oscillations is generally much smaller than in the adiabatic case (more than two orders of magnitude for the p- and g-modes) reflecting the effect of thermal dissipation. Both the isothermal and adiabatic limits are recovered in our treatment and we study in more detail the intermediate regime. Our formalism finds its natural astrophysical applic...
Steam bottoming cycle for an adiabatic diesel engine
Poulin, E.; Demler, R.; Krepchin, I.; Walker, D.
1984-03-01
A study of steam bottoming cycles using adiabatic diesel engine exhaust heat projected substantial performance and economic benefits for long haul trucks. A parametric analysis of steam cycle and system component variables, system cost, size and performance was conducted. An 811 K/6.90 MPa state-of-the-art reciprocating expander steam system with a monotube boiler and radiator core condenser was selected for preliminary design. When applied to a NASA specified turbo-charged adiabatic diesel the bottoming system increased the diesel output by almost 18%. In a comparison of the costs of the diesel with bottoming system (TC/B) and a NASA specified turbocompound adiabatic diesel with after-cooling with the same total output, the annual fuel savings less the added maintenance cost was determined to cover the increased initial cost of the TC/B system in a payback period of 2.3 years. Also during this program steam bottoming system freeze protection strategies were developed, technological advances required for improved system reliability were considered and the cost and performance of advanced systems were evaluated.
Quantum Adiabatic Algorithms, Small Gaps, and Different Paths
Farhi, Edward; Gosset, David; Gutmann, Sam; Meyer, Harvey B; Shor, Peter
2011-01-01
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then penalizing one of them with a single additional clause. We argue that by randomly modifying the beginning Hamiltonian, one obtains (with substantial probability) an adiabatic path that removes this difficulty. This suggests that the quantum adiabatic algorithm should in general be run on each instance with many different random paths leading to the problem Hamiltonian. We do not know whether this trick will help for a random instance of 3SAT (as opposed to an instance from the particular set we consider), especially if the instance has an exponential number of disparate assignments that violate few clauses. We use a continuous imaginary time Quantum Monte Carlo algorithm in a novel way to numerically investigate the ground state as well as the first excited state of our system...
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.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
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...
Two Timescale Approximation Applied to Gravitational Waves from Eccentric EMRIs
Moxon, Jordan; Flanagan, Eanna; Hinderer, Tanja; Pound, Adam
2016-03-01
Gravitational-wave driven inspirals of compact objects into massive black holes (Extreme Mass Ratio Inspirals - EMRIs) form an interesting, long-lived signal for future space-based gravitational wave detectors. Accurate signal predictions will be necessary to take full advantage of matched filtering techniques, motivating the development of a calculational technique for deriving the gravitational wave signal to good approximation throughout the inspiral. We report on recent work on developing the two-timescale technique with the goal of predicting waveforms from eccentric equatorial systems to subleading (post-adiabatic) order in the phase, building on recent work by Pound in the scalar case. The computation requires us to understand the dissipative component of the second-order self force. It also demands careful consideration of how the two timescale (near-zone) approximation should match with the post-Minkowski approximation of the gravitational waves at great distances.
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.
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
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.
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
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.
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
Mineo, H.; Niu, Y. L.; Kuo, J. L.; Lin, S. H.; Fujimura, Y.
2015-08-01
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.
Compressible Quasi-geostrophic Convection without the Anelastic Approximation
Calkins, M. A.; Marti, P.; Julien, K. A.
2014-12-01
Fluid compressibility is known to be an important, non-negligible component of the dynamics of many planetary atmospheres and stellar convection zones, yet imposes severe computational constraints on numerical simulations of the compressible Navier-Stokes equations (NSE). An often employed reduced form of the NSE are the anelastic equations, which maintain fluid compressibility in the form of a depth varying, adiabatic background state onto which the perturbations cannot feed back. We present the linear theory of compressible rotating convection in a local-area, plane layer geometry. An important dimensionless parameter in convection is the ratio of kinematic viscosity to thermal diffusivity, or the Prandtl number, Pr. It is shown that the anelastic approximation cannot capture the linear instability of gases with Prandtl numbers less than approximately 0.5 in the limit of rapid rotation; the time derivative of the density fluctuation appearing in the conservation of mass equation remains important for these cases and cannot be neglected. An alternative compressible, geostrophically balanced equation set has been derived and preliminary results utilizing this new equation set are presented. Notably, this new set of equations satisfies the Proudman-Taylor theorem on small axial scales even for strongly compressible flows, does not require the flow to be nearly adiabatic, and thus allows for feedback onto the background state.
Approximate Bayesian computation.
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
An, Shuoming; Lv, Dingshun; Del Campo, Adolfo; Kim, Kihwan
2016-09-01
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. Here we report the experimental implementation of counterdiabatic driving in a continuous variable system, a shortcut to the adiabatic transport of a trapped ion in phase space. The resulting dynamics is equivalent to a `fast-motion video' of the adiabatic trajectory. The robustness of this protocol is shown to surpass that of competing schemes based on classical local controls and Fourier optimization methods. Our results demonstrate that shortcuts to adiabaticity provide a robust speedup of quantum protocols of wide applicability in quantum technologies.
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 ...
Adiabatic quantum computing with spin qubits hosted by molecules.
Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji
2015-01-28
A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.
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.
Stimulated Raman adiabatic passage analogues in classical physics
Rangelov, A A [University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel (Germany); Vitanov, N V [Department of Physics, Sofia University, James Bourchier 5 blvd., 1164 Sofia (Bulgaria); Shore, B W [618 Escondido Cir., Livermore, CA (United States)
2009-03-14
Stimulated Raman adiabatic passage (STIRAP) is a well-established technique for producing coherent population transfer in a three-state quantum system. We here exploit the resemblance between the Schroedinger equation for such a quantum system and the Newton equation of motion for a classical system undergoing torque to discuss several classical analogues of STIRAP, notably the motion of a moving charged particle subject to the Lorentz force of a quasistatic magnetic field, the orientation of a magnetic moment in a slowly varying magnetic field and the Coriolis effect. Like STIRAP, these phenomena occur for counterintuitive motion of the torque and are robustly insensitive to small changes in the interaction properties.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
Diabatic Versus Adiabatic Calculation of Torsion-Vibration Interactions
Hougen, Jon T.
2013-06-01
The introductory part of this talk will deal briefly with two historical topics: (i) use of the words adiabatic, nonadiabatic, and diabatic in thermodynamics and quantum mechanics, and (ii) application of diabatic and adiabatic ideas to vibrational energy level calculations for a pair of diatomic-molecule potential energy curves exhibiting an avoided crossing. The main part of the talk will be devoted to recent work with Li-Hong Xu and Ron Lees on how ab initio projected frequency calculations for small-amplitude vibrations along the large-amplitude internal rotation path in methanol can best be used to help guide experimental assignments and fits in the IR vibrational spectrum. The three CH stretching vibrations for CH_{3}OH can conveniently be represented as coefficients multiplying three different types of basis vibrations, i.e., as coefficients of: (i) the local mode C-H_i bond displacements δr_{i} for hydrogens H_{1}, H_{2} and H_{3} of the methyl top, (ii) symmetrized linear combinations of the three δr_{i} of species A_{1} oplus E in the permutation-inversion group G_{6} = C_{3v} appropriate for methanol, or (iii) symmetrized linear combinations of the three δr_{i} of species 2A_{1} oplus A_{2} in the permutation-inversion group G_{6}. In this talk, we will focus on diabatic and adiabatic computations for the A_{1} oplus E basis vibrations of case (ii) above. We will briefly explain how Jahn-Teller-like and Renner-Teller-like torsion-vibration interaction terms occurring in the potential energy expression in the diabatic calculation become torsion-vibration Coriolis interaction terms occurring in the kinetic energy expression of the adiabatic calculations, and also show how, for algebraically solvable parameter choices, the same energy levels are obtained from either calculation. A final conclusion as to which approach is computationally superior for the numerical data given in a quantum chemistry output file has not yet been arrived at.
Power comparison of CMOS and adiabatic full adder circuit
Reddy, Sunil Gavaskar; 10.5121/vlsic.2011.2306
2011-01-01
Full adders are important components in applications such as digital signal processors (DSP) architectures and microprocessors. Apart from the basic addition adders also used in performing useful operations such as subtraction, multiplication, division, address calculation, etc. In most of these systems the adder lies in the critical path that determines the overall performance of the system. In this paper conventional complementary metal oxide semiconductor (CMOS) and adiabatic adder circuits are analyzed in terms of power and transistor count using 0.18UM technology.
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.
Adiabatic regularization of power spectra in nonminimally coupled chaotic inflation
Alinea, Allan L.
2016-10-01
We investigate the effect of adiabatic regularization on both the tensor- and scalar-perturbation power spectra in nonminimally coupled chaotic inflation. Similar to that of the 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 regularized power spectrum tends to the ``bare'' power spectrum. This study justifies the use of the unregularized (``bare'') power spectrum in standard calculations.
Adiabaticity and Reversibility Studies for Beam Splitting using Stable Resonances
Franchi, A; Giovannozzi, M
2008-01-01
At the CERN Proton Synchrotron, a series of beam experiments proved beam splitting by crossing the one-fourth resonance. Depending on the speed at which the horizontal resonance is crossed, the splitting process is more or less adiabatic, and a different fraction of the initial beam is trapped in the islands. Experiments prove that when the trapping process is reversed and the islands merged together, the final distribution features thick tails. The beam population in such tails is correlated to the speed of the resonance crossing and to the fraction of the beam trapped in the stable islands. Experiments and possible theoretical explanations are discussed.
Metallization of Nanofilms in Strong Adiabatic Electric Fields
Durach, Maxim; Rusina, Anastasia; Kling, Matthias F.; Stockman, Mark I.
2010-08-01
We introduce an effect of metallization of dielectric nanofilms by strong, adiabatically varying electric fields. The metallization causes optical properties of a dielectric film to become similar to those of a plasmonic metal (strong absorption and negative permittivity at low optical frequencies). This is a quantum effect, which is exponentially size-dependent, occurring at fields on the order of 0.1V/Å and pulse durations ranging from ˜1fs to ˜10ns for a film thickness of 3-10 nm.
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.
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
ADELE adiabatic compressed air energy storage. Status and perspectives
Freund, Sebastian [General Electric Deutschland Holding GmbH, Garching (Germany). GE Global Research Renewable Energy Systems Lab.; Marquardt, Roland; Moser, Peter [RWE Power AG, Essen (Germany). Research and Development Innovative Power Plant Technology
2013-06-01
This paper gives an overview about compressed air energy storage (CAES) technology and a summary of the ADELE programme, a multi-year R and D programme undertaken by a consortium led by RWE Power to develop adiabatic (A) CAES technology and commercialise the first plant. The ACAES technology is to utilise waste heat developing upon compression in order to increase the entire efficiency. The ADELE-ING project is to provide the basis for making the decision on the construction of a 85 MW prototype. (orig.)
Adiabatic Passage of Collective Excitations in Atomic Ensembles
LIYong; MIAOYuan-Xiu; SUNChang-Pu
2004-01-01
We describe a theoretical scheme that allows for transfer of quantum states of atomic collective excitation between two macroscopic atomic ensembles localized in two spatially-separated domains. The conception is based on the occurrence of double-exciton dark states due to the collective destructive quantum interference of the emissions from the two atomic ensembles. With an adiabatically coherence manipulation for the atom-field couplings by stimulated Rmann scattering, the dark states will extrapolate from an exciton state of an ensemble to that of another. This realizes the transport of quantum information among atomic ensembles.
Adiabatic Passage of Collective Excitations in Atomic Ensembles
LI Yong; MIAO Yuan-Xiu; SUN Chang-Pu
2004-01-01
We describe a theoretical scheme that allows for transfer of quantum states of atomic collective excitation between two macroscopic atomic ensembles localized in two spatially-separated domains. The conception is based on the occurrence of double-exciton dark states due to the collective destructive quantum interference of the emissions from the two atomic ensembles. With an adiabatically coherence manipulation for the atom-field couplings by stimulated Ramann scattering, the dark states will extrapolate from an exciton state of an ensemble to that of another. This realizes the transport of quantum information among atomic ensembles.
Fast CNOT gate via shortcuts to adiabatic passage
Wang, Zhe; Xia, Yan; Chen, Ye-Hong; Song, Jie
2016-10-01
Based on the shortcuts to adiabatic passage, we propose a scheme for directly implementing a controlled-not (CNOT) gate in a cavity quantum electrodynamics system. Moreover, we generalize the scheme to realize a CNOT gate in two separate cavities connected by an optical fiber. The strictly numerical simulation shows that the schemes are fast and insensitive to the decoherence caused by atomic spontaneous emission and photon leakage. In addition, the schemes can provide a theoretical basis for the manipulation of the multiqubit quantum gates in distant nodes of a quantum network.
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.
Salt materials testing for a spacecraft adiabatic demagnetization refrigerator
Savage, M. L.; Kittel, P.; Roellig, T.
As part of a technology development effort to qualify adiabatic demagnetization refrigerators for use in a NASA spacecraft, such as the Space Infrared Telescope Facility, a study of low temperature characteristics, heat capacity and resistance to dehydration was conducted for different salt materials. This report includes results of testing with cerrous metaphosphate, several synthetic rubies, and chromic potassium alum (CPA). Preliminary results show that CPA may be suitable for long-term spacecraft use, provided that the salt is property encapsulated. Methods of salt pill construction and testing for all materials are discussed, as well as reliability tests. Also, the temperature regulation scheme and the test cryostat design are briefly discussed.
无
2005-01-01
Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic system in terms of quasi-coordinates are studied. The perturbation to symmetries for the nonholonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the forms of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
CHEN Xiang-Wei; WANG Ming-Quan; WANG Xin-Min
2005-01-01
Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
WANG Yu-Sheng; ZHANG Xiao-Ni; YUAN Bao-He; FANG Jian-Hui; YANG Guo-Hong; LIN Peng; PANG Ting
2008-01-01
Based on the concept of higher-order adiabatic invariants of mechanical system with action of a small perturbation, the perturbation to Lie symmetry and generalized Hojman adiabatic invariants for the relativistic Hamilton system are studied. Perturbation to Lie symmetry is discussed under general infinitesimal transformation of groups in which time is variable. The form and the criterion of generalized Hojman adiabatic invariants for this system are obtained. Finally, an example is given to illustrate the results.
Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equation
Chen Xiang-Wei; Liu Cui-Mei; Li Yan-Min
2006-01-01
Based on the invariance of differential equations under infinitesimal transformations,Lie symmetry,laws of conservations,perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed.The conditions for existence of the exact invariants and adiabatic invariants are proved,and their forms are also given.In addition,an example is presented to illustrate these results.
Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems
DING Ning; FANG Jian-Hui; WANG Peng; ZHANG Xiao-Ni
2007-01-01
Based on the concept of adiabatic invariant, the perturbation to the Lie symmetry and adiabatic invariants for general holonomic mechanical systems are studied. The exact invariants induced directly from the Lie symmetry of the system without perturbation are given. The perturbation to the Lie symmetry is discussed and the adiabatic invariants that have the different form from that in [Act. Phys. Sin. 55 (2006) 3236 (in Chinese)] of the perturbed system, are obtained.
Exact invariants and adiabatic invariants of dynamical system of relative motion
Chen Xiang-Wei; Wang Xin-Min; Wang Ming-Quan
2004-01-01
Based on the theory of symmetries and conserved quantities, the exact inwriants and adiabatic inwriants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
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.
Roy, Swapnoneel; Thakur, Ashok Kumar
2008-01-01
Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.
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 projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....
Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems
Luo Shao-Kai; Cai Jian-Le; Jia Li-Qun
2008-01-01
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 invaxiants 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.
Wu, Jin-Lei; Ji, Xin; Zhang, Shou
2017-01-01
We propose a dressed-state scheme to achieve shortcuts to adiabaticity in atom-cavity quantum electrodynamics for speeding up adiabatic two-atom quantum state transfer and maximum entanglement generation. Compared with stimulated Raman adiabatic passage, the dressed-state scheme greatly shortens the operation time in a non-adiabatic way. By means of some numerical simulations, we determine the parameters which can guarantee the feasibility and efficiency both in theory and experiment. Besides, numerical simulations also show the scheme is robust against the variations in the parameters, atomic spontaneous emissions and the photon leakages from the cavity.
A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics
Zhang Yi
2006-01-01
The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.
S-Approximation: A New Approach to Algebraic Approximation
M. R. Hooshmandasl
2014-01-01
Full Text Available We intend to study a new class of algebraic approximations, called S-approximations, and their properties. We have shown that S-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of S-approximations, called Sℳ-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusionbased. The paper concludes by studying some basic operations on S-approximations and counting the number of S-min functions.
Adiabatic Compression of Compact Tori for Current Drive and Heating
Woodruff, Simon; McNab, Angus; Miller, Kenneth; Ziemba, Tim
2008-11-01
Several critical issues stand in the development path for compact tori. An important one is the production of strong magnetic fields, (or large flux amplifications) by use of a low current source. The Pulsed Build-up Experiment is a Phase II SBIR project in which we aim to show a new means for generating strong magnetic fields from a low current source, namely, the repetitive injection of helicity-bearing plasma that also undergoes an acceleration and compression. In the Phase I SBIR, advanced computations were benchmarked against analytic theory and run to determine the best means for the acceleration and compression of a compact torus plasma. The study included detailed simulations of magnetic reconnection. In Phase II, an experiment has been designed and is being built to produce strong magnetic fields in a spheromak by the repetitive injection of magnetic helicity from a low current coaxial plasma source. The plasma will be accelerated and compressed in a similar manner to a traveling wave adiabatic compression scheme that was previously applied to a mirror plasma [1]. [1] P. M. Bellan Scalings for a Traveling Mirror Adiabatic Magnetic Compressor Rev. Sci. Instrum. 53(8) 1214 (1982) Work supported by DOE Grant No. DE-FG02-06ER84449.
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...
Shortcut to adiabaticity for an anisotropic unitary Fermi gas
Deng, Shujin; Yu, Qianli; Wu, Haibin
2016-01-01
Coherent control of complex quantum systems is a fundamental requirement in quantum information processing and engineering. Recently developed notion of shortcut to adiabaticity (STA) has spawned intriguing prospects. So far, the most experimental investigations of STA are implemented in the ideal thermal gas or the weakly interacting ultracold Bose gases. Here we report the first demonstration of a many-body STA in a 3D anisotropically trapped unitary Fermi gas. A new dynamical scaling law is demonstrated on such a strongly interacting quantum gas. By simply engineering the frequency aspect ratio of a harmonic trap, the dynamics of the gas can be manipulated and the many-body state can be transferred adiabatically from one stationary state to another one in short time scale without the excitation. The universal scaling both for non-interacting and unitary Fermi gas is also verified. This could be very important for future many-body quantum engineering and the exploration of the fundamental law of the thermod...
Adiabatic Berry Phase and Hannay Angle for Open Paths
Pati, A K
1998-01-01
We obtain the adiabatic Berry phase by defining a generalised gauge potential whose line integral gives the phase holonomy for arbitrary evolutions of parameters. Keeping in mind that for classical integrable systems it is hardly clear how to obtain open-path Hannay angle, we establish a connection between the open-path Berry phase and Hannay angle by using the parametrised coherent state approach. Using the semiclassical wavefunction we analyse the open-path Berry phase and obtain the open-path Hannay angle. Further, by expressing the adiabatic Berry phase in terms of the commutator of instantaneous projectors with its differential and using Wigner representation of operators we obtain the Poisson bracket between distribution function and its differential. This enables us to talk about the classical limit of the phase holonomy which yields the angle holonomy for open-paths. An operational definition of Hannay angle is provided based on the idea of classical limit of quantum mechanical inner product. A probab...
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.
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.
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.
Rajinder Pal
2016-03-01
Full Text Available 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. The entropy generation rate per unit pipe length is affected by the type of the emulsion as well as its stability. Unstable emulsions without any surfactant present at the interface generate less entropy in the turbulent regime as compared with the surfactant-stabilized emulsions of the same viscosity and density. The effect of surfactant is particularly severe in the case of W/O emulsions. In the turbulent regime, the rate of entropy generation in unstable W/O emulsions is much lower in comparison with that observed in the stable W/O emulsions. A significant delay in the transition from laminar to turbulent regime is also observed in the case of unstable W/O emulsion. Finally, the analysis and simulation results are presented on non-adiabatic pipeline flow of emulsions.
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 ...
Zhao, Z.P.; Iwasa, Y. (Massachusetts Inst. of Tech., Cambridge, MA (United States). Francis Bitter National Magnet Lab. Massachusetts Inst. of Tech., Cambridge, MA (United States). Plasma Fusion Center)
1991-09-01
A normal zone propagation model has been developed for superconducting composites under adiabatic conditions. It is based on the Whetstone-Roos model, originally developed for normal zone propagation in adiabatic wires of unclad superconductor. The model takes into account the temperature and magnetic field dependent material properties, for both superconductor and matrix metal. Analytical results agree well with experimental data. (author).
Dzyaloshinskii-Moriya interactions and adiabatic magnetization dynamics in molecular magnets
De Raedt, H; Miyashita, S; Michielsen, K; Machida, M
A microscopic model of the molecular magnet V-15 is used to study mechanisms for the adiabatic change of the magnetization in time-dependent magnetic fields. The effects of the Dzyaloshinskii-Moriya interaction, the most plausible source for the energy-level repulsions that lead to adiabatic changes
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.
Duality in adiabatic level crossing Quantum coherence and complete reflection
Fujikawa, K; Fujikawa, Kazuo; Suzuki, Hiroshi
1997-01-01
A field dependent su(2) gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) level crossing problem. It is pointed out that weak and strong level crossing interactions are interchanged under this transformation, and thus realizing a naive strong and weak duality. A reliable perturbation theory is thus formulated in the both limits of weak and strong interactions. Main characteristics of the level crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double well potential is generally suppressed by the effect of level crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Antonio Enea Romano
2016-04-01
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.
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...
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.
Adiabatic pumping of Chern-Simons axion coupling.
Taherinejad, Maryam; Vanderbilt, David
2015-03-06
We study the adiabatic pumping of the Chern-Simons axion (CSA) coupling along a parametric loop characterized by a nonzero second Chern number C^{(2)} from the viewpoint of the hybrid Wannier representation, in which the Wannier charge centers are visualized as sheets defined over a projected 2D Brillouin zone. We derive a new formula for the CSA coupling, expressing it as an integral involving Berry curvatures and potentials defined on the Wannier charge center sheets. We show that a loop characterized by a nonzero C^{(2)} requires a series of sheet-touching events at which 2π quanta of Berry curvature are passed from sheet to sheet, in such a way that e^{2}/h units of CSA coupling are pumped by a lattice vector by the end of the cycle. We illustrate these behaviors via explicit calculations on a model tight-binding Hamiltonian and discuss their implications.
Diffusion of the adiabatic invariant for modulated symplectic maps
Bazzani, A.; Brini, F.; Turchetti, G. [University of Bologna, INFN sezione di Bologna via Irnerio n.46, I-40126 Bologna (Italy)
1997-02-01
We consider the diffusion of the orbits due to a slow modulation of a parameter in an almost integrable symplectic map. This phenomenon (modulational diffusion) is relevant for the stability of the betatronic motion when the ripples are present in the feeding currents of the magnets. In the limit of a slow periodic modulation when the theory of Neishtadt applies, the diffusion takes place in the region swept by a nonlinear resonance and a random walk is defined in the space of the adiabatic invariant. The effect of the boundaries is reproduced by introducing an absorbing boundary condition (dynamical aperture) or a reflecting boundary condition. The analytical result for the action distribution function reproduces very well the numerical distribution function both when the diffusion takes place in a bounded region and when the orbits reach the dynamical aperture. {copyright} {ital 1997 American Institute of Physics.}
Yang-Mills moduli space in the adiabatic limit
Lechtenfeld, Olaf
2015-01-01
We consider the Yang-Mills equations for a matrix gauge group $G$ inside the future light cone of 4-dimensional Minkowski space, which can be viewed as a Lorentzian cone $C(H^3)$ over the 3-dimensional hyperbolic space $H^3$. Using the conformal equivalence of $C(H^3)$ and the cylinder $R\\times H^3$, we show that, in the adiabatic limit when the metric on $H^3$ is scaled down, classical Yang-Mills dynamics is described by geodesic motion in the infinite-dimensional group manifold $C^\\infty (S^2_\\infty,G)$ of smooth maps from the boundary 2-sphere $S^2_\\infty=\\partial H^3$ into the gauge group $G$.
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.
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.
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.
Adiabatic Dynamics of Edge Waves in Photonic Graphene
Ablowitz, M J; Ma, Y -P
2014-01-01
The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying dynamics. Depending on parameters, edge states can exist over an entire period or only part of a period; in the latter case an edge mode can effectively disintegrate and scatter into the bulk. In the presence of nonlinearity, a `time'-dependent one-dimensional nonlinear Schr\\"odinger (NLS) equation describes the envelope dynamics of edge modes. When the average of the `time varying' coefficients yields a focusing NLS equation, soliton propagation is exhibited. For both linear and nonlinear systems, certain long lived traveling modes with minimal backscattering are found; they exhibit properties of topologically protected states.
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...
A Random Matrix Model of Adiabatic Quantum Computing
Mitchell, D R; Lue, W; Williams, C P; Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2004-01-01
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances, i.e., those having a critical ratio of clauses to variables, the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathemat...
Hydroxylamine nitrate self-catalytic kinetics study with adiabatic calorimetry.
Liu, Lijun; Wei, Chunyang; Guo, Yuyan; Rogers, William J; Sam Mannan, M
2009-03-15
Hydroxylamine nitrate (HAN) is an important member of the hydroxylamine compound family with applications that include equipment decontamination in the nuclear industry and aqueous or solid propellants. Due to its instability and autocatalytic behavior, HAN has been involved in several incidents at the Hanford and Savannah River Site (SRS) [Technical Report on Hydroxylamine Nitrate, US Department of Energy, 1998]. Much research has been conducted on HAN in different areas, such as combustion mechanism, decomposition mechanism, and runaway behavior. However, the autocatalytic decomposition behavior of HAN at runaway stage has not been fully addressed due to its highly exothermic and rapid decomposition behavior. This work is focused on extracting HAN autocatalytic kinetics and analyzing HAN critical behavior from adiabatic calorimetry measurements. A lumped autocatalytic kinetic model for HAN and associated model parameters are determined. Also the storage and handling critical conditions of diluted HAN solution without metal presence are quantified.
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.
On the adiabatic ionization energy of the propargyl radical
Jacovella, U.; Gans, B.; Merkt, F.
2013-08-01
The photoionization and pulsed-field-ionization zero-kinetic-energy photoelectron spectra of the propargyl radical have been recorded in the vicinity of the origin of the tilde{X}^+ ^1A_1 leftarrow tilde{X} ^2B_1 photoionizing transition. An internally cold sample of propargyl with a rotational temperature of ˜45 K was produced in a supersonic expansion of 1,3-butadiene in helium. Propargyl was generated by excimer laser (ArF, 193 nm) photolysis of 1,3-butadiene in a quartz capillary mounted at the exit of a pulsed valve. The rotational structure of the origin band of the photoelectron spectrum was partially resolved and an improved value of the adiabatic ionization energy of propargyl (EI/hc = 70174.5(20) cm-1) was determined.
Adiabatic Cooling for Rovibrational Spectroscopy of Molecular Ions
Fisher, Karin
2017-01-01
The field of cold molecular ions is a fast growing one, with applications in high resolution spectroscopy and metrology, the search for time variations of fundamental constants, cold chemistry and collisions, and quantum information processing, to name a few. The study of single molecular ions...... is attractive as it enables one to push the limits of spectroscopic accuracy. Non-destructive spectroscopic detection of molecular ions can be achieved by co-trapping with an easier to detect atomic ion. The ion chain has coupled motion, and transitions which change both the internal and motional states...... to the measured heating rates, almost perfectly fitting existing heating rate theory. Further, the same model successfully predicted the heating rates of the in-phase mode of a two-ion crystal, indicating that we can use it to predict the heating rates in experiments on molecule-atom chains. Adiabatic cooling...
Filtering of matter wave vibrational states via spatial adiabatic passage
Loiko, Yu; Corbalán, R; Birkl, G; Mompart, J; 10.1103/PhysRevA.83.033629
2011-01-01
We discuss the filtering of the vibrational states of a cold atom in an optical trap, by chaining this trap with two empty ones and controlling adiabatically the tunneling. Matter wave filtering is performed by selectively transferring the population of the highest populated vibrational state to the most distant trap while the population of the rest of the states remains in the initial trap. Analytical conditions for two-state filtering are derived and then applied to an arbitrary number of populated bound states. Realistic numerical simulations close to state-of-the-art experimental arrangements are performed by modeling the triple well with time dependent P\\"oschl-Teller potentials. In addition to filtering of vibrational states, we discuss applications for quantum tomography of the initial population distribution and engineering of atomic Fock states that, eventually, could be used for tunneling assisted evaporative cooling.
Adiabatic pumping solutions in global AdS
Carracedo, Pablo; Mas, Javier; Musso, Daniele; Serantes, Alexandre
2017-05-01
We construct a family of very simple stationary solutions to gravity coupled to a massless scalar field in global AdS. They involve a constantly rising source for the scalar field at the boundary and thereby we name them pumping solutions. We construct them numerically in D = 4. They are regular and, generically, have negative mass. We perform a study of linear and nonlinear stability and find both stable and unstable branches. In the latter case, solutions belonging to different sub-branches can either decay to black holes or to limiting cycles. This observation motivates the search for non-stationary exactly timeperiodic solutions which we actually construct. We clarify the role of pumping solutions in the context of quasistatic adiabatic quenches. In D = 3 the pumping solutions can be related to other previously known solutions, like magnetic or translationally-breaking backgrounds. From this we derive an analytic expression.
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)...
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Collisionless magnetic reconnection under anisotropic MHD approximation
Hirabayashi, Kota; Hoshino, Masahiro
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless magneto-hydro-dynamic (MHD) simulations based on the double adiabatic approximation, which is an important step to bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observation. According to our results, a pair of slow shocks does form in the reconnection layer. The resultant shock waves, however, are quite weak compared with those in an isotropic MHD from the point of view of the plasma compression and the amount of the magnetic energy released across the shock. Once the slow shock forms, the downstream plasma are heated in highly anisotropic manner and a firehose-sense (P_{||}>P_{⊥}) pressure anisotropy arises. The maximum anisotropy is limited by the marginal firehose criterion, 1-(P_{||}-P_{⊥})/B(2) =0. In spite of the weakness of the shocks, the resultant reconnection rate is kept at the same level compared with that in the corresponding ordinary MHD simulations. It is also revealed that the sequential order of propagation of the slow shock and the rotational discontinuity, which appears when the guide field component exists, changes depending on the magnitude of the guide field. Especially, when no guide field exists, the rotational discontinuity degenerates with the contact discontinuity remaining at the position of the initial current sheet, while with the slow shock in the isotropic MHD. Our result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.
Wei, Chia-Chien
2012-11-05
This work theoretically studies the transmission performance of a DML-based OFDM system by small-signal approximation, and the model considers both the transient and adiabatic chirps. The dispersion-induced distortion is modeled as subcarrier-to-subcarrier intermixing interference (SSII), and the theoretical SSII agrees with the distortion obtained from large-signal simulation statistically and deterministically. The analysis shows that the presence of the adiabatic chirp will ease power fading or even provide gain, but will increase the SSII to deteriorate OFDM signals after dispersive transmission. Furthermore, this work also proposes a novel iterative equalization to eliminate the SSII. From the simulation, the distortion could be effectively mitigated by the proposed equalization such that the maximum transmission distance of the DML-based OFDM signal is significantly improved. For instance, the transmission distance of a 30-Gbps DML-based OFDM signal can be extended from 10 km to more than 100 km. Besides, since the dispersion-induced distortion could be effectively mitigated by the equalization, negative power penalties are observed at some distances due to chirp-induced power gain.
Omiste, J J; Schmelcher, P; González-Férez, R; Holmegaard, L; Nielsen, J H; Stapelfeldt, H; Küpper, J
2011-01-01
We present a theoretical study of recent laser-alignment and mixed-field-orientation experiments of asymmetric top molecules. In these experiments, pendular states were created using linearly polarized strong ac electric fields from pulsed lasers in combination with weak electrostatic fields. We compare the outcome of our calculations with experimental results obtained for the prototypical large molecule benzonitrile (C$_7$H$_5$N) [J.L. Hansen et al, Phys. Rev. A, 83, 023406 (2011)] and explore the directional properties of the molecular ensemble for several field configurations, i.e., for various field strengths and angles between ac and dc fields. For perpendicular fields one obtains pure alignment, which is well reproduced by the simulations. For tilted fields, we show that a fully adiabatic description of the process does not reproduce the experimentally observed orientation, and it is mandatory to use a diabatic model for population transfer between rotational states. We develop such a model and compare ...
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
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 + ...
Two-level system in spin baths: non-adiabatic dynamics and heat transport.
Segal, Dvira
2014-04-28
We study the non-adiabatic dynamics of a two-state subsystem in a bath of independent spins using the non-interacting blip approximation, and derive an exact analytic expression for the relevant memory kernel. We show that in the thermodynamic limit, when the subsystem-bath coupling is diluted (uniformly) over many (infinite) degrees of freedom, our expression reduces to known results, corresponding to the harmonic bath with an effective, temperature-dependent, spectral density function. We then proceed and study the heat current characteristics in the out-of-equilibrium spin-spin-bath model, with a two-state subsystem bridging two thermal spin-baths of different temperatures. We compare the behavior of this model to the case of a spin connecting boson baths, and demonstrate pronounced qualitative differences between the two models. Specifically, we focus on the development of the thermal diode effect, and show that the spin-spin-bath model cannot support it at weak (subsystem-bath) coupling, while in the intermediate-strong coupling regime its rectifying performance outplays the spin-boson model.
Evaporative cooling of air in an adiabatic channel with partially wetted zones
Terekhov, V. I.; Gorbachev, M. V.; Khafaji, H. Q.
2016-03-01
The paper deals with the numerical study of heat and mass transfer in the process of direct evaporation air cooling in the laminar flow of forced convection in a channel between two parallel insulated plates with alternating wet and dry zones along the length. The system of Navier-Stokes equations and equations of energy and steam diffusion are being solved in two-dimensional approximation. At the channel inlet, all thermal gas-dynamic parameters are constant over the cross section, and the channel walls are adiabatic. The studies were carried out with varying number of dry zones ( n = 0-16), their relative length ( s/l = 0-1) and Reynolds number Re = 50-1000 in the flow of dry air (φ0 = 0) with a constant temperature at the inlet (T 0 = 30 °C). The main attention is paid to optimization analysis of evaporation cell characteristics. It is shown that an increase in the number of alternating steps leads to an increase in the parameters of thermal and humid efficiency. With an increase in Re number and a decrease in the extent of wet areas, the efficiency parameter reduces.
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
Approximation by Multivariate Singular Integrals
Anastassiou, George A
2011-01-01
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last cha
Approximations of fractional Brownian motion
Li, Yuqiang; 10.3150/10-BEJ319
2012-01-01
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
Approximation by planar elastic curves
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
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....
Energy-Efficient and Secure S-Box circuit using Symmetric Pass Gate Adiabatic Logic
Kumar, Dinesh [University of Kentucky, Lexington; Thapliyal, Himanshu [ORNL; 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.
Recent developments in trapping and manipulation of atoms with adiabatic potentials
Garraway, Barry M.; Perrin, Hélène
2016-09-01
A combination of static and oscillating magnetic fields can be used to ‘dress’ atoms with radio-frequency (RF), or microwave, radiation. The spatial variation of these fields can be used to create an enormous variety of traps for ultra-cold atoms and quantum gases. This article reviews the type and character of these adiabatic traps and the applications which include atom interferometry and the study of low-dimensional quantum systems. We introduce the main concepts of magnetic traps leading to adiabatic dressed traps. The concept of adiabaticity is discussed in the context of the Landau-Zener model. The first bubble trap experiment is reviewed together with the method used for loading it. Experiments based on atom chips show the production of double wells and ring traps. Dressed atom traps can be evaporatively cooled with an additional RF field, and a weak RF field can be used to probe the spectroscopy of the adiabatic potentials. Several approaches to ring traps formed from adiabatic potentials are discussed, including those based on atom chips, time-averaged adiabatic potentials and induction methods. Several proposals for adiabatic lattices with dressed atoms are also reviewed.
Mitra, Avik; Ghosh, Arindam; Das, Ranabir; Patel, Apoorva; Kumar, Anil
2005-12-01
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.
Rossby wave extra invariant in the Galerkin approximation
Balk, Alexander M.
2017-08-01
The non-linear system of Rossby waves or plasma drift waves is known to have a unique adiabatic-like extra invariant in addition to the energy and enstrophy. This invariant is physically significant because its presence implies the generation of zonal flow. The latter is known to slow down the anomalous transport of temperature and particles in nuclear fusion with magnetic confinement. However, the derivation of the extra invariant - unlike the energy and enstrophy - is based on the continuum of resonances, while in numerical simulations there are only finite number of resonances. We show that precisely the same invariant takes place in the Galerkin approximations (even of low order, with a few ODEs). To show this we make variation of boundary conditions, when the solution is periodic in different directions. We also simplify the derivation of the extra conservation.
P. Savoini
2005-12-01
Full Text Available Test particle simulations are performed in order to analyze in detail the dynamics of transmitted electrons through a supercritical, strictly perpendicular, collisionless shock. In addition to adiabatic particles, two distinct nonadiabatic populations are observed surprisingly: (i first, an over-adiabatic population characterized by an increase in the gyrating velocity higher than that expected from the conservation of the magnetic moment µ, and (ii second, an under-adiabatic population characterized by a decrease in this velocity. Results show that both nonadiabatic populations have their pitch angle more aligned along the magnetic field than the adiabatic one at the time these hit the shock front. The formation of "under" and "over-adiabatic" particles strongly depends on their local injection conditions through the large amplitude cross-shock potential present within the shock front. A simplified theoretical model validates these results and points out the important role of the electric field as seen by the electrons. A classification shows that both nonadiabatic electrons are issued from the core part of the upstream distributionÊ function. In contrast, suprathermal and tail electrons only contribute to the adiabatic population; nevertheless, the core part of the upstream distribution contributes at a lower percentage to the adiabatic electrons. Under-adiabatic electrons are characterized by small injection angles θ_{inj}≤90°, whereas "over-adiabatic" particles have high injection angles θ_{inj}>90° (where θ_{inj} is the angle between the local gyrating velocity vector and the shock normal.
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.
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
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai; ZHANG Ke-Jun; LI Yan
2009-01-01
The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied.First,the discrete Noether exact invariant induced directly from the Noether symmetry of the system without perturbation is given.Secondly,the concept of discrete high-order adiabatic invariant is presented,the criterion of the perturbation to Noether symmetry is established,and the discrete Noether adiabatic invariant induced directly from the perturbation to Noether symmetry is obtained.Lastly,an example is discussed to illustrate the application of the results.
Peter Keefe
2004-03-01
Full Text Available Abstract: The nature of the thermodynamic behavior of Type I superconductor particles, having a cross section less than the Ginzburg-Landau temperature dependent coherence length is discussed for magnetic field induced adiabatic phase transitions from the superconductive state to the normal state. Argument is advanced supporting the view that when the adiabatic magneto-caloric process is applied to particles, the phase transition is characterized by a decrease in entropy in violation of traditional formulations of the Second Law, evidenced by attainment of a final process temperature below that which would result from an adiabatic magneto-caloric process applied to bulk dimensioned specimens.
Adiabatic Floquet Picture for Hydrogen Atom in an Intense Laser Field
Wang, Yujun; Esry, B D
2010-01-01
We develop an adiabatic Floquet picture in the length gauge to describe the dynamics of a hydrogen atom in an intense laser field. In this picture, we discuss the roles played by frequency and intensity in terms of adiabatic potentials and the couplings between them, which gives a physical and intuitive picture for quantum systems exposed to a laser field. For simplicity, analyze hydrogen and give the adiabatic potential curves as well as some physical quantities that can be readily calculated for the ground state. Both linearly and circularly polarized laser fields are discussed.
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.
Solitary shock waves and adiabatic phase transition in lipid interfaces and nerves.
Shrivastava, Shamit; Kang, Kevin Heeyong; Schneider, Matthias F
2015-01-01
This study shows that the stability of solitary waves excited in a lipid monolayer near a phase transition requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the condition results in a threshold for excitation, saturation of the wave's amplitude, and the splitting of the wave at the phase boundaries. Splitting in particular confirms that a hydrated lipid interface can undergo condensation on adiabatic heating, thus showing retrograde behavior. Finally, using the theoretical insights and state dependence of conduction velocity in nerves, the curvature of the adiabatic state diagram is shown to be closely tied to the thermodynamic blockage of nerve pulse propagation.
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.
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.
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.
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...
Random Matrix Approach to Quantum Adiabatic Evolution Algorithms
Boulatov, Alexei; Smelyanskiy, Vadier N.
2004-01-01
We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.
Development of a semi-adiabatic isoperibol solution calorimeter
Venkata Krishnan, R.; Jogeswararao, G.; Parthasarathy, R.; Premalatha, S.; Prabhakar Rao, J.; Gunasekaran, G.; Ananthasivan, K.
2014-12-01
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%.
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.
Stimulated Raman adiabatic passage in physics, chemistry, and beyond
Vitanov, Nikolay V.; Rangelov, Andon A.; Shore, Bruce W.; Bergmann, Klaas
2017-01-01
The technique of stimulated Raman adiabatic passage (STIRAP), which allows efficient and selective population transfer between quantum states without suffering loss due to spontaneous emission, was introduced in 1990 by Gaubatz et al.. Since then STIRAP has emerged as an enabling methodology with widespread successful applications in many fields of physics, chemistry, and beyond. This article reviews the many applications of STIRAP emphasizing the developments since 2001, the time when the last major review on the topic was written (Vitanov, Fleischhauer et al.). A brief introduction into the theory of STIRAP and the early applications for population transfer within three-level systems is followed by the discussion of several extensions to multilevel systems, including multistate chains and tripod systems. The main emphasis is on the wide range of applications in atomic and molecular physics (including atom optics, cavity quantum electrodynamics, formation of ultracold molecules, etc.), quantum information (including single- and two-qubit gates, entangled-state preparation, etc.), solid-state physics (including processes in doped crystals, nitrogen-vacancy centers, superconducting circuits, semiconductor quantum dots and wells), and even some applications in classical physics (including waveguide optics, polarization optics, frequency conversion, etc.). Promising new prospects for STIRAP are also presented (including processes in optomechanics, precision experiments, detection of parity violation in molecules, spectroscopy of core-nonpenetrating Rydberg states, population transfer with x-ray pulses, etc.).
Thermodynamics Analysis of Refinery Sludge Gasification in Adiabatic Updraft Gasifier
Reem Ahmed
2014-01-01
Full Text Available 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.
Development of a semi-adiabatic isoperibol solution calorimeter.
Venkata Krishnan, R; Jogeswararao, G; Parthasarathy, R; Premalatha, S; Prabhakar Rao, J; Gunasekaran, G; Ananthasivan, K
2014-12-01
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%.
Nonequilibrium adiabatic molecular dynamics simulations of methane clathrate hydrate decomposition
Alavi, Saman; Ripmeester, J. A.
2010-04-01
Nonequilibrium, constant energy, constant volume (NVE) molecular dynamics simulations are used to study the decomposition of methane clathrate hydrate in contact with water. Under adiabatic conditions, the rate of methane clathrate decomposition is affected by heat and mass transfer arising from the breakup of the clathrate hydrate framework and release of the methane gas at the solid-liquid interface and diffusion of methane through water. We observe that temperature gradients are established between the clathrate and solution phases as a result of the endothermic clathrate decomposition process and this factor must be considered when modeling the decomposition process. Additionally we observe that clathrate decomposition does not occur gradually with breakup of individual cages, but rather in a concerted fashion with rows of structure I cages parallel to the interface decomposing simultaneously. Due to the concerted breakup of layers of the hydrate, large amounts of methane gas are released near the surface which can form bubbles that will greatly affect the rate of mass transfer near the surface of the clathrate phase. The effects of these phenomena on the rate of methane hydrate decomposition are determined and implications on hydrate dissociation in natural methane hydrate reservoirs are discussed.
Adiabatic calorimetric decomposition studies of 50 wt.% hydroxylamine/water.
Cisneros, L O; Rogers, W J; Mannan, M S
2001-03-19
Calorimetric data can provide a basis for determining potential hazards in reactions, storage, and transportation of process chemicals. This work provides calorimetric data for the thermal decomposition behavior in air of 50wt.% hydroxylamine/water (HA), both with and without added stabilizers, which was measured in closed cells with an automatic pressure tracking adiabatic calorimeter (APTAC). Among the data provided are onset temperatures, reaction order, activation energies, pressures of noncondensable products, thermal stability at 100 degrees C, and the effect of HA storage time. Discussed also are the catalytic effects of carbon steel, stainless steel, stainless steel with silica coating, inconel, titanium, and titanium with silica coating on the reaction self-heat rates and onset temperatures. In borosilicate glass cells, HA was relatively stable at temperatures up to 133 degrees C, where the HA decomposition self-heat rate reached 0.05 degrees C/min. The added stabilizers appeared to reduce HA decomposition rates in glass cells and at ambient temperatures. The tested metals and metal surfaces coated with silica acted as catalysts to lower the onset temperatures and increase the self-heat rates.
Progress in the Development of a Continuous Adiabatic Demagnetization Refrigerator
Shirron, Peter; Canavan, Edgar; DiPirro, Michael; Jackson, Michael; King, Todd; Tuttle, James; Krebs, Carolyn A. (Technical Monitor)
2002-01-01
We report on recent progress in the development of a continuous adiabatic demagnetization refrigerator (CADR). Continuous operation avoids the constraints of long hold times and short recycle times that lead to the generally large mass of single-shot ADRs, allowing us to achieve an order of magnitude larger cooling power per unit mass. Our current design goal is 10 micro W of cooling at 50 mK using a 6-10 K heat sink. The estimated mass is less than 10 kg, including magnetic shielding of each stage. The relatively high heat rejection capability allows it to operate with a mechanical cryocooler as part of a cryogen-free, low temperature cooling system. This has the advantages of long mission life and reduced complexity and cost. We have assembled a three-stage CADR and have demonstrated continuous cooling using a superfluid helium bath as the heat sink. The temperature stability is 8 micro K rms or better over the entire cycle, and the cooling power is 2.5 micro W at 60 mK rising to 10 micro W at 100 mK.
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%.
Salt Pill Design and Fabrication for Adiabatic Demagnetization Refrigerators
Shirron, Peter J.; Mccammon, Dan
2014-01-01
The performance of an adiabatic demagnetization refrigerator (ADR) is critically dependent on the design and construction of the salt pills that produce cooling. In most cases, the primary goal is to obtain the largest cooling capacity at the low temperature end of the operating range. The realizable cooling capacity depends on a number of factors, including refrigerant mass, and how efficiently it absorbs heat from the various instrument loads. The design and optimization of "salt pills" for ADR systems depend not only on the mechanical, chemical and thermal properties of the refrigerant, but also on the range of heat fluxes that the salt pill must accommodate. Despite the fairly wide variety of refrigerants available, those used at very low temperature tend to be hydrated salts that require a dedicated thermal bus and must be hermetically sealed, while those used at higher temperature - greater than about 0.5 K - tend to be single-- or poly--crystals that have much simpler requirements for thermal and mechanical packaging. This paper presents a summary of strategies and techniques for designing, optimizing and fabricating salt pills for both low-- and mid--temperature applications.
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.
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
Calculating excitation energies by extrapolation along adiabatic connections
Rebolini, Elisa; Teale, Andrew M; Helgaker, Trygve; Savin, Andreas
2015-01-01
In this paper, an alternative method to range-separated linear-response time-dependent density-functional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially interacting system around the physical system, we use an extrapolation scheme to improve the estimation of the energies of the physical system at an intermediate point of the range-separated or linear adiabatic connection where either the electron--electron interaction is scaled or only the long-range part of the Coulomb interaction is included. The extrapolation scheme is first applied to the range-separated energies of the helium and beryllium atoms and of the hydrogen molecule at its equilibrium and stretched geometries. It improves significantly the convergence rate of the energies toward their exact limit with respect to the range-separation parameter. The range...
Adiabatic Demagnetisation Refrigerators for Future Sub-Millimetre Space Missions
Hepburn, I. D.; Davenport, I.; Smith, A.
1995-10-01
Space worthy refrigeration capable of providing a 100 mK and below heat load sink for bolometric detectors will be required for the next generation of sub-millimetre space missions. Adiabatic demagnetisation refrigeration (ADR), being a gravity independent laboratory method for obtaining such temperatures, is a favourable technique for utilisation in space. We show that by considering a 3 salt pill refrigerator rather than the classic single salt pill design the space prohibitive laboratory ADR properties of high magnetic field (6 Tesla) and alow temperature hold time and short recycle time. The additional salt pills, composed of Gadolinium Gallium Garnet (GGG) provide intermediate cooling stages, enabling operation from a 4 K environment provided by a single 4 K mechanical cooler, thereby providing consumable free operation. Such ADRs could operate with fields as low as 1 Tesla allowing the use of high temperature, mechanically cooled superconducting magnets and so effectively remove the risk of quenching. We discuss the possibility of increasing the hold time from 3 hours, for the model presented, to between 40 and 80 hours, plus reducing the number of salt pills to two, through the use of a more efficient Garnet. We believe the technical advances necessitated by the envisaged ADRs are minimal and conclude that such ADRs offer a long orbital life time, consumable free, high efficiency means of milli-Kelvin cooling, requiring relatively little laboratory development.
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...
Tree wavelet approximations with applications
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
Adiabatic Heavy Ion Fusion Potentials for Fusion at Deep Sub-barrier Energies
Sastry, S V S; Mohanty, A K; Saxena, A
2003-01-01
The fusion cross sections from well above barrier to extreme sub-barrier energies have been analysed using the energy (E) and angular momentum (L) dependent barrier penetration model ({\\small{ELDBPM}}). From this analysis, the adiabatic limits of fusion barriers have been determined for a wide range of heavy ion systems. The empirical prescription of Wilzynska and Wilzynski has been used with modified radius parameter and surface tension coefficient values consistent with the parameterization of the nuclear masses. The adiabatic fusion barriers calculated from this prescription are in good agreement with the adiabatic barriers deduced from {\\small{ELDBPM}} fits to fusion data. The nuclear potential diffuseness is larger at adiabatic limit, resulting in a lower $\\hbar\\omega$ leading to increase of "logarithmic slope" observed at energies well below the barrier. The effective fusion barrier radius and curvature values are anomalously smaller than the predictions of known empirical prescriptions. A detailed comp...
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.
Luo Shao-Kai; Chen Xiang-Wei; Guo Yong-Xin
2007-01-01
Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries,exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
Rapid adiabatic passage in quantum dots: Influence of scattering and dephasing
Schuh, K.; Jahnke, F.; Lorke, Michael
2011-01-01
Theoretical investigations for the realization of population inversion of semiconductor quantum dot ground-state transitions by means of adiabatic passage with chirped optical pulses are presented. While the inversion due to Rabi oscillations depends sensitively on the resonance condition...
Time-resolved photoelectron spectroscopy of non-adiabatic dynamics in polyatomic molecules
Stolow, Albert
2015-01-01
This review article discusses advances in the use of time-resolved photoelectron spectroscopy for the study of non-adiabatic processes in molecules. A theoretical treatment of the experiments is presented together with a number of experimental examples.
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.
Quantum state engineering in a cavity by Stark chirped rapid adiabatic passage
Amniat-Talab, M; Guérin, S
2006-01-01
We propose a robust scheme to generate single-photon Fock states and atom-photon and atom-atom entanglement in atom-cavity systems. We also present a scheme for quantum networking between two cavity nodes using an atomic channel. The mechanism is based on Stark-chirped rapid adiabatic passage (SCRAP) and half-SCRAP processes in a microwave cavity. The engineering of these states depends on the design of the adiabatic dynamics through the static and dynamic Stark shifts.
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.
Adiabatic criteria for outer-sphere bimolecular electron-transfer reactions
Onuchic, Jose Nelson; Beratan, David N.
1988-01-01
A model is presented for outer-sphere bimolecular electron-transfer reactions which is correct in the adiabatic, nonadiabatic, and intermediate dynamical regimes for an overdamped solvent coordinate. From this model, the conditions for the transfer to be adiabatic or nonadiabatic are deduced. The time-scale separations needed to adequately describe the process as an average over (distant dependent) unimolecular rates are described.
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....
Unified Dark Fluid with Constant Adiabatic Sound Speed: Including Entropic Perturbations
Xu, Lixin
2012-01-01
In this paper, we continue to study a unified dark fluid model with a constant adiabatic sound speed but with the entropic perturbations. When the entropic perturbations are included, an effective sound speed, which reduces to the adiabatic sound speed when the entropic perturbations are zero, has to be specified as an additional free model parameter. Due to the relations between the adiabatic sound speed and equations of state (EoS) $c^2_{s,ad}(a)=w(a)-d\\ln(1+w(a))/3 d\\ln a$, the equation of state can be determined up to an integration constant in principle when an adiabatic sound speed is given. Then there are two degrees of freedom to describe the linear perturbations for a fluid. Its micro-scale properties are characterized by its EoS or adiabatic sound speed and an effective sound speed. We take the effective sound speed and adiabatic sound speed as free model parameters and then use the currently available cosmic observational data sets, which include type Ia supernova Union 2.1, baryon acoustic oscilla...
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.
2017-08-01
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.
Diophantine approximation and automorphic spectrum
Ghosh, Anish; Nevo, Amos
2010-01-01
The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.
Some results in Diophantine approximation
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered...
Uniform approximation by (quantum) polynomials
Drucker, A.; de Wolf, R.
2011-01-01
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectivel
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
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.
Commercial concepts for adiabatic compressed air energy storage
Freund, Sebastian [General Electric Global Research, Garching (Germany); Schainker, Robert [Electric Power Research Institute, Palo Alto, CA (United States); Moreau, Robert [General Electric Oil and Gas, Florence (Italy)
2012-07-01
Adiabatic compressed air energy storage (ACAES) systems offer the potential for efficient large-scale energy storage, almost approaching values typical for pumped hydro. In an ACAES plant, the heat of compression is stored and utilized during the expansion of the air instead of firing natural gas like in commercial CAES. However, no ACAES plants have been commercialized due to challenges with respect to the cost and the heat storage technology. In this study, conducted by EPRI, GE Global Research and GE Oil and Gas, several concepts for ACAES plants are analyzed and their efficiency, complexity and technical risk compared. The components selected for the plants are available either off-the-shelf or near-commercial within a short development time and without the high costs associated with developing a new generation of large custom-made compressors and turbines. The most promising concept for near-term commercialization and low costs turns out to be a two-stage, low-temperature ACAES system. A regenerative (solid) and a recuperative (liquid) thermal storage system have been designed and analyzed for this concept, with the result that the liquid-recuperative system offers a much lower cost and comparable performance. Performance and cost targets for the concepts are 100 MW output per plant for 6 h with a round-trip efficiency above 60% and a capital cost of about $1000/kW. Selections of the turbomachinery for the compression and expansion train from General Electric Oil and Gas are presented for several plant options along with their expansion power range (25..100 MW), round-trip efficiency (66%..70%) and preliminary capital cost estimates (1100..1200 $/kW).
Towards robust dynamical decoupling and high fidelity adiabatic quantum computation
Quiroz, Gregory
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum
Classical molecular dynamics simulation of electronically non-adiabatic processes.
Miller, William H; Cotton, Stephen J
2016-12-22
Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born-Oppenheimer electronic state). This paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides "quantization" of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. Also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).