Bond selective chemistry beyond the adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
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.
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
A 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 for the evolution generated by an A-uniformly pseudo-Hermitian Hamiltonian
Wang, Wenhua; Cao, Huaixin; Chen, Zhengli
2017-09-01
We discuss an adiabatic approximation for the evolution generated by an A-uniformly pseudo-Hermitian Hamiltonian H(t). Such a Hamiltonian is a time-dependent operator H(t) similar to a time-dependent Hermitian Hamiltonian G(t) under a time-independent invertible operator A. Using the relation between the solutions of the evolution equations H(t) and G(t), we prove that H(t) and H† (t) have the same real eigenvalues and the corresponding eigenvectors form two biorthogonal Riesz bases for the state space. For the adiabatic approximate solution in case of the minimum eigenvalue and the ground state of the operator H(t), we prove that this solution coincides with the system state at every instant if and only if the ground eigenvector is time-independent. We also find two upper bounds for the adiabatic approximation error in terms of the norm distance and in terms of the generalized fidelity. We illustrate the obtained results with several examples.
Energy Technology Data Exchange (ETDEWEB)
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.
Directory of Open Access Journals (Sweden)
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.
Effenberger, Frederic; Litvinenko, Yuri E.
2014-03-01
The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wave-like aspects of the cosmic-ray transport.
Tremblay, Jean Christophe
2013-06-28
A model for treating excitation and relaxation of adsorbates at metallic surfaces induced by non-adiabatic coupling is developed. The derivation is based on the concept of resonant electron transfer, where the adsorbate serves as a molecular bridge for the inelastic transition between an electron source and a sink. In this picture, energy relaxation and scanning tunneling microscopy (STM) at metallic surfaces are treated on an equal footing as a quasi-thermal process. The model goes beyond the local harmonic approximation and allows for an unbiased description of floppy systems with multiple potential wells. Further, the limitation of the product ansatz for the vibronic wave function to include the position-dependence of the non-adiabatic couplings is avoided by explicitly enforcing detailed balance. The theory is applied to the excitation of hydrogen on palladium, which has multiple local potential minima connected by low energy barriers. The main aspects investigated are the lifetimes of adsorbate vibrations in different adsorption sites, as well as the dependence of the excitation, response, and transfer rates on an applied potential bias. The excitation and relaxation simulations reveal intricate population dynamics that depart significantly from the simplistic tunneling model in a truncated harmonic potential. In particular, the population decay from an initially occupied local minimum induced by the contact with an STM tip is found to be better described by a double exponential. The two rates are interpreted as a response to the system perturbation and a transfer rate following the perturbation. The transfer rate is found to obey a power law, as was the case in previous experimental and theoretical work.
Transitionless driving on adiabatic search algorithm
Oh, Sangchul; Kais, Sabre
2014-12-01
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
Quantum adiabatic Markovian master equations
Albash, Tameem; Boixo, Sergio; Lidar, Daniel A.; Zanardi, Paolo
2012-12-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state.
Directory of Open Access Journals (Sweden)
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.
Semi adiabatic theory of seasonal Markov processes
Energy Technology Data Exchange (ETDEWEB)
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 Cooling of Antiprotons
Gabrielse, G; McConnell, R; Richerme, P; Kalra, R; Novitski, E; Grzonka, D; Oelert, W; Sefzick, T; Zielinski, M; Fitzakerley, D; George, M C; Hessels, E A; Storry, C H; Weel, M; Mullers, A; Walz, J
2011-01-01
Adiabatic cooling is shown to be a simple and effective method to cool many charged particles in a trap to very low temperatures. Up to 3 x 10(6) (p) over bar are cooled to 3.5 K-10(3) times more cold (p) over bar and a 3 times lower (p) over bar temperature than previously reported. A second cooling method cools (p) over bar plasmas via the synchrotron radiation of embedded (p) over bar (with many fewer (p) over bar than (p) over bar) in preparation for adiabatic cooling. No (p) over bar are lost during either process-a significant advantage for rare particles.
Adiabatic Interactions of Manakov Solitons -- Effects of Cross-modulation
Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V.
2016-01-01
We investigate the asymptotic behavior of the Manakov soliton trains perturbed by cross-modulation in the adiabatic approximation. The multisoliton interactions in the adiabatic approximation are modeled by a generalized Complex Toda chain (GCTC). The cross-modulation requires special treating for the evolution of the polarization vectors of the solitons. The numerical predictions of the Manakov system are compared with the perturbed GCTC. For certain set of initial parameters GCTC describes ...
Semiconductor adiabatic qubits
Energy Technology Data Exchange (ETDEWEB)
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.
Quantum Adiabatic Brachistochrone
Rezakhani, A. T.; Kuo, W.-J.; Hamma, A.; Lidar, D. A.; Zanardi, P.
2009-08-01
We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.
Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system.
Sun, Xiankai; Liu, Hsi-Chun; Yariv, Amnon
2009-02-01
By analyzing the propagating behavior of the supermodes in a coupled-waveguide system, we have derived a universal criterion for designing adiabatic mode transformers. The criterion relates epsilon, the fraction of power scattered into the unwanted mode, to waveguide design parameters and gives the shortest possible length of an adiabatic mode transformer, which is approximately 2/piepsilon1/2 times the distance of maximal power transfer between the waveguides. The results from numerical calculations based on a transfer-matrix formalism support this theory very well.
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.
Geometrizing adiabatic quantum computation
Rezakhani, Ali; Kuo, Wan-Jung; Hamma, Alioscia; Lidar, Daniel; Zanardi, Paolo
2010-03-01
A time-optimal approach to adiabatic quantum computation (AQC) is formulated. The corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. We demonstrate this geometrization through some examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance. The underlying connection with quantum phase transitions is also explored.
Albash, Tameem; Lidar, Daniel A.
2018-01-01
Adiabatic quantum computing (AQC) started as an approach to solving optimization problems and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. This review gives an account of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. Several variants are presented of the adiabatic theorem, the cornerstone of AQC, and examples are given of explicit AQC algorithms that exhibit a quantum speedup. An overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory is given. Considerable space is devoted to stoquastic AQC, the setting of most AQC work to date, where obstructions to success and their possible resolutions are discussed.
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.
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.…
Adiabatic vs. non-adiabatic determination of specific absorption rate of ferrofluids
Energy Technology Data Exchange (ETDEWEB)
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.
Adiabatic thermal models for planetary bodies
Spohn, T.
1985-01-01
In a number of recent experiments it was found that the logarithmic derivative with respect to volume of the adiabatic temperature increase with pressure P to be an approximately constant quantity n. It was found that n decreases slightly with temperature, to be virtually unaffected by increasing pressure and to take values between 4 and 8 for a wide variety of materials. It is shown that these findings can be substantiated from thermodynamic arguments, finite strain theory, atomic potential theory and experimental data on the thermal expansion coefficient and the bulk modulus B. It will be shown that n is independent of pressure if it is exactly equal to dB/dP + 1. For these materials d log gamma/d log v = -1, where gamma is the thermodynamic Gruneisenparameter. It will increase with P during an isothermal transformation if n dB/dP + 1 and decrease of n dB/dP + 1. For most materials n is close to dB/dP and the changes will be slight if pressures do not become too extreme. During an adiabatic transformation n is virtually constant. Adiabatic thermal models for planetary bodies were calculated and are presented.
Classical nuclear motion coupled to electronic non-adiabatic transitions.
Agostini, Federica; Abedi, Ali; Gross, E K U
2014-12-07
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Analysis of Adiabatic Batch Reactor
Directory of Open Access Journals (Sweden)
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 continuous stirred tank reactor
DEFF Research Database (Denmark)
Schroll-Fleischer, Eskild; Wu, Hao; Huusom, Jakob Kjøbsted
The present report documents the adiabatic CSTR experimental setup after it was refurbished in September 2017. The goal of the refurbishment was firstly to enable computer control of the experiment using the Open Process Control Unified Architecture (OPC-UA) standard, and secondly to improve...
Studies in Chaotic adiabatic dynamics
Energy Technology Data Exchange (ETDEWEB)
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the {open_quotes}goodness{close_quotes} of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees).
An Adiabatic Phase-Matching Accelerator
Energy Technology Data Exchange (ETDEWEB)
Lemery, Francois [DESY; Floettmann, Klaus [DESY; Piot, Philippe [Northern Illinois U.; Kaertner, Franz X. [Hamburg U.; Assmann, Ralph [DESY
2017-12-22
We present a general concept to accelerate non-relativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell's equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program {\\sc astra} and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of 100~MV/m. The numerical simulations indicate that a $\\sim 200$-keV electron beam can be accelerated to an energy of $\\sim10$~MeV over $\\sim 10$~cm. The novel scheme is also found to form electron beams with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.
Adiabatic Mass Loss Model in Binary Stars
Ge, H. W.
2012-07-01
Rapid mass transfer process in the interacting binary systems is very complicated. It relates to two basic problems in the binary star evolution, i.e., the dynamically unstable Roche-lobe overflow and the common envelope evolution. Both of the problems are very important and difficult to be modeled. In this PhD thesis, we focus on the rapid mass loss process of the donor in interacting binary systems. The application to the criterion of dynamically unstable mass transfer and the common envelope evolution are also included. Our results based on the adiabatic mass loss model could be used to improve the binary evolution theory, the binary population synthetic method, and other related aspects. We build up the adiabatic mass loss model. In this model, two approximations are included. The first one is that the energy generation and heat flow through the stellar interior can be neglected, hence the restructuring is adiabatic. The second one is that he stellar interior remains in hydrostatic equilibrium. We model this response by constructing model sequences, beginning with a donor star filling its Roche lobe at an arbitrary point in its evolution, holding its specific entropy and composition profiles fixed. These approximations are validated by the comparison with the time-dependent binary mass transfer calculations and the polytropic model for low mass zero-age main-sequence stars. In the dynamical time scale mass transfer, the adiabatic response of the donor star drives it to expand beyond its Roche lobe, leading to runaway mass transfer and the formation of a common envelope with its companion star. For donor stars with surface convection zones of any significant depth, this runaway condition is encountered early in mass transfer, if at all; but for main sequence stars with radiative envelopes, it may be encountered after a prolonged phase of thermal time scale mass transfer, so-called delayed dynamical instability. We identify the critical binary mass ratio for the
A Many Particle Adiabatic Invariant
DEFF Research Database (Denmark)
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 in...... in terms of Hamiltonian dynamics is given. The relation to the Equipartition Theorem of statistical Mechanics is briefly discussed....
Quantum Computation by Adiabatic Evolution
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 ...
Adiabaticity in open quantum systems
Venuti, Lorenzo Campos; Albash, Tameem; Lidar, Daniel A.; Zanardi, Paolo
2016-03-01
We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian L (t ) . We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of L (t ) will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time T . In the case of a finite number of level crossings, the scaling becomes T-η with an exponent η that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time T should be long compared to the corresponding minimum inverse gap squared of L (t ) . Our results are illustrated with several examples.
Theory of Adiabatic Fountain Resonance
Williams, Gary A.
2017-06-01
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.
Laser cooling by adiabatic transfer
Norcia, Matthew; Cline, Julia; Bartolotta, John; Holland, Murray; Thompson, James
2017-04-01
We have demonstrated a new method of laser cooling applicable to particles with narrow linewidth optical transitions. This simple and robust cooling mechanism uses a frequency-swept laser to adiabatically transfer atoms between internal and motional states. The role of spontaneous emission is reduced (though is still critical) compared to Doppler cooling. This allows us to achieve greater slowing forces than would be possible with Doppler cooling, and may make this an appealing technique for cooling molecules. In this talk, I will present a demonstration of this technique in a cold strontium system. DARPA QUASAR, NIST, NSF PFC.
QCD string model for hybrid adiabatic potentials
Kalashnikova, Yu. S.; Kuzmenko, D. S.
2001-01-01
Hybrid adiabatic potentials are considered in the framework of the QCD string model. The einbein field formalism is applied to obtain the large-distance behaviour of adiabatic potentials. The calculated excitation curves are shown to be the result of interplay between potential-type longitudinal and string-type transverse vibrations. The results are compared with recent lattice data.
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Approximation Clustering. Clustering within (1+ ε) of the optimum cost. ε is user defined tolerance. For metric spaces even approximating is. hard (below, say 30%). Euclidean k-median in fixed dimension can. be approximated in polynomial time.
Dispersive Readout of Adiabatic Phases
Kohler, Sigmund
2017-11-01
We propose a protocol for the measurement of adiabatic phases of periodically driven quantum systems coupled to an open cavity that enables dispersive readout. It turns out that the cavity transmission exhibits peaks at frequencies determined by a resonance condition that involves the dynamical and the geometric phase. Since these phases scale differently with the driving frequency, one can determine them by fitting the peak positions to the theoretically expected behavior. For the derivation of the resonance condition and for a numerical study, we develop a Floquet theory for the dispersive readout of ac driven quantum systems. The feasibility is demonstrated for two test cases that generalize Landau-Zener-Stückelberg-Majorana interference to two-parameter driving.
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.
Adiabatic limit in perturbation theory
Epstein, H
1976-01-01
It is shown that, with correct mass and wave function renormalization, the time-ordered products for Wick polynomials T(L(y/sub 1/)...L(y/sub n/)) constructed by a method outlined in a previous paper (Epstein and Glaser, 1970) are such that the vectors of the form integral T(L(y/sub 1/)...L(y/sub n/)) g(y/sub 1/)...g(y/sub n/) psi dy/sub 1/...dy/sub n/ have limits when g tends to a constant, provided psi is chosen in a suitable dense domain. It follows that the S-matrix has unitary adiabatic limit as an operator-valued formal power series in Fock space. (4 refs).
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
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 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original “global" one, this “new" algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M = 1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed.
Quantum adiabatic protocols using emergent local Hamiltonians.
Modak, Ranjan; Vidmar, Lev; Rigol, Marcos
2017-10-01
We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work from initial band-insulating states, and how to adiabatically transfer systems from linear and harmonic traps into box traps. Our protocols consist of two stages. The first one involves a free expansion followed by a quench to an emergent local Hamiltonian. In the second stage, the emergent local Hamiltonian is "turned off" quasistatically. For the adiabatic transfer from a harmonic trap, we consider both zero- and nonzero-temperature initial states.
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
Energy Technology Data Exchange (ETDEWEB)
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.
Thermoelectric Effects under Adiabatic Conditions
Directory of Open Access Journals (Sweden)
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.
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.
Electron Correlation from the Adiabatic Connection for Multireference Wave Functions
Pernal, Katarzyna
2018-01-01
An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.
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...
Non-adiabatic rotational excitation of dipolar molecule under the ...
Indian Academy of Sciences (India)
adiabatically by half cycle pulse. (HCP) is controlled using the second ultrashort HCP. ... excited to create a rotational quantum wave packet, a .... Non-adiabatic rotational excitation of dipolar molecule under the influence of delayed pulses. 1215.
Adiabatic pumping through interacting quantum dots
Splettstoesser, Janine; Governale, Michele; König, Jürgen; Fazio, Rosario
2005-01-01
We present a general formalism to study adiabatic pumping through interacting quantum dots. We derive a formula that relates the pumped charge to the local, instantaneous Green function of the dot. This formula is then applied to the infinite-U Anderson model both for weak and strong tunnel-coupling strengths.
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
Improving the positive feedback adiabatic logic familiy
Directory of Open Access Journals (Sweden)
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.
Wigner phase space distribution via classical adiabatic switching
Energy Technology Data Exchange (ETDEWEB)
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.
Non-adiabatic perturbations in multi-component perfect fluids
Energy Technology Data Exchange (ETDEWEB)
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.
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.
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.
Pulsed Adiabatic Photoassociation via Scattering Resonances
Han, Alex C.; Shapiro, Evgeny A.; Shapiro, Moshe
2011-01-01
We develop the theory for the Adiabatic Raman Photoassociation (ARPA) of ultracold atoms to form ultracold molecules in the presence of scattering resonances. Based on a computational method in which we replace the continuum with a discrete set of "effective modes", we show that the existence of resonances greatly aids in the formation of deeply bound molecular states. We illustrate our general theory by computationally studying the formation of $^{85}$Rb$_2$ molecules from pairs of colliding...
Adiabatic heating in impulsive solar flares
Maetzler, C.; Bai, T.; Crannell, C. J.; Frost, K. J.
1978-01-01
A study is made of adiabatic heating in two impulsive solar flares on the basis of dynamic X-ray spectra in the 28-254 keV range, H-alpha, microwave, and meter-wave radio observations. It is found that the X-ray spectra of the events are like those of thermal bremsstrahlung from single-temperature plasmas in the 10-60 keV range if photospheric albedo is taken into account. The temperature-emission correlation indicates adiabatic compression followed by adiabatic expansion and that the electron distribution remains isotropic. H-alpha data suggest compressive energy transfer. The projected areas and volumes of the flares are estimated assuming that X-ray and microwave emissions are produced in a single thermal plasma. Electron densities of about 10 to the 9th/cu cm are found for homogeneous, spherically symmetric sources. It is noted that the strong self-absorption of hot-plasma gyrosynchrotron radiation reveals low magnetic field strengths.
Narrow Linewidth Laser Cooling via Adiabatic Transfer
Bartolotta, John; Holland, Murray; Norcia, Matthew; Thompson, James; Cline, Julia
2017-04-01
We simulate and provide a theoretical framework for a new cooling method applicable to particles with narrow-linewidth optical transitions. The particles are adiabatically transferred to lower momentum states upon interaction with counter-propagating laser beams that are repeatedly swept over the transition frequency. A reduced reliance on spontaneous emission (compared to Doppler cooling) allows for larger slowing forces. Cooling via a 7.6 kHz dipole forbidden transition in Strontium-88 is simulated using one-dimensional quantum jump and c-number Langevin equation methods. This ``sweep cooling'' mechanism also shows promise for application to systems lacking closed cycling transitions, such as molecules.
Green's Functions and the Adiabatic Hyperspherical Method
Rittenhouse, Seth T; Greene, Chris H
2010-01-01
We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in $d$-dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of three-particles with s-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semi-analytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom-loss due to three-body recombination for a three-component fermi-gas of $^{6}$Li atoms is presented.
Inversion produced and reversed by adiabatic passage
Liedenbaum, C.; Stolte, S.; Reuss, J.
1989-06-01
This report deals with non-linear effects produced in molecules by strong laser fields. The molecules experience these laser fields during their passage through the laser waists. We present results on rapid adiabatic passage processes which move the molecules up and down the energy ladder, the latter due to stimulated emission. Experimentally, stimulated emission is observed by opto-thermal detection of a molecular beam where de-excitation by stimulated emission leads to negative signals as compared to straightforward excitation processes. Two-level, three-level and multi-level systems are covered by the following discussion.
The Effect of non-Hermiticity on Adiabatic Elimination
Sharaf, Rahman; Dehghani, Mojgan; Darbari, Sara; Ramezani, Hamidreza
2017-01-01
We investigate the influence of non-Hermiticity on the adiabatic elimination in coupled waveguides. We show that adiabatic elimination is not affected when the system is in parity-time symmetric phase. However, in the broken phase the eliminated waveguide loses its darkness namely its amplitude starts increasing, which means adiabatic elimination does not hold in the broken phase. Our results can advance the control of the dynamics in coupled laser cavities, and help the design of controllabl...
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.
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...
Symmetry of the adiabatic condition in the piston problem
Energy Technology Data Exchange (ETDEWEB)
Anacleto, Joaquim; Ferreira, J M, E-mail: anacleto@utad.pt [Departamento de Fisica, Escola de Ciencias e Tecnologia, Universidade de Tras-os-Montes e Alto Douro, Apartado 1013, 5001-801 Vila Real (Portugal)
2011-11-15
This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be compatible with the invariance of total entropy under a system-surroundings interchange. This paper also strengthens some recently published ideas concerning the concepts of heat and dissipative work, and is primarily intended for teachers and graduate students, as well as for all who are interested in this fascinating problem.
Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H2 reaction
Mielke, Steven L.; Garrett, Bruce C.; Fleming, Donald G.; Truhlar, Donald G.
2015-01-01
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 in this journal of the thermal and vibrationally state-selected 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 non-adiabatic transitions cannot be understood by considering tunnelling 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.
Symmetry-broken effects on electron momentum spectroscopy caused by adiabatic vibration
Zhu, Yinghao; Ma, Xiaoguang; Lou, Wenhua; Wang, Meishan; Yang, Chuanlu
2017-11-01
The vibronic coupling effect is usually studied by invoking the breakdown of Born-Oppenheimer approximation. The present study shows that the symmetry-broken effect induced by nuclei vibrations can also lead strong impact on the electronic states under the framework of Born-Oppenheimer approximation. This adiabatic-invoking vibrational effect on electron momentum spectroscopy of ethylene (C2H4), ethane (C2H6) and methanol (CH3OH) was studied with quantum mechanical method. The results show that electron momentum spectroscopy of localized electrons, especially core electrons in axial symmetric geometry molecules can be affected unusually and strongly by several asymmetric vibrational modes.
Adiabatic capture theory applied to N+NH-->N2+H at low temperature.
Frankcombe, Terry J; Nyman, Gunnar
2007-12-20
The adiabatic capture centrifugal sudden approximation (ACCSA) has been applied to the ground state reaction N+NH-->N2+H over the temperature range 2-300 K using an existent potential energy surface. The resultant thermal rate constants are in agreement with available rate constants from quasi-classical trajectory calculations but are significantly larger than the available experimentally derived rate. The calculated rate constants monotonically increase with increasing temperature but could only be approximately described with a simple Arrhenius-like form. Subtle quantum effects are evident in the initial rotational state resolved cross sections and rate constants.
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.
Non-adiabatic corrections to the energies of the pure vibrational states of H2
Bubin, Sergiy; Leonarski, Filip; Stanke, Monika; Adamowicz, Ludwik
2009-07-01
Nonrelativistic energies of all fifteen pure vibrational states of the H molecule have been recalculated with much higher accuracy than before. In the calculations we employed explicitly correlated Gaussian functions and an approach where the Born-Oppenheimer (BO) approximation is not assumed. The wave function of each state was expanded in terms of 10 000 Gaussians whose nonlinear parameters were optimized using a procedure involving the analytical energy gradient. The obtained non-BO energies combined with the recent BO adiabatic energies of Pachucki and Komasa [K. Pachucki, J. Komasa, J. Chem. Phys. 129 (2008) 034102] allowed us to determine new improved values of the non-adiabatic corrections for the considered states.
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.
Adiabatic heavy-ion fusion potentials for fusion at deep sub-barrier ...
Indian Academy of Sciences (India)
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 ...
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.
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.
Reversible logic gate using adiabatic superconducting devices.
Takeuchi, N; Yamanashi, Y; Yoshikawa, N
2014-09-15
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
Energy Technology Data Exchange (ETDEWEB)
Pawlak, Mariusz [Schulich Faculty of Chemistry, Technion–Israel Institute of Technology, Haifa 32000 (Israel); Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń (Poland); Shagam, Yuval; Narevicius, Edvardas [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel); Moiseyev, Nimrod [Schulich Faculty of Chemistry, Technion–Israel Institute of Technology, Haifa 32000 (Israel); Faculty of Physics, Technion–Israel Institute of Technology, Haifa 32000 (Israel)
2015-08-21
We developed an adiabatic theory for cold anisotropic collisions between slow atoms and cold molecules. It enables us to investigate the importance of the couplings between the projection states of the rotational motion of the atom about the molecular axis of the diatom. We tested our theory using the recent results from the Penning ionization reaction experiment {sup 4}He(1s2s {sup 3}S) + HD(1s{sup 2}) → {sup 4}He(1s{sup 2}) + HD{sup +}(1s) + e{sup −} [Lavert-Ofir et al., Nat. Chem. 6, 332 (2014)] and demonstrated that the couplings have strong effect on positions of shape resonances. The theory we derived provides cross sections which are in a very good agreement with the experimental findings.
Adiabatic Rearrangement of Hollow PV Towers
Directory of Open Access Journals (Sweden)
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
Quasiadiabatic Grover search via the Wentzel-Kramers-Brillouin approximation
Muthukrishnan, Siddharth; Lidar, Daniel A.
2017-07-01
In various applications one is interested in quantum dynamics at intermediate evolution times, for which the adiabatic approximation is inadequate. Here we develop a quasiadiabatic approximation based on the WKB method, designed to work for such intermediate evolution times. We apply it to the problem of a single qubit in a time-varying magnetic field, and to the Hamiltonian Grover search problem, and show that already at first order the quasiadiabatic WKB captures subtle features of the dynamics that are missed by the adiabatic approximation. However, we also find that the method is sensitive to the type of interpolation schedule used in the Grover problem and can give rise to nonsensical results for the wrong schedule. Conversely, it reproduces the quadratic Grover speedup when the well-known optimal schedule is used.
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.
Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
Rezakhani, A. T.; Abasto, D. F.; Lidar, D. A.; Zanardi, P.
2010-07-01
We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity, we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric description of quantum adiabatic evolution and quantum phase transitions that generalizes previous treatments to allow for degeneracy. The same structure is relevant for applications in quantum information processing, including adiabatic and holonomic quantum computing, where geodesics over the manifold of control parameters correspond to paths which minimize errors. We illustrate this geometric structure with examples, for which we explicitly find adiabatic geodesics. By solving the geodesic equations in the vicinity of a quantum critical point, we identify universal characteristics of optimal adiabatic passage through a quantum phase transition. In particular, we show that in the vicinity of a critical point describing a second-order quantum phase transition, the geodesic exhibits power-law scaling with an exponent given by twice the inverse of the product of the spatial and scaling dimensions.
Constraints on the Adiabatic Temperature Change in Magnetocaloric Materials
DEFF Research Database (Denmark)
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......-order materials. For materials with a continuous adiabatic temperature change as a function of temperature, this inequality is shown to hold for all temperatures. However, discontinuous materials may violate the inequality. We compare our results with measured results in the literature and discuss...
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 Computation with Neutral Atoms
Biedermann, Grant
2013-03-01
We are implementing a new platform for adiabatic quantum computation (AQC)[2] based on trapped neutral atoms whose coupling is mediated by the dipole-dipole interactions of Rydberg states. Ground state cesium atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism,[3,4] thereby providing the requisite entangling interactions. As a benchmark we study a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. In collaboration with Lambert Parazzoli, Sandia National Laboratories; Aaron Hankin, Center for Quantum Information and Control (CQuIC), University of New Mexico; James Chin-Wen Chou, Yuan-Yu Jau, Peter Schwindt, Cort Johnson, and George Burns, Sandia National Laboratories; Tyler Keating, Krittika Goyal, and Ivan Deutsch, Center for Quantum Information and Control (CQuIC), University of New Mexico; and Andrew Landahl, Sandia National Laboratories. This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories
On the persistence of adiabatic shear bands
Boakye-Yiadom, S.; Bassim, M. N.; Al-Ameeri, S.
2012-08-01
It is generally agreed that the initiation and development of adiabatic shear bands (ASBs) are manifestations of damage in metallic materials subjected to high strain rates and large strains as those due to impact in a Hopkinson Bar system. Models for evolution of these bands have been described in the literature. One question that has not received attention is how persistent these bands are and whether their presence and effect can be reversed or eliminated by using a process of thermal (heat treatment) or thermo-mechanical treatment that would relieve the material from the high strain associated with ASBs and their role as precursors to crack initiation and subsequent failure. Since ASBs are more prevalent and more defined in BCC metals including steels, a study was conducted to investigate the best conditions of generating ASBs in a heat treatable steel, followed by determining the best conditions for heat treatment of specimens already damaged by the presence of ASBs in order to relieve the strains due to ASBs and restore the material to an apparent microstructure without the "scars" due to the previous presence of ASBs. It was found that heat treatment achieves the curing from ASBs. This presentation documents the process undertaken to achieve this objective.
On the persistence of adiabatic shear bands
Directory of Open Access Journals (Sweden)
Bassim M.N.
2012-08-01
Full Text Available It is generally agreed that the initiation and development of adiabatic shear bands (ASBs are manifestations of damage in metallic materials subjected to high strain rates and large strains as those due to impact in a Hopkinson Bar system. Models for evolution of these bands have been described in the literature. One question that has not received attention is how persistent these bands are and whether their presence and effect can be reversed or eliminated by using a process of thermal (heat treatment or thermo-mechanical treatment that would relieve the material from the high strain associated with ASBs and their role as precursors to crack initiation and subsequent failure. Since ASBs are more prevalent and more defined in BCC metals including steels, a study was conducted to investigate the best conditions of generating ASBs in a heat treatable steel, followed by determining the best conditions for heat treatment of specimens already damaged by the presence of ASBs in order to relieve the strains due to ASBs and restore the material to an apparent microstructure without the “scars” due to the previous presence of ASBs. It was found that heat treatment achieves the curing from ASBs. This presentation documents the process undertaken to achieve this objective.
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.
Spatial non-adiabatic passage using geometric phases
Energy Technology Data Exchange (ETDEWEB)
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.)
Adiabatic projection method for scattering and reactions on the lattice
Energy Technology Data Exchange (ETDEWEB)
Pine, Michelle; Lee, Dean [North Carolina State University, Department of Physics, Raleigh, NC (United States); Rupak, Gautam [Mississippi State University, Department of Physics and Astronomy and HPC2 Center for Computational Sciences, Mississippi State, MS (United States)
2013-12-15
We demonstrate and test the adiabatic projection method, a general new framework for calculating scattering and reactions on the lattice. The method is based upon calculating a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. As a detailed example we calculate the adiabatic two-body Hamiltonian for elastic fermion-dimer scattering in lattice effective field theory. Our calculation corresponds to neutron-deuteron scattering in the spin-quartet channel at leading order in pionless effective field theory. We show that the spectrum of the adiabatic Hamiltonian reproduces the spectrum of the original Hamiltonian below the inelastic threshold to arbitrary accuracy. We also show that the calculated s -wave phase shift reproduces the known exact result in the continuum and infinite-volume limits. When extended to more than one scattering channel, the adiabatic projection method can be used to calculate inelastic reactions on the lattice in future work. (orig.)
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...
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...
Low-power adiabatic 9T static random access memory
Directory of Open Access Journals (Sweden)
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.
Adiabatic Cooling for Rovibrational Spectroscopy of Molecular Ions
DEFF Research Database (Denmark)
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...... proposes to adiabatically relax the trapping potential, called adiabatic cooling, when performing rovibrational excitations of the molecular ion to reduce the energy spacing of the harmonic motional levels, thus increasing the likelihood of a motional transition. The work presented in this thesis covers...... the implementation of adiabatic cooling for the application of rovibrational spectroscopy on single molecular ions. This entailed constructing and testing a new DC supply capable of employing adiabatic ramps of the ion's axial frequency on the 100's of us timescale. The DC supply went through several iterations...
Adiabatic regularization for spin-1/2 fields
Landete, Aitor; Navarro-Salas, José; Torrentí, Francisco
2013-09-01
We extend the adiabatic regularization method to spin-1/2 fields. The ansatz for the adiabatic expansion for fermionic modes differs significantly from the WKB-type template that works for scalar modes. We give explicit expressions for the first adiabatic orders and analyze particle creation in de Sitter spacetime. As for scalar fields, the adiabatic method can be distinguished by its capability to overcome the UV divergences of the particle number operator. We also test the consistency of the extended method by working out the conformal and axial anomalies for a Dirac field in a Friedmann-Lemaître-Robertson-Walker spacetime, in exact agreement with those obtained from other renormalization prescriptions. We finally show its power by computing the renormalized stress-energy tensor for Dirac fermions in de Sitter space.
Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing
O'Hara, Michael J.; O'Leary, Dianne P.
2008-01-01
Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the J...
Hybrid adiabatic potentials in the QCD string model
Kalashnikova, Yu. S.; Kuzmenko, D. S.
2002-01-01
The short- and intermediate-distance behaviour of the hybrid adiabatic potentials is calculated in the framework of the QCD string model. The calculations are performed with the inclusion of Coulomb force. Spin-dependent force and the so-called string correction term are treated as perturbation at the leading potential-type regime. Reasonably good agreement with lattice measurements takes place for adiabatic curves excited with magnetic components of field strength correlators.
Electron Scattering on a Magnetic Skyrmion in the Nonadiabatic Approximation.
Denisov, K S; Rozhansky, I V; Averkiev, N S; Lähderanta, E
2016-07-08
We present a theory of electron scattering on a magnetic Skyrmion for the case when the exchange interaction is moderate so that the adiabatic approximation and the Berry phase approach are not applicable. The theory explains the appearance of a topological Hall current in the systems with magnetic Skyrmions, the special importance of which is its applicability to dilute magnetic semiconductors with a weak exchange interaction.
Energy Technology Data Exchange (ETDEWEB)
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)
Response of quasi-adiabatic ions to magnetotail reconfigurations
Delcourt, D.; Malova, H. V.; Zelenyi, L. M.
2016-12-01
Particles traveling in sharp field reversals like in the Earth's magnetotail may not conserve their magnetic moment (first adiabatic invariant) due to significant variation of the magnetic field on the length scale of their Larmor radius. Although their motion is non-adiabatic per say and differs from a regular helical one, some particles may experience negligible net change of magnetic moment, a behavior that is referred to as quasi-adiabatic [Büchner and Zelenyi, 1989] like in the well-known Speiser orbit [Speiser, 1965]. Such a behavior is more pronounced at specific values of the adiabaticity parameter κ (square root of the minimum curvature radius to maximum Larmor radius ratio) due to resonance between the slow gyromotion in the tail midplane and the fast oscillation in the direction perpendicular to it. On the other hand, during rapid reconfigurations of the magnetotail as observed during substorms, the impulsive electric field induced by the time-varying magnetic field may lead to non-adiabatic behaviors as well, with large variations of the magnetic moment for particles that have cyclotron periods comparable to the field variation time scale. In this case, the κ parameter that is used to characterize spatial non-adiabaticity cannot be used since magnetic field lines are rapidly evolving in time. We examine the response of quasi-adiabatic ions in the presence of such short-lived reconfigurations of the magnetic field lines using single particle calculations. We demonstrate that quasi-adiabatic ions may remain quasi-adiabatic while experiencing an impulsive energization under the effect of the induced electric field ; hence, their faster oscillations about the tail midplane and their higher resonance order. Systematic acceleration up to about 3VE (where VE is the peak ExB drift speed during field line reconfiguration) is found for the lowest energy particles. We show that, altogether, impulsive transport and energization may be responsible for short
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.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Pu, Jin; Jiang, Qing-Quan; Zu, Xiao-Tao
2017-05-01
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 Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant I_adia = \\oint p_i dq_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.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Energy Technology Data Exchange (ETDEWEB)
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.)
Interplay between electric and magnetic effect in adiabatic polaritonic systems.
Alabastri, Alessandro; Toma, Andrea; Liberale, Carlo; Chirumamilla, Manohar; Giugni, Andrea; De Angelis, Francesco; Das, Gobind; Di Fabrizio, Enzo; Zaccaria, Remo Proietti
2013-03-25
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.
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...
Non-adiabatic effects in elementary reaction processes at metal surfaces
Alducin, M.; Díez Muiño, R.; Juaristi, J. I.
2017-12-01
Great success has been achieved in the modeling of gas-surface elementary processes by the use of the Born-Oppenheimer approximation. However, in metal surfaces low energy electronic excitations are generated even by thermal and hyperthermal molecules due to the absence of band gaps in the electronic structure. This shows the importance of performing dynamical simulations that incorporate non-adiabatic effects to analyze in which way they affect most common gas-surface reactions. Here we review recent theoretical developments in this problem and their application to the study of the effect of electronic excitations in the adsorption and relaxation of atoms and molecules in metal surfaces, in scattering processes, and also in recombinative processes between impinging atoms and adsorbates at the surface. All these studies serve us to establish what properties of the gas-surface interaction favor the excitation of low-energy electron-hole pairs. A general observation is that the nature of these excitations usually requires long lasting interactions at the surface in order to observe deviations from the adiabatic behaviour. We also provide the basis of the local density friction approximation (LDFA) that have been used in all these studies, and show how it has been employed to perform ab initio molecular dynamics with electronic friction (AIMDEF). As a final remark, we will shortly review on recent applications of the LDFA to successfully simulate desorption processes induced by intense femtosecond laser pulses.
Energy Technology Data Exchange (ETDEWEB)
Ananth, V.; Venkataraman, C.; Miller, W.H.
2007-06-22
The initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the Meyer-Miller/Stock-Thoss description of electronic degrees of freedom in order to treat electronically non-adiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wavefunction), but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SC-IVR framework. For example, in the traditional Ehrenfest model (a mixed quantum-classical approach) the nuclear motion emerges from a non-adiabatic encounter on an average potential energy surface (a weighted average according to the population in the various electronic states), while the SC-IVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forward-backward versions of SC-IVR theory (FB-IVR) are presented to illustrate this behavior. An even more approximate version of the SC-IVR, the linearized approximation (LSC-IVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSC-IVR is also not able to describe the correct correlation between nuclear and electronic dynamics.
Computing approximate diagnoses by using approximate entailment
Teije, A. ten; Harmelen, van F.A.H.
1996-01-01
The most widely accepted models of diagnostic reasoning are all phrased in terms of the logical consequence relations. In work in recent years, Schaerf and Cadoli have proposed efficient approximations of the classical consequence relation. The central idea of this paper is to parameterise the
High beta lasing in micropillar cavities with adiabatic layer design
DEFF Research Database (Denmark)
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......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 threshold pump power by over 2 orders of magnitude from dc = 2.25 μm down to 0.95 μm. Lasing with β factors exceeding 0.5 shows that adiabatic micropillars are operating deeply in the cavity quantum electrodynamics regime....
A Novel Cold Cathode Fluorescent Lamp with an Adiabatic Layer
Nishimura, Kiyoshi; Yajima, Jun; Yuasa, Kunio
A novel cold cathode fluorescent lamp (CCFL) with an adiabatic layer suitable for backlighting in PDAs (Personal Data Assistants) is described. The adiabatic layer (100-200 μm) is formed between a light tube and an outer tube and is filled with low-pressure gases. This raises the temperature of the light tube to the suitable value (50-70°C), which maximizes luminous efficacy even in low lamp wattage operation and at low ambient temperatures. The results of experiments and heat transfer analyses show that the optimum pressure in an adiabatic layer lies between 1Pa and 10Pa. At a pressure of less than 1Pa, the lamp temperature maintains a constant level because the conduction loss is lower than the radiation loss.
Lin, Tzung-Yi; Hsiao, Fu-Chen; Jhang, Yao-Wun; Hu, Chieh; Tseng, Shuo-Yen
2012-10-08
A shortcut to adiabatic mode conversion in multimode waveguides using optical analogy of stimulated Raman adiabatic passage is investigated. The design of mode converters using the shortcut scheme is discussed. Computer-generated planar holograms are used to mimic the shaped pulses used to speed up adiabatic passage in quantum systems based on the transitionless quantum driving algorithm. The mode coupling properties are analyzed using the coupled mode theory and beam propagation simulations. We show reduced device length using the shortcut scheme as compared to the common adiabatic scheme. Modal evolution in the shortened device indeed follows the adiabatic eigenmode exactly amid the violation of adiabatic criterion.
On the adiabatic theorem when eigenvalues dive into the continuum
DEFF Research Database (Denmark)
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....
Niiniluoto, Ilkka
2014-03-01
Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).
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.
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...
Wei, Xin; Chen, Mei-Feng
2015-07-01
We propose an efficient scheme to prepare W state of superconducting (SC) qubits in spatially separated coplanar waveguide (CPW) resonators via adiabatic passage. The CPW resonators, each trapping a SC qubit, are coupled only by a superconducting coupler (SCC) qubit. Based on a circuit quantum electrodynamics system, our scheme can be controlled and implemented easily in experiment. As a model of a plurality of separated cavities coupled to a SCC qubit, our protocol can be useful in scalable distributed quantum networks. By introducing adiabatic passage into our model, there is no need to control the Rabi frequency of classical field and the interaction time precisely during the whole operation. Also, the dissipation from the resonators and the energy relaxation can be omitted approximately.
Energy Technology Data Exchange (ETDEWEB)
Taioli, Simone [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Department of Physics, University of Trento, Trento (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (Italy); Department of Chemistry, University of Bologna, Bologna (Italy); Garberoglio, Giovanni [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Simonucci, Stefano [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (Italy); Department of Physics, University of Camerino, Camerino (Italy); Beccara, Silvio a [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Department of Physics, University of Trento, Trento (Italy); Aversa, Lucrezia [Institute of Materials for Electronics and Magnetism, IMEM-CNR, Trento (Italy); Nardi, Marco [Institute of Materials for Electronics and Magnetism, IMEM-CNR, Trento (Italy); Institut fuer Physik, Humboldt-Universitaet zu Berlin, Berlin (Germany); Verucchi, Roberto [Institute of Materials for Electronics and Magnetism, FBK-CNR, Trento (Italy); Iannotta, Salvatore [Institute of Materials for Electronics and Magnetism, IMEM-CNR, Parma (Italy); Dapor, Maurizio [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Department of Materials Engineering and Industrial Technologies, University of Trento, Trento (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Padova (Italy); and others
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{sub 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{sub 60} impact on the Si surface is in good agreement with our experimental findings.
Rodriguez-Cancio, Marcelino; Combemale, Benoit; Baudry, Benoit
2016-01-01
We introduce Approximate Unrolling, a loop optimization that reduces execution time and energy consumption, exploiting the existence of code regions that can endure some degree of approximation while still producing acceptable results. This work focuses on a specific kind of forgiving region: counted loops that map a given functions over the elements of an array. Approximate Unrolling transforms loops in a similar way Loop Unrolling does. However, unlike its exact counterpart, our optimizatio...
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.
Adiabatic CMB perturbations in pre-big bang string cosmology
DEFF Research Database (Denmark)
Enqvist, Kari; Sloth, Martin Snoager
2001-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations in ...
Generalized Design Procedure for Short, Efficient Adiabatic Mode Converters
2016-05-20
ideally follow this trend. This gives an important rule of thumb in adiabatic mode converter design, in that beyond a certain "knee" significant increases...Each section of the linear taper between two cuts is stretched or squeezed based on the calcu- lated value from Eqn. 11. Fig. 2. Shapes of the two
On adiabatic perturbation theory for the energy eigenvalue problem
Michels, M.A.J.; Suttorp, L.G.
1978-01-01
The adiabatic perturbation formalism is used to derive several alternative expressions for the effective Hamiltonian of a discrete energy level. In the nondegenerate case these expressions may be cast in the form of linked-cluster expansions. The connection between the energy shifts and the
Experimental adiabatic vortex ratchet effect in Nb films with ...
Indian Academy of Sciences (India)
Nb films grown on top of an array of asymmetric pinning centers show a vortex ratchet effect. A net flow of vortices is induced when the vortex lattice is driven by fluctuating forces on an array of pinning centers without reflection symmetry. This effect occurs in the adiabatic regime and it could be mimiced only by reversible DC ...
Adiabatic invariants of the extended KdV equation
Energy Technology Data Exchange (ETDEWEB)
Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)
2017-01-30
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.
Monte Carlo Simulation of Adiabatic Cooling and Nuclear Magnetism
DEFF Research Database (Denmark)
Lindgård, Per-Anker; Viertiö, H. E.; Mouritsen, Ole G.
1988-01-01
in experimental studies of nuclear magnetism using adiabatic demagnetization methods. It is found that, although fluctuations reduce the transition temperatures by 40%, the isentropes are reduced by less than 10% relative to those calculated by mean-field theory. The dynamics of the ordering process following...
Start up of an industrial adiabatic tubular reactor
Verwijs, J.W.; Verwijs, J.W.; van den Berg, Henderikus; 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
Adiabatic and diabatic aerosol transport to the Jungfraujoch
Energy Technology Data Exchange (ETDEWEB)
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.
Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems
Directory of Open Access Journals (Sweden)
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.
Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions
Directory of Open Access Journals (Sweden)
Philipp eHauke
2015-04-01
Full Text Available Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.
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.…
Adiabatic perturbation theory and geometry of periodically-driven systems
Weinberg, Phillip; Bukov, Marin; D'Alessio, Luca; Polkovnikov, Anatoli; Vajna, Szabolcs; Kolodrubetz, Michael
2017-05-01
We give a systematic review of the adiabatic theorem and the leading non-adiabatic corrections in periodically-driven (Floquet) systems. These corrections have a two-fold origin: (i) conventional ones originating from the gradually changing Floquet Hamiltonian and (ii) corrections originating from changing the micro-motion operator. These corrections conspire to give a Hall-type linear response for non-stroboscopic (time-averaged) observables allowing one to measure the Berry curvature and the Chern number related to the Floquet Hamiltonian, thus extending these concepts to periodically-driven many-body systems. The non-zero Floquet Chern number allows one to realize a Thouless energy pump, where one can adiabatically add energy to the system in discrete units of the driving frequency. We discuss the validity of Floquet Adiabatic Perturbation Theory (FAPT) using five different models covering linear and non-linear few and many-particle systems. We argue that in interacting systems, even in the stable high-frequency regimes, FAPT breaks down at ultra slow ramp rates due to avoided crossings of photon resonances, not captured by the inverse-frequency expansion, leading to a counter-intuitive stronger heating at slower ramp rates. Nevertheless, large windows in the ramp rate are shown to exist for which the physics of interacting driven systems is well captured by FAPT.
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.
Test of adiabatic spin flippers for application at pulsed neutron sources
Energy Technology Data Exchange (ETDEWEB)
Kraan, W.H. E-mail: kraan@iri.tudelft.nl; Grigoriev, S.V.; Rekveldt, M.Th.; Fredrikze, H.; Vroege, C.F. de; Plomp, J
2003-09-11
Experimental results on the flipping efficiency are shown for a set of 2 V-coils as spin flipper and for a high-frequency flipper with adiabatic transition. The influence of the adiabaticity parameter is discussed. The merits of these adiabatic flippers are compared with the use of 'monochromatic' flippers, when operated in a beam from a pulsed neutron source. It is concluded that for 'long pulse' sources adiabatic flippers will be superior.
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
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...
A subgradient approach for constrained binary optimization via quantum adiabatic evolution
Karimi, Sahar; Ronagh, Pooya
2017-08-01
Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.
de Villiers, Johan
2012-01-01
The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in
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
Approximation Behooves Calibration
DEFF Research Database (Denmark)
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....
Bosma, Wieb
1990-01-01
The distribution is determined of some sequences that measure how well a number is approximated by its mediants (or intermediate continued fraction convergents). The connection with a theorem of Fatou, as well as a new proof of this, is given.
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
Manipulation of ultracold atoms in dressed adiabatic radio-frequency potentials
DEFF Research Database (Denmark)
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....
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.
Adiabatic Evolution of an Open Quantum System in its Instantaneous Steady State
Li, Dongxiao; Wu, Songlin; Shen, Hongzhi; Yi, Xuexi
2017-11-01
In this paper, we derive an adiabatic condition for an quantum system subject to environment. The adiabaticity defined here dicates that the open quantum system prepared initially in its steady state would adiabatically follow its instantaneous steady state. We find that if the driving on the open system does not induce transition between the eigenstates of the instantaneous steady state, the open system can evolve adiabatically. In order to examine the validity of the adiabatic condition, a two-band model is exemplified. The results show that the topological quantum phase transition presented in the two-band model is caused by the competition between the effect of decay and the spoiling of the adiabaticity. The geometric phase is also calculated and discussed when the adiabatic condition is satisfied.
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.
Reverse engineering of a nonlossy adiabatic Hamiltonian for non-Hermitian systems
Wu, Qi-Cheng; Chen, Ye-Hong; Huang, Bi-Hua; Xia, Yan; Song, Jie
2016-11-01
We generalize the quantum adiabatic theorem to the non-Hermitian system and build a strict adiabaticity condition to make the adiabatic evolution nonlossy when taking into account the effect of the adiabatic phase. According to the strict adiabaticity condition, the nonadiabatic couplings and the effect of the imaginary part of adiabatic phase should be eliminated as much as possible. Also, the non-Hermitian Hamiltonian reverse-engineering method is proposed for adiabatically driving an artificial quantum state. A concrete two-level system is adopted to show the usefulness of the reverse-engineering method. We obtain the desired target state by adjusting extra rotating magnetic fields at a predefined time. Furthermore, the numerical simulation shows that certain noise and dissipation in the systems are no longer undesirable but play a positive role in the scheme. Therefore, the scheme is quite useful for quantum information processing in some dissipative systems.
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.
Fast forward of the adiabatic spin dynamics of entangled states
Setiawan, Iwan; Eka Gunara, Bobby; Masuda, Shumpei; Nakamura, Katsuhiro
2017-11-01
We develop a fast-forward scheme of the adiabatic spin dynamics of quantum entangled states. We settle the quasiadiabatic dynamics by adding the regularization terms to the original Hamiltonian and then accelerate it with the use of a large time-scaling factor. Assuming the experimentally realizable candidate Hamiltonian consisting of the exchange interactions and magnetic field, we solve the regularization terms. These terms, multiplied by the velocity function, give rise to the state-dependent counterdiabatic terms. The scheme needs neither knowledge of full spectral properties of the system nor solving the initial- and boundary-value problem. Our fast forward Hamiltonian generates a variety of state-dependent counterdiabatic terms for each of adiabatic states, which can include the state-independent one. We highlight this fact by using minimum (two-spin) models for a simple transverse Ising model, quantum annealing, and generation of entanglement.
Crack propagation of Ti alloy via adiabatic shear bands
Energy Technology Data Exchange (ETDEWEB)
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.
The telegraph equation for cosmic-ray transport with weak adiabatic focusing
Litvinenko, Y. E.; Schlickeiser, R.
2013-06-01
Time-dependent solutions of a spatial diffusion equation are often used to describe the transport of solar energetic particles, accelerated in large solar flares. Approximate analytical solutions of the diffusion approximation can complement and guide detailed numerical solutions of the Fokker-Planck equation for the particle distribution function. The accuracy of the diffusion approximation is limited, however, because the signal propagation speed is infinite in the diffusion limit. An improved description of cosmic-ray transport is provided by the telegraph equation, characterised by a finite signal propagation speed. We derive the telegraph equation for the particle density, taking into account adiabatic focusing in a large-scale interplanetary magnetic field in a weak focusing limit. As an illustration, we calculate a propagating pulse solution of the telegraph equation, determine the rise time when the maximum particle intensity is reached at a given distance from the Sun, and compare the results with those obtained in the diffusion approximation. In comparison with the diffusion equation, the telegraph equation predicts an asymmetrical shape of the pulse and a shorter rise time. These potentially significant differences suggest that the more accurate telegraph equation should be used in analysis of the solar energetic particle data, at least to quantify the accuracy of the focused diffusion model. Appendix A is available in electronic form at http://www.aanda.org
A field theory characterization of interacting adiabatic particles in cosmology
Energy Technology Data Exchange (ETDEWEB)
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.
Analysis of adiabatic transfer in cavity quantum electrodynamics
Indian Academy of Sciences (India)
2015-11-27
Nov 27, 2015 ... 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.
The Adiabatic Piston and the Second Law of Thermodynamics
Crosignani, Bruno; Di Porto, Paolo; Conti, Claudio
2002-11-01
A detailed analysis of the adiabatic-piston problem reveals peculiar dynamical features that challenge the general belief that isolated systems necessarily reach a static equilibrium state. In particular, the fact that the piston behaves like a perpetuum mobile, i.e., it never stops but keeps wandering, undergoing sizable oscillations, around the position corresponding to maximum entropy, has remarkable implications on the entropy variations of the system and on the validity of the second law when dealing with systems of mesoscopic dimensions.
The adiabatic piston: a perpetuum mobile in the mesoscopic realm
Crosignani, Bruno; Di Porto, Paolo; Conti, Claudio
2004-01-01
Abstract: A detailed analysis of the adiabatic-piston problem reveals, for a finely-tuned choice of the spatial dimensions of the system, peculiar dynamical features that challenge the statement that an isolated system necessarily reaches a time-independent equilibrium state. In particular, the piston behaves like a perpetuum mobile, i.e., it never comes to a stop but keeps wandering, undergoing sizeable oscillations around the position corresponding to maximum entropy; this has remarkable im...
Lahiri, B. B.; Ranoo, Surojit; Philip, John
2017-11-01
Magnetic fluid hyperthermia (MFH) is becoming a viable cancer treatment methodology where the alternating magnetic field induced heating of magnetic fluid is utilized for ablating the cancerous cells or making them more susceptible to the conventional treatments. The heating efficiency in MFH is quantified in terms of specific absorption rate (SAR), which is defined as the heating power generated per unit mass. In majority of the experimental studies, SAR is evaluated from the temperature rise curves, obtained under non-adiabatic experimental conditions, which is prone to various thermodynamic uncertainties. A proper understanding of the experimental uncertainties and its remedies is a prerequisite for obtaining accurate and reproducible SAR. Here, we study the thermodynamic uncertainties associated with peripheral heating, delayed heating, heat loss from the sample and spatial variation in the temperature profile within the sample. Using first order approximations, an adiabatic reconstruction protocol for the measured temperature rise curves is developed for SAR estimation, which is found to be in good agreement with those obtained from the computationally intense slope corrected method. Our experimental findings clearly show that the peripheral and delayed heating are due to radiation heat transfer from the heating coils and slower response time of the sensor, respectively. Our results suggest that the peripheral heating is linearly proportional to the sample area to volume ratio and coil temperature. It is also observed that peripheral heating decreases in presence of a non-magnetic insulating shielding. The delayed heating is found to contribute up to ~25% uncertainties in SAR values. As the SAR values are very sensitive to the initial slope determination method, explicit mention of the range of linear regression analysis is appropriate to reproduce the results. The effect of sample volume to area ratio on linear heat loss rate is systematically studied and the
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.
Dynamical Cluster Approximation
Fotso, H.; Yang, S.; Chen, K.; Pathak, S.; Moreno, J.; Jarrell, M.; Mikelsons, K.; Khatami, E.; Galanakis, D.
The dynamical cluster approximation (DCA) is a method which systematically incorporates nonlocal corrections to the dynamical mean-field approximation. Here we present a pedagogical discussion of the DCA by describing it as a Φ-derivable coarse-graining approximation in k-space, which maps an infinite lattice problem onto a periodic finite-sized cluster embedded in a self-consistently determined effective medium. We demonstrate the method by applying it to the two-dimensional Hubbard model. From this application, we show evidences of the presence of a quantum critical point (QCP) at a finite doping underneath the superconducting dome. The QCP is associated with the second-order terminus of a line of first order phase separation transitions. This critical point is driven to zero temperature by varying the band parameters, generating the QCP. The effect of the proximity of the QCP to the superconducting dome is also discussed.
Covariant approximation averaging
Shintani, Eigo; Arthur, Rudy; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2015-06-01
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 Nf=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.
Thermal reservoir sizing for adiabatic compressed air energy storage
Energy Technology Data Exchange (ETDEWEB)
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.
Introduction to Diophantine Approximation
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-06-01
Full Text Available In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842 of existence of the solution [12], [1].
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.
Approximate and Incomplete Factorizations
Chan, T.F.; Vorst, H.A. van der
1997-01-01
In this chapter, we give a brief overview of a particular class of preconditioners known as incomplete factorizations. They can be thought of as approximating the exact LU factorization of a given matrix A (e.g. computed via Gaussian elimination) by disallowing certain ll-ins. As opposed to other
Directory of Open Access Journals (Sweden)
Lacroix D.
2010-03-01
Full Text Available Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in 238U [1]. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn’t seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in 238U and 239U for an excitation energy of 2.3 MeV above the barrier [2–4]. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.
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.
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...
Pumping approximately integrable systems
Lange, Florian; Lenarčič, Zala; Rosch, Achim
2017-06-01
Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose-Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here, we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps.
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.
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
Approximation and perturbation methods
Iyer, B R
1993-01-01
Few problems in nature are amenable to an exact solution and hence when one proceeds from elegant problems of theory to messy complicated problems of practice one is forced to recourse to methods of approximation and perturbation. The development of such techniques has been natural in attempts to extract physically veriﬁable consequences from either exact solutions of general relativity or from speciﬁc astrophysical systems for which an exact solution is impossible to ﬁnd. However, this should not be taken to imply giving up of mathematical rigour and an appeal to only physical intuition.
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.
Planetary Ices and the Linear Mixing Approximation
Bethkenhagen, M.; Meyer, E. R.; Hamel, S.; Nettelmann, N.; French, M.; Scheibe, L.; Ticknor, C.; Collins, L. A.; Kress, J. D.; Fortney, J. J.; Redmer, R.
2017-10-01
The validity of the widely used linear mixing approximation (LMA) for the equations of state (EOSs) of planetary ices is investigated at pressure-temperature conditions typical for the interiors of Uranus and Neptune. The basis of this study is ab initio data ranging up to 1000 GPa and 20,000 K, calculated via density functional theory molecular dynamics simulations. In particular, we determine a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the LMA from the results of the real mixture are generally small; for the thermal EOSs they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior ({T}{core}˜ 4000 K).
Optimized sympathetic cooling of atomic mixtures via fast adiabatic strategies
Energy Technology Data Exchange (ETDEWEB)
Choi, Stephen; Sundaram, Bala [Department of Physics, University of Massachusetts, Boston, Massachusetts 02125 (United States); Onofrio, Roberto [Dipartimento di Fisica ' ' Galileo Galilei' ' , Universita di Padova, Via Marzolo 8, Padova I-35131 (Italy); Department of Physics, University of Massachusetts, Boston, Massachusetts 02125 (United States); Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP), Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138 (United States)
2011-11-15
We discuss fast frictionless cooling techniques in the framework of sympathetic cooling of cold atomic mixtures. It is argued that optimal cooling of an atomic species--in which the deepest quantum degeneracy regime is achieved--may be obtained by means of sympathetic cooling with another species whose trapping frequency is dynamically changed to maintain constancy of the Lewis-Riesenfeld adiabatic invariant. Advantages and limitations of this cooling strategy are discussed, with particular regard to the possibility of cooling Fermi gases to a deeper degenerate regime.
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.
Designing single-qutrit quantum gates via tripod adiabatic passage
Directory of Open Access Journals (Sweden)
M. Amniat-Talab
2014-04-01
Full Text Available In this paper, we use stimulated Raman adiabatic passage technique to implement single-qutrit quantum gates in tripod systems. It is shown by using the Morris-Shore (MS transformation, the six-state problem with 5 pulsed fields can be reduced to a basis that decouples two states from the others. This imposes three pulses not connected to the initial condition with have the same shape. Using this method, the six-state penta-pod system is reduced to a tripod system. We can design single-qutrit quantum gates by ignoring the fragile dynamical phase, and by suitable design of Rabi frequencies of the effective Hamiltonian
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 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
Ultrasonic velocity and adiabatic compressibility in dioxane-water mixtures
Ciupe, A.; Auslaender, D.
1974-01-01
Using a method of diffraction of light on an ultrasonic beam, the velocity of ultrasounds and the adiabatic compressibility in dioxane-water mixtures were determined. The dependence of these quantities on the temperature (in the 15-50 C range) and on the concentration (0-100%) were studied. For each temperature there was found a velocity maximum and a compressibility minimum for a given value of the dioxane concentration. The different behavior of these mixtures is due to intense interactions between the molecules of the two liquids composing the mixture.
η condensate of fermionic atom pairs via adiabatic state preparation.
Kantian, A; Daley, A J; Zoller, P
2010-06-18
We discuss how an η condensate, corresponding to an exact excited eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an optical lattice. Using time-dependent density matrix renormalization group methods, we analyze a state preparation scheme beginning from a band insulator state in an optical superlattice. This state can act as an important test case, both for adiabatic preparation methods and the implementation of the many-body Hamiltonian, and measurements on the final state can be used to help detect associated errors.
The adiabatic piston: a perpetuum mobile in the mesoscopic realm
Crosignani, Bruno; Porto, Paolo; Conti, Claudio
2004-03-01
A detailed analysis of the adiabatic-piston problem reveals, for a finely-tuned choice of the spatial dimensions of the system, peculiar dynamical features that challenge the statement that an isolated system necessarily reaches a time-independent equilibrium state. In particular, the piston behaves like a perpetuum mobile, i.e., it never comes to a stop but keeps wandering, undergoing sizeable oscillations around the position corresponding to maximum entropy; this has remarkable implications on the entropy changes of a mesoscopic isolated system and on the limits of validity of the second law of thermodynamics in the mesoscopic realm.
The adiabatic piston: a perpetuum mobile in the mesoscopic realm
Directory of Open Access Journals (Sweden)
Claudio Conti
2004-03-01
Full Text Available Abstract: A detailed analysis of the adiabatic-piston problem reveals, for a finely-tuned choice of the spatial dimensions of the system, peculiar dynamical features that challenge the statement that an isolated system necessarily reaches a time-independent equilibrium state. In particular, the piston behaves like a perpetuum mobile, i.e., it never comes to a stop but keeps wandering, undergoing sizeable oscillations around the position corresponding to maximum entropy; this has remarkable implications on the entropy changes of a mesoscopic isolated system and on the limits of validity of the second law of thermodynamics in the mesoscopic realm.
Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems
Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.
2018-02-01
A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.
Tensile Deformation and Adiabatic Heating in Post-Yield Response of Polycarbonate
2015-11-01
ARL-TR-7531 ● NOV 2015 US Army Research Laboratory Tensile Deformation and Adiabatic Heating in Post-Yield Response of...Army Research Laboratory Tensile Deformation and Adiabatic Heating in Post-Yield Response of Polycarbonate by C. Allan Gunnarsson, Bryan Love...REPORT TYPE Final 3. DATES COVERED (From - To) January 2014–August 2015 4. TITLE AND SUBTITLE Tensile Deformation and Adiabatic Heating in Post
Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and Rydberg blockade
Beterov, I. I.; Saffman, M.; Yakshina, E. A.; Zhukov, V. P.; Tretyakov, D. B.; Entin, V. M.; Ryabtsev, I. I.; Mansell, C. W.; MacCormick, C.; Bergamini, S.; Fedoruk, M. P.
2012-01-01
We present schemes for geometric phase compensation in adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer wit...
Approximate Bayesian Computation
Sunnåker, Mikael; Corander, Jukka; Foll, Matthieu; Dessimoz, Christophe
2013-01-01
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). PMID:23341757
Wu, Jin-Lei; Ji, Xin; Zhang, Shou
2017-04-11
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.
Wu, Jin-Lei; Ji, Xin; Zhang, Shou
2017-04-01
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.
Shortcuts to Adiabaticity in the Infinite-Range Ising Model by Mean-Field Counter-Diabatic Driving
Hatomura, Takuya
2017-09-01
The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an original Hamiltonian to cancel out diabatic transitions. The counter-diabatic Hamiltonian is constructed by using the eigenstates of the original Hamiltonian. Therefore, it is in general difficult to construct the counter-diabatic Hamiltonian for quantum many-body systems. Even if the counter-diabatic Hamiltonian for quantum many-body systems is obtained, it is generally non-local and even diverges at critical points. We construct an approximated counter-diabatic Hamiltonian for the infinite-range Ising model by making use of the mean-field approximation. An advantage of this method is that the mean-field counter-diabatic Hamiltonian is constructed by only local operators. We numerically demonstrate the effectiveness of this method through quantum annealing processes going the vicinity of the critical point. It is also confirmed that the mean-field counter-diabatic Hamiltonian is still well-defined in the limit to the critical point for a certain class of schedules. The present method can take higher order contributions into account and is consistent with the variational approach for local counter-diabatic driving.
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
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....
Sliding Seal Materials for Adiabatic Engines, Phase 2
Lankford, J.; Wei, W.
1986-01-01
An essential task in the development of the heavy-duty adiabatic diesel engine is identification and improvements of reliable, low-friction piston seal materials. In the present study, the sliding friction coefficients and wear rates of promising carbide, oxide, and nitride materials were measured under temperature, environmental, velocity, and loading conditions that are representative of the adiabatic engine environment. In addition, silicon nitride and partially stabilized zirconia disks were ion implanted with TiNi, Ni, Co, and Cr, and subsequently run against carbide pins, with the objective of producing reduced friction via solid lubrication at elevated temperature. 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. Electron microscopy was used to elucidate the micromechanisms of wear following wear testing, and Auger electron spectroscopy was used to evaluate interface/environment interactions which seemed to be important in the friction and wear process. Unmodified ceramic sliding couples were characterized at all temperatures by friction coefficients of 0.24 and above. The coefficient at 800 C in an oxidizing environment was reduced to below 0.1, for certain material combinations, by the ion implanation of TiNi or Co. This beneficial effect was found to derive from lubricious Ti, Ni, and Co oxides.
Conditions for super-adiabatic droplet growth after entrainment mixing
Directory of Open Access Journals (Sweden)
F. Yang
2016-07-01
Full Text Available Cloud droplet response to entrainment and mixing between a cloud and its environment is considered, accounting for subsequent droplet growth during adiabatic ascent following a mixing event. The vertical profile for liquid water mixing ratio after a mixing event is derived analytically, allowing the reduction to be predicted from the mixing fraction and from the temperature and humidity for both the cloud and environment. It is derived for the limit of homogeneous mixing. The expression leads to a critical height above the mixing level: at the critical height the cloud droplet radius is the same for both mixed and unmixed parcels, and the critical height is independent of the updraft velocity and mixing fraction. Cloud droplets in a mixed parcel are larger than in an unmixed parcel above the critical height, which we refer to as the “super-adiabatic” growth region. Analytical results are confirmed with a bin microphysics cloud model. Using the model, we explore the effects of updraft velocity, aerosol source in the environmental air, and polydisperse cloud droplets. Results show that the mixed parcel is more likely to reach the super-adiabatic growth region when the environmental air is humid and clean. It is also confirmed that the analytical predictions are matched by the volume-mean cloud droplet radius for polydisperse size distributions. The findings have implications for the origin of large cloud droplets that may contribute to onset of collision–coalescence in warm clouds.
An Adiabatic Quantum Algorithm for Determining Gracefulness of a Graph
Hosseini, Sayed Mohammad; Davoudi Darareh, Mahdi; Janbaz, Shahrooz; Zaghian, Ali
2017-07-01
Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph G with e edges, is to label the vertices of G with 0, 1, ℒ, e such that, if we specify to each edge the difference value between its two ends, then any of 1, 2, ℒ, e appears exactly once as an edge label. For a given graph, there are still few efficient classical algorithms that determine either it is graceful or not, even for trees - as a well-known class of graphs. In this paper, we introduce an adiabatic quantum algorithm, which for a graceful graph G finds a graceful labelling. Also, this algorithm can determine if G is not graceful. Numerical simulations of the algorithm reveal that its time complexity has a polynomial behaviour with the problem size up to the range of 15 qubits. A general sufficient condition for a combinatorial optimization problem to have a satisfying adiabatic solution is also derived.
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.
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 ...
Energy Technology Data Exchange (ETDEWEB)
Krix, David; Nienhaus, Hermann, E-mail: hermann.nienhaus@uni-due.de [Faculty of Physics, University of Duisburg-Essen and Center of Nanointegration Duisburg-Essen (CENIDE), Lotharstr. 1, D-47048 Duisburg (Germany)
2014-08-21
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K{sub 2}O{sub 2} is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period.
Adiabatic heavy-ion fusion potentials for fusion at deep sub-barrier ...
Indian Academy of Sciences (India)
Abstract. 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 adia- batic barriers are consistent with the adiabatic fusion barriers ...
Quantum adiabatic computation with a constant gap is not useful in one dimension
Energy Technology Data Exchange (ETDEWEB)
Hastings, Matthew [Los Alamos National Laboratory
2009-01-01
We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state. The proof relies on a recently proven area law for such systems, implying the existence of a good matrix product representation of the ground state, combined with an appropriate algorithm to update the matrix product state as the Hamiltonian is changed. This implies that adiabatic evolution with such Hamiltonians is not useful for universal quantum computation. Therefore, adiabatic algorithms which are useful for universal quantum computation either require a spectral gap tending to zero or need to be implemented in more than one dimension (we leave open the question of the computational power of adiabatic simulation with a constant gap in more than one dimension).
Perspective: Stimulated Raman adiabatic passage: The status after 25 years
Bergmann, Klaas; Vitanov, Nikolay V.; Shore, Bruce W.
2015-05-01
The first presentation of the STIRAP (stimulated Raman adiabatic passage) technique with proper theoretical foundation and convincing experimental data appeared 25 years ago, in the May 1st, 1990 issue of The Journal of Chemical Physics. By now, the STIRAP concept has been successfully applied in many different fields of physics, chemistry, and beyond. In this article, we comment briefly on the initial motivation of the work, namely, the study of reaction dynamics of vibrationally excited small molecules, and how this initial idea led to the documented success. We proceed by providing a brief discussion of the physics of STIRAP and how the method was developed over the years, before discussing a few examples from the amazingly wide range of applications which STIRAP now enjoys, with the aim to stimulate further use of the concept. Finally, we mention some promising future directions.
Properties of a two stage adiabatic demagnetization refrigerator
Fukuda, H.; Ueda, S.; Arai, R.; Li, J.; Saito, A. T.; Nakagome, H.; Numazawa, T.
2015-12-01
Currently, many space missions using cryogenic temperatures are being planned. In particular, high resolution sensors such as Transition Edge Sensors need very low temperatures, below 100 mK. It is well known that the adiabatic demagnetization refrigerator (ADR) is one of most useful tools for producing ultra-low temperatures in space because it is gravity independent. We studied a continuous ADR system consisting of 4 stages and demonstrated it could provide continuous temperatures around 100 mK. However, there was some heat leakage from the power leads which resulted in reduced cooling power. Our efforts to upgrade our ADR system are presented. We show the effect of using the HTS power leads and discuss a cascaded Carnot cycle consisting of 2 ADR units.
Adiabatic ground state preparation in an expanding lattice
Gazit, Snir; Olund, Chris; Yao, Norman
2017-04-01
We numerically investigate the newly proposed s-source framework for constructing ground state wave functions of gapped Hamiltonians. The key idea is to utilize the adiabatic principle to build a tensor network representation that smoothly interpolates between the ground state of system sizes L and 2L via an interleaved set of ancillary degrees of freedom. Repeatedly applying this procedure reproduces the thermodynamic limit. The scheme should be contrasted with conventional tensor network methods that rely on the variational principle to target the ground state by iteratively improving a variational energy. We introduce a simple yet flexible tensor network structure and an optimization protocol borrowing techniques from quantum control theory. We anticipate that this approach can, in principle, allow access to problems beyond current tensor network technology and even serve as an experimental scheme for ground state preparation in quantum engineered systems.
Optical waveguide device with an adiabatically-varying width
Energy Technology Data Exchange (ETDEWEB)
Watts,; Michael R. (Albuquerque, NM), Nielson; Gregory, N [Albuquerque, NM
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.
Quasi-adiabatic compression heating of selected foods
Landfeld, Ales; Strohalm, Jan; Halama, Radek; Houska, Milan
2011-03-01
The quasi-adiabatic temperature increase due to compression heating, during high-pressure (HP) processing (HPP), was studied using specially designed equipment. The temperature increase was evaluated as the difference in temperature, during compression, between atmospheric pressure and nominal pressure. The temperature was measured using a thermocouple in the center of a polyoxymethylene cup, which contained the sample. Fresh meat balls, pork meat pate, and tomato purée temperature increases were measured at three initial temperature levels between 40 and 80 °C. Nominal pressure was either 400 or 500 MPa. Results showed that the fat content had a positive effect on temperature increases. Empirical equations were developed to calculate the temperature increase during HPP at different initial temperatures for pressures of 400 and 500 MPa. This thermal effect data can be used for numerical modeling of temperature histories of foods during HP-assisted pasteurization or sterilization processes.
Towards generic adiabatic elimination for bipartite open quantum systems
Azouit, R.; Chittaro, F.; Sarlette, A.; Rouchon, P.
2017-12-01
We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow subsystem. The method, based on an asymptotic expansion and geometric singular perturbation theory, ensures the physical interpretation of the reduced second-order model by giving the reduced dynamics in a Lindblad form and the state reduction in Kraus map form. We give explicit second-order formulas for Hamiltonian or cascade coupling between the two subsystems. These formulas can be used to engineer, via a careful choice of the fast subsystem, the Hamiltonian and Lindbald operators governing the dissipative dynamics of the slow subsystem.
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.
DEFF Research Database (Denmark)
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...
Coherent state mapping ring polymer molecular dynamics for non-adiabatic quantum propagations
Chowdhury, Sutirtha N.; Huo, Pengfei
2017-12-01
We introduce the coherent-state mapping ring polymer molecular dynamics (CS-RPMD), a new method that accurately describes electronic non-adiabatic dynamics with explicit nuclear quantization. This new approach is derived by using coherent-state mapping representation for the electronic degrees of freedom (DOF) and the ring-polymer path-integral representation for the nuclear DOF. The CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the state-dependent potential and correctly describes electronic Rabi oscillations. A classical equation of motion is used to sample initial configurations and propagate the trajectories from the CS-RPMD Hamiltonian. At the time equivalent to zero, the quantum Boltzmann distribution (QBD) is recovered by reweighting the sampled distribution with an additional phase factor. In a special limit that there is one bead for mapping variables and multiple beads for nuclei, CS-RPMD satisfies detailed balance and preserves an approximate QBD. Numerical tests of this method with a two-state model system show very good agreement with exact quantum results over a broad range of electronic couplings.
Energy-Efficient and Secure S-Box circuit using Symmetric Pass Gate Adiabatic Logic
Energy Technology Data Exchange (ETDEWEB)
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.
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.
INHOMOGENEOUS DIOPHANTINE APPROXIMATION WITH PRIME ...
Indian Academy of Sciences (India)
50
INHOMOGENEOUS DIOPHANTINE APPROXIMATION WITH PRIME. CONSTRAINTS. STEPHAN BAIER AND ANISH GHOSH. Abstract. We study the problem of ... this area under primality constraints. Indeed, the ...... [7] A. Ghosh, Diophantine approximation on subspaces of Rn and dynamics on homogeneous spaces, to.
Diophantine approximation in prescribed degree
Schleischitz, Johannes
2017-01-01
We investigate approximation to a given real number by algebraic numbers and algebraic integers of prescribed degree. We deal with both best and uniform approximation, and highlight the similarities and differences compared with the intensely studied problem of approximation by algebraic numbers (and integers) of bounded degree. We establish the answer to a question of Bugeaud concerning approximation to transcendental real numbers by quadratic irrational numbers, and thereby we refine a resu...
Adiabatic regularization and particle creation for spin one-half fields
Landete, Aitor; Navarro-Salas, José; Torrentí, Francisco
2014-02-01
The extension of the adiabatic regularization method to spin-1/2 fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-1/2 fields. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.
Directory of Open Access Journals (Sweden)
Elham Moomivand
2017-05-01
Full Text Available We investigate adiabatic pumping current in a graphene based normal-insulator-superconductor (NIS junction with Corbino disk structure. The adiabatic pumping current is generated by two electrostatic potentials, oscillating periodically and out of phase, applied to the insulating and superconducting regions. Using the extended Brouwer’s formula for the adiabatic pumping current, which is based on the scattering theory, the pumping current is obtained. The results of this calculation show the pumped current oscillates as a function of the barrier strength and it has maximums at resonances with a π/2 phase shift in comparison to the planar NIS junction.
Conical Intersections Between Vibrationally Adiabatic Surfaces in Methanol
Dawadi, Mahesh B.; Perry, David S.
2014-06-01
The discovery of a set of seven conical intersections (CI's) between vibrationally adiabatic surfaces in methanol is reported. The intersecting surfaces represent the energies of the two asymmetric CH stretch vibrations, νb{2} and νb{9}, regarded as adiabatic functions of the torsional angle, γ, and COH bend angle, ρ. One conical intersection, required by symmetry, is located at the C3v geometry where the COH group is linear (ρ = 0°); the other six are in eclipsed conformations with ρ = 62° and 94°. The three CI's at ρ = 62° are close to the equilibrium geometry (ρ = 71.4°), within the zero-point amplitude of the COH bending vibration. CI's between electronic surfaces have long been recognized as crucial conduits for ultrafast relaxation, and recently Hamm, and Stock have shown that vibrational CI's may also provide a mechanism for ultrafast vibrational relaxation. The ab initio data reported here are well described by an extended Zwanziger and Grant model for E ⊗ e Jahn-Teller systems in which Renner-Teller coupling is also active. However, in the present case, the distortion ρ from C3v symmetry is much larger than is typical in the Jahn-Teller coupling of electronic surfaces and accordingly higher-order terms in ρ are required. The present results are also consistent with the two-state model of Xu et al. The cusp-like features, which they found along the internal-rotation path, are explained in the context of the present work in terms of proximity to the CI's. The presence of multiple CI's near the torsional minimum energy path impacts the role of geometric phase in this three-fold internal-rotor system. When the dimensionality of the low-frequency space is extended to include the CO bond length as well as γ and ρ, the individual CI's become seams of CI's. It is shown that the CI's at ρ = 62° and 94° lie along the same seam of CI's in this higher dimensional space. P. Hamm and G. Stock, Phys. Rev. Lett., 109, 173201, (2012) P. Hamm, and G
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Nonequilibrium adiabatic molecular dynamics simulations of methane clathrate hydrate decomposition.
Alavi, Saman; Ripmeester, J A
2010-04-14
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.
Resource efficient gadgets for compiling adiabatic quantum optimization problems
Babbush, Ryan; O'Gorman, Bryan; Aspuru-Guzik, Alán
2013-11-01
We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, we optimize methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits. Next, we show a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision. Finally, we present numerics which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.
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.
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.
Adiabatic interpretation of particle creation in a de Sitter universe
Energy Technology Data Exchange (ETDEWEB)
Molina-Paris, C.
1998-06-10
The choice of vacuum state for a quantum scalar field propagating in a de Sitter spacetime (massive and arbitrarily coupled to the gravitational field) is discussed. The problem of finite-time initial conditions for the mode functions is analyzed, as well as how these determine the vacuum state of the quantum system. The principle guiding the choice of vacuum state is the following: one wants the vacuum contribution to the energy-momentum tensor to contain all the ultraviolet divergent terms, so that the particle creation terms are finite, and covariantly conserved. There is a suitable set of modes (instantaneous adiabatic basis) in which this splitting of the expectation value of the energy-momentum tensor can be carried out. Numerical results are presented for different finite-time initial conditions (m = 0.6, {zeta} = 1/6). The nature of the particle creation effect is described and its relationship to the concept of a horizon crossing time is shown. These numerical results imply that back-reaction can be important and should be the subject of further research.
Adiabatic, Shock, and Plastic Work Heating of Solids and the Cylinder Test
National Research Council Canada - National Science Library
Ruden, E
2000-01-01
Solids subjected to high pressures, shocks, and/or deformation experience an increase in internal energy density and temperature due to adiabatic compression, shock heating, and plastic work heating, respectively...
Adiabatic Low-Pass J Filters for Artifact Suppression in Heteronuclear NMR
DEFF Research Database (Denmark)
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....
Scaled hydrogenic approximation wavefunctions. [Hartree-Fock approximation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1979-09-01
Although widespread use of computer codes for the solution of Schrodinger equations makes available numerical Hartree-Fock model radial wave functions, there remains persistant interest in simple analytic expressions for atomic wave functions. One such frequency favored approach employs hydrogenic functions, suitably scaled, as approximate wave functions. The following note displays typical inaccuracies to be expected from such approximations. 13 references.
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare......-unilateral has an approximation ratio between 0.610 and 0.611, the best ordinal mechanism has an approximation ratio between 0.616 and 0.641, while the best mixed-unilateral mechanism has an approximation ratio bigger than 0.660. In particular, the best mixed-unilateral non-ordinal (i.e., cardinal) mechanism...
On the response of quasi-adiabatic particles to magnetotail reconfigurations
Delcourt, Dominique C.; Malova, Helmi V.; Zelenyi, Lev M.
2017-01-01
We investigate the response of quasi-adiabatic particles to dynamical reconfigurations of the magnetotail field lines. Although they travel through a sharp field reversal with a characteristic length scale smaller than their Larmor radii, these quasi-adiabatic particles experience a negligible net change in magnetic moment. We examine the robustness of such a quasi-adiabatic behavior in the presence of a large surging electric field induced by magnetic field line reconfiguration as observed during the expansion phase of substorms. We demonstrate that, although such a short-lived electric field can lead to substantial nonadiabatic heating, quasi-adiabaticity is conserved for particles with velocities larger than the peak ExB drift speed. Because of the time-varying character of the magnetic field, it is not possible to use the adiabaticity parameter κ in a straightforward manner to characterize the particle behavior. We rather consider a κ parameter that is averaged over equatorial crossings. We demonstrate that particles intercepting the field reversal in the early stage of the magnetic transition may experience significant energization and enhanced oscillating motion in the direction normal to the midplane. In contrast, particles interacting with the field reversal in the late stage of the magnetic transition experience weaker energization and slower oscillations about the midplane. We show that quasi-adiabatic particles accelerated during such events can lead to energy-time dispersion signatures at low altitudes as is observed in the plasma sheet boundary layer.
On the response of quasi-adiabatic particles to magnetotail reconfigurations
Directory of Open Access Journals (Sweden)
D. C. Delcourt
2017-01-01
Full Text Available We investigate the response of quasi-adiabatic particles to dynamical reconfigurations of the magnetotail field lines. Although they travel through a sharp field reversal with a characteristic length scale smaller than their Larmor radii, these quasi-adiabatic particles experience a negligible net change in magnetic moment. We examine the robustness of such a quasi-adiabatic behavior in the presence of a large surging electric field induced by magnetic field line reconfiguration as observed during the expansion phase of substorms. We demonstrate that, although such a short-lived electric field can lead to substantial nonadiabatic heating, quasi-adiabaticity is conserved for particles with velocities larger than the peak ExB drift speed. Because of the time-varying character of the magnetic field, it is not possible to use the adiabaticity parameter κ in a straightforward manner to characterize the particle behavior. We rather consider a κ parameter that is averaged over equatorial crossings. We demonstrate that particles intercepting the field reversal in the early stage of the magnetic transition may experience significant energization and enhanced oscillating motion in the direction normal to the midplane. In contrast, particles interacting with the field reversal in the late stage of the magnetic transition experience weaker energization and slower oscillations about the midplane. We show that quasi-adiabatic particles accelerated during such events can lead to energy–time dispersion signatures at low altitudes as is observed in the plasma sheet boundary layer.
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.
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
Energy Technology Data Exchange (ETDEWEB)
Wang, J. F.; Ma, Q. M.; Song, T.; Yuan, S. B. [Research Department of Biomedical Engineering, Institute of Electrical Engineering, Chinese Academy of Science, Beijing 100190 (China); Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn [School of Science, Harbin Institute of Technology, Shenzhen 518055 (China)
2017-08-20
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.
General background conditions for K-bounce and adiabaticity
Energy Technology Data Exchange (ETDEWEB)
Romano, Antonio Enea [University of Crete, Department of Physics, Heraklion (Greece); Kyoto University, Yukawa Institute for Theoretical Physics, Kyoto (Japan); Universidad de Antioquia, Instituto de Fisica, A.A.1226, Medellin (Colombia)
2017-03-15
We study the background conditions for a bounce uniquely driven by a single scalar field model with a generalized kinetic term K(X), without any additional matter field. 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(X), and the other on a K(X) 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, or oscillations of H. In the region where these models have a constant potential they are adiabatic on any scale and because of this they may not conserve curvature perturbations on super-horizon scales. While at the perturbation level one class of models is free from ghosts and singularities of the classical equations of motion, in general gradient instabilities are present around the bounce time, because the sign of the squared speed of sound is opposite to the sign of the time derivative of H. We discuss how this kind of instabilities could be avoided by modifying the Lagrangian by introducing Galilean terms in order to prevent a negative squared speed of sound around the bounce. (orig.)
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
Energy Technology Data Exchange (ETDEWEB)
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.
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
-commuting maps and invariant approximations
Directory of Open Access Journals (Sweden)
Rhoades BE
2006-01-01
Full Text Available We obtain common fixed point results for generalized -nonexpansive -commuting maps. As applications, various best approximation results for this class of maps are derived in the setup of certain metrizable topological vector spaces.
Some results in Diophantine approximation
DEFF Research Database (Denmark)
Pedersen, Steffen Højris
This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...... 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....... The first part is about a failed attempt of applying dynamical methods to obtain results and is not part of the paper. It explains the ideas of how the real case works and what goes wrong in the case of the formal Laurent series. The second part contains the results of the paper and sketches of the proofs....
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...
He, Shuang; Su, Shi-Lei; Wang, Dong-Yang; Sun, Wen-Mei; Bai, Cheng-Hua; Zhu, Ai-Dong; Wang, Hong-Fu; Zhang, Shou
2016-08-08
We propose an effective scheme of shortcuts to adiabaticity for generating a three-dimensional entanglement of two atoms trapped in a cavity using the transitionless quantum driving (TQD) approach. The key point of this approach is to construct an effective Hamiltonian that drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final state as that of an adiabatic process within a much shorter time. In this paper, the shortcuts to adiabatic passage are constructed by introducing two auxiliary excited levels in each atom and applying extra cavity modes and classical fields to drive the relevant transitions. Thereby, the three-dimensional entanglement is obtained with a faster rate than that in the adiabatic passage. Moreover, the influences of atomic spontaneous emission and photon loss on the fidelity are discussed by numerical simulation. The results show that the speed of entanglement implementation is greatly improved by the use of adiabatic shortcuts and that this entanglement implementation is robust against decoherence. This will be beneficial to the preparation of high-dimensional entanglement in experiment and provides the necessary conditions for the application of high-dimensional entangled states in quantum information processing.
Selective excitation in a three-state system using a hybrid adiabatic-nonadiabatic interaction
Song, Yunheung; Jo, Hanlae; Ahn, Jaewook
2016-01-01
The chirped-pulse interaction in the adiabatic coupling regime induces cyclic permutations of the energy states of a three-level system in the $V$-type configuration, which process is known as the three-level chirped rapid adiabatic passage. Here we show that a spectral hole in a chirped pulse can turn on and off one of the two adiabatic crossing points of this process, reducing the system to an effective two-level system. The given hybrid adiabatic-nonadiabatic transition results in selective excitation of the three-level system, controlled by the laser intensity and spectral position of the hole as well as the sign of the chirp parameter. Experiments are performed with shaped femtosecond laser pulses and the three lowest energy-levels (5S$_{1/2}$, 5P$_{1/2}$, and 5P$_{3/2}$) of atomic rubidium ($^{85}$Rb), of which the result shows good agreement with the theoretically analyzed dynamics. The result indicates that our method, being combined with the ordinary chirped-RAP, implements an adiabatic transitions b...
Predicting the effect of relaxation during frequency-selective adiabatic pulses.
Pfaff, Annalise R; McKee, Cailyn E; Woelk, Klaus
2017-10-03
Adiabatic half and full passages are invaluable for achieving uniform, B1-insensitive excitation or inversion of macroscopic magnetization across a well-defined range of NMR frequencies. To accomplish narrow frequency ranges with adiabatic pulses (<100Hz), long pulse durations at low RF power levels are necessary, and relaxation during these pulses may no longer be negligible. A numerical, discrete recursive combination of the Bloch equations for longitudinal and transverse relaxation with the optimized equation for adiabatic angular motion of magnetization is used to calculate the trajectory of magnetization including its relaxation during adiabatic hyperbolic secant pulses. The agreement of computer-calculated data with experimental results demonstrates that, in non-viscous, small-molecule fluids, it is possible to model magnetization and relaxation by considering standard T1 and T2 relaxation in the traditional rotating frame. The proposed model is aimed at performance optimizations of applications in which these pulses are employed. It differs from previous reports which focused on short high-power adiabatic pulses and relaxation that is governed by dipole-dipole interactions, cross polarization, or chemical exchange. Copyright © 2017. Published by Elsevier Inc.
Approximate number sense theory or approximate theory of magnitude?
Content, Alain; Velde, Michael Vande; Adriano, Andrea
2017-01-01
Leibovich et al. argue that the evidence in favor of a perceptual mechanism devoted to the extraction of numerosity from visual collections is unsatisfactory and propose to replace it with an unspecific mechanism capturing approximate magnitudes from continuous dimensions. We argue that their representation of the evidence is incomplete and that their theoretical proposal is too vague to be useful.
Approximate entropy of network parameters
West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew
2012-04-01
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Twist angle determination in liquid crystal displays by location of local adiabatic points
Moreno, Ignacio; Bennis, Noureddine; Davis, Jeffrey A.; Ferreira, Carlos
1998-12-01
In this work we present a method for the determination of the twist angle of an arbitrary twisted nematic liquid crystal spatial light modulator. The method is based on the location of local adiabatic points, i.e., situations in which the liquid crystal SLM acts only as a rotation device. For these cases, the rotation induced on the polarization of the incident beam is equal to the twist angle. Consequently, the twist angle can be determined with high precision. We show that local adiabatic regime may be achieved in two ways, either by changing the incident beam wavelength, or by applying a voltage to the electrodes of the display. However, the simple model that describes the SLM in the off-state, may break down when a voltage is applied to the display, and it may affect the local adiabatic behaviour. We present theoretical and experimental results.
Rabi oscillations produced by adiabatic pulse due to initial atomic coherence.
Svidzinsky, Anatoly A; Eleuch, Hichem; Scully, Marlan O
2017-01-01
If an electromagnetic pulse is detuned from atomic transition frequency by amount Δ>1/τ, where τ is the turn-on time of the pulse, then atomic population adiabatically follows the pulse intensity without causing Rabi oscillations. Here we show that, if initially, the atom has nonzero coherence, then the adiabatic pulse yields Rabi oscillations of atomic population ρaa(t), and we obtain analytical solutions for ρaa(t). Our findings can be useful for achieving generation of coherent light in the backward direction in the QASER scheme in which modulation of the coupling between light and atoms is produced by Rabi oscillations. Initial coherence can be created by sending a short resonant pulse into the medium followed by a long adiabatic pulse, which leads to the light amplification in the backward direction.
Optimal control of the power adiabatic stroke of an optomechanical heat engine.
Bathaee, M; Bahrampour, A R
2016-08-01
We consider the power adiabatic stroke of the Otto optomechanical heat engine introduced in Phys. Rev. Lett. 112, 150602 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.150602. We derive the maximum extractable work of both optomechanical normal modes in the minimum time while the system experiences quantum friction effects. We show that the total work done by the system in the power adiabatic stroke is optimized by a bang-bang control. The time duration of the power adiabatic stroke is of the order of the inverse of the effective optomechanical-coupling coefficient. The optimal phase-space trajectory of the Otto cycle for both optomechanical normal modes is also obtained.
Analysis of adiabatic trapping for quasi-integrable area-preserving maps
Bazzani, A; Giovannozzi, M; Hernalsteens, C
2014-01-01
Trapping phenomena involving non-linear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of non-linear resonances and slow time-variation of some system parameters is considered. The focus of this paper is on discrete-time dynamical systems generated by two-dimensional symplectic maps. The possibility of extending the results of neo-adiabatic theory to quasi-integrable area-preserving maps is discussed. Scaling laws are derived, which describe the adiabatic transport as a function of the system parameters using a probabilistic point of view. These laws can be particularly relevant for physical applications. The outcome of extensive numerical simulations showing the excellent agreement with the analytical estimates and scaling laws is presented and discussed in detail.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Svrček, M.; Baňacký, P.; Biskupič, S.; Noga, J.; Pelikán, P.; Zajac, A.
1999-01-01
The Born-Handy formula, recently shown by Kutzelnigg to be a rigorous expression for the calculation of the adiabatic correction, has been, on the level of a ground state SCF wavefunction, reformulated and linked to the coefficients of the standard coupled perturbed Hartree-Fock (CPHF) method. The contribution of the electron correlation via second-order perturbation theory is also presented. The solution of the corresponding secular equation of the nuclear motion enables the calculation of the adiabatic correction over the particular normal modes. The method offers the possibility of extending high-precision calculations of the adiabatic correction to more complex systems. Test calculations have been performed for H 2, HD and D 2 and the results are in satisfactory agreement with the exact figures.
Best Approximation in Numerical Radius
Aksoy, Asuman Guven; Lewicki, Grzegorz
2010-01-01
Let $X$ be a reflexive Banach space. In this paper we give a necessary and sufficient condition for an operator $T\\in \\mathcal{K}(X)$ to have the best approximation in numerical radius from the convex subset $\\mathcal{U} \\subset \\mathcal{K}(X),$ where $\\mathcal{K}(X)$ denotes the set of all linear, compact operators from $X$ into $X.$ We will also present an application to minimal extensions with respect to the numerical radius. In particular some results on best approximation in norm will be...
Face Recognition using Approximate Arithmetic
DEFF Research Database (Denmark)
Marso, Karol
Face recognition is image processing technique which aims to identify human faces and found its use in various diﬀerent ﬁelds for example in security. Throughout the years this ﬁeld evolved and there are many approaches and many diﬀerent algorithms which aim to make the face recognition as eﬀective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
Approximation by Penultimate Stable Laws
L.F.M. de Haan (Laurens); L. Peng (Liang); H. Iglesias Pereira
1997-01-01
textabstractIn certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\\\alpha_n \\\\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
APPROXIMATE MODELS FOR FLOOD ROUTING
African Journals Online (AJOL)
kinematic model and a nonlinear convection-diffusion model are extracted from a normalized form of the St. Venant equations, and applied to ... normal ﬂow condition is moderate. Keywords: approximate models, nonlinear kinematic ... The concern here is with the movement of an abnormal amount of water along a river or ...
Approximation for Bayesian Ability Estimation.
1987-02-18
two-way contingency tables. Journal of Educational Statistics, 11, 33-56. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos Estadistica , 31...Sloan-Kettering Cancer Center 1275 York Avenue New York, NY 10021 Dr. Wallace Wulfeck, 11 Navy Personnel R&D Center San Diego, CA 92152-6800 Dr. Wendy
Protecting and accelerating adiabatic passage with time-delayed pulse sequences
Sampedro, Pablo; Sola, Ignacio R
2016-01-01
Using numerical simulations of two-photon electronic absorption with femtosecond pulses in Na$_2$ we show that: i) it is possible to avoid the characteristic saturation or dumped Rabi oscillations in the yield of absorption by time-delaying the laser pulses; ii) it is possible to accelerate the onset of adiabatic passage by using the vibrational coherence starting in a wave packet; and iii) it is possible to prepare the initial wave packet in order to achieve full state-selective transitions with broadband pulses. The findings can be used, for instance, to achieve ultrafast adiabatic passage by light-induced potentials and understand its intrinsic robustness.
Adiabatic response and quantum thermoelectrics for ac-driven quantum systems
Ludovico, María Florencia; Battista, Francesca; von Oppen, Felix; Arrachea, Liliana
2016-02-01
We generalize the theory of thermoelectrics to include coherent electron systems under adiabatic ac driving, accounting for quantum pumping of charge and heat, as well as for the work exchanged between the electron system and driving potentials. We derive the relevant response coefficients in the adiabatic regime and show that they obey generalized Onsager reciprocity relations. We analyze the consequences of our generalized thermoelectric framework for quantum motors, generators, heat engines, and heat pumps, characterizing them in terms of efficiencies and figures of merit. We illustrate these concepts in a model for a quantum pump.
Spectroscopy of the Rotating Kaluza-Klein Spacetime via Revisited Adiabatic Invariant Quantity
Yu, Li; Qi, De-Jiang
2017-07-01
In this paper, we have investigated the spectroscopy of the rotating Kaluza-Klein spacetime by applying Bohr-Sommerfeld quantization rule and the first law of thermodynamics. we derived the expression of the adiabatic invariant quantity in the dragged-Painlevé coordinate system. Then, via revisited adiabatic invariant quantity, we derive the area and entropy spectra of the spacetime. We obtained the area spectrum of the Kaluza-Klein spacetime is {Δ } A=8π {lP2}, and the entropy spectrum is Δ S = 2 π. This result is consistent with the Bekenstein's original result, which imply the entropy and horizon area are discrete and equidistant for the spacetime.
Energy Technology Data Exchange (ETDEWEB)
Olazabal-Loume, M.; Hallo, L. [Bordeaux-1 Univ., CELIA UMR 5107, 33 - Talence (France)
2006-06-15
This study deals with the hydrodynamic stability of a planar target in the context of inertial confinement fusion direct drive. Recently, different schemes have been proposed in order to reduce ablative Rayleigh-Taylor growth. They are based on the target adiabatic shaping in the ablation zone. In this work, we consider an adiabatic shaping scheme by relaxation: a prepulse is followed by a relaxation period where the laser is turned off. A numerical study is performed with a perturbation code dedicated to the linear stability analysis. The simulations show stabilizing effects of the relaxation scheme on the linear Rayleigh-Taylor growth rate. Influence of the picket parameters is also discussed. (authors)
Magnetic Skyrmion Transport in a Nanotrack With Spatially Varying Damping and Non-adiabatic Torque
Zhang, Xichao; Xia, Jing; Zhao, G. P.; Liu, Xiaoxi; Zhou, Yan
2016-01-01
Reliable transport of magnetic skyrmions is required for any future skyrmion-based information processing devices. Here we present a micromagnetic study of the in-plane current-driven motion of a skyrmion in a ferromagnetic nanotrack with spatially sinusoidally varying Gilbert damping and/or non-adiabatic spin-transfer torque coefficients. It is found that the skyrmion moves in a sinusoidal pattern as a result of the spatially varying Gilbert damping and/or non-adiabatic spin-transfer torque ...
Rapid adiabatic passage in quantum dots: Influence of scattering and dephasing
DEFF Research Database (Denmark)
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......, the pulse area, as well as on the absence of carrier scattering and dephasing, we find that adiabatic passage is surprisingly insensitive to the excitation conditions and carrier scattering effects. Quantum kinetic models for the interaction of quantum-dot carriers with longitudinal optical phonons are used...
Performance Limits of Nanoelectromechanical Switches (NEMS-Based Adiabatic Logic Circuits
Directory of Open Access Journals (Sweden)
Samer Houri
2013-12-01
Full Text Available This paper qualitatively explores the performance limits, i.e., energy vs. frequency, of adiabatic logic circuits based on nanoelectromechanical (NEM switches. It is shown that the contact resistance and the electro-mechanical switching behavior of the NEM switches dictate the performance of such circuits. Simplified analytical expressions are derived based on a 1-dimensional reduced order model (ROM of the switch; the results given by this simplified model are compared to classical CMOS-based, and sub-threshold CMOS-based adiabatic logic circuits. NEMS-based circuits and CMOS-based circuits show different optimum operating conditions, depending on the device parameters and circuit operating frequency.
Vashaee, S; Newling, B; Balcom, B J
2015-12-01
Band selective adiabatic inversion radio frequency pulses were employed for multi-slice T2 distribution measurements in porous media samples. Multi-slice T2 measurement employing longitudinal Hadamard encoding has an inherent sensitivity advantage over slice-by-slice local T2 measurements. The slice selection process is rendered largely immune to B1 variation by employing hyperbolic secant adiabatic inversion pulses, which simultaneously invert spins in several well-defined slices. While Hadamard encoding is well established for local spectroscopy, the current work is the first use of Hadamard encoding for local T2 measurement. Copyright © 2015 Elsevier Inc. All rights reserved.
Transient Particle Energies in Shortcuts to Adiabatic Expansions of Harmonic Traps.
Cui, Yang-Yang; Chen, Xi; Muga, J G
2016-05-19
The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be reduced to zero, practical limitations and constraints impose minimal finite times for the externally controlled time-dependent frequency protocols. We examine the role of different time-averaged energies (total, kinetic, potential, nonadiabatic) and of the instantaneous power in characterizing or selecting different protocols. Specifically, we prove a virial theorem for STA processes, set minimal energies (or times) for given times (or energies), and discuss their realizability by means of Dirac impulses or otherwise.
Localization and adiabatic pumping in a generalized Aubry-André-Harper model
Liu, Fangli; Ghosh, Somnath; Chong, Y. D.
2015-01-01
A generalization of the Aubry-André-Harper (AAH) model is developed, containing a tunable phase shift between on-site and off-diagonal modulations. A localization transition can be induced by varying just this phase, keeping all other model parameters constant. The complete localization phase diagram is obtained. Unlike the original AAH model, the generalized model can exhibit a transition between topologically trivial band structures and topologically nontrivial band structures containing protected boundary states. These boundary states can be pumped across the system by adiabatic variations in the phase shift parameter. The model can also be used to demonstrate the phenomenon of adiabatic pumping breakdown due to localization.
Trigonometric protocols for shortcuts to adiabatic transport of cold atoms in anharmonic traps
Li, Jing; Zhang, Qi; Chen, Xi
2017-10-01
Shortcuts to adiabaticity have been proposed to speed up the ;slow; adiabatic transport of ultracold atoms. Their realizations, using inverse engineering protocols, provide families of trajectories with appropriate boundary conditions. These trajectories can be optimized with respect to the operation time and the energy input. In this paper we propose trigonometric protocols for fast and robust atomic transport, taking into account cubic or quartic anharmonicities of the trapping potential. Numerical analysis demonstrates that this choice of the trajectory minimizes the final residual energy efficiently, and shows extraordinary robustness against anharmonic parameters. These results might be of interest for the state-of-the-art experiments on ultracold atoms and ions.
Mussard, Bastien; Jansen, Georg; Angyan, Janos
2016-01-01
Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the co...
Fishchuk, A.V.; Merritt, J.M.; Avoird, A. van der
2007-01-01
The three adiabatic potential surfaces of the Br(P-2)-HCN complex that correlate to the P-2 ground state of the Br atom were calculated ab initio. With the aid of a geometry-dependent diabatic mixing angle, also calculated ab initio, these adiabatic potential surfaces were transformed into a set of
Dyvorne, Hadrien; O'Halloran, Rafael; Balchandani, Priti
2016-05-01
To improve ultrahigh field diffusion-weighted imaging (DWI) in the presence of inhomogeneous transmit B1 field by designing a novel semi-adiabatic single-refocused DWI technique. A 180° slice-selective, adiabatic radiofrequency (RF) pulse of 4 ms duration was designed using the adiabatic Shinnar-Le Roux algorithm. A matched-phase slice-selective 90° RF pulse of 8 ms duration was designed to compensate the nonlinear phase of the adiabatic 180° RF pulse. The resulting RF pulse combination, matched-phase adiabatic spin echo (MASE), was integrated into a single-shot echo planar DWI sequence. The performance of this sequence was compared with single-refocused Stejskal-Tanner (ST), twice-refocused spin echo (TRSE) and twice-refocused adiabatic spin echo (TRASE) in simulations, phantoms, and healthy volunteers at 7 Tesla (T). In regions with inhomogeneous B1 , MASE resulted in increased signal intensity compared with ST (up to 64%). Moderate increase in specific absorption rate (35-39%) was observed for adiabatic RF pulses. MASE resulted in higher signal homogeneity at 7T, leading to improved visualization of measures derived from diffusion-weighted images such as white matter tractography and track density images. Efficient adiabatic SLR pulses can be adapted to single-refocused DWI, leading to substantially improved signal uniformity when compared with conventional acquisitions. © 2015 Wiley Periodicals, Inc.
CSIR Research Space (South Africa)
Baloyi, J
2014-06-01
Full Text Available An analysis of irreversibilities generated due to combustion in an adiabatic combustor burning wood was conducted. This was done for a reactant mixture varying from a rich to a lean mixture. A non-adiabatic non-premixed combustion model of a...
Towards 1H-MRSI of the human brain at 7T with slice-selective adiabatic refocusing pulses.
Scheenen, T.W.J.; Heerschap, A.; Klomp, D.W.J.
2008-01-01
OBJECTIVE: To explore the possibilities of proton spectroscopic imaging (1H-MRSI) of the human brain at 7 Tesla with adiabatic refocusing pulses. MATERIALS AND METHODS: A combination of conventional slice selective excitation and two pairs of slice selective adiabatic refocusing pulses (semi-LASER)
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Good points for diophantine approximation
Indian Academy of Sciences (India)
Given a sequence ( x n ) n = 1 ∞ of real numbers in the interval [0,1) and a sequence ( n ) n = 1 ∞ of positive numbers tending to zero, we consider the size of the set of numbers in [0,1] which can be `well approximated' by terms of the first sequence, namely, those y ∈ [ 0 , 1 ] for which the inequality | y − x n | < n holds ...
Computer Experiments for Function Approximations
Energy Technology Data Exchange (ETDEWEB)
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Many Faces of Boussinesq Approximations
Vladimirov, Vladimir A
2016-01-01
The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of velocity, time, viscosity, \\emph{etc.} Increasing $q$ improves the quality of a model, but narrows the limits of its applicability. Parameter $k$ allows us to vary the scales of time, velocity and viscosity and gives us the possibility to consider any initial and boundary conditions. In general, we discover and classify a rich variety of possibilities and restrictions, which are hidden behind the routine use of the Boussinesq...
Non-adiabatic collisions in H + O2 system: An ab initio study
Indian Academy of Sciences (India)
WINTEC
mentioned above. The degeneracy of the second and the third CT channels which also belongs to the Π symmetry in the collinear approach, is also lifted into A′ and A″ as shown in figure 2. The adiabatic PECs for the same three orientations as shown in figure 2, but as a function of r (internu- clear distance of the diatom) ...
Preparation of Quantum States of H2 using Stark-induced Adiabatic Raman Passage (SARP)
2013-12-02
The Journal of Chemical Physics , (07 2011): 24201. doi: Nandini Mukherjee...Richard N. Zare. Can stimulated Raman pumping cause large population transfers in isolated molecules?, The Journal of Chemical Physics , (11 2011): 0...population to a selected rovibrational state of H2 by Stark-induced adiabatic Raman passage, THE JOURNAL OF CHEMICAL PHYSICS , (02 2013): 51101.
Non-adiabatic radiative collapse of a relativistic star under different ...
Indian Academy of Sciences (India)
We examine the role of space-time geometry in the non-adiabatic collapse of a star dissipating energy in the form of radial heat flow, studying its evolution under different initial conditions. The collapse of a star filled with a homogeneous perfect fluid is compared with that of a star filled with inhomogeneous imperfect fluid ...
Adiabatic flame temperature of sodium combustion and sodium-water reaction
Energy Technology Data Exchange (ETDEWEB)
Okano, Y.; Yamaguchi, A. [Japan Nuclear Cycle Development Institute, Ibaraki (Japan)
2001-07-01
In this paper, background information of sodium fire and sodium-water reaction accidents of LMFBR (liquid metal fast breeder reactor) is mentioned at first. Next, numerical analysis method of GENESYS is described in detail. Next, adiabatic flame temperature and composition of sodium combustion are analyzed, and affect of reactant composition, such oxygen and moisture, is discussed. Finally, adiabatic reaction zone temperature and composition of sodium-water reaction are calculated, and affects of reactant composition, sodium vaporization, and pressure are stated. Chemical equilibrium calculation program for generic chemical system (GENESYS) is developed in this study for the research on adiabatic flame temperature of sodium combustion and adiabatic reaction zone temperature of sodium-water reaction. The maximum flame temperature of the sodium combustion is 1,950 K at the standard atmospheric condition, and is not affected by the existence of moisture. The main reaction product is Na{sub 2}O{sub (l)}, and in combustion in moist air, with NaOH{sub (g)}. The maximum reaction zone temperature of the sodium-water reaction is 1,600 K, and increases with the system pressure. The main products are NaOH{sub (g)}, NaOH{sub (l)} and H2{sub (g)}. Sodium evaporation should be considered in the cases of sodium-rich and high pressure above 10 bar.
Between ethylene and polyenes--the non-adiabatic dynamics of cis-dienes
DEFF Research Database (Denmark)
Kuhlman, Thomas Scheby; Glover, William J; Mori, Toshifumi
2012-01-01
Using Ab Initio Multiple Spawning (AIMS) with a Multi-State Multi-Reference Perturbation theory (MS-MR-CASPT2) treatment of the electronic structure, we have simulated the non-adiabatic excited state dynamics of cyclopentadiene (CPD) and 1,2,3,4-tetramethyl-cyclopentadiene (Me4-CPD) following exc...
Saline Cavern Adiabatic Compressed Air Energy Storage Using Sand as Heat Storage Material
Directory of Open Access Journals (Sweden)
Martin Haemmerle
2017-03-01
Full Text Available Adiabatic compressed air energy storage systems offer large energy storage capacities and power outputs beyond 100MWel. Salt production in Austria produces large caverns which are able to hold pressure up to 100 bar, thus providing low cost pressurized air storage reservoirs for adiabatic compressed air energy storage plants. In this paper the results of a feasibility study is presented, which was financed by the Austrian Research Promotion Agency, with the objective to determine the adiabatic compressed air energy storage potential of Austria’s salt caverns. The study contains designs of realisable plants with capacities between 10 and 50 MWel, applying a high temperature energy storage system currently developed at the Institute for Energy Systems and Thermodynamics in Vienna. It could be shown that the overall storage potential of Austria’s salt caverns exceeds a total of 4GWhel in the year 2030 and, assuming an adequate performance of the heat exchanger, that a 10MWel adiabatic compressed air energy storage plant in Upper Austria is currently feasible using state of the art thermal turbomachinery which is able to provide a compressor discharge temperature of 400 °C.
Adiabatic superconducting cells for ultra-low-power artificial neural networks
Directory of Open Access Journals (Sweden)
Andrey E. Schegolev
2016-10-01
Full Text Available We propose the concept of using superconducting quantum interferometers for the implementation of neural network algorithms with extremely low power dissipation. These adiabatic elements are Josephson cells with sigmoid- and Gaussian-like activation functions. We optimize their parameters for application in three-layer perceptron and radial basis function networks.
Correction for adiabatic effects in lethe calculated instantaneous gas consumption of scuba dives
Schellart, Nico A. M.; Le Péchon, Jean-Claude
2015-01-01
Introduction: In scuba-diving practice, instantaneous gas consumption is generally calculated from the fall in cylinder pressure without considering the effects of water temperature (heat transfer) and adiabatic processes. We aimed to develop a simple but precise method for calculating the
An integrated optic adiabatic TE/TM mode splitter on silicon
de Ridder, R.M.; Sander, A.F.M.; Driessen, A.; Fluitman, J.H.J.
1993-01-01
A compact integrated optic fundamental TE/TM mode splitter, based on the mode-sorting characteristics of an asymmetrical adiabatic Y junction of optical waveguides exhibiting shape birefringence, operating at 1550 nm, has been designed using the discrete sine method (DSM) and the beam propagation
Modelling of an adiabatic trickle-bed reactor with phase change
DEFF Research Database (Denmark)
Ramirez Castelan, Carlos Eduardo; Hidalgo-Vivas, Angelica; Brix, Jacob
2017-01-01
This paper describes a modelling approach of the behavior of trickle-bed reactors used for catalytic hydrotreating of oil fractions. A dynamic plug-flow heterogeneous one-dimensional adiabatic model was used to describe the main reactions present in the hydrotreating process: hydrodesulfurization...
Adiabatic partition effect on natural convection heat transfer inside a square cavity
DEFF Research Database (Denmark)
Mahmoudi Nezhad, Sajjad; Rezaniakolaei, Alireza; yousefi, Tooraj
2017-01-01
A steady state and two-dimensional laminar free convection heat transfer in a partitioned cavity with horizontal adiabatic and isothermal side walls is investigated using both experimental and numerical approaches. The experiments and numerical simulations are carried out using a Mach-Zehnder int...
Alos-Palop, M.; Blaauboer, M.
2011-01-01
We investigate adiabatic quantum pumping through a normal-metal–“insulator”–superconductor (NIS) junction in a monolayer of graphene. The pumped current is generated by periodic modulation of two gate voltages, applied to the insulating and superconducting regions, respectively. In the bilinear
Directory of Open Access Journals (Sweden)
Salem M. Osta-Omar
2016-11-01
Full Text Available The objective of this paper is to develop a mathematical model for thermodynamic analysis of an absorption refrigeration system equipped with an adiabatic absorber using a lithium-bromide/water (LiBr/water pair as the working fluid. The working temperature of the generator, adiabatic absorber, condenser, evaporator, the cooling capacity of the system, and the ratio of the solution mass flow rate at the circulation pump to that at the solution pump are used as input data. The model evaluates the thermodynamic properties of all state points, the heat transfer in each component, the various mass flow rates, and the coefficient of performance (COP of the cycle. The results are used to investigate the effect of key parameters on the overall performance of the system. For instance, increasing the generator temperatures and decreasing the adiabatic absorber temperatures can increase the COP of the cycle. The results of this mathematical model can be used for designing and sizing new LiBr/water absorption refrigeration systems equipped with an adiabatic absorber or for optimizing existing aforementioned systems.
DEFF Research Database (Denmark)
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 general...
Directory of Open Access Journals (Sweden)
Min-Suk Jo
2017-11-01
Full Text Available This paper aimed to evaluate the applicability of adiabatic humidification in the heating, ventilation, and air conditioning (HVAC systems of semiconductor cleanrooms. Accurate temperature and humidity control are essential in semiconductor cleanrooms and high energy consumption steam humidification is commonly used. Therefore, we propose an adiabatic humidification system employing a pressurized water atomizer to reduce the energy consumption. The annual energy consumption of three different HVAC systems were analyzed to evaluate the applicability of adiabatic humidification. The studied cases were as follows: (1 CASE 1: a make-up air unit (MAU with a steam humidifier, a dry cooling coil (DCC, and a fan filter unit (FFU; (2 CASE 2: a MAU with the pressurized water atomizer, a DCC, and a FFU; and (3 CASE 3: a MAU, a DCC, and a FFU, and the pressurized water atomizer installed in the return duct. The energy saving potential of adiabatic humidification over steam humidification has been proved, with savings of 8% and 23% in CASE 2 and CASE 3 compared to CASE 1, respectively. Furthermore, the pressurized water atomizer installed in the return duct exhibits greater energy saving effect than when installed in the MAU.
Non-adiabatic molecular dynamic simulations of opening reaction of molecular junctions
Czech Academy of Sciences Publication Activity Database
Zobač, Vladimír; Lewis, J.P.; Jelínek, Pavel
2016-01-01
Roč. 27, č. 28 (2016), 1-8, č. článku 285202. ISSN 0957-4484 R&D Projects: GA ČR(CZ) GA14-02079S Institutional support: RVO:68378271 Keywords : non-adiabatic molecular dynamics * molecular junctions * molecular switches * DFT Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.440, year: 2016
Gas phase adiabatic electron affinities of cyclopenta-fused polycyclic aromatic hydrocarbons
Todorov, P.D.; Koper, C.; van Lenthe, J.H.; Jenneskens, L.W.
2008-01-01
The B3LYP/DZP++ adiabatic electron affinity (AEA) of nine (non)-alternant polycyclic aromatic hydrocarbons are reported and discussed. Calculations became feasible for molecules this size by projecting out the near-linearly dependent part of the one-electron basis. Non-alternant PAH consisting of an
Reconfigurable CPLAG and Modified PFAL Adiabatic Logic Circuits
Directory of Open Access Journals (Sweden)
Manoj Sharma
2015-01-01
Full Text Available Previously, authors have proposed CPLAG and MCPLAG circuits extracting benefits of CPL family implemented based upon semiadiabatic logic for low power VLSI circuit design along with gating concept. Also authors have communicated RCPLAG circuits adding another dimension of reconfigurability into CPLAG/MCPLAG circuits. Moving ahead, in this paper, authors have implemented/reconfigured RCPLAG universal Nand/And gate and universal Nor/Or gate for extracting behavior of dynamic positive edge triggered DFF. Authors have also implemented Adder/Subtractor circuit using different techniques. Authors have also reported modification in PFAL semiadiabatic circuit family to further reduce the power dissipation. Functionality of these is verified and found to be satisfactory. Further these are examined rigorously with voltage, Cload, temperature, and transistor size variation. Performance of these is examined with these variations with power dissipation, delays, rise, and fall times associated. From the analysis it is found that best operating condition for DFF based upon RCPLAG universal gate can be achieved at supply voltage lower than 3 V which can be used for different transistor size up to 36 μm. Average power dissipation is 0.2 μW at 1 V and 30 μW at 2 V at 100 ff Cload 25°C approximately. Average power dissipated by CPLAG Adder/Subtractot is 58 μW. Modified PFAL circuit reduces average power by 9% approximately.
Approximate treatment of the continuum
Energy Technology Data Exchange (ETDEWEB)
Vertse, T. (Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen (Hungary)); Curutchet, P.; Liotta, R.J. (Research Institute of Physics, S-10405 Stockholm (Sweden))
1990-12-01
Pole expansions of the Green function (Berggren and Mittag-Leffler) are used to calculate single-particle and particle-hole response functions for a square well plus Coulomb potential and the results are compared with the corresponding exact ones. The approximate and exact response functions agree well with each other in the resonant energy region. The Mittag-Leffler expansion is shown to be valid even for the long-range Coulomb potential. The computation time needed for the calculation of the particle-hole response function can be reduced considerably by using the pole expansions.
Convex approximations of quantum channels
Sacchi, Massimiliano F.; Sacchi, Tito
2017-09-01
We address the problem of optimally approximating the action of a desired and unavailable quantum channel Φ having at our disposal a single use of a given set of other channels {Ψi} . The problem is recast to look for the least distinguishable channel from Φ among the convex set ∑ipiΨi , and the corresponding optimal weights {pi} provide the optimal convex mixing of the available channels {Ψi} . For single-qubit channels we study specifically cases where the available convex set corresponds to covariant channels or to Pauli channels, and the desired target map is an arbitrary unitary transformation or a generalized damping channel.
Approximate Solution for Choked Flow in Gas Seal Pads
Fleming, David P.
2004-01-01
Previous analyses of high pressure seals have considered adiabatic flow with friction but neglected effects of seal rotation. Most of this work analyzed a one-dimensional flow field. This works well to calculate stiffness and leakage of full circular seals, either face seals or annular ring seals. However, it cannot provide accurate results for a rectangular seal pad with its strongly two-dimensional flow field and its reliance on hydrodynamic forces to maintain a full fluid film. On the other hand, solutions of Reynolds lubrication equation have been obtained for the two-dimensional flow in a seal pad. But these solutions do not account for choking which occurs at high seal pressure ratios, nor do they consider the pressure loss that occurs in the entrance region of the flow field. The aim of the present work is to build on the Reynolds equation solution by use of an approximate choked flow analysis. This will account for the pressure losses in the flow entrance region, ensure that fluid velocities remain subsonic, and enable fluid inertial effects within the pad film to be accounted for. Results show that, in general, fluid inertia acts to decrease pad film load capacity and leakage, and increase film stiffness.
Toyota, Koudai
2016-01-01
The method of the envelope Hamiltonian [K. Toyota, U. Saalmann, and J. M. Rost, New J. Phys. {\\bf 17}, 073005~(2015)] is applied to further study a detachment dynamics of a model negative ion in one-dimension in high-frequency regime. This method is based on the Floquet approach, but the time-dependency of an envelope function is explicitly kept for arbitrary pulse durations. Therefore, it is capable of describing not only a photo absorption/emission but also a non-adiabatic transition which is induced by the time-varying envelope of the pulse. It was shown that the envelope Hamiltonian accurately retrieves the results obtained by the time-dependent Schr\\"odinger equation, and underlying physics were well understood by the adiabatic approximation based on the envelope Hamiltonian. In this paper, we further explore two more aspects of the detachment dynamics, which were not done in our previous work. First, we find out features of both a {\\it spatial} and {\\it temporal} interference of photo electron wave pack...
Approximating distributions in stochastic learning.
Leen, Todd K; Friel, Robert; Nielsen, David
2012-08-01
On-line machine learning algorithms, many biological spike-timing-dependent plasticity (STDP) learning rules, and stochastic neural dynamics evolve by Markov processes. A complete description of such systems gives the probability densities for the variables. The evolution and equilibrium state of these densities are given by a Chapman-Kolmogorov equation in discrete time, or a master equation in continuous time. These formulations are analytically intractable for most cases of interest, and to make progress a nonlinear Fokker-Planck equation (FPE) is often used in their place. The FPE is limited, and some argue that its application to describe jump processes (such as in these problems) is fundamentally flawed. We develop a well-grounded perturbation expansion that provides approximations for both the density and its moments. The approach is based on the system size expansion in statistical physics (which does not give approximations for the density), but our simple development makes the methods accessible and invites application to diverse problems. We apply the method to calculate the equilibrium distributions for two biologically-observed STDP learning rules and for a simple nonlinear machine-learning problem. In all three examples, we show that our perturbation series provides good agreement with Monte-Carlo simulations in regimes where the FPE breaks down. Copyright © 2012 Elsevier Ltd. All rights reserved.
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
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....
Mass distribution of fission fragments within the Born-Oppenheimer approximation
Energy Technology Data Exchange (ETDEWEB)
Pomorski, K.; Nerlo-Pomorska, B. [M.C.S. University, Department of Theoretical Physics, Lublin (Poland); Ivanyuk, F.A. [Institute for Nuclear Research, Kiev (Ukraine)
2017-03-15
The fission fragments mass-yield of {sup 236} U is obtained by an approximate solution of the eigenvalue problem of the collective Hamiltonian that describes the dynamics of the fission process whose degrees of freedom are: the fission (elongation), the neck and mass-asymmetry modes. The macroscopic-microscopic method is used to evaluate the potential energy surface. The macroscopic energy part is calculated using the liquid drop model and the microscopic corrections are obtained using a Woods-Saxon single-particle levels. The four-dimensional modified Cassini ovals shape parametrization is used to describe the shape of the fissioning nucleus. The mass tensor is taken within a cranking-type approximation. The final fragment mass distribution is obtained by weighting the adiabatic density distribution in the collective space with the neck-dependent fission probability. The neck degree of freedom is found to play a significant role in determining the final fragment mass distribution. (orig.)
Coarse-graining stochastic biochemical networks: adiabaticity and fast simulations
Energy Technology Data Exchange (ETDEWEB)
Nemenman, Ilya [Los Alamos National Laboratory; Sinitsyn, Nikolai [Los Alamos National Laboratory; Hengartner, Nick [Los Alamos National Laboratory
2008-01-01
We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscoplc, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenhelmer approximation in quantum mechanics, follows from the stochastic path Integral representation of the cumulant generating function of reaction events. In applications with a small number of chemIcal reactions, It produces analytical expressions for cumulants of chemical fluxes between the slow variables. This allows for a low-dimensional, Interpretable representation and can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we derive the coarse-grained description for a chain of biochemical reactions, and show that the coarse-grained and the microscopic simulations are in an agreement, but the coarse-gralned simulations are three orders of magnitude faster.
Chapman, Craig T.; Cina, Jeffrey A.
2007-09-01
Time-resolved coherent nonlinear optical experiments on small molecules in low-temperature host crystals are exposing valuable information on quantum mechanical dynamics in condensed media. We make use of generic features of these systems to frame two simple, comprehensive theories that will enable the efficient calculations of their ultrafast spectroscopic signals and support their interpretation in terms of the underlying chemical dynamics. Without resorting to a simple harmonic analysis, both treatments rely on the identification of normal coordinates to unambiguously partition the well-structured guest-host complex into a system and a bath. Both approaches expand the overall wave function as a sum of product states between fully anharmonic vibrational basis states for the system and approximate Gaussian wave packets for the bath degrees of freedom. The theories exploit the fact that ultrafast experiments typically drive large-amplitude motion in a few intermolecular degrees of freedom of higher frequency than the crystal phonons, while these intramolecular vibrations indirectly induce smaller-amplitude—but still perhaps coherent—motion among the lattice modes. The equations of motion for the time-dependent parameters of the bath wave packets are fairly compact in a fixed vibrational basis/Gaussian bath (FVB/GB) approach. An alternative adiabatic vibrational basis/Gaussian bath (AVB/GB) treatment leads to more complicated equations of motion involving adiabatic and nonadiabatic vector potentials. Computational demands for propagation of the parameter equations of motion appear quite manageable for tens or hundreds of atoms and scale similarly with system size in the two cases. Because of the time-scale separation between intermolecular and lattice vibrations, the AVB/GB theory may in some instances require fewer vibrational basis states than the FVB/GB approach. Either framework should enable practical first-principles calculations of nonlinear optical
Approximate cohomology in Banach algebras | Pourabbas ...
African Journals Online (AJOL)
We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...
Monte Carlo modeling of Lead-Cooled Fast Reactor in adiabatic equilibrium state
Energy Technology Data Exchange (ETDEWEB)
Stanisz, Przemysław, E-mail: pstanisz@agh.edu.pl; Oettingen, Mikołaj, E-mail: moettin@agh.edu.pl; Cetnar, Jerzy, E-mail: cetnar@mail.ftj.agh.edu.pl
2016-05-15
Graphical abstract: - Highlights: • We present the Monte Carlo modeling of the LFR in the adiabatic equilibrium state. • We assess the adiabatic equilibrium fuel composition using the MCB code. • We define the self-adjusting process of breeding gain by the control rod operation. • The designed LFR can work in the adiabatic cycle with zero fuel breeding. - Abstract: Nuclear power would appear to be the only energy source able to satisfy the global energy demand while also achieving a significant reduction of greenhouse gas emissions. Moreover, it can provide a stable and secure source of electricity, and plays an important role in many European countries. However, nuclear power generation from its birth has been doomed by the legacy of radioactive nuclear waste. In addition, the looming decrease in the available resources of fissile U235 may influence the future sustainability of nuclear energy. The integrated solution to both problems is not trivial, and postulates the introduction of a closed-fuel cycle strategy based on breeder reactors. The perfect choice of a novel reactor system fulfilling both requirements is the Lead-Cooled Fast Reactor operating in the adiabatic equilibrium state. In such a state, the reactor converts depleted or natural uranium into plutonium while consuming any self-generated minor actinides and transferring only fission products as waste. We present the preliminary design of a Lead-Cooled Fast Reactor operating in the adiabatic equilibrium state with the Monte Carlo Continuous Energy Burnup Code – MCB. As a reference reactor model we apply the core design developed initially under the framework of the European Lead-cooled SYstem (ELSY) project and refined in the follow-up Lead-cooled European Advanced DEmonstration Reactor (LEADER) project. The major objective of the study is to show to what extent the constraints of the adiabatic cycle are maintained and to indicate the phase space for further improvements. The analysis
Energy Technology Data Exchange (ETDEWEB)
Peña-Monferrer, C., E-mail: cmonfer@upv.es [Institute for Energy Engineering, Universitat Politècnica de València, 46022 València (Spain); Passalacqua, A., E-mail: albertop@iastate.edu [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States); Chiva, S., E-mail: schiva@emc.uji.es [Department of Mechanical Engineering and Construction, Universitat Jaume I, 12080 Castelló de la Plana (Spain); Muñoz-Cobo, J.L., E-mail: jlcobos@iqn.upv.es [Institute for Energy Engineering, Universitat Politècnica de València, 46022 València (Spain)
2016-05-15
Highlights: • A population balance equation solved with QMOM approximation is implemented in OpenFOAM. • Available models for interfacial forces and bubble induced turbulence are analyzed. • A vertical pipe flow is simulated for different bubbly flow conditions. • Two-phase flow characteristics in vertical pipes are properly predicted. - Abstract: An Eulerian–Eulerian approach was investigated to model adiabatic bubbly flow with CFD techniques. In the framework of the OpenFOAM{sup ®} software, a two-fluid model solver was modified to include a population balance equation, solved with the quadrature method of moments approximation to predict upward bubbly flow in vertical pipes considering the polydisperse nature of two-phase flow. Some progress have been made recently solving population balance equations in OpenFOAM{sup ®} and this research aims to extend its application to the case of vertical pipes under different conditions of liquid and gas velocities. In order to test the solver for nuclear applications, interfacial forces and bubble induced turbulence models were included to provide to this solver the capability to correctly predict the behavior of the continuous and disperse phases. Two-phase flow experiments with different superficial velocities of gas and liquid are used to validate the model and its implementation. Radial profiles of void fraction, gas and liquid velocities, Sauter mean diameter and turbulence intensity are compared to the computational results. These results are in satisfactory agreement with the experiments, showing the capability of the solver to predict two-phase flow characteristics.
Ultrafast hydrogen migration in acetylene cation driven by non-adiabatic effects.
Madjet, Mohamed El-Amine; Li, Zheng; Vendrell, Oriol
2013-03-07
Non-adiabatic dynamics of the acetylene cation is investigated using mixed quantum-classical dynamics based on trajectory surface hopping. To describe the non-adiabatic effects, two surface hopping methods are used, namely, Tully's fewest switches and Landau-Zener surface hopping. Similarities and differences between the results based on those two methods are discussed. We find that the photoionization of acetylene into the first excited state A(2)Σg(+) drives the molecule from the linear structure to a trans-bent structure. Through a conical intersection the acetylene cation can relax back to either the ground state of acetylene or vinylidene. We conclude that hydrogen migration always takes place after non-radiative electronic relaxation to the ground state of the monocation. Based on the analysis of correlation functions we identify coherent oscillations between acetylene and vinylidene with a period of about 70 fs after the electronic relaxation.
A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems
Tamascelli, Dario; Zanetti, Luca
2014-08-01
We present a quantum algorithm for solving graph isomorphism problems that is based on an adiabatic protocol. We use a collection of continuous time quantum walks, each one generated by an XY Hamiltonian, to visit the configuration space. In this way we avoid a diffusion over all the possible configurations and significantly reduce the dimensionality of the accessible Hilbert space. Within this restricted space, the graph isomorphism problem can be translated into searching for a satisfying assignment to a 2-SAT (satisfiable) formula and mapped onto a 2-local Hamiltonian without resorting to perturbation gadgets or projective techniques. We present an analysis of the time for execution of the algorithm on small graph isomorphism problem instances and discuss the issue of an implementation of the proposed adiabatic scheme on current quantum computing hardware.
Raefat, Saad; Garoum, Mohammed; Laaroussi, Najma; Thiam, Macodou; Amarray, Khaoula
2017-07-01
In this work experimental investigation of apparent thermal diffusivity and adiabatic limit temperature of expanded granular perlite mixes has been made using the flash technic. Perlite granulates were sieved to produce essentially three characteristic grain sizes. The consolidated samples were manufactured by mixing controlled proportions of the plaster and water. The effect of the particle size on the diffusivity was examined. The inverse estimation of the diffusivity and the adiabatic limit temperature at the rear face as well as the heat losses coefficients were performed using several numerical global minimization procedures. The function to be minimized is the quadratic distance between the experimental temperature rise at the rear face and the analytical model derived from the one dimension heat conduction. It is shown that, for all granulometry tested, the estimated parameters lead to a good agreement between the mathematical model and experimental data.
Adiabatic nanofocusing: Spectroscopy, transport and imaging investigation of the nano world
Giugni, Andrea
2014-11-01
Adiabatic compression plays a fundamental role in the realization of localized enhanced electromagnetic field hot spots, it provides the possibility to focus at nanoscale optical excitation. It differs from the well-known lightning rod effect since it is based on the lossless propagation of surface plasmon polaritons (SPPs) up to a nano-sized metal tip where the energy density is largely enhanced. Here we discuss two important applications of adiabatic compression: Raman and hot electron spectroscopy at nanometric resolution. The underlying phenomena are the conversion of SPPs into photons or hot electrons. New scanning probe spectroscopy techniques along with experimental results are discussed. We foresee that these techniques will play a key role in relating the functional and structural properties of matter at the nanoscale.
Optically driven Rabi oscillations and adiabatic passage of single electron spins in diamond.
Golter, D Andrew; Wang, Hailin
2014-03-21
Rabi oscillations and adiabatic passage of single electron spins in a diamond nitrogen vacancy center are demonstrated with two Raman-resonant optical pulses that are detuned from the respective dipole optical transitions. We show that the optical spin control is nuclear-spin selective and can be robust against rapid decoherence, including radiative decay and spectral diffusion, of the underlying optical transitions. A direct comparison between the Rabi oscillation and the adiabatic passage, along with a detailed theoretical analysis, provides significant physical insights into the connections and differences between these coherent spin processes and also elucidates the role of spectral diffusion in these processes. The optically driven coherent spin processes enable the use of nitrogen vacancy excited states to mediate coherent spin-phonon coupling, opening the door to combining optical control of both spin and mechanical degrees of freedom.
DFT Study on Adiabatic and Vertical Ionization Potentials of Graphene Sheets
Directory of Open Access Journals (Sweden)
Igor K. Petrushenko
2015-01-01
Full Text Available Adiabatic and vertical ionization potentials (IPs of finite-size graphene sheets as a function of size were determined by using density functional theory. In the case of graphene a very moderate gap between vertical and adiabatic IPs was observed, whereas for coronene molecule as a model compound these values differ considerably. The ionization process induces large changes in the structure of the studied sheets of graphene; “horizontal” and “vertical” bond lengths have different patterns of alternation. It was also established that the HOMO electron density distribution in the neutral graphene sheet affects its size upon ionization. The evolution of IPs of graphene sheets towards their work functions was discussed.
The adiabatic strictly-correlated-electrons functional: kernel and exact properties.
Lani, Giovanna; Di Marino, Simone; Gerolin, Augusto; van Leeuwen, Robert; Gori-Giorgi, Paola
2016-08-03
We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.
Adiabatic measurements of magneto-caloric effects in pulsed high magnetic fields up to 55 T
Kihara, T.; Kohama, Y.; Hashimoto, Y.; Katsumoto, S.; Tokunaga, M.
2013-07-01
Magneto-caloric effects (MCEs) measurement system in adiabatic condition is proposed to investigate the thermodynamic properties in pulsed magnetic fields up to 55 T. With taking the advantage of the fast field-sweep rate in pulsed field, adiabatic measurements of MCEs were carried out at various temperatures. To obtain the prompt response of the thermometer in the pulsed field, a thin film thermometer is grown directly on the sample surfaces. The validity of the present setup was demonstrated in the wide temperature range through the measurements on Gd at about room temperature and on Gd3Ga5O12 at low temperatures. The both results show reasonable agreement with the data reported earlier. By comparing the MCE data with the specific heat data, we could estimate the entropy as functions of magnetic field and temperature. The results demonstrate the possibility that our approach can trace the change in transition temperature caused by the external field.
Energy Technology Data Exchange (ETDEWEB)
Nebogatov, V. A.; Pastukhov, V. P., E-mail: past@nfi.kiae.ru [National Research Centre Kurchatov Institute (Russian Federation)
2013-06-15
A closed set of reduced equations describing low-frequency nonlinear flute magnetohydrodynamic (MHD) convection and the resulting nondiffusive processes of particle and energy transport in a weakly collisional cylindrical plasma with an anisotropic pressure is derived. The Chew-Goldberger-Low anisotropic magnetohydrodynamics is used as the basic dynamic model, because this model is applicable to describing flute convection in a cylindrical plasma column even in the low-frequency limit. The reduced set of equations was derived using the method of adiabatic separation of fast and slow motions. It is shown that the structure of the adiabatic transformation and the corresponding velocity field are identical to those obtained earlier in the isotropic MHD model. However, the derived heat transfer equations differ drastically from the isotropic pressure model. In particular, they indicate a tendency toward maintaining different radial profiles of the longitudinal and transverse pressures.
Sato, Yukio; Kono, Hirohiko; Koseki, Shiro; Fujimura, Yuichi
2003-07-02
We theoretically investigated the dynamics of structural deformations of CO(2) and its cations in near-infrared intense laser fields (approximately 10(15) W cm(-2)) by using the time-dependent adiabatic state approach. To obtain "field-following" adiabatic potentials for nuclear dynamics, the electronic Hamiltonian including the interaction with the instantaneous laser electric field is diagonalized by the multiconfiguration self-consistent-field molecular orbital method. In the CO(2) and CO(2+) stages, ionization occurs before the field intensity becomes high enough to deform the molecule. In the CO(2)(2+) stage, simultaneous symmetric two-bond stretching occurs as well as one-bond stretching. Two-bond stretching is induced by an intense field in the lowest time-dependent adiabatic state |1> of CO(2)(2+), and this two-bond stretching is followed by the occurrence of a large-amplitude bending motion mainly in the second-lowest adiabatic state |2> nonadiabatically created at large internuclear distances by the field from |1>. It is concluded that the experimentally observed stretched and bent structure of CO(2)(3+) just before Coulomb explosions originates from the structural deformation of CO(2)(2+). We also show in this report that the concept of "optical-cycle-averaged potential" is useful for designing schemes to control molecular (reaction) dynamics, such as dissociation dynamics of CO(2), in intense fields. The present approach is simple but has wide applicability for analysis and prediction of electronic and nuclear dynamics of polyatomic molecules in intense laser fields.
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
Lloyd, Seth; Terhal, Barbara
2016-01-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a mode...
Spherical collapse of a unified dark fluid with constant adiabatic sound speed
Xu, Lixin
2013-03-01
In this paper, we test the spherical collapse of a unified dark fluid (UDF) which has constant adiabatic sound speed. By choosing the different values of model parameters B s and α, we show the non-linear collapse for UDF and baryons which are considered for their formation of the large scale structure of our Universe. The analyzed results show that larger values of α and B s make the structure formation faster and earlier.
Spherical collapse of a unified dark fluid with constant adiabatic sound speed
Energy Technology Data Exchange (ETDEWEB)
Xu, Lixin [Dalian University of Technology, Institute of Theoretical Physics, School of Physics and Optoelectronic Technology, Dalian (China); Dalian University of Technology, College of Advanced Science and Technology, Dalian (China)
2013-03-15
In this paper, we test the spherical collapse of a unified dark fluid (UDF) which has constant adiabatic sound speed. By choosing the different values of model parameters B{sub s} and {alpha}, we show the non-linear collapse for UDF and baryons which are considered for their formation of the large scale structure of our Universe. The analyzed results show that larger values of {alpha} and B{sub s} make the structure formation faster and earlier. (orig.)
High-Energy, Multi-Octave-Spanning Mid-IR Sources via Adiabatic Difference Frequency Generation
2016-10-17
ABSTRACT The creation of energetic , arbitrarily shapeable, multi-octave-spanning, coherent sources of short-wave, mid-wave, and long-wave mid-IR...plan. We have evaluated a brand-new concept in nonlinear optics, adiabatic difference frequency generation (ADFG) for the efficient transfer of...generation: limited bandwidth and limited conversion efficiency . 15. SUBJECT TERMS Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18 Page 1 of
Thermal explosion hazards on 18650 lithium ion batteries with a VSP2 adiabatic calorimeter
Energy Technology Data Exchange (ETDEWEB)
Jhu, Can-Yong [Doctoral Program, Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology (NYUST), 123, University Rd., Sec. 3, Douliou, Yunlin 64002, Taiwan, ROC (China); Wang, Yih-Wen, E-mail: g9410825@yuntech.edu.tw [Department of Occupational Safety and Health, Jen-Teh Junior College of Medicine, Nursing and Management, 79-9, Sha-Luen-Hu, Xi-Zhou-Li, Houlong, Miaoli 35664, Taiwan, ROC (China); Shu, Chi-Min [Doctoral Program, Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology (NYUST), 123, University Rd., Sec. 3, Douliou, Yunlin 64002, Taiwan, ROC (China); Chang, Jian-Chuang; Wu, Hung-Chun [Material and Chemical Research Laboratories, Industrial Technology Research Institute (ITRI), Rm. 222, Bldg. 77, 2F, 195, Sec. 4, Chung Hsing Rd., Chutung, Hsinchu 31040, Taiwan, ROC (China)
2011-08-15
Thermal abuse behaviors relating to adiabatic runaway reactions in commercial 18650 lithium ion batteries (LiCoO{sub 2}) are being studied in an adiabatic calorimeter, vent sizing package 2 (VSP2). We select four worldwide battery producers, Sony, Sanyo, Samsung and LG, and tested their Li-ion batteries, which have LiCoO{sub 2} cathodes, to determine their thermal instabilities and adiabatic runaway features. The charged (4.2 V) and uncharged (3.7 V) 18650 Li-ion batteries are tested using a VSP2 with a customized stainless steel test can to evaluate their thermal hazard characteristics, such as the initial exothermic temperature (T{sub 0}), the self-heating rate (dT/dt), the pressure rise rate (dP/dt), the pressure-temperature profiles and the maximum temperature (T{sub max}) and pressure (P{sub max}). The T{sub max} and P{sub max} of the charged Li-ion battery during the runaway reaction reach 903.0 {sup o}C and 1565.9 psig (pound-force per square inch gauge), respectively. This result leads to a thermal explosion, and the heat of reaction is 26.2 kJ. The thermokinetic parameters of the reaction of LiCoO{sub 2} batteries are also determined using the Arrhenius model. The thermal reaction mechanism of the Li-ion battery (pack) proved to be an important safety concern for energy storage. Additionally, use of the VSP2 to classify the self-reactive ratings of the various Li-ion batteries demonstrates a new application of the adiabatic calorimetric methodology.
A scalable control system for a superconducting adiabatic quantum optimization processor
Johnson, M. W.; Bunyk, P.; Maibaum, F.; Tolkacheva, E.; Berkley, A. J.; Chapple, E. M.; Harris, R.; Johansson, J.; Lanting, T.; Perminov, I.; Ladizinsky, E.; Oh, T.; Rose, G.
2010-06-01
We have designed, fabricated and operated a scalable system for applying independently programmable time-independent, and limited time-dependent flux biases to control superconducting devices in an integrated circuit. Here we report on the operation of a system designed to supply 64 flux biases to devices in a circuit designed to be a unit cell for a superconducting adiabatic quantum optimization system. The system requires six digital address lines, two power lines, and a handful of global analog lines.
Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion
Palamaru, Mirel; Lalanne, Philippe
2001-01-01
International audience; An accurate model for the out-of-plane radiation losses occurring when a guided wave propagating in a conventional waveguide impinges on a photonic crystal waveguide is presented. The model makes clear that the losses originate from insertion losses resulting from a mode mismatch. A generic taper structure realizing an adiabatic modal conversion is proposed and validated through numerical computations for cavities with large Q's and large peak transmission.
Adiabatic radio-frequency potentials for the coherent manipulation of matter waves
DEFF Research Database (Denmark)
Lesanovsky, Igor; Schumm, Thorsten; Hofferberth, S.
2006-01-01
Adiabatic dressed state potentials are created when magnetic substates of trapped atoms are coupled by a radio-frequency field. We discuss their theoretical foundations and point out fundamental advantages over potentials purely based on static fields. The enhanced flexibility enables one...... to implement numerous configurations, including double wells, Mach-Zehnder, and Sagnac interferometers which even allows for internal state-dependent atom manipulation. These can be realized using simple and highly integrated wire geometries on atom chips....
General laser interaction theory in atom-diatom systems for both adiabatic and nonadiabatic cases.
Li, Xuan; Brue, Daniel A; Parker, Gregory A; Chang, Sin-Tarng
2006-04-27
This paper develops the general theory for laser fields interacting with bimolecular systems. In this study, we choose to use the multipolar gauge on the basis of gauge invariance. We consider both the adiabatic and nonadiabatic cases and find they produce similar interaction pictures. As an application of this theory, we present the study of rovibrational energy transfer in Ar + CO collisions in the presence of an intense laser field.
Deterministic single-atom excitation via adiabatic passage and Rydberg blockade
Beterov, I. I.; Tretyakov, D. B.; Entin, V. M.; Yakshina, E. A.; Ryabtsev, I. I.; MacCormick, C.; Bergamini, S.
2011-01-01
We propose to use adiabatic rapid passage with a chirped laser pulse in the strong dipole blockade regime to deterministically excite only one Rydberg atom from randomly loaded optical dipole traps or optical lattices. The chirped laser excitation is shown to be insensitive to the random number \\textit{N} of the atoms in the traps. Our method overcomes the problem of the $\\sqrt {N} $ dependence of the collective Rabi frequency, which was the main obstacle for deterministic single-atom excitat...
Oscillating potential well in the complex plane and the adiabatic theorem
Longhi, Stefano
2017-10-01
A quantum particle in a slowly changing potential well V (x ,t ) =V ( x -x0(ɛ t ) ) , periodically shaken in time at a slow frequency ɛ , provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than ˜1 /ɛ . Specifically, we consider a double-well potential V (x ) sustaining two bound states spaced in frequency by ω0 and periodically shaken in a complex plane. Two different spatial displacements x0(t ) are assumed: the real spatial displacement x0(ɛ t ) =A sin(ɛ t ) , corresponding to ordinary Hermitian shaking, and the complex one x0(ɛ t ) =A -A exp(-i ɛ t ) , corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency ɛ is close to an odd resonance of ω0. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.
Ultra Low Power Adiabatic Logic Using Diode Connected DC Biased PFAL Logic
Directory of Open Access Journals (Sweden)
Akash Agrawal
2017-01-01
Full Text Available With the continuous scaling down of technology in the field of integrated circuit design, low power dissipation has become one of the primary focuses of the research. With the increasing demand for low power devices, adiabatic logic gates prove to be an effective solution. This paper briefs on different adiabatic logic families such as ECRL (Efficient Charge Recovery Logic, 2N-2N2P and PFAL (Positive Feedback Adiabatic Logic, and presents a new proposed circuit based on the PFAL logic circuit. The aim of this paper is to simulate various logic gates using PFAL logic circuits and with the proposed logic circuit, and hence to compare the effectiveness in terms of average power dissipation and delay at different frequencies. This paper further presents implementation of C17 and C432 benchmark circuits, using the proposed logic circuit and the conventional PFAL logic circuit to compare effectiveness of the proposed logic circuit in terms of average power dissipation at different frequencies. All simulations are carried out by using HSPICE Simulator at 65 nm technology at different frequency ranges. Finally, average power dissipation characteristics are plotted with the help of graphs, and comparisons are made between PFAL logic family and new proposed PFAL logic family.
Energy Technology Data Exchange (ETDEWEB)
Coïsson, M. [INRIM, strada delle Cacce 91, 10135 Torino (Italy); Barrera, G. [INRIM, strada delle Cacce 91, 10135 Torino (Italy); University of Torino, Chemistry Department, via P. Giuria 7, 10125 Torino (Italy); Celegato, F.; Martino, L.; Vinai, F. [INRIM, strada delle Cacce 91, 10135 Torino (Italy); Martino, P. [Politronica srl, via Livorno 60, 10144 Torino (Italy); Ferraro, G. [Center for Space Human Robotics, Istituto Italiano di Tecnologia - IIT, corso Trento 21, 10129 Torino (Italy); Tiberto, P. [INRIM, strada delle Cacce 91, 10135 Torino (Italy)
2016-10-01
An experimental setup for magnetic hyperthermia operating in non-adiabatic conditions is described. A thermodynamic model that takes into account the heat exchanged by the sample with the surrounding environment is developed. A suitable calibration procedure is proposed that allows the experimental validation of the model. Specific absorption rate can then be accurately determined just from the measurement of the sample temperature at the equilibrium steady state. The setup and the measurement procedure represent a simplification with respect to other systems requiring calorimeters or crucial corrections for heat flow. Two families of magnetic nanoparticles, one superparamagnetic and one characterised by larger sizes and static hysteresis, have been characterised as a function of field intensity, and specific absorption rate and intrinsic loss power have been obtained. - Highlights: • Development and thermodynamic modelling of a hyperthermia setup operating in non-adiabatic conditions. • Calibration of the experimental setup and validation of the model. • Accurate measurement of specific absorption rate and intrinsic loss power in non-adiabatic conditions.
A scalable readout system for a superconducting adiabatic quantum optimization system
Berkley, A. J.; Johnson, M. W.; Bunyk, P.; Harris, R.; Johansson, J.; Lanting, T.; Ladizinsky, E.; Tolkacheva, E.; Amin, M. H. S.; Rose, G.
2010-10-01
We have designed, fabricated and tested an XY-addressable readout system that is specifically tailored for the reading of superconducting flux qubits in an integrated circuit that could enable adiabatic quantum optimization. In such a system, the flux qubits only need to be read at the end of an adiabatic evolution when quantum mechanical tunneling has been suppressed, thus simplifying many aspects of the readout process. The readout architecture for an N-qubit adiabatic quantum optimization system comprises N hysteretic dc SQUIDs and N rf SQUID latches controlled by 2\\sqrt {N}+2 bias lines. The latching elements are coupled to the qubits and the dc SQUIDs are then coupled to the latching elements. This readout scheme provides two key advantages: first, the latching elements provide exceptional flux sensitivity that significantly exceeds what may be achieved by directly coupling the flux qubits to the dc SQUIDs using a practical mutual inductance. Second, the states of the latching elements are robust against the influence of ac currents generated by the switching of the hysteretic dc SQUIDs, thus allowing one to interrogate the latching elements repeatedly so as to mitigate the effects of stochastic switching of the dc SQUIDs. We demonstrate that it is possible to achieve single-qubit read error rates of < 10 - 6 with this readout scheme. We have characterized the system level performance of a 128-qubit readout system and have measured a readout error probability of 8 × 10 - 5 in the presence of optimal latching element bias conditions.
Impact of Turbocharger Non-Adiabatic Operation on Engine Volumetric Efficiency and Turbo Lag
Directory of Open Access Journals (Sweden)
S. Shaaban
2012-01-01
Full Text Available Turbocharger performance significantly affects the thermodynamic properties of the working fluid at engine boundaries and hence engine performance. Heat transfer takes place under all circumstances during turbocharger operation. This heat transfer affects the power produced by the turbine, the power consumed by the compressor, and the engine volumetric efficiency. Therefore, non-adiabatic turbocharger performance can restrict the engine charging process and hence engine performance. The present research work investigates the effect of turbocharger non-adiabatic performance on the engine charging process and turbo lag. Two passenger car turbochargers are experimentally and theoretically investigated. The effect of turbine casing insulation is also explored. The present investigation shows that thermal energy is transferred to the compressor under all circumstances. At high rotational speeds, thermal energy is first transferred to the compressor and latter from the compressor to the ambient. Therefore, the compressor appears to be “adiabatic” at high rotational speeds despite the complex heat transfer processes inside the compressor. A tangible effect of turbocharger non-adiabatic performance on the charging process is identified at turbocharger part load operation. The turbine power is the most affected operating parameter, followed by the engine volumetric efficiency. Insulating the turbine is recommended for reducing the turbine size and the turbo lag.
(Non-adiabatic) string creation on nice slices in Schwarzschild black holes
Puhm, Andrea; Rojas, Francisco; Ugajin, Tomonori
2017-04-01
Nice slices have played a pivotal role in the discussion of the black hole information paradox as they avoid regions of strong spacetime curvature and yet smoothly cut through the infalling matter and the outgoing Hawking radiation, thus, justifying the use of low energy field theory. To avoid information loss it has been argued recently, however, that local effective field theory has to break down at the horizon. To assess the extent of this breakdown in a UV complete framework we study string-theoretic effects on nice slices in Schwarzschild black holes. Our purpose is two-fold. First, we use nice slices to address various open questions and caveats of [1] where it was argued that boost-enhanced non-adiabatic string-theoretic effects at the horizon could provide a dynamical mechanism for the firewall. Second, we identify two non-adiabatic effects on nice slices in Schwarzschild black holes: pair production of open strings near the horizon enhanced by the presence of the infinite tower of highly excited string states and a late-time non-adiabatic effect intrinsic to nice slices.
Adiabatic reduction of a model of stochastic gene expression with jump Markov process.
Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C
2014-04-01
This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.
Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions.
Menzeleev, Artur R; Bell, Franziska; Miller, Thomas F
2014-02-14
We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically non-adiabatic dynamics of the system. KC-RPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, time-reversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of position-representation RPMD by enabling the description of non-adiabatic transitions between states associated with general, many-electron wavefunctions and by accurately describing deep-tunneling processes across asymmetric barriers. We demonstrate that KC-RPMD yields excellent numerical results for a range of model systems, including a simple avoided-crossing reaction and condensed-phase electron-transfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force.
Extension of the adiabatic regularization method to spin-1/2 fields
Landete, Aitor
2015-04-01
The adiabatic regularization method was designed by L. Parker [1] for scalar fields in order to to subtract the potentially UV divergences that appear in the particle number operator. After that the method was generalized [2] to remove, in a consistent way, the UV divergences that appear in the expectation value of the stress-energy tensor in homogeneous cosmological backgrounds. We are going to provide here the extension of the adiabatic regularization method to spin-1/2 fields first given in [3]. In order to achieve this extension we will show the generalization of the adiabatic expansion for fermionic fields which differs significantly from the WKB-type expansion that works for the scalar modes. We will also show the consistency of the extended method computing well-known results, computed by other renormalization methods for a Dirac field in a FLRW spacetime, like the conformal and axial anomalies. Finally we will compute the expectation value of the stress-energy tensor for a Dirac field in a de Sitter spacetime.
Low-Power Adiabatic Computing with Improved Quasistatic Energy Recovery Logic
Directory of Open Access Journals (Sweden)
Shipra Upadhyay
2013-01-01
Full Text Available Efficiency of adiabatic logic circuits is determined by the adiabatic and non-adiabatic losses incurred by them during the charging and recovery operations. The lesser will be these losses circuit will be more energy efficient. In this paper, a new approach is presented for minimizing power consumption in quasistatic energy recovery logic (QSERL circuit which involves optimization by removing the nonadiabatic losses completely by replacing the diodes with MOSFETs whose gates are controlled by power clocks. Proposed circuit inherits the advantages of quasistatic ERL (QSERL family but is with improved power efficiency and driving ability. In order to demonstrate workability of the newly developed circuit, a 4 × 4 bit array multiplier circuit has been designed. A mathematical expression to calculate energy dissipation in proposed inverter is developed. Performance of the proposed logic (improved quasistatic energy recovery logic (IQSERL is analyzed and compared with CMOS and reported QSERL in their representative inverters and multipliers in VIRTUOSO SPECTRE simulator of Cadence in 0.18 μm UMC technology. In our proposed (IQSERL inverter the power efficiency has been improved to almost 20% up to 50 MHz and 300 fF external load capacitance in comparison to CMOS and QSERL circuits.
Chandrashekar, R.; Segar, J
2012-01-01
A unified framework to describe the adiabatic class of ensembles in the generalized statistical mechanics based on Schwammle-Tsallis two parameter (q, q') entropy is proposed. The generalized form of the equipartition theorem, virial theorem and the adiabatic theorem are derived. Each member of the class of ensembles is illustrated using the classical nonrelativistic ideal gas and we observe that the heat functions could be written in terms of the Lambert's W-function in the large N limit. In...
National Oceanic and Atmospheric Administration, Department of Commerce — WBAN-31 is a form on which the Weather Bureau, Army and Navy recorded weather observations in the upper air as observed by rawinsonde and radiosonde. The collection...
On martingale approximation of adapted processes
Queffélec, Hervé; Volný, Dalibor
2011-01-01
We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration, but no approximation with respect to a larger filtration with respect to wich it is adapted and regular. There exists a stationary process adapted, regular, and having a martingale approximation with respect to a given filtration but not (regular and having...
Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states.
Humeniuk, Alexander; Mitrić, Roland
2016-06-21
A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected by...... on the sparse approximation process. Our experimental results show the locally constant form of SPARROW performs competitively....
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
Abstract. In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable dis- crete metric space. Moreover, we use the techniques of Ozawa's to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Approximate Nearest Neighbor Queries among Parallel Segments
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias
2010-01-01
We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...
Exploiting domain knowledge for approximate diagnosis
Teije, A. ten; Harmelen, van F.A.H.
1997-01-01
The AI literature contains many definitions of diagnostic reasoning most of which are defined in terms of the logical entailment relation. We use existing work on approximate entailment to define notions of approximation in diagnosis. We show how such a notion of approximate diagnosis can be
Truth Approximation, Social Epistemology, and Opinion Dynamics
Douven, Igor; Kelp, Christoph
This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the
Axiomatic Characterizations of IVF Rough Approximation Operators
Yu, Guangji
2014-01-01
This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa's to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Mátyus, Edit; Szidarovszky, Tamás; Császár, Attila G
2014-10-21
Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H3(+), for which a global adiabatic potential energy surface accurate to better than 0.1 cm(-1) exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D(3h) point-group symmetry is employed. The vibrational mass of the proton in H3(+) is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m(opt,p)((v))=m(nuc,p)+0.31224m(e). This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.
Energy Technology Data Exchange (ETDEWEB)
Mátyus, Edit, E-mail: matyus@chem.elte.hu [Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518 Budapest 112 (Hungary); Szidarovszky, Tamás [MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest (Hungary); Császár, Attila G., E-mail: csaszar@chem.elte.hu [Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518, Budapest 112, Hungary and MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest (Hungary)
2014-10-21
Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H{sub 3}{sup +}, for which a global adiabatic potential energy surface accurate to better than 0.1 cm{sup −1} exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D{sub 3h} point-group symmetry is employed. The vibrational mass of the proton in H{sub 3}{sup +} is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m{sub opt,p}{sup (v)}=m{sub nuc,p}+0.31224 m{sub e}. This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.
Feller, David
2017-07-01
Benchmark adiabatic ionization potentials were obtained with the Feller-Peterson-Dixon (FPD) theoretical method for a collection of 48 atoms and small molecules. In previous studies, the FPD method demonstrated an ability to predict atomization energies (heats of formation) and electron affinities well within a 95% confidence level of ±1 kcal/mol. Large 1-particle expansions involving correlation consistent basis sets (up to aug-cc-pV8Z in many cases and aug-cc-pV9Z for some atoms) were chosen for the valence CCSD(T) starting point calculations. Despite their cost, these large basis sets were chosen in order to help minimize the residual basis set truncation error and reduce dependence on approximate basis set limit extrapolation formulas. The complementary n-particle expansion included higher order CCSDT, CCSDTQ, or CCSDTQ5 (coupled cluster theory with iterative triple, quadruple, and quintuple excitations) corrections. For all of the chemical systems examined here, it was also possible to either perform explicit full configuration interaction (CI) calculations or to otherwise estimate the full CI limit. Additionally, corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, non-adiabatic effects, and other minor factors were considered. The root mean square deviation with respect to experiment for the ionization potentials was 0.21 kcal/mol (0.009 eV). The corresponding level of agreement for molecular enthalpies of formation was 0.37 kcal/mol and for electron affinities 0.20 kcal/mol. Similar good agreement with experiment was found in the case of molecular structures and harmonic frequencies. Overall, the combination of energetic, structural, and vibrational data (655 comparisons) reflects the consistent ability of the FPD method to achieve close agreement with experiment for small molecules using the level of theory applied in this study.
Richards, Paul L.
2005-01-01
Mechanical heat switches are used in conjunction with sorption refrigerators, adiabatic demagnetization refrigerators and for other cryogenic tasks including the pre-cooling cryogenic systems. They use a mechanical actuator which closes Au plated Cu jaws on an Au plated Cu bar. The thermal conductance in the closed position is essentially independent of the area of the jaws and proportional to the force applied. It varies linearly with T. It is approximately 10mW/K for 200 N at 1.5K. In some applications, the heat switch can be driven from outside the cryostat by a rotating rod and a screw. Such heat switches are available commercially from several sources. In other applications, including systems for space, it is desirable to drive the switch using a cold linear motor, or solenoid. Superconducting windings are used at temperatures s 4.2K to minimize power dissipation, but are not appropriate for pre-cooling a system at higher temperatures. This project was intended to improve the design of solenoid activated mechanical heat switches and to provide such switches as required to support the development of Advanced Adiabatic Demagnetization Refrigerators for Continuous Cooling from 10 K to 50 mK at GSFC. By the time funding began in 5/1/01, the immediate need for mechanical heat switches at GSFC had subsided but, at the same time, the opportunity had arisen to improve the design of mechanical heat switching by incorporating a "latching solenoid". In this device, the solenoid current is required only for changing the state of the switch and not during the whole time that the switch is closed.
Generalized adiabatic polaron hopping: Meyer-Neldel compensation and Poole-Frenkel behavior.
Emin, David
2008-04-25
The commonly employed adiabatic treatment of polaron hopping is extended to treat the continuous alteration of a carrier wave function with the atoms' movements and a carrier's long-range interaction with a polar surrounding. These features, respectively, introduce carrier-induced softening of the atoms' vibrations and a hopping activation energy that depends on hopping distance. The Meyer-Neldel compensation effect results from carrier-induced softening of vibrations. Poole-Frenkel behavior emerges for electric-field driven polaron hopping in ionic and polar media.
Adiabatically switched-on electrical bias and the Landauer-Buttiker formula
DEFF Research Database (Denmark)
Cornean, Horia; Duclos, P.; Nenciu, G.
2008-01-01
Consider a three dimensional system which looks like a cross connected pipe system, i.e., a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we adiabatically turn on an electrical bias between leads....... The main technical tool is the use of a finite volume regularization, which allows us to define the current coming out of a lead as the time derivative of its charge. We finally prove that in virtually all physically interesting situations, the conductivity tensor is given by a Landauer-Büttiker type...
Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Büttiker formula
DEFF Research Database (Denmark)
Cornean, Horia; Duclos, Pierre; Nenciu, Gheorghe
Consider a three dimensional system which looks like a cross-connected pipe system, i.e. a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we adiabatically turn on an electrical bias between leads....... The main technical tool is the use of a finite volume regularization, which allows us to define the current coming out of a lead as the time derivative of its charge. We finally prove that in virtually all physically interesting situations, the conductivity tensor is given by a Landauer-Büttiker type...
Chen, Xi; Wang, Hong-Wei; Ban, Yue; Tseng, Shuo-Yen
2014-10-06
Conventional narrowband spectrum polarization devices are short but not robust, based on quasi-phase matching (QPM) technique, in periodically poled lithium niobate (PPLN) crystal. In this paper, we propose short-length and robust polarization rotators by using shortcuts to adiabaticity. Beyond the QPM condition, the electric field and period of PPLN crystal are designed in terms of invariant dynamics, and further optimized with respect to input wavelength/refractive index variations. In addition, the stability of conversion efficiency on the electric field and period of PPLN crystal is also discussed. As a consequence, the optimal shortcuts are fast as well as robust, which provide broadband spectrum polarization devices with short length.
Enqvist, Kari; Kasuya, Shinta; Mazumdar, Anupam
2003-03-07
We propose that the inflaton is coupled to ordinary matter only gravitationally and that it decays into a completely hidden sector. In this scenario both baryonic and dark matter originate from the decay of a flat direction of the minimal supersymmetric standard model, which is shown to generate the desired adiabatic perturbation spectrum via the curvaton mechanism. The requirement that the energy density along the flat direction dominates over the inflaton decay products fixes the flat direction almost uniquely. The present residual energy density in the hidden sector is typically shown to be small.
Adiabatic wall temperature and heat transfer coefficient influenced by separated supersonic flow
Directory of Open Access Journals (Sweden)
Leontiev Alexander
2017-01-01
Full Text Available Investigations of supersonic air flow around plane surface behind a rib perpendicular to the flow direction are performed. Research was carried out for free stream Mach number 2.25 and turbulent flow regime - Rex>2·107. Rib height was varied in range from 2 to 8 mm while boundary layer thickness at the nozzle exit section was about 6 mm. As a result adiabatic wall temperature and heat transfer coefficient are obtained for flow around plane surface behind a rib incontrast with the flow around plane surface without any disturbances.
Döppner, T; Thomas, C A; Divol, L; Dewald, E L; Celliers, P M; Bradley, D K; Callahan, D A; Dixit, S N; Harte, J A; Glenn, S M; Haan, S W; Izumi, N; Kyrala, G A; LaCaille, G; Kline, J K; Kruer, W L; Ma, T; MacKinnon, A J; McNaney, J M; Meezan, N B; Robey, H F; Salmonson, J D; Suter, L J; Zimmerman, G B; Edwards, M J; MacGowan, B J; Kilkenny, J D; Lindl, J D; Van Wonterghem, B M; Atherton, L J; Moses, E I; Glenzer, S H; Landen, O L
2012-03-30
We have imaged hard x-ray (>100 keV) bremsstrahlung emission from energetic electrons slowing in a plastic ablator shell during indirectly driven implosions at the National Ignition Facility. We measure 570 J in electrons with E>100 keV impinging on the fusion capsule under ignition drive conditions. This translates into an acceptable increase in the adiabat α, defined as the ratio of total deuterium-tritium fuel pressure to Fermi pressure, of 3.5%. The hard x-ray observables are consistent with detailed radiative-hydrodynamics simulations, including the sourcing and transport of these high energy electrons.
DEFF Research Database (Denmark)
von Moos, Lars; Bahl, Christian R.H.; Nielsen, Kaspar Kirstein
2014-01-01
description of the phase transition at varying magnetic fields and temperatures. Using detailed experimental property data, a Preisach type model is used to describe the thermal hysteresis effects and simulate the material under realistic working conditions. We find that the adiabatic temperature change......We quantify the effect of hysteresis on the performance of the magnetocaloric first order material Gd5Si2Ge2 undergoing an ideal active magnetic regenerator (AMR) cycle. The material is carefully characterized through magnetometry (VSM) and calorimetry (DSC) in order to enable an accurate model...
Deterministic single-atom excitation via adiabatic passage and Rydberg blockade
Beterov, I. I.; Tretyakov, D. B.; Entin, V. M.; Yakshina, E. A.; Ryabtsev, I. I.; MacCormick, C.; Bergamini, S.
2011-08-01
We propose to use adiabatic rapid passage with a chirped laser pulse in the strong dipole blockade regime to deterministically excite only one Rydberg atom from randomly loaded optical dipole traps or optical lattices. The chirped laser excitation is shown to be insensitive to the random number N of the atoms in the traps. Our method overcomes the problem of the N dependence of the collective Rabi frequency, which was the main obstacle for deterministic single-atom excitation in the ensembles with unknown N, and can be applied for single-atom loading of dipole traps and optical lattices.
Adiabatic tapered optical fiber fabrication for exciting whispering gallery modes in microcavities
Chenari, Z.; Latifi, H.; Hashemi, R. S.; Doroudmand, F.
2014-05-01
This article demonstrates an investigation and analysis of a tapered fiber fabrication using an etchant droplet method. To achieve precise control on process, a two-step etching method is proposed (using 48% concentration of HF acid and Buffered HF) which results in low-loss adiabatic tapered fiber. A spectrum analysis monitoring in addition to a microscopy system was used to verify the etching progress. Tapers with losses less than 0.4 dB in air and 4.5 dB in water are demonstrated. A biconical fiber taper fabricated using this method was used to excite the WGMs on a microsphere surface in aquatic environment.
Adiabatic cooling of a tunable Bose-Fermi mixture in an optical lattice
DEFF Research Database (Denmark)
Sørensen, Ole Søe; Nygaard, Nicolai; Blakie, P.B.
2009-01-01
We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. Thus by adjusting the magnetic field the portion of fermionic and bosonic particles in the system can be continuously...... varied. We analyze the statistical mechanics of this system and consider the interplay of the lattice physics with the atom-molecule conversion. We study the entropic behavior of the system and characterize the temperature changes that occur during adiabatic ramps across the Feshbach resonance. We show...... that an appropriate choice of filling fraction can be used to reduce the system temperature during such ramps....
Implementation of one-qubit holonomic rotation gate by adiabatic passage
Directory of Open Access Journals (Sweden)
R Nader-Ali
2010-06-01
Full Text Available We propose a robust scheme, using tripod stimulated Raman adiabatic passage, to generate one-qubit rotation gate. In this scheme, a four-level atom interacts with three resonant laser pulses and time evolution of the corresponding coherent system is designed such that the rotation gate is implemented at the end of process. Rotation angle in this gate is holonomic and has a geometrical basis in the parameter space. We also explore the effect of spontaneous emission on the population transfer with numerical solution of Schrödinger and Liouville equations.
Adiabatic tapered optical fiber Fabry-Perot structure as a refractive index sensor
Ranjbar-Naeini, O. R.; Chenari, Z.; Zarafshani, P.; Jafari, F.; Latifi, H.
2017-04-01
In this article, an Adiabatic Tapered Optical Fiber - Fabry Perot (ATOF-FP) Sensor is introduced as a simple refractive index sensor. This FP Cavity relies upon reflection from two cleave ends of ATOF sensor's arms. Its spectrum was investigated with Distributed Feedback (DFB) tunable laser and photo detector. With analyzing the change in Optical Transmission Power (OTP) versus refractive index changes, the sensitivity of ATOF was -66.21 dB/RIU. In addition, the visibility of FP was studied. Its RI sensitivity was -0.975 1/RIU. The sensor resolution was 2.3 × 10-5 RIU with consideration of minimum detectable signal of acquisition system.
Exact analysis of gate noise effects on non-adiabatic transformations of spin-orbit qubits
Ulčakar, Lara; Ramšak, Anton
2017-09-01
We considered various types of potential noise in gates controlling non-adiabatic holonomic transformations of spin-qubits in one and two-dimensional systems with the Rashba interaction. It is shown how exact results can be derived for deviations of spin rotation angle and fidelity of the qubit transformation after a completed transformation. Errors in initial values of gate potentials and time-dependent drivings are considered and exact results for white gate noise are derived and analysed in detail. It is demonstrated how the drivings can be tuned to optimise the final fidelity of the transformation and to minimise the variances of qubit transformations.
Deterministic single-atom excitation via adiabatic passage and Rydberg blockade
Energy Technology Data Exchange (ETDEWEB)
Beterov, I. I.; Tretyakov, D. B.; Entin, V. M.; Yakshina, E. A.; Ryabtsev, I. I.; MacCormick, C.; Bergamini, S. [A. V. Rzhanov Institute of Semiconductor Physics SB RAS, Prospekt Lavrentieva 13, 630090 Novosibirsk (Russian Federation); Open University, Walton Hall, Milton Keynes MK6 7AA (United Kingdom)
2011-08-15
We propose to use adiabatic rapid passage with a chirped laser pulse in the strong dipole blockade regime to deterministically excite only one Rydberg atom from randomly loaded optical dipole traps or optical lattices. The chirped laser excitation is shown to be insensitive to the random number N of the atoms in the traps. Our method overcomes the problem of the {radical}(N) dependence of the collective Rabi frequency, which was the main obstacle for deterministic single-atom excitation in the ensembles with unknown N, and can be applied for single-atom loading of dipole traps and optical lattices.
Directory of Open Access Journals (Sweden)
Choong Leng Ng
2013-10-01
Full Text Available We demonstrate a refractive index sensor based on a long period grating (LPG inscribed in a special photosensitive microfiber with double-clad profile. The fiber is tapered gradually enough to ensure the adiabaticity of the fiber taper. In other words, the resulting insertion loss is sufficiently small. The boron and germanium co-doped inner cladding makes it suitable for inscribing gratings into its tapered form. The manner of wavelength shift for refractive indices (RIs differs from conventional LPG, and the refractive index detection limit is 1.67 × 10−5.
DEFF Research Database (Denmark)
Gammelmark, Søren; Eckardt, André
2013-01-01
We theoretically study the adiabatic preparation of an antiferromagnetic phase in a mixed Mott insulator of two bosonic atom species in a one-dimensional optical lattice. In such a system one can engineer a tunable parabolic inhomogeneity by controlling the difference of the trapping potentials f...... that during the preparation finite size effects will play a crucial role for a system of realistic size. The experiment that we propose can be realized, for example, using atomic mixtures of rubidium 87 with potassium 41, or ytterbium 168 with ytterbium 174....
Pure spin current induced by adiabatic quantum pumping in zigzag-edged graphene nanoribbons
Energy Technology Data Exchange (ETDEWEB)
Souma, Satofumi, E-mail: ssouma@harbor.kobe-u.ac.jp; Ogawa, Matsuto [Department of Electrical and Electronic Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501 (Japan)
2014-05-05
We show theoretically that pure spin current can be generated in zigzag edged graphene nanoribbons through the adiabatic pumping by edge selective pumping potentials. The origin of such pure spin current is the spin splitting of the edge localized states, which are oppositely spin polarized at opposite edges. In the proposed device, each edge of the ribbon is covered by two independent time-periodic local gate potentials with a definite phase difference, inducing the edge spin polarized current. When the pumping phase difference is opposite in sign between two edges, the total charge currents is zero and the pure edge spin current is generated.
The Primordial Inflation Polarization ExploreR Continuous Adiabatic Demagnetization Refrigerator
Pawlyk, Samuel; Ade, Peter; Benford, Dominic; Bennett, Charles; Chuss, David; Datta, Rahul; Dotson, Jessie; Essinger-Hileman, Thomas; Fixsen, Dale; Halpern, Mark; Hilton, Gene; Hinshaw, Gary; Irwin, Kent; Jhabvala, Christine; Kimball, Mark; Kogut, Al; Lowe, Luke; McMahon, Jeff; Miller, Timothy; Mirel, Paul; Moseley, Samuel Harvey; Rodriguez, Samelys; Sharp, Elmer; Shirron, Peter; Staguhn, Johannes G.; Sullivan, Dan; Switzer, Eric; Taraschi, Peter; Tucker, Carole; Wollack, Edward; Walts, Alexander
2018-01-01
The Primordial Inflation Polarization ExploreR (PIPER) uses a Continuous Adiabatic Demagnetization Refrigerator (CADR) to cool its detectors. The CADR consists of four independent stages with adjacent stages connected by gas gap (GG) or superconducting (SC) heat switches. The three warm stages cycle to transfer heat from the 100 mK detector package to the 1.5 K liquid helium bath. The coldest stage maintains a continuous temperature of 100 mK for the detector package with 10 uW cooling power. We describe the mechanical, electrical, and software design of the CADR and present recent results.
Plasmonic black gold by adiabatic nanofocusing and absorption of light in ultra-sharp convex grooves
DEFF Research Database (Denmark)
Søndergaard, Thomas; Novikov, Sergey M.; Stær, Tobias Holmgaard
2012-01-01
of surface plasmon excitations involved. Nonresonant absorption has so far been achieved by using combined nano- and micro-structural surface modifications and with composite materials involving metal nanoparticles embedded in dielectric layers. Here we realize nonresonant light absorption in a well......-defined geometry by using ultra-sharp convex metal grooves via adiabatic nanofocusing of gap surface plasmon modes excited by scattering off subwavelength-sized wedges. We demonstrate experimentally that two-dimensional arrays of sharp convex grooves in gold ensure efficient (>87%) broadband (450-850 nm...
Strecka, Jozef; Cisarova, Jana
2013-01-01
A full energy spectrum of the spin-1/2 Heisenberg cubic cluster is used to investigate a low-temperature magnetization process and adiabatic demagnetization of this zero-dimensional 2x2x2 quantum spin system. It is shown that the antiferromagnetic spin-1/2 Heisenberg cube exhibits at low enough temperatures a stepwise magnetization curve with four intermediate plateaux at zero, one quarter, one half, and three quarters of the saturation magnetization. We have also found the enhanced magnetoca...
Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering
Tang, K. T.; Karplus, M.
1970-10-01
A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the “linear model” is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.
The adiabatic/entropy decomposition in $P(\\phi^I,X^{IJ})$ theories with multiple sound speeds
Longden, Chris
2016-01-01
We consider $P(\\phi^I,X^{IJ})$ theories of multi-field inflation and ask the question of how to define the adiabatic and entropy perturbations, widely used in calculating the curvature and isocurvature power spectra, in this general context. It is found that when the field perturbations propagate with different speeds, these adiabatic and entropy modes are not generally the fundamental (most natural to canonically quantise) degrees of freedom that propagate with a single speed. The alternative fields which do propagate with a single speed are found to be a rotation in field space of the adiabatic and entropy perturbations. We show how this affects the form of the horizon-crossing power spectrum, when there is not a single "adiabatic sound speed" sourcing the curvature perturbation. Special cases of our results are discussed, including $P(X)$ theories where the adiabatic and entropy perturbations are fundamental. We finally look at physical motivations for considering multi-speed models of inflation, particula...
Mapping moveout approximations in TI media
Stovas, Alexey
2013-11-21
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
Role of adiabaticity in controlling alkali-metal fine-structure mixing induced by rare gases
Eshel, Ben; Cardoza, Joseph A.; Weeks, David E.; Perram, Glen P.
2017-04-01
The collision cross sections for alkali-metal-rare-gas spin orbit mixing between the n2P3 /2→n2P1 /2 levels trend strongly with the Massey parameter, or adiabaticity of the collisions. The strength of the interaction, as characterized by the C6 dispersion coefficient, is a secondary influence on the rates. An analytic expression for the probability of energy transfer in alkali-metal-rare-gas collisions is derived using time-dependent perturbation theory. The model agrees well with a broad literature survey of the observed temperature-dependent cross sections. A simple interaction potential successfully organizes the alkali-metal-rare-gas database. The rates become very large for high-lying states, as the collisions are quite sudden and the radius of the valence electron is large. In contrast, the highly adiabatic cesium 62P mixing rates are six to eight orders of magnitude smaller. The mixing rate for the Rb-He diode pumped alkali laser system varies from 0.20 -1.53 ×10-11cm 3/at .s for T =279 -893 K .
Ma, Rui; Wang, Bingfeng; Zhang, Xiaoyong; Zhou, Bingqing
2018-01-01
Adiabatic shear localization plays an important role in the deformation and failure of ultrafine grained 6061 aluminum alloy processed by friction stir processing. To understand the effects of temperature and strain on adiabatic shear localization in the ultrafine grained 6061 aluminum alloy, it has been investigated dynamic mechanical behavior of ultrafine grained 6061 aluminum alloy under the controlled shock loading experiments. Deformation characteristics and microstructures in the shear band were performed by optical microscopy and transmission electron microscopy. The shear band in the ultrafine grained aluminum alloy is a long and straight band distinguished from the matrix. The width of the shear band decreases with increasing nominal strain. The results show that the grains in the boundary of the shear band are highly elongated along the shear direction and form the elongated cell structures (0.2 μ in width), and the core of the shear band consists of a number of recrystallized equiaxed grains 0.2-0.3 μ in diameters and the second phases distribute in both the boundary and the inner of the equiaxed new grains. The calculated temperature in the shear band is about 692 K. Rotational dynamic recrystallization mechanism is responsible for the formation of the microstructure in the shear band.
Time Scale for Adiabaticity Breakdown in Driven Many-Body Systems and Orthogonality Catastrophe
Lychkovskiy, Oleg; Gamayun, Oleksandr; Cheianov, Vadim
2017-11-01
The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely, many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter-dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving nonautonomous time evolution in a large Hilbert space.
Rapid Manipulation of Bose-Einstein Condensates using Shortcuts to Adiabaticity
Samson, E. Carlo; Ryu, Changhyun; Boshier, Malcolm; Del Campo, Adolfo
2015-05-01
We are investigating practical methods based on shortcuts to adiabaticity (STA) for rapid manipulation of BECs. STA is an emergent field in quantum science that develops nonadiabatic protocols to drive a system into a target state much faster than the conventional slow adiabatic process. The first STA method that we are developing involves the ultrafast expansion (or compression) of a trapped BEC, as initially proposed by Del Campo and Boshier. We discuss our experimental implementation of this protocol, and our studies of the BEC dynamics and the fidelity of the final state. The other STA method is a launching protocol, in which we accelerate a trapped BEC to a target speed. We show through numerical GPE simulations that the target speed can be achieved in short durations and short launching distances with minimal excitations to the BEC, despite the nonadiabatic nature of the method. We also present initial results from the experimental implementation of this launching protocol. These STA-based experimental techniques would prove beneficial in systems that require fast initial state preparation and cycle time, without loss of coherence nor emergence of perturbations, such as in matter wave circuits, atom interferometry, and quantum heat engines. Supported by LANL/LDRD.
Controlling vibrational cooling with zero-width resonances: An adiabatic Floquet approach
Leclerc, Arnaud; Viennot, David; Jolicard, Georges; Lefebvre, Roland; Atabek, Osman
2016-10-01
In molecular photodissociation, some specific combinations of laser parameters (wavelength and intensity) lead to unexpected zero-width resonances (ZWRs) with, in principle, infinite lifetimes. Their potential to induce basic quenching mechanisms has recently been devised in the laser control of vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev. A 87, 031403(R) (2013), 10.1103/PhysRevA.87.031403]. A full quantum adiabatic control theory based on the adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be envelope-shaped and frequency-chirped so as to protect a given initial vibrational state against dissociation, taking advantage of its continuous transport on the corresponding ZWR all along the pulse duration. As compared with previous control scenarios that actually suffered from nonadiabatic contamination, drastically different and much more efficient filtration goals are achieved. A semiclassical analysis helps us to find and interpret a complete map of ZWRs in the laser parameter plane. In addition, the choice of a given ZWR path, among the complete series identified by the semiclassical approach, turns out to be crucial for the cooling scheme, targeting a single vibrational state population left at the end of the pulse, while all others have almost completely decayed. The illustrative example, which has the potential to be transposed to other diatomics, is Na2 prepared by photoassociation in vibrationally hot but translationally and rotationally cold states.
Hoang, Thai M; Bharath, Hebbe M; Boguslawski, Matthew J; Anquez, Martin; Robbins, Bryce A; Chapman, Michael S
2016-08-23
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.
Dissipation in adiabatic quantum computers: lessons from an exactly solvable model
Keck, Maximilian; Montangero, Simone; Santoro, Giuseppe E.; Fazio, Rosario; Rossini, Davide
2017-11-01
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-product-operator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.
Adiabatic preparation of Rydberg crystals in a cold lattice gas: Influence of atomic relaxations
Petrosyan, David; Molmer, Klaus; Fleischhauer, Michael
2017-04-01
Strong, long-range interactions between atoms in high-lying Rydberg states make them attractive systems for the studies of ordered phases and phase transitions of interacting many-body systems. Different approaches have been explored, both theoretically and experimentally, for the preparation of crystalline order of Rydberg excitations in spatially-extended ensembles of cold atoms. These include direct (near-)resonant laser excitation of interacting Rydberg states in a lattice gas, and adiabatic preparation of crystalline phases of Rydberg excitations in a one-dimensional optical lattice by adiabatic frequency sweep of the excitation laser. We show, however, that taking into account realistic relaxation processes affecting the atoms severely complicates the prospects of attaining sizable crystals of Rydberg excitations in laser-driven atomic media. Our many-body simulations well reproduce the experimental observations of spatial ordering of Rydberg excitations in driven dissipative lattice gases, as well as highly sub-Poissonian probability distribution of the excitation number. We find that the excitations essentially form liquid rather than crystal phases with long-range order.
Directory of Open Access Journals (Sweden)
Hossein Safaei
2017-07-01
Full Text Available We present analyses of three families of compressed air energy storage (CAES systems: conventional CAES, in which the heat released during air compression is not stored and natural gas is combusted to provide heat during discharge; adiabatic CAES, in which the compression heat is stored; and CAES in which the compression heat is used to assist water electrolysis for hydrogen storage. The latter two methods involve no fossil fuel combustion. We modeled both a low-temperature and a high-temperature electrolysis process for hydrogen production. Adiabatic CAES (A-CAES with physical storage of heat is the most efficient option with an exergy efficiency of 69.5% for energy storage. The exergy efficiency of the conventional CAES system is estimated to be 54.3%. Both high-temperature and low-temperature electrolysis CAES systems result in similar exergy efficiencies (35.6% and 34.2%, partly due to low efficiency of the electrolyzer cell. CAES with high-temperature electrolysis has the highest energy storage density (7.9 kWh per m3 of air storage volume, followed by A-CAES (5.2 kWh/m3. Conventional CAES and CAES with low-temperature electrolysis have similar energy densities of 3.1 kWh/m3.
Gate Leakage Reduction by Clocked Power Supply of Adiabatic Logic Circuits
Directory of Open Access Journals (Sweden)
Ph. Teichmann
2005-01-01
Full Text Available Losses due to gate-leakage-currents become more dominant in new technologies as gate leakage currents increase exponentially with decreasing gate oxide thickness. The most promising Adiabatic Logic (AL families use a clocked power supply with four states. Hence, the full VDD voltage drops over an AL gate only for a quarter of the clock cycle, causing a full gate leakage only for a quarter of the clock period. The rising and falling ramps of the clocked power supply lead to an additional energy consumption by gate leakage. This energy is smaller than the fraction caused by the constant VDD drop, because the gate leakage exponentially depends on the voltage across the oxide. To obtain smaller energy consumption, Improved Adiabatic Logic (IAL has been introduced. IAL swaps all n- and p-channel transistors. The logic blocks are built of p-channel devices which show gate tunneling currents significantly smaller than in n-channel devices. Using IAL instead of conventional AL allows an additional reduction of the energy consumption caused by gate leakage. Simulations based on a 90nm CMOS process show a lowering in gate leakage energy consumption for AL by a factor of 1.5 compared to static CMOS. For IAL the factor is up to 4. The achievable reduction varies depending on the considered AL family and the complexity of the gate.
Taple-top imaging of the non-adiabatically driven isomerization in the acetylene cation
Beaulieu, Samuel; Ibrahim, Heide; Wales, Benji; Schmidt, Bruno E.; Thiré, Nicolas; Bisson, Éric; Hebeisen, Christoph T.; Wanie, Vincent; Giguere, Mathieu; Kieffer, Jean-Claude; Sanderson, Joe; Schuurman, Michael S.; Légaré, François
2014-05-01
One of the primary goals of modern ultrafast science is to follow nuclear and electronic evolution of molecules as they undergo a photo-chemical reaction. Most of the interesting dynamics phenomena in molecules occur when an electronically excited state is populated. When the energy difference between electronic ground and excited states is large, Free Electron Laser (FEL) and HHG-based VUV sources were, up to date, the only light sources able to efficiently initiate those non-adiabatic dynamics. We have developed a simple table-top approach to initiate those rich dynamics via multiphoton absorption. As a proof of principle, we studied the ultrafast isomerization of the acetylene cation. We have chosen this model system for isomerization since the internal conversion mechanism which leads to proton migration is still under debate since decades. Using 266 nm multiphoton absorption as a pump and 800 nm induced Coulomb Explosion as a probe, we have shoot the first high-resolution molecular movie of the non-adiabatically driven proton migration in the acetylene cation. The experimental results are in excellent agreement with high level ab initio trajectory simulations.
From sudden quench to adiabatic dynamics in the attractive Hubbard model
Mazza, Giacomo
2017-11-01
We study the crossover between the sudden quench limit and the adiabatic dynamics of superconducting states in the attractive Hubbard model. We focus on the dynamics induced by the change of the attractive interaction during a finite ramp time. The ramp time is varied in order to track the evolution of the dynamical phase diagram from the sudden quench to the equilibrium limit. Two different dynamical regimes are realized for quenches towards weak and strong coupling interactions. At weak coupling the dynamics depends only on the energy injected into the system, whereas a dynamics retaining memory of the initial state takes place at strong coupling. We show that this is related to a sharp transition between a weak and a strong coupling quench dynamical regime, which defines the boundaries beyond which a dynamics independent from the initial state is recovered. Comparing the dynamics in the superconducting and nonsuperconducting phases, we argue that this is due to the lack of an adiabatic connection to the equilibrium ground state for nonequilibrium superconducting states in the strong coupling quench regime.
Changing role of carrier gas in formation of ethanol clusters by adiabatic expansion
Abu-samha, Mahmoud; Ryding, Mauritz J.; Uggerud, Einar; Sæthre, Leif J.; Børve, Knut J.
2017-07-01
Adiabatic expansion of molecular vapors is a celebrated method for producing pure and mixed clusters of relevance in both applied and fundamental studies. The present understanding of the relationship between experimental conditions and the structure of the clusters formed is incomplete. We explore the role of the backing/carrier gas during adiabatic expansion of ethanol vapors with regard to cluster production and composition. Single-component clusters of ethanol were produced over a wide size-range by varying the rare gas (He, Ar) backing pressure, with Ar being more efficient than He in promoting the formation of pure ethanol clusters. However, at stagnation pressures Ps>1.34 (4 ) bar and temperature 49 (2) °C, synchrotron-based valence and inner-shell photoelectron spectroscopy reveals condensation of Ar carrier gas on the clusters. Theoretical calculations of cluster geometries as well as chemical shifts in carbon 1s ionization energies confirm that the experimental observations are consistent with an ethanol core covered by an outer shell of argon. Experiments on the 1-propanol/Ar system display a similar pattern as described for ethanol/Ar, indicating a broader range of validity of the results.
Froment, P; Delbar, T; Ryckewaert, G; Tilquin, I; Vervier, J
2002-01-01
The Transmutation by Adiabatic Resonance Crossing (TARC) technique has been proposed by Rubbia (Resonance enhanced neutron captures for element activation and waste transmutation, CERN-LHC/97-0040EET, 1997; TARC collaboration, Neutron-driven nuclear transmutation by adiabatic resonance crossing, CERN-SL-99-036EET, 1999; Abanades et al., Nucl. Instr. and Meth. A 487 (2002) 577) for element activation and waste transmutation. We investigate the possibility to use this technique for the industrial production of **9**9Mo and **1**2**5Xe by resonance neutron capture in **9**8Mo and **1**2**4Xe, respectively. Their daughters, i.e. **9**9**mTc and **1**2**5I, are widely used in medical applications. The high neutron flux needed is produced by bombarding a thick Be target with 65 or 75 MeV proton beam (few microamperes). This target is placed at the centre of a large cubic lead assembly (1.6 m side, purity: 99.999%). The neutrons are progressively slowed down by elastic scattering on lead, and their energies "scan" t...
Non-adiabatic approach to optical conductivity in the one-dimensional half-filled Holstein model
Energy Technology Data Exchange (ETDEWEB)
Wang, Qin; Zheng, Hang
2003-08-04
The optical conductivity in the one-dimensional half-filled Holstein model of spin-((1)/(2)) electrons is investigated by developing an analytical non-adiabatic approach based on the unitary transformation method. The non-adiabatic effects due to finite phonon frequency {omega}{sub 0}>0 are treated through an energy-dependent electron-phonon scattering function {delta}(k',k) and the Green's function method is used to implement the perturbation treatment. The calculated optical conductivity and the density of states of electrons do not have the inverse-square-root singularity but have a peak above the gap edge and there exists a significant tail below the peak. This indicates that due to the non-adiabatic effects the Peierls gap shifts and the optical excitation spectrum does not peak at the correspondingly renormalized gap edge.
Directory of Open Access Journals (Sweden)
Jeong Ryeol Choi
2015-01-01
Full Text Available An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.
Multilevel Monte Carlo in Approximate Bayesian Computation
Jasra, Ajay
2017-02-13
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen
2015-01-01
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high-dimensional Euclid......Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high...
Abánades, A; Andriamonje, Samuel A; Angelopoulos, Angelos; Apostolakis, Alcibiades J; Arnould, H; Belle, E; Bompas, C A; Brozzi, Delecurgo; Bueno, J; Buono, S; Carminati, F; Casagrande, Federico; Cennini, P; Collar, J I; Cerro, E; Del Moral, R; Díez, S; Dumps, Ludwig; Eleftheriadis, C; Embid, M; Fernández, R; Gálvez, J; García, J; Gelès, C; Giorni, A; González, E; González, O; Goulas, I; Heuer, R D; Hussonnois, M; Kadi, Y; Karaiskos, P; Kitis, G; Klapisch, Robert; Kokkas, P; Lacoste, V; Le Naour, C; Lèpez, C; Loiseaux, J M; Martínez-Val, J M; Méplan, O; Nifenecker, H; Oropesa, J; Papadopoulos, I M; Pavlopoulos, P; Pérez-Enciso, E; Pérez-Navarro, A; Perlado, M; Placci, A; Poza, M; Revol, Jean Pierre Charles; Rubbia, Carlo; Rubio, J A; Sakelliou, L; Saldaña, F; Savvidis, E; Schussler, F; Sirvent, C; Tamarit, J; Trubert, D; Tzima, A; Viano, J B; Vieira, S L; Vlachoudis, V; Zioutas, Konstantin; CERN. Geneva. SPS and LEP Division
2000-01-01
The Transmutation by Adiabatic Resonance Crossing (TARC) experiment was carried out as PS211 at the CERN PS from 1996 to 1999. Energy and space distributions of spallation neutrons (from 2.5 and 3.57 GeV/c CERN proton beams) slowing down in a 3.3x3.3x3 m3 lead volume and neutron capture rates on long-lived fission fragements 99Tc and 129I demonstrate that Adiabatic Resonance Crossing (ARC) can be used to eliminate efficiently such nuclear waste and validate innovative simulation.
Muszyński, Tomasz; Andrzejczyk, Rafał; Dorao, Carlos A.
2017-09-01
The article presents detailed two-phase adiabatic pressure drops data for refrigerant R134a. Study cases have been set for a mass flux varying from 200 to 400 kg/m2s, at the saturation temperature of 19.4 °C. Obtained experimental data was compared with the available correlations from the literature for the frictional pressure drop during adiabatic flow. Influence of mixture preparation on pressure drop was investigated, for varying inlet subcooling temperature in the heated section. The flow patterns have also been obtained by means of a high-speed camera placed in the visualization section and compared with literature observations.
Lifetime of the Nonlinear Geometric Optics Approximation
DEFF Research Database (Denmark)
Binzer, Knud Andreas
The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations.......The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations....
Hardness of approximation for Knapsack problems
Buhrman, H.; Loff, B.; Torenvliet, L.
2015-01-01
We show various hardness results for knapsack and related problems; in particular we will show that unless the Exponential-Time Hypothesis is false, subset-sum cannot be approximated any better than with an FPTAS. We also provide new unconditional lower bounds for approximating knapsack in Ketan
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Approximate Solution of Rod Heating Problem
Directory of Open Access Journals (Sweden)
P. Lasy
2013-01-01
Full Text Available Contains exact and approximate analytic representations pertaining to the solution of a homogeneous mixed problem for a non-homogeneous one-dimensional equation of heat conduction using a special psi-function. The order of an approximate formula accuracy is given in the paper.
Inversion and approximation of Laplace transforms
Lear, W. M.
1980-01-01
A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.
Polynomial approximation approach to transient heat conduction ...
African Journals Online (AJOL)
This work reports polynomial approximation approach to transient heat conduction in a long slab, long cylinder and sphere with linear internal heat generation. It has been shown that the polynomial approximation method is able to calculate average temperature as a function of time for higher value of Biot numbers.
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
On approximating multi-criteria TSP
Manthey, Bodo; Albers, S.; Marion, J.-Y.
2009-01-01
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized
On approximating multi-criteria TSP
Manthey, Bodo
We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be
Boundary Value Problems and Approximate Solutions ...
African Journals Online (AJOL)
In this paper, we discuss about some basic things of boundary value problems. Secondly, we study boundary conditions involving derivatives and obtain finite difference approximations of partial derivatives of boundary value problems. The last section is devoted to determine an approximate solution for boundary value ...
Ravi, M. U.; Reddy, C. P.; Ravindranath, K.
2013-04-01
In view of fast depletion of fossil fuels and the rapid rate at which the fuel consumption is taking place all over the world, scientists are searching for alternate fuels for maintaining the growth industrially and economically. Hence search for alternate fuel(s) has become imminent. Out of the limited options for internal combustion engines, the bio diesel fuel appears to be the best. Many advanced countries are implementing several biodiesel initiatives and developmental programmes in order to become self sufficient and reduce the import bills. Biodiesel is biodegradable and renewable fuel with the potential to enhance the performance and reduce engine exhaust emissions. This is due to ready usage of existing diesel engines, fuel distribution pattern, reduced emission profiles, and eco-friendly properties of biodiesel. Simarouba biodiesel (SBD), the methyl ester of Simarouba oil is one such alternative fuel which can be used as substitute to conventional petro-diesel. The present work involves experimental investigation on the use of SBD blends as fuel in conventional diesel engine and semi-adiabatic diesel engine. The oil was triple filtered to eliminate particulate matter and then transesterified to obtain biodiesel. The project envisaged aims at conducting analysis of diesel with SBD blends (10, 20, 30 and 40 %) in conventional engine and semi-adiabatic engine. Also it was decided to vary the injection pressure (180, 190 and 200 bar) and observe its effect on performance and also suggest better value of injection pressure. The engine was made semi adiabatic by coating the piston crown with partially stabilized zirconia (PSZ). Kirloskar AV I make (3.67 kW) vertical, single cylinder, water cooled diesel engine coupled to an eddy current dynamometer with suitable measuring instrumentation/accessories used for the study. Experiments were initially carried out using pure diesel fuel to provide base line data. The test results were compared based on the performance
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
Orienting polar molecules without hexapoles: Optical state selection with adiabatic orientation
Schäfer, Tim; Bartels, Nils; Hocke, Nils; Yang, Xueming; Wodtke, Alec M.
2012-05-01
A pedagogic review of technology used to orient polar molecules is presented to place in context the report of a new approach to this problem. Laboratory frame orientation of polar molecules is achieved by state-specific optical pumping in a region free of electric fields followed by adiabatic transport into a static electric field. This approach overcomes some of the limitations of the more common hexapole focusing method. In particular the method is nearly insensitive to the kinetic energy of the sample. We demonstrate production of oriented samples of NO (μel = 0.15 D) with translational energies above 1 eV in both high- and low-field seeking states. The method can be extended to many other classes of molecules, including near symmetric tops and ions.
Khorshidi, Abdollah; Pazirandeh, Ali; Tenreiro, Claudio; Kadi, Yacine
2014-01-01
In this study, the transmutation adiabatic resonance crossing (TARC) concept was estimated in Mo-99 radioisotope production via radiative capture reaction in two designs. The TARC method was composed of moderating neutrons in lead or a composition of lead and water. Additionally, the target was surrounded by a moderator assembly and a graphite reflector district. Produced neutrons were investigated by (p,xn) interactions with 30 MeV and 300 mu A proton beam on tungsten, beryllium, and tantalum targets. The Mo-99 production yield was related to the moderator property, cross section, and sample positioning inside the distinct region of neutron storage as must be proper to achieve gains. Gathered thermal flux of neutrons can contribute to molybdenum isotope production. Moreover, the sample positioning to gain higher production yield was dependent on a greater flux in the length of thermal neutrons and region materials inside the moderator or reflector. When the sample radial distance from Be was 38 cm inside the...
Berman, G P; Chapline, G; Gurvitz, S A; Hammel, P C; Pelekhov, D V; Suter, A; Tsifrinovich, V I
2003-01-01
We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) with a cyclic adiabatic inversion (CAI). This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a cantilever modelled by a quantum oscillator in a coherent state in a quasi-classical range of parameters. The entire system is treated rigorously within the framework of the Schroedinger equation. For a many-spin system our equations accurately describe conventional MRFM experiments involving CAI of the spin system. Our computer simulations of the quantum spin-cantilever dynamics show that the probability distribution for the cantilever position develops two asymmetric peaks with the total relative probabilities mainly dependent on the initial angle between the directions of the average spin and the effective magnetic field, in the rotating frame. We show that each of th...
Adiabatic Gasification and Pyrolysis of Coffee Husk Using Air-Steam for Partial Oxidation
Directory of Open Access Journals (Sweden)
Catalina Rodriguez
2011-01-01
Full Text Available Colombian coffee industry produces about 0.6 million tons of husk (CH per year which could serve as feedstock for thermal gasification to produce gaseous and liquid fuels. The current paper deals with: (i CH adiabatic gasification modeling using air-steam blends for partial oxidation and (ii experimental thermogravimetric analysis to determine the CH activation energy (E. The Chemical Equilibrium with Applications Program (CEA, developed by NASA, was used to estimate the effect of equivalence ratio (ER and steam to fuel ratio (S : F on equilibrium temperature and gas composition of ~150 species. Also, an atom balance model was developed for comparison purposes. The results showed that increased ER and (S : F ratios produce mixtures that are rich in H2 and CO2 but poor in CO. The value for the activation energy was estimated to be 221 kJ/kmol.
Rapid Adiabatic Preparation of Injective Projected Entangled Pair States and Gibbs States
Ge, Yimin; Molnár, András; Cirac, J. Ignacio
2016-02-01
We propose a quantum algorithm for many-body state preparation. It is especially suited for injective projected entangled pair states and thermal states of local commuting Hamiltonians on a lattice. We show that for a uniform gap and sufficiently smooth paths, an adiabatic runtime and circuit depth of O (polylog N ) can be achieved for O (N ) spins. This is an almost exponential improvement over previous bounds. The total number of elementary gates scales as O (N p o l y l o g N ) . This is also faster than the best known upper bound of O (N2) on the mixing times of Monte Carlo Markov chain algorithms for sampling classical systems in thermal equilibrium.
Investigation of spontaneous Brillouin scattering generation based on non-adiabatic microfibres
Zarei, A.; Jasim, A. A.; Harun, S. W.; Ahmad, H.
2014-12-01
Brillouin Stokes and anti-Stokes generation is successfully demonstrated in backward direction using a non-adiabatic microfibre as the gain medium. The Stokes light wavelength is up-shifted by 0.088 nm (10 GHz) from the BP wavelength as monitored by using an optical spectrum analyzer. The Brillouin scattering can also be enhanced by employing a microfibre based inline Mach-Zehnder interferometer (IMZI) as the gain medium due to its stronger multimode interference effect. It is shown that the microfibre geometry plays an important role in the spontaneous Brillouin scattering generation and gain bandwidth broadening due to its effect on irritation of the acoustic modes inside the microfibre.
Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization
Energy Technology Data Exchange (ETDEWEB)
Imam, Neena [ORNL; Humble, Travis S. [ORNL; McCaskey, Alex [ORNL; Schrock, Jonathan [ORNL; Hamilton, Kathleen E. [ORNL
2017-09-01
A content-addressable memory (CAM) stores key-value associations such that the key is recalled by providing its associated value. While CAM recall is traditionally performed using recurrent neural network models, we show how to solve this problem using adiabatic quantum optimization. Our approach maps the recurrent neural network to a commercially available quantum processing unit by taking advantage of the common underlying Ising spin model. We then assess the accuracy of the quantum processor to store key-value associations by quantifying recall performance against an ensemble of problem sets. We observe that different learning rules from the neural network community influence recall accuracy but performance appears to be limited by potential noise in the processor. The strong connection established between quantum processors and neural network problems supports the growing intersection of these two ideas.
Octave-spanning coherent mid-IR generation via adiabatic difference frequency conversion.
Suchowski, Haim; Krogen, Peter R; Huang, Shu-Wei; Kärtner, Franz X; Moses, Jeffrey
2013-11-18
We demonstrate efficient downconversion of a near-IR broadband optical parametric chirped pulse amplifier (OPCPA) pulse to a 1.1-octave-spanning mid-IR pulse (measured at -10 dB of peak) via a single nonlinearly and adiabatically chirped quasi-phase-matching grating in magnesium oxide doped lithium niobate. We report a spectrum spanning from 2 to 5 μm and obtained by near full photon number conversion of μJ-energy OPCPA pulses spanning 680-870 nm mixed with a narrowband 1047-nm pulse. The conversion process is shown to be robust for various input broadband OPA pulses and suitable for post-amplification conversion for many near-IR systems.
Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity.
Tu, Z C
2014-05-01
When a Brownian particle in contact with a heat bath at a constant temperature is controlled by a time-dependent harmonic potential, its distribution function can be rigorously derived from the Kramers equation with the consideration of the inertial effect of the Brownian particle. Based on this rigorous solution and the concept of shortcuts to adiabaticity, we construct a stochastic heat engine by employing the time-dependent harmonic potential to manipulate the Brownian particle to complete a thermodynamic cycle. We find that the efficiency at maximum power of this stochastic heat engine is equal to 1-sqrt[T(c)/T(h)], where T(c) and T(h) are the temperatures of the cold bath and the hot one in the thermodynamic cycle, respectively.
Multiturn extraction and injection by means of adiabatic capture in stable islands of phase space
Cappi, R
2004-01-01
Recently a novel approach has been proposed for performing multiturn extraction from a circular machine. Such a technique consists of splitting the beam by means of stable islands created in transverse phase space by magnetic elements creating nonlinear fields, such as sextupoles and octupoles. Provided a slow time variation of the linear tune is applied, adiabatic with respect to the betatron motion, the islands can be moved in phase space and eventually charged particles may be trapped inside the stable structures. This generates a certain number of well-separated beamlets. Originally, this principle was successfully tested using a fourth-order resonance. In this paper the approach is generalized by considering other types of resonances as well as the possibility of performing multiple multiturn extractions. The results of numerical simulations are presented and described in detail. Of course, by time reversal, the proposed approach could be used also for multiturn injection.
The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers.
Oskooi, Ardavan F; Zhang, Lei; Avniel, Yehuda; Johnson, Steven G
2008-07-21
Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).
Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
Chen, Hsing-Ta; Reichman, David R
2016-01-01
In this paper we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while the companion paper provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each.
Heaps, Charles W
2016-01-01
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schr\\"{o}dinger equation with $N$ Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from $\\mathcal{O}(N^2)$ to $\\mathcal{O}(N)$. By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems; the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-d...
Quantum state specific reactant preparation in a molecular beam by rapid adiabatic passage
Energy Technology Data Exchange (ETDEWEB)
Chadwick, Helen, E-mail: helen.chadwick@epfl.ch; Hundt, P. Morten; Reijzen, Maarten E. van; Yoder, Bruce L.; Beck, Rainer D. [Laboratoire de Chimie Physique Moléculaire, Ecole Polytechnique Fédérale de Lausanne, Lausanne (Switzerland)
2014-01-21
Highly efficient preparation of molecules in a specific rovibrationally excited state for gas/surface reactivity measurements is achieved in a molecular beam using tunable infrared (IR) radiation from a single mode continuous wave optical parametric oscillator (cw-OPO). We demonstrate that with appropriate focusing of the IR radiation, molecules in the molecular beam crossing the fixed frequency IR field experience a Doppler tuning that can be adjusted to achieve complete population inversion of a two-level system by rapid adiabatic passage (RAP). A room temperature pyroelectric detector is used to monitor the excited fraction in the molecular beam and the population inversion is detected and quantified using IR bleaching by a second IR-OPO. The second OPO is also used for complete population transfer to an overtone or combination vibration via double resonance excitation using two spatially separated RAP processes.
Directory of Open Access Journals (Sweden)
López-Castillo A.
1998-01-01
Full Text Available Full quantum charge transfer study of the process B3+ + He -> B2+ + He+ has been investigated in the collision energy range 1-102 eV using an ab-initio interaction potential. A new method to solve the Schrödinger equation in an adiabatic basis was used, where the radial and rotational coupling were taken into account, and the importance of the coupling between states of different symmetry was discussed. Moreover, by using the well known Landau-Zener model, it was concluded that the two state model cannot be applied for the present system, and this might indicate that such a model should be applied carefully for other systems when a charge transfer process is considered. Finally, the quantum total cross sections were compared with the previous published work of Gargaud and co-workers and a fair agreement was achieved.
Directory of Open Access Journals (Sweden)
A. Franchi
2009-01-01
Full Text Available The multiturn extraction from a circular particle accelerator is performed by trapping the beam inside stable islands of the horizontal phase space. In general, by crossing a resonance of order n, n+1 beamlets are created whenever the resonance is stable, whereas if the resonance is unstable the beam is split in n parts. Islands are generated by nonlinear magnetic fields, whereas the trapping is realized by means of a given tune variation so to cross adiabatically a resonance. Experiments at the CERN Proton Synchrotron carried out in 2007 gave the evidence of protons trapped in stable islands while crossing the one-third and one-fifth resonances. Dedicated experiments were also carried out to study the trapping process and its reversibility properties. The results of these measurement campaigns are presented and discussed in this paper.
Adiabatic Non-resonant Acceleration in Magnetic Turbulence and Hard Spectra of Gamma-Ray Bursts
Xu, Siyao; Zhang, Bing
2017-09-01
We introduce a non-resonant acceleration mechanism arising from the second adiabatic invariant in magnetic turbulence and apply it to study the prompt emission spectra of gamma-ray bursts (GRBs). The mechanism contains both the first- and second-order Fermi acceleration, originating from the interacting turbulent reconnection and dynamo processes. It leads to a hard electron energy distribution up to a cutoff energy at the balance between the acceleration and synchrotron cooling. The sufficient acceleration rate ensures a rapid hardening of any initial energy distribution to a power-law distribution with the index p˜ 1, which naturally produces a low-energy photon index α ˜ -1 via the synchrotron radiation. For typical GRB parameters, the synchrotron emission can extend to a characteristic photon energy on the order of ˜100 keV.
Connecting orbits near the adiabatic limit of Lagrangian systems with turning points
Ivanov, Alexey V.
2017-09-01
We consider a natural Lagrangian system defined on a complete Riemannian manifold being subjected to action of a time-periodic force field with potential U( q, t, ɛ) = f( ɛt) V( q) depending slowly on time. It is assumed that the factor f( τ) is periodic and vanishes at least at one point on the period. Let X c denote a set of isolated critical points of V( x) at which V( x) distinguishes its maximum or minimum. In the adiabatic limit ɛ → 0 we prove the existence of a set E h such that the system possesses a rich class of doubly asymptotic trajectories connecting points of X c for ɛ ∈ E h .
Franchi, A; Giovannozzi, M; CERN. Geneva. BE Department
2009-01-01
The multi-turn extraction from a circular particle accelerator is performed by trapping the beam inside stable islands of the horizontal phase space. In general, by crossing a resonance of order n, n+1 beamlets are created whenever the resonance is stable, whereas if the resonance is unstable the beam is split in n parts. Islands are generated by non-linear magnetic fields, whereas the trapping is realized by means of a given tune variation so to cross adiabatically a resonance. Experiments at the CERN Proton Synchrotron carried out in 2007 gave the evidence of protons trapped in stable islands while crossing the one-third and one-fifth resonances. Dedicated experiments were also carried out to study the trapping process and its reversibility properties. The results of these measurement campaigns are presented and discussed in this paper.
The tendon approximator device in traumatic injuries.
Forootan, Kamal S; Karimi, Hamid; Forootan, Nazilla-Sadat S
2015-01-01
Precise and tension-free approximation of two tendon endings is the key predictor of outcomes following tendon lacerations and repairs. We evaluate the efficacy of a new tendon approximator device in tendon laceration repairs. In a comparative study, we used our new tendon approximator device in 99 consecutive patients with laceration of 266 tendons who attend a university hospital and evaluated the operative time to repair the tendons, surgeons' satisfaction as well as patient's outcomes in a long-term follow-up. Data were compared with the data of control patients undergoing tendon repair by conventional method. Totally 266 tendons were repaired by approximator device and 199 tendons by conventional technique. 78.7% of patients in first group were male and 21.2% were female. In approximator group 38% of patients had secondary repair of cut tendons and 62% had primary repair. Patients were followed for a mean period of 3years (14-60 months). Time required for repair of each tendon was significantly reduced with the approximator device (2 min vs. 5.5 min, ptendon repair were identical in the two groups and were not significantly different. 1% of tendons in group A and 1.2% in group B had rupture that was not significantly different. The new nerve approximator device is cheap, feasible to use and reduces the time of tendon repair with sustained outcomes comparable to the conventional methods.
Effects of Adiabatic Heating on the High Strain Rate Deformation of Polymer Matrix Composites
Sorini, Chris; Chattopadhyay, Aditi; Goldberg, Robert K.
2017-01-01
Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures.
Directory of Open Access Journals (Sweden)
R. Becchi
2015-12-01
Full Text Available Nowadays total inlet temperature of gas turbine is far above the permissible metal temperature; as a consequence, advanced cooling techniques must be applied to protect from thermal stresses, oxidation and corrosion the components located in the high pressure stages, such as the blade trailing edge. A suitable design of the cooling system for the trailing edge has to cope with geometric constraints and aerodynamic demands; state-of-the-art of cooling concepts often use film cooling on blade pressure side: the air taken from last compressor stages is ejected through discrete holes or slots to provide a cold layer between hot mainstream and the blade surface. With the goal of ensuring a satisfactory lifetime of blades, the design of efficient trailing edge film cooling schemes and, moreover, the possibility to check carefully their behavior, are hence necessary to guarantee an appropriate metal temperature distribution. For this purpose an experimental survey was carried out to investigate the film covering performance of different pressure side trailing edge cooling systems for turbine blades. The experimental test section consists of a scaled-up trailing edge model installed in an open loop suction type test rig. Measurements of adiabatic effectiveness distributions were carried out on three trailing edge cooling system configurations. The baseline geometry is composed by inclined slots separated by elongated pedestals; the second geometry shares the same cutback configuration, with an additional row of circular film cooling holes located upstream; the third model is equipped with three rows of in-line film cooling holes. Experiments have been performed at nearly ambient conditions imposing several blowing ratio values and using carbon dioxide as coolant in order to reproduce a density ratio close to the engine conditions (DR=1.52. To extend the validity of the survey a comparison between adiabatic effectiveness measurements and a prediction by
Revisiting the theory of the evolution of pick-up ion distributions: magnetic or adiabatic cooling?
Directory of Open Access Journals (Sweden)
H. J. Fahr
2008-01-01
Full Text Available We study the phasespace behaviour of heliospheric pick-up ions after the time of their injection as newly created ions into the solar wind bulk flow from either charge exchange or photoionization of interplanetary neutral atoms. As interaction with the ambient MHD wave fields we allow for rapid pitch angle diffusion, but for the beginning of this paper we shall neglect the effect of quasilinear or nonlinear energy diffusion (Fermi-2 acceleration induced by counterflowing ambient waves. In the up-to-now literature connected with the convection of pick-up ions by the solar wind only adiabatic cooling of these ions is considered which in the solar wind frame takes care of filling the gap between the injection energy and energies of the thermal bulk of solar wind ions. Here we reinvestigate the basics of the theory behind this assumption of adiabatic pick-up ion reactions and correlated predictions derived from it. We then compare it with the new assumption of a pure magnetic cooling of pick-up ions simply resulting from their being convected in an interplanetary magnetic field which decreases in magnitude with increase of solar distance. We compare the results for pick-up ion distribution functions derived along both ways and can point out essential differences of observational and diagnostic relevance. Furthermore we then include stochastic acceleration processes by wave-particle interactions. As we can show, magnetic cooling in conjunction with diffusive acceleration by wave-particle interaction allows for an unbroken power law with the unique power index γ=−5 beginning from lowest velocities up to highest energy particles of about 100 KeV which just marginally can be in resonance with magnetoacoustic turbulences. Consequences for the resulting pick-up ion pressures are also analysed.
Adiabatic perturbation theory for atoms and molecules in the low-frequency regime
Martiskainen, Hanna; Moiseyev, Nimrod
2017-12-01
There is an increasing interest in the photoinduced dynamics in the low frequency, ω, regime. The multiphoton absorptions by molecules in strong laser fields depend on the polarization of the laser and on the molecular structure. The unique properties of the interaction of atoms and molecules with lasers in the low-frequency regime imply new concepts and directions in strong-field light-matter interactions. Here we represent a perturbational approach for the calculations of the quasi-energy spectrum in the low-frequency regime, which avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. This is in the spirit of the first step in the Corkum three-step model. The second-order perturbation correction terms are obtained when i ℏ ω ∂/∂ τ serves as a perturbation and τ is a dimensionless variable. The second-order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement the perturbation approach presented here for calculating atomic and molecular energy shifts (positions) due to the interaction with low-frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. In addition to the shift of the energy positions, the energy widths (inverse lifetimes) can be obtained at the same level of theory. These energy shifts are functions of the laser parameters (low frequency, intensity, and polarization).
Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.
Chao, Fa-An; Byrd, R Andrew
2017-04-01
The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', Cα, Hα, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.
Application of geometric approximation to the CPMG experiment: Two- and three-site exchange
Chao, Fa-An; Byrd, R. Andrew
2017-04-01
The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C‧, Cα, Hα, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.
Gonen, S.
2014-01-01
The present study was carried out with 46 teacher candidates taking the course of "Thermodynamics" in the Department of Physics Teaching. The purpose of the study was to determine the difficulties that teacher candidates experienced in explaining the heat, work and internal energy relationships in the processes of adiabatic compression…
Loverude, Michael E.; Kautz, Christian H.; Heron, Paula R. L.
2002-01-01
Reports on an investigation of student understanding of the first law of thermodynamics. Involves students from a first-year university physics course and a second-year thermal physics course. Focuses on the ability of students to relate the first law to the adiabatic physics course. Discusses implications for thermal physics and mechanics…
DEFF Research Database (Denmark)
Denisov, S.; Flach, S.; Ovchinnikov, A. A.
2002-01-01
We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is em...
Determination of adiabatic temperature change in MnFe(P,Ge) compounds with pulse-field method
Trung, N.T.; Klaasse, J.C.P.; Tegus, O.; Cam Thanh, D.T.; Buschow, K.H.J.; Brück, E.
2009-01-01
Fast magnetic measurements performed by means of a 20 T pulse-field magnet provide a good approach for directly monitoring the magnetocaloric effect of the MnFe(P,Ge) compounds. Based on the comparison of magnetization curves obtained either in an adiabatic or isothermal process, we propose that the
Approximation of the semi-infinite interval
Directory of Open Access Journals (Sweden)
A. McD. Mercer
1980-01-01
Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Conditional Density Approximations with Mixtures of Polynomials
DEFF Research Database (Denmark)
Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre
2015-01-01
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...
Fractional Mathematical Operators and Their Computational Approximation
Directory of Open Access Journals (Sweden)
José Crespo
2016-01-01
Full Text Available Usual applied mathematics employs three fundamental arithmetical operators: addition, multiplication, and exponentiation. However, for example, transcendental numbers are said not to be attainable via algebraic combination with these fundamental operators. At the same time, simulation and modelling frequently have to rely on expensive numerical approximations of the exact solution. The main purpose of this article is to analyze new fractional arithmetical operators, explore some of their properties, and devise ways of computing them. These new operators may bring new possibilities, for example, in approximation theory and in obtaining closed forms of those approximations and solutions. We show some simple demonstrative examples.
Directory of Open Access Journals (Sweden)
W. W. Grabowski
2009-04-01
Full Text Available A large set of rising adiabatic parcel simulations is executed to investigate the combined diffusional and accretional growth of cloud droplets in maritime and continental conditions, and to assess the impact of enhanced droplet collisions due to small-scale cloud turbulence. The microphysical model applies the droplet number density function to represent spectral evolution of cloud and rain/drizzle drops, and various numbers of bins in the numerical implementation, ranging from 40 to 320. Simulations are performed applying two traditional gravitational collection kernels and two kernels representing collisions of cloud droplets in the turbulent environment, with turbulent kinetic energy dissipation rates of 100 and 400 cm^{2} s^{−3}. The overall result is that the rain initiation time significantly depends on the number of bins used, with earlier initiation of rain when the number of bins is low. This is explained as a combination of the increase of the width of activated droplet spectrum and enhanced numerical spreading of the spectrum during diffusional and collisional growth when the number of model bins is low. Simulations applying around 300 bins seem to produce rain at times which no longer depend on the number of bins, but the activation spectra are unrealistically narrow. These results call for an improved representation of droplet activation in numerical models of the type used in this study.
Despite the numerical effects that impact the rain initiation time in different simulations, the turbulent speedup factor, the ratio of the rain initiation time for the turbulent collection kernel and the corresponding time for the gravitational kernel, is approximately independent of aerosol characteristics, parcel vertical velocity, and the number of bins used in the numerical model. The turbulent speedup factor is in the range 0.75–0.85 and 0.60–0.75 for the turbulent kinetic energy dissipation rates of 100 and
Analytical Ballistic Trajectories with Approximately Linear Drag
National Research Council Canada - National Science Library
Giliam J. P. de Carpentier
2014-01-01
This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories...
Broadband Approximations for Doubly Curved Reflector Antenna
Directory of Open Access Journals (Sweden)
V. Schejbal
2010-12-01
Full Text Available The broadband approximations for shaped-beam doubly curved reflector antennas with primary feed (rectangular horn producing uniform amplitude and phase aperture distribution are derived and analyzed. They are very valuable for electromagnetic compatibility analyses both from electromagnetic interference and susceptibility point of view, because specialized more accurate methods such as physical optics are only used by antenna designers. To allow quick EMC analyses, typical values, beamwidth changes, sidelobe levels and aperture efficiencies are given for frequency changes approximately up to four times operating frequency. A comparison of approximated and measured patterns of doubly curved reflector antennas shows that the given approximation could be reliably used for analyses of pattern changes due to very broad frequency changes.
Saddlepoint approximation methods in financial engineering
Kwok, Yue Kuen
2018-01-01
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...
Low Rank Approximation Algorithms, Implementation, Applications
Markovsky, Ivan
2012-01-01
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...
Degree of Approximation and Green Potential
Directory of Open Access Journals (Sweden)
M. Simkani
2009-03-01
Full Text Available We will relate the degree of rational approximation of a meromorphic function f to the minimum value, on the natural boundary of f, of Green potential of the weak∗ limit of the normalized pole-counting measures
Cq-commuting maps and invariant approximations
Directory of Open Access Journals (Sweden)
B. E. Rhoades
2006-06-01
Full Text Available We obtain common fixed point results for generalized I-nonexpansive Cq-commuting maps. As applications, various best approximation results for this class of maps are derived in the setup of certain metrizable topological vector spaces.
An approximation of solutions of variational inequalities
Directory of Open Access Journals (Sweden)
B. E. Rhoades
2005-10-01
Full Text Available We use a Mann-type iteration scheme and the metric projection operator (the nearest-point projection operator to approximate the solutions of variational inequalities in uniformly convex and uniformly smooth Banach spaces.
Approximate substitutions and the normal ordering problem
Energy Technology Data Exchange (ETDEWEB)
Cheballah, H; Duchamp, G H E [Universite Paris 13 Laboratoire d' Informatique Paris Nord, CNRS UMR 7030 99 Av. J-B. Clement, F 93430 Villetaneuse (France); Penson, K A [Laboratoire de Physique Theorique de la Matiere Condensee Universite Pierre et Marie Curie, CNRS UMR 7600 Tour 24 - 2e et., 4 pl. Jussieu, F 75252 Paris Cedex 05 (France)], E-mail: hayat.cheballah@lipn-univ.paris13.fr, E-mail: ghed@lipn-univ.paris13.fr, E-mail: penson@lptl.jussieu.fr
2008-03-01
In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations.
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION
Directory of Open Access Journals (Sweden)
Mădălina Roxana Buneci
2016-12-01
Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
An overview on Approximate Bayesian computation*
Directory of Open Access Journals (Sweden)
Baragatti Meïli
2014-01-01
Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.
An approximation of solutions of variational inequalities
Directory of Open Access Journals (Sweden)
Rhoades BE
2005-01-01
Full Text Available We use a Mann-type iteration scheme and the metric projection operator (the nearest-point projection operator to approximate the solutions of variational inequalities in uniformly convex and uniformly smooth Banach spaces.
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach...... for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy....
The closure approximation in the hierarchy equations.
Adomian, G.
1971-01-01
The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.
Adaptive and Approximate Orthogonal Range Counting
DEFF Research Database (Denmark)
Chan, Timothy M.; Wilkinson, Bryan Thomas
2013-01-01
]. •We give an O(n loglog n)-space data structure for approximate 2-D orthogonal range counting that can compute a (1+δ)-factor approximation to the count in O(loglog n) time for any fixed constant δ>0. Again, our bounds match the state of the art for the 2-D orthogonal range emptiness problem. •Lastly...
Seismic modeling using the frozen Gaussian approximation
Yang, Xu; Lu, Jianfeng; Fomel, Sergey
2013-01-01
We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian functions along appropriate ray paths. As opposed to the classic Gaussian-beam method, FGA keeps the Gaussians frozen (at a fixed width) during the propagation process and adjusts their amplitudes to produce an accurate approximation after summation. We perform t...
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, S.
1998-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding....
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, s.
1999-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding. (C) 1999 Academic Press....
Nonlinear approximation with nonstationary Gabor frames
DEFF Research Database (Denmark)
Ottosen, Emil Solsbæk; Nielsen, Morten
2018-01-01
We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions...... resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding...
Adiabatic excitation for (31) P MR spectroscopy in the human heart at 7 T: A feasibility study.
Valkovič, Ladislav; Clarke, William T; Purvis, Lucian A B; Schaller, Benoit; Robson, Matthew D; Rodgers, Christopher T
2017-11-01
Phosphorus magnetic resonance spectroscopy ((31) P-MRS) provides a unique tool for assessing cardiac energy metabolism, often quantified using the phosphocreatine (PCr)/adenosine triphosphate (ATP) ratio. Surface coils are typically used for excitation for (31) P-MRS, but they create an inhomogeneous excitation field across the myocardium, producing undesirable, spatially varying partial saturation. Therefore, we implemented adiabatic excitation in a 3D chemical shift imaging (CSI) sequence for cardiac (31) P-MRS at 7 Tesla (T). We optimized an adiabatic half passage pulse with bandwidth sufficient to excite PCr and γ-ATP together. In addition, the CSI sequence was modified to allow interleaved excitation of PCr and γ-ATP, then 2,3-DPG, to enable PCr/ATP determination with blood correction. Nine volunteers were scanned at 2 transmit voltages to confirm that measured PCr/ATP was independent of B1+ (i.e. over the adiabatic threshold). Six septal voxels were evaluated for each volunteer. Phantom experiments showed that adiabatic excitation can be reached at the depth of the heart using our pulse. The mean evaluated cardiac PCr/ATP ratio from all 9 volunteers corrected for blood signal was 2.14 ± 0.16. Comparing the two acquisitions with different voltages resulted in a minimal mean difference of -0.005. Adiabatic excitation is possible in the human heart at 7 T, and gives consistent PCr/ATP ratios. Magn Reson Med 78:1667-1673, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.
Approximating centrality in evolving graphs: toward sublinearity
Priest, Benjamin W.; Cybenko, George
2017-05-01
The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.
Memory-optimal neural network approximation
Bölcskei, Helmut; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp
2017-08-01
We summarize the main results of a recent theory-developed by the authors-establishing fundamental lower bounds on the connectivity and memory requirements of deep neural networks as a function of the complexity of the function class to be approximated by the network. These bounds are shown to be achievable. Specifically, all function classes that are optimally approximated by a general class of representation systems-so-called affine systems-can be approximated by deep neural networks with minimal connectivity and memory requirements. Affine systems encompass a wealth of representation systems from applied harmonic analysis such as wavelets, shearlets, ridgelets, α-shearlets, and more generally α-molecules. This result elucidates a remarkable universality property of deep neural networks and shows that they achieve the optimum approximation properties of all affine systems combined. Finally, we present numerical experiments demonstrating that the standard stochastic gradient descent algorithm generates deep neural networks which provide close-to-optimal approximation rates at minimal connectivity. Moreover, stochastic gradient descent is found to actually learn approximations that are sparse in the representation system optimally sparsifying the function class the network is trained on.
Matsubara, T.; Yoshisato, A.; Morikawa, M.
We investigate the reason why Zel'dovich-type approximations work accurately beyond the linear regime from the following two points of view: (1) Dimensionality of the system and (2) the Lagrangian scheme on which the Zel'dovich approximation is grounded. We introduce a model with spheroidal mass distribution and the Padé approximation in Eulerian scheme. We clarify which of these aspects supports the accuracy of the Zel'dovich-type approximations.
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
Energy Technology Data Exchange (ETDEWEB)
Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
2015-07-20
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
A new six-dimensional potential energy surface for H2-N2O and its adiabatic-hindered-rotor treatment
Wang, Lecheng; Xie, Daiqian; Le Roy, Robert J.; Roy, Pierre-Nicholas
2013-07-01
A six-dimensional ab initio potential energy surface (PES) for H2-N2O which explicitly includes the symmetric and asymmetric vibrational coordinates Q1 and Q3 of N2O is calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triple level using an augmented correlation-consistent polarized-valence quadruple-zeta basis set together with midpoint bond functions. Four-dimensional intermolecular PESs are then obtained by fitting the vibrationally averaged interactions energies for υ3(N2O) = 0 and 1 to the Morse/long-range analytical form. In the fits, fixing the long-range parameters at theoretical values smoothes over the numerical noise in the ab initio points in the long-range region of the potential. Using the adiabatic hindered-rotor approximation, two-dimensional PESs for hydrogen-N2O complexes with different isotopomers of hydrogen are generated by averaging the 4D PES over the rotation of the hydrogen molecule within the complex. The band-origin shifts for the hydrogen-N2O dimers calculated using both the 4D PESs and the angle-averaged 2D PESs are all in good agreement with each other and with the available experimental observations. The predicted infrared transition frequencies for para-H2-N2O and ortho-D2-N2O are also consistent with the observed spectra.
Shirron, Peter; Kimball, Mark; James, Bryan; Muench, Theodore; Canavan, Edgar; DiPirro, Michael; Bialas, Thomas; Sneiderman, Gary; Boyce, Kevin; Kilbourne, Caroline;
2016-01-01
The Soft X-ray Spectrometer instrument on the Astro-H observatory contains a 6x6 array of x-ray microcalorimeters, which is cooled to 50 mK by an adiabatic demagnetization refrigerator (ADR). The ADR consists of three stages in order to provide stable detector cooling using either a 1.2 K superfluid helium bath or a 4.5 K Joule-Thomson (JT) cryocooler as its heat sink. When liquid helium is present, two of the ADRs stages are used to single-shot cool the detectors while rejecting heat to the helium. After the helium is depleted, all three stages are used to cool both the helium tank (to about 1.5 K) and the detectors (to 50 mK) using the JT cryocooler as its heat sink. The Astro-H observatory, renamed Hitomi after its successful launch in February 2016, carried approximately 36 liters of helium into orbit. On day 5, the helium had cooled sufficiently (1.4 K) to allow operation of the ADR. This paper describes the design, operation and on-orbit performance of the ADR.
Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory
Richter, Martin; Fingerhut, Benjamin P.
2017-06-01
The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.
The grammar of approximating number pairs.
Eriksson, Kimmo; Bailey, Drew H; Geary, David C
2010-04-01
In the present article, we studied approximating pairs of numbers (a, b) that were used to estimate quantity in a single phrase ("two, three years ago"). Pollmann and Jansen (1996) found that only a few of the many possible pairs are actually used, suggesting an interaction between the ways in which people estimate quantity and their use of quantitative phrases in colloquial speech. They proposed a set of rules that describe which approximating pairs are used in Dutch phrases. We revisited this issue in an analysis of Swedish and American language corpora and in a series of three experiments in which Swedish and American adults rated the acceptability of various approximating pairs and created approximating pairs of their own in response to various estimation tasks. We found evidence for Pollmann and Jansen's rules in both Swedish and English phrases, but we also identified additional rules and substantial individual and cross-language variation. We will discuss implications for the origin of this loose "grammar" of approximating pairs.
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef
2017-06-30
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.
Semiclassical initial value approximation for Green's function.
Kay, Kenneth G
2010-06-28
A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-10-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
Tree-fold loop approximation of AMD
Energy Technology Data Exchange (ETDEWEB)
Ono, Akira [Tohoku Univ., Sendai (Japan). Faculty of Science
1997-05-01
AMD (antisymmetrized molecular dynamics) is a frame work for describing a wave function of nucleon multi-body system by Slater determinant of Gaussian wave flux, and a theory for integrally describing a wide range of nuclear reactions such as intermittent energy heavy ion reaction, nucleon incident reaction and so forth. The aim of this study is induction on approximation equation of expected value, {nu}, in correlation capable of calculation with time proportional A (exp 3) (or lower), and to make AMD applicable to the heavier system such as Au+Au. As it must be avoided to break characteristics of AMD, it needs not to be anxious only by approximating the {nu}-value. However, in order to give this approximation any meaning, error of this approximation will have to be sufficiently small in comparison with bond energy of atomic nucleus and smaller than 1 MeV/nucleon. As the absolute expected value in correlation may be larger than 50 MeV/nucleon, the approximation is required to have a high accuracy within 2 percent. (G.K.)
Numerical approximation of partial differential equations
Bartels, Sören
2016-01-01
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular ...
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Variational algorithms for approximate Bayesian inference
Beal, Matthew James
The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propagation algorithms. Chapter 2 forms the theoretical core of the thesis, generalising the expectation- maximisation (EM) algorithm for learning maximum likelihood parameters to the VB EM algorithm which integrates over model parameters. The algorithm is then specialised to the large family of conjugate-exponential (CE) graphical models, and several theorems are presented to pave the road for automated VB derivation procedures in both directed and undirected graphs (Bayesian and Markov networks, respectively). Chapters 3--5 derive and apply the VB EM algorithm to three commonly-used and important models: mixtures of factor analysers, linear dynamical systems, and hidden Markov models. It is shown how model selection tasks such as determining the dimensionality, cardinality, or number of variables are possible using VB approximations. Also explored are methods for combining sampling procedures with variational approximations, to estimate the tightness of VB bounds and to obtain more effective sampling algorithms. Chapter 6 applies VB learning to a long-standing problem of scoring discrete-variable directed acyclic graphs, and compares the performance to annealed importance sampling amongst other methods. Throughout, the VB approximation is compared to other methods including sampling, Cheeseman-Stutz, and asymptotic approximations such as BIC. The thesis concludes with a discussion of evolving directions for model selection
Exact and approximate calculation of giant resonances
Energy Technology Data Exchange (ETDEWEB)
Vertse, T. [Magyar Tudomanyos Akademia, Debrecen (Hungary). Atommag Kutato Intezete; Liotta, R.J. [Royal Inst. of Tech., Stockholm (Sweden); Maglione, E. [Padua Univ. (Italy). Ist. di Fisica
1995-02-13
Energies, sum rules and partial decay widths of giant resonances in {sup 208}Pb are calculated solving exactly the continuum RPA equations corresponding to a central Woods-Saxon potential. For comparison an approximate treatment of those quantities in terms of pole expansions of the Green function (Berggren and Mittag-Leffler) is also performed. It is found that the approximated results agree well with the exact ones. Comparison with experimental data is made and a search for physically meaningful resonances is carried out. ((orig.))
Approximate Inference and Deep Generative Models
CERN. Geneva
2018-01-01
Advances in deep generative models are at the forefront of deep learning research because of the promise they offer for allowing data-efficient learning, and for model-based reinforcement learning. In this talk I'll review a few standard methods for approximate inference and introduce modern approximations which allow for efficient large-scale training of a wide variety of generative models. Finally, I'll demonstrate several important application of these models to density estimation, missing data imputation, data compression and planning.
Optimal convex approximations of quantum states
Sacchi, Massimiliano F.
2017-10-01
We consider the problem of optimally approximating an unavailable quantum state ρ by the convex mixing of states drawn from a set of available states {νi} . The problem is recast to look for the least distinguishable state from ρ among the convex set ∑ipiνi , and the corresponding optimal weights {pi} provide the optimal convex mixing. We present the complete solution for the optimal convex approximation of a qubit mixed state when the set of available states comprises the three bases of the Pauli matrices.
Approximations in the PE-method
DEFF Research Database (Denmark)
Arranz, Marta Galindo
1996-01-01
Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed...... for a case where the normal mode solution to the wave equation is valid, when the sound is propagated in a downward refracting atmosphere. The angular limitations for the different parabolic approximations are deduced, and calculations showing shifts in the starter as the second source of error...
Approximating hidden chaotic attractors via parameter switching
Danca, Marius-F.; Kuznetsov, Nikolay V.; Chen, Guanrong
2018-01-01
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration.
An Approximate Bayesian Fundamental Frequency Estimator
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2012-01-01
and the model order is based on a probability model which corresponds to a minimum of prior information. From this probability model, we give the exact posterior distributions on the fundamental frequency and the model order, and we also present analytical approximations of these distributions which lower......Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency...
Approximate Networking for Universal Internet Access
Directory of Open Access Journals (Sweden)
Junaid Qadir
2017-12-01
Full Text Available Despite the best efforts of networking researchers and practitioners, an ideal Internet experience is inaccessible to an overwhelming majority of people the world over, mainly due to the lack of cost-efficient ways of provisioning high-performance, global Internet. In this paper, we argue that instead of an exclusive focus on a utopian goal of universally accessible “ideal networking” (in which we have a high throughput and quality of service as well as low latency and congestion, we should consider providing “approximate networking” through the adoption of context-appropriate trade-offs. In this regard, we propose to leverage the advances in the emerging trend of “approximate computing” that rely on relaxing the bounds of precise/exact computing to provide new opportunities for improving the area, power, and performance efficiency of systems by orders of magnitude by embracing output errors in resilient applications. Furthermore, we propose to extend the dimensions of approximate computing towards various knobs available at network layers. Approximate networking can be used to provision “Global Access to the Internet for All” (GAIA in a pragmatically tiered fashion, in which different users around the world are provided a different context-appropriate (but still contextually functional Internet experience.
Approximate Symbolic Model Checking Using Overlapping Projections
1999-01-01
Abstract Symbolic Model Checking extends the scope of verification algorithms that can be handled automatically, by using symbolic representations...many of today’s large designs because of the state explosion problem. Approximate symbolic model checking is an attempt to trade off accuracy with
Static correlation beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
We investigate various approximations to the correlation energy of a H2 molecule in the dissociation limit, where the ground state is poorly described by a single Slater determinant. The correlation energies are derived from the density response function and it is shown that response functions de...
Markov operators, positive semigroups and approximation processes
Altomare, Francesco; Leonessa, Vita; Rasa, Ioan
2015-01-01
In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Approximate Equilibrium Problems and Fixed Points
Directory of Open Access Journals (Sweden)
H. Mazaheri
2013-01-01
Full Text Available We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block...
On the Subspace Projected Approximate Matrix method
Brandts, J.H.; Reis da Silva, R.
2015-01-01
We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix A. It falls in the category of inner-outer iteration methods and aims to reduce the costs of
Approximability of Minimum AND-Circuits
Arpe, J.; Manthey, Bodo
Given a set of monomials, the {\\sc Minimum AND-Circuit} problem asks for a circuit that computes these monomials using AND-gates of fan-in two and being of minimum size. We prove that the problem is not polynomial-time approximable within a factor of less than 1.0051 unless {\\sc P = NP}, even if the
Uncertainty relations for approximation and estimation
Energy Technology Data Exchange (ETDEWEB)
Lee, Jaeha, E-mail: jlee@post.kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tsutsui, Izumi, E-mail: izumi.tsutsui@kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)
2016-05-27
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.