Bast, Radovan; Jensen, Hans Jørgen Aagaard; Saue, Trond
2009-01-01
We report an implementation of adiabatic time-dependent density functional theory based on the 4-component relativistic Dirac-Coulomb Hamiltonian and a closed-shell reference. The implementation includes noncollinear spin magnetization and full derivatives of functionals, including hybrid...... and time reversal symmetry on trial vectors to obtain even better reductions in terms of memory and run time, and without invoking approximations. Further reductions are obtained by exploiting point group symmetries for D2h and subgroups in a symmetry scheme where symmetry reductions translate...... into reduction of algebra from quaternion to complex or real. For hybrid GGAs with noncollinear spin magnetization we derive a new computationally advantageous equation for the full second variational derivatives of such exchange-correlation functionals. We apply our implementation to calculations on the ns2...
Similarity solutions for radiation in time-dependent relativistic flows
Lucy, L B
2004-01-01
Exact analytic solutions are derived for radiation in time-dependent relativistic flows. The flows are spherically-symmetric homologous explosions or implosions of matter with a grey extinction coefficient. The solutions are suitable for testing numerical transfer codes, and this is illustrated for a fully relativistic Monte Carlo code.
Invariant Hermitian Operator and Density Operator for the Adiabatically Time-Dependent System
YAN Feng-Li; YANG Lin-Guang
2001-01-01
The density operator is approximately expressed as a function of the invariant Hermitian operator for the adiabatically time-dependent system. Using this method, the calculation of the density operator for the Heisenberg spin system in a weakly time-dependent magnetic field is exemplified. By virtue of the density operator, we obtain equilibrium.``
TIME-DEPENDENT LANDAU SYSTEM AND NON-ADIABATIC BERRY PHASE IN TWO DIMENSIONS
Jing Hui; Wu Jian-sheng
2000-01-01
By applying the time-independent unitary transformation, thetime-dependent Landau system is transformed into a product of atime-independent Landau system's Hamiltonian and a factor only dependingon time, which can be solved exactly. Both the invariant operator andthe eigenstate are obtained. In the periodical time-dependent case, thenon-adiabatic Berry's phase is also presented.
Adiabatic approximation of time-dependent density matrix functional response theory.
Pernal, Katarzyna; Giesbertz, Klaas; Gritsenko, Oleg; Baerends, Evert Jan
2007-12-07
Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.
Time-dependent closure relations for relativistic collisionless fluid equations.
Bendib-Kalache, K; Bendib, A; El Hadj, K Mohammed
2010-11-01
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space (ω,k), where ω and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter ω/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc²/T , where m is the particle rest mass and T, the plasma temperature in energy units.
Oh, Yun-Tak; Higashi, Yoichi; Chan, Ching-Kit; Han, Jung Hoon
2016-08-01
The Lang-Firsov Hamiltonian, a well-known solvable model of interacting fermion-boson system with sideband features in the fermion spectral weight, is generalized to have the time-dependent fermion-boson coupling constant. We show how to derive the two-time Green's function for the time-dependent problem in the adiabatic limit, defined as the slow temporal variation of the coupling over the characteristic oscillator period. The idea we use in deriving the Green's function is akin to the use of instantaneous basis states in solving the adiabatic evolution problem in quantum mechanics. With such "adiabatic Green's function" at hand we analyze the transient behavior of the spectral weight as the coupling is gradually tuned to zero. Time-dependent generalization of a related model, the spin-boson Hamiltonian, is analyzed in the same way. In both cases the sidebands arising from the fermion-boson coupling can be seen to gradually lose their spectral weights over time. Connections of our solution to the two-dimensional Dirac electrons coupled to quantized photons are discussed.
Leclerc, Arnaud; Viennot, David; Killingbeck, John P; 10.1063/1.3673320
2012-01-01
The Constrained Adiabatic Trajectory Method (CATM) is reexamined as an integrator for the Schr\\"odinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet and the (t,t') theories is presented in detail. Two points are then more particularly analysed and illustrated by a numerical calculation describing the $H_2^+$ ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to...
Leclerc, A.; Jolicard, G.; Viennot, D.; Killingbeck, J. P.
2012-01-01
The constrained adiabatic trajectory method (CATM) is reexamined as an integrator for the Schrödinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet, and the (t, t') theories is presented in detail. Two points are then more particularly analyzed and illustrated by a numerical calculation describing the H_2^+ ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to integrate the system.
Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
Chen, Xi
2010-01-01
There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
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...
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.
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai; PANG Ting; LIN Peng
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.
Time-dependent relativistic density functional study of Yb and YbO
XU WenHua; ZHANG Yong; LIU WenJian
2009-01-01
The low-lying electronic states of Yb and YbO are investigated by using time-dependent relativistic density functional theory,which is based on the newly developed exact two-component Hamiltonian resulting from symmetrized elimination of the small component.The nature of the excited states is analyzed by using the full molecular symmetry.The calculated results support the previous experimental assignment of the ground and excited states of YbO.
Kullie, Ossama, E-mail: kullie@uni-kassel.de [Institute de Chimie de Strasbourg, CNRS et Université de Strasbourg, Laboratoire de Chimie Quantique, 4 rue Blaise Pascal, 67070 Strasbourg (France); Theoretical Physics, Institute for Physics, Department of Mathematics and Natural Science, University of Kassel (Germany)
2013-03-29
Highlights: ► The achievement of CAMB3LYP functional for excited states in framework of TD-DFT. ► Relativistic 4-components calculations for the excited states of the Cd{sub 2} dimer. ► Relativistic Spin-Free calculations for the excited states of Cd{sub 2} dimer. ► A comparison of the achievements of different types of DFT approximations upon Cd{sub 2}. - Abstract: In this paper we present a time-dependent density functional study for the ground-state as well the 20-lowest laying excited states of the cadmium dimer Cd{sub 2}, we analyze its spectrum obtained from all electrons calculations performed with time-depended density functional for the relativistic Dirac-Coulomb- and relativistic spin-free-Hamiltonian as implemented in DIRAC-PACKAGE. The calculations were obtained with different density functional approximations, and a comparison with the literature is given as far as available. Our result is very encouraging, especially for the lowest excited states of this dimer, and is expected to be enlightened for similar systems. The result shows that only long-range corrected functionals such as CAMB3LYP, gives the correct asymptotic behavior for the higher states. A comparable but less satisfactory results were obtained with B3LYP and PBE0 functionals. Spin-free-Hamiltonian is shown to be very efficient for systems containing heavy elements such as Cd{sub 2} in frameworks of (time-dependent) density functional without introducing large errors.
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)
2015-12-31
We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.
Adiabatic theorem for non-hermitian time-dependent open systems
Fleischer, A; Fleischer, Avner; Moiseyev, Nimrod
2005-01-01
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t') formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criteria for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a 1D model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the gener- ation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived.
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-gang
2001-01-01
The relativistic random phase approximation (RRPA) is derived from the time-dependent relativistic mean field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also ah configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that
Spitkovsky, A; Spitkovsky, Anatoly; Arons, Jonathan
2004-01-01
We describe results from time-dependent numerical modeling of the collisionless reverse shock terminating the pulsar wind in the Crab Nebula. We treat the upstream relativistic wind as composed of ions and electron-positron plasma embedded in a toroidal magnetic field, flowing radially outward from the pulsar in a sector around the rotational equator. The relativistic cyclotron instability of the ion gyrational orbit downstream of the leading shock in the electron-positron pairs launches outward propagating magnetosonic waves. Because of the fresh supply of ions crossing the shock, this time-dependent process achieves a limit-cycle, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in the magnetic field and pair density associated with these waves, as well as their propagation speed, semi-quantitatively reproduce the behavior of the wisp and ring features described in recent observations obtained using the Hubble Space Telescope and the Chandra X-Ray Observator...
Zhang, Ruili; He, Yang; Xiao, Jianyuan; Liu, Jian; Qin, Hong; Tang, Yifa
2016-01-01
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using symplectic integrators. For modern large-scale particle simulations in complex, time-dependent electromagnetic field, explicit symplectic algorithms are much more preferable. In this paper, we treat the relativistic dynamics of a particle as a Hamiltonian system on the cotangent space of the space-time, and construct for the first time explicit symplectic algorithms for relativistic charged particles of order 2 and 3 using the sum-split technique and generating functions.
WANG Yu-Sheng; ZHANG Xiao-Ni; YUAN Bao-He; FANG Jian-Hui; YANG Guo-Hong; LIN Peng; PANG Ting
2008-01-01
Based on the concept of higher-order adiabatic invariants of mechanical system with action of a small perturbation, the perturbation to Lie symmetry and generalized Hojman adiabatic invariants for the relativistic Hamilton system are studied. Perturbation to Lie symmetry is discussed under general infinitesimal transformation of groups in which time is variable. The form and the criterion of generalized Hojman adiabatic invariants for this system are obtained. Finally, an example is given to illustrate the results.
A relativistic time-dependent density functional study of the excited states of the mercury dimer
Kullie, Ossama, E-mail: kullie@uni-kassel.de, E-mail: ossama.kullie@unistra.fr [Institute de Chimie de Strasbourg, CNRS et Université de Strasbourg, Laboratoire de Chimie Quantique, 4 rue Blaise Pascal, 67070 Strasbourg, France and Theoretical Physics, Institute for Physics, Department of Mathematics and Natural Science, University of Kassel, D-34127 Kassel (Germany)
2014-01-14
In previous works on Zn{sub 2} and Cd{sub 2} dimers we found that the long-range corrected CAMB3LYP gives better results than other density functional approximations for the excited states, especially in the asymptotic region. In this paper, we use it to present a time-dependent density functional (TDDFT) study for the ground-state as well as the excited states corresponding to the (6s{sup 2} + 6s6p), (6s{sup 2} + 6s7s), and (6s{sup 2} + 6s7p) atomic asymptotes for the mercury dimer Hg{sub 2}. We analyze its spectrum obtained from all-electron calculations performed with the relativistic Dirac-Coulomb and relativistic spinfree Hamiltonian as implemented in DIRAC-PACKAGE. A comparison with the literature is given as far as available. Our result is excellent for the most of the lower excited states and very encouraging for the higher excited states, it shows generally good agreements with experimental results and outperforms other theoretical results. This enables us to give a detailed analysis of the spectrum of the Hg{sub 2} including a comparative analysis with the lighter dimers of the group 12, Cd{sub 2}, and Zn{sub 2}, especially for the relativistic effects, the spin-orbit interaction, and the performance of CAMB3LYP and is enlightened for similar systems. The result shows, as expected, that spinfree Hamiltonian is less efficient than Dirac-Coulomb Hamiltonian for systems containing heavy elements such as Hg{sub 2}.
Wells, J C; Eichler, J
1999-01-01
We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.
Tominaga, Nozomu; Blinnikov, Sergei I
2015-01-01
We develop a time-dependent multi-group multidimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) that evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with a ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed frame approach; the source function is evaluated in the comoving frame whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated with various test problems and comparisons with results of a relativistic Monte Carlo code. These validations confirm that the code ...
Avron, Joseph
2016-01-01
We derive the relativistically exact Eikonal equation for ring interferometers undergoing adiabatic deformations. The leading term in the adiabatic expansion of the phase shift is independent of the refraction index $n$ and is given by a line integral generalizing results going back to Sagnac to all orders in $\\beta$. The next term in the adiabaticity is of lower order in $\\beta$ and may be as important as the first in nonrelativistic cases. This term is proportional to $n^2$ and has the form of a double integral. It generalizes previous results to fibers with chromatic dispersion and puts Sagnac and Fizeau interferometers under a single umbrella.
Pétri, J
2014-01-01
Pulsars are believed to loose their rotational kinetic energy primarily by a large amplitude low frequency electromagnetic wave which is eventually converted into particle creation, acceleration and followed by a broad band radiation spectrum. To date, there exist no detailed calculation of the exact spin-down luminosity with respect to the neutron star magnetic moment and spin frequency, including general-relativistic effects. Estimates are usually given according to the flat spacetime magnetodipole formula. The present paper pursue our effort to look for accurate solutions of the general-relativistic electromagnetic field around a slowly rotating magnetized neutron star. In a previous work, we already found approximate stationary solutions to this problem. Here we address again this problem but using a more general approach. We indeed solve the full set of time-dependent Maxwell equations in a curved vacuum space-time following the 3+1 formalism. The numerical code is based on our pseudo-spectral method exp...
Avron, Joseph; Kenneth, Oded
2016-12-01
We derive the relativistically exact eikonal equation for ring interferometers undergoing deformation. For ring interferometers that undergo slow deformation we describe the two leading terms in the adiabatic expansion of the phase shift. The leading term is independent of the refraction index n and is given by a line integral generalizing results going back to Sagnac for nondeforming interferometers to all orders in β =|v |/c . In the nonrelativistic limit this term is O (β ) . The next term in the adiabaticity has the form of a double integral, it is of order β0 and depends on the refractive index n . It accounts for nonreciprocity due to changing circumstances in the fiber. The adiabatic correction is often comparable to the Sagnac term. In particular, this is the case in Fizeau's interferometer. Besides providing a mathematical framework that puts all ring interferometers under a single umbrella, our results strengthen earlier results and generalize them to fibers with chromatic dispersion.
Kullie, Ossama [CNRS et Universite de Strasbourg, Institut de Chimie, Laboratoire de Chimie Quantique, 1 Rue Blaise Pascal, F- 67008 Strasbourg cedex (France)
2012-07-01
In this poster I present a (time-dependent) density functional study of the 20 low-lying excited states as well the ground states of the zinc dimer Zn{sub 2}. I analyze the spectrum of the dimer obtained form all electrons calculations which are performed using time-depended density functional with a relativistic 4-components-, and spin-free-Hamiltonian. I show results for different well-known density functional approximations, in comparing with literature and experimental values, the results are very encouraging, especially for the lowest excited states of these dimers. However, the results show that only the long-range corrected functionals such CAMB3LYP gives the correct asymptotic behavior for the higher states, for which the best result is obtained, and a comparable result is obtained from PBE0 functional.
Ji, Min; Lan, Xin; Han, Zhenping; Hao, Ce; Qiu, Jieshan
2012-11-19
The electronically excited state and luminescence property of metal-organic framework MOF-5 were investigated using relativistic density functional theory (DFT) and time-dependent DFT (TDDFT). The geometry, IR spectra, and UV-vis spectra of MOF-5 in the ground state were calculated using relativistic DFT, leading to good agreement between the experimental and theoretical results. The frontier molecular orbitals and electronic configuration indicated that the luminescence mechanism in MOF-5 follows ligand-to-ligand charge transfer (LLCT), namely, π* → π, rather than emission with the ZnO quantum dot (QD) proposed by Bordiga et al. The geometry and IR spectra of MOF-5 in the electronically excited state have been calculated using the relativistic TDDFT and compared with those for the ground state. The comparison reveals that the Zn4O13 QD is rigid, whereas the ligands BDC(2-) are nonrigid. In addition, the calculated emission band of MOF-5 is in good agreement with the experimental result and is similar to that of the ligand H2BDC. The combined results confirmed that the luminescence mechanism for MOF-5 should be LLCT with little mixing of the ligand-to-metal charge transfer. The reason for the MOF-5 luminescence is explained by the excellent coplanarity between the six-membered ring consisting of zinc, oxygen, carbon, and the benzene ring.
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 ...
Kutnink, Timothy; Santrach, Amelia; Hockett, Sarah; Barcus, Scott; Petridis, Athanasios
2016-09-01
The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the staggered-leap-frog algorithm with reflecting boundary conditions. The stability region of the method versus the interaction strength and the spatial-grid size over time-step ratio is established. The expectation values of several dynamic operators are then evaluated as functions of time. These include the fermion and electromagnetic energies and the fermion dynamic mass, as the self-interacting spinors are no longer mass-eigenfunctions. There is a characteristic, non-exponential, oscillatory dependence leading to asymptotic constants of these expectation values. In the case of the fermion mass this amounts to renormalization. The dependence of the expectation values on the spatial-grid size is evaluated in detail. Statistical regularization, employing a canonical ensemble whose temperature is the inverse of the grid size, is used to remove the grid-size dependence and produce a finite result in the continuum limit.
Hossen, M. R.; Nahar, L.; Mamun, A. A. [Jahangirnagar University,Savar, Dhaka (Bangladesh)
2014-12-15
The properties of time-dependent cylindrical and spherical, modified ion-acoustic (mIA) solitary structures in relativistic degenerate multi-ion plasmas (containing degenerate electron fluids, inertial positively-, as well as negatively-, charged light ions, and positively-charged static heavy ions) have been investigated theoretically. This investigation is valid for both non-relativistic and ultrarelativistic limits. The well-known reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV) and the mK-dV equations for studying the basic features of solitary waves. The fundamental characteristics of mIA solitary waves are found to be significantly modified by the effects of the degenerate pressures of the electron and the ion fluids, their number densities, and the various charge states of heavy ions. The relevance of our results in astrophysical compact objects like white dwarfs and neutron stars, which are of scientific interest, is briefly discussed.
Imamura, Yutaka; Kamiya, Muneaki; Nakajima, Takahito
2016-03-01
We study spin-forbidden transitions of Os polypyridyl sensitizers by two-component relativistic time-dependent density functional theory with the spin-orbit interaction based on Tamm-Dancoff approximation. The absorption spectra, including spin-forbidden-transition peaks, for the Os complexes are reasonably reproduced in comparison with the experimental ones. The extension of the conjugated lengths in the Os complexes is investigated and found to be effective to enhance photo absorption for spin-allowed transitions as well as spin-forbidden ones. This study provides fruitful information for a design of new dyes in terms of conjugation lengths.
Nakata, Ayako; Tsuneda, Takao; Hirao, Kimihiko
2011-12-14
A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Gholibeigian, Hassan; Amirshahkarami, Abdolazim; Gholibeigian, Kazem
2017-01-01
In special relativity theory, time dilates in velocity of near light speed. Also based on ``Substantial motion'' theory of Sadra, relative time (time flux); R = f (mv , σ , τ) , for each atom is momentum of its involved fundamental particles, which is different from the other atoms. In this way, for modification of the relativistic classical equation of string theory and getting more precise results, we should use effect of dilation and contraction of time in equation. So we propose to add two derivatives of the time's flux to the equation as follows: n.tp∂/R ∂ τ +∂2Xμ/(σ , τ) ∂τ2 = n .tp (∂/R ∂ σ ) +c2∂2Xμ/(σ , τ) ∂σ2 In which, Xμ is space-time coordinates of the string, σ & τ are coordinates on the string world sheet, respectively space and time along the string, string's mass m , velocity of string's motion v , factor n depends on geometry of each hidden extra dimension which relates to its own flux time, and tp is Planck's time. AmirKabir University of Technology, Tehran, Iran.
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.
Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index
Mignone, A
2007-01-01
The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $\\Gamma$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of ast...
The stability of relativistic stars and the role of the adiabatic index
Moustakidis, Ch. C.
2017-05-01
We study the stability of three analytical solutions of the Einstein's field equations for spheres of fluid. These solutions are suitable to describe compact objects including white dwarfs, neutron stars and supermassive stars and they have been extensively employed in the literature. We re-examine the range of stability of the Tolman VII solution, we focus on the stability of the Buchdahl solution which is under contradiction in the literature and we examine the stability of the Nariai IV solution. We found that all the mentioned solutions are stable in an extensive range of the compactness parameter. We also concentrate on the effect of the adiabatic index on the instability condition. We found that the critical adiabatic index, depends linearly on the ratio of central pressure over central energy density P_c/{E}_c, up to high values of the compactness. Finally, we examine the possibility to impose constraints, via the adiabatic index, on realistic equations of state in order to ensure stable configurations of compact objects.
Equation of state in relativistic magnetohydrodynamics: variable versus constant adiabatic index
Mignone, A.; McKinney, Jonathan C.
2007-07-01
The role of the equation of state (EoS) for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant Γ-law EoS, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic EoS that better approximates the single-specie relativistic gas. The paper focuses on three different topics. First, the influence of a more realistic EoS on the propagation of fast magnetosonic shocks is investigated. This calls into question the validity of the constant Γ-law EoS in problems where the temperature of the gas substantially changes across hydromagnetic waves. Secondly, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general EoS and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic EoS can considerably bear upon the solution when transitions from cold to hot gas (or vice versa) are present. Under these circumstances, a polytropic EoS can significantly endanger the solution.
Non-adiabatic radiative collapse of a relativistic star under different initial conditions
Ranjan Sharma; Ramesh Tikekar
2012-09-01
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 under anisotropic pressure. Both the configurations are spherically symmetric. However, in the latter case, the physical space = constant of the configurations endowed with spheroidal or pseudospheroidal geometry is assumed to be inhomogeneous. It is observed that as long as the collapse is shear-free, its evolution depends only on the mass and size of the star at the onset of collapse.
Entropy density of an adiabatic relativistic Bose-Einstein condensate star
Khaidir, Ahmad Firdaus; Kassim, Hasan Abu; Yusof, Norhasliza [Theoretical Physics Lab., Department of Physics, Faculty of Science Building, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2015-04-24
Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of T due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.
Cencek, Wojciech; Przybytek, Michał; Komasa, Jacek; Mehl, James B; Jeziorski, Bogumił; Szalewicz, Krzysztof
2012-06-14
The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound
Gritsenko, Oleg V; Baerends, Evert Jan
2009-06-14
Time-dependent density functional (response) theory (TDDF(R)T) is applied almost exclusively in its adiabatic approximation (ATDDFT), which is restricted to predominantly single electronic excitations and neglects additional roots of the TDDFT eigenvalue problem stemming from the interaction between single and double excitations. We incorporate the effect of the latter interaction into a non-adiabatic frequency-dependent and spatially non-local Hartree-exchange-correlation (Hxc) kernel fCEDAHxc (r1, r2, omega), the explicit analytical expression of which is derived for interacting single and double excitations well separated from the other excitations, within the common energy denominator approximation (CEDA) for the Kohn-Sham (KS) and interacting density response functions, chis and chi, respectively. The kernel fCEDAHxc (r1, r2, omega) obtained from the direct analytical inverse of chiCEDAs and chiCEDA is a sum of the delta-function and non-local orbital-dependent spatial terms with frequency-dependent factors, with which fCEDAHxc acquires a modulated quadratic dependence on omega. The effective incorporation in fCEDAHxc of the complete manifold of excited states (through the delta function term) represents an extension of the kernel reported by Maitra, Zhang, Cave, and Burke [J. Chem. Phys., 2004, 120, 5932]. In the TDDFT eigenvalue equations considered in the diagonal approximation, fCEDAHxc generates two excitation energies omegaq and omegaq+1, which both correspond to the same single KS excitation omegasq, thus producing the effect of the single-double excitation interaction.
Casida, Mark E; Huix-Rotllant, Miquel
2016-01-01
In their famous paper, Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays, however, the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very similar to what the local density approximation (LDA) is to conventional ground-state DFT. Although some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.
Yb、Ybo电子激发态的相对论含时密度泛函理论研究%Time-dependent relativistic density functional study of Yb and YbO
许文华; 张勇; 刘文剑
2009-01-01
The low-lying electronic states of Yb and YbO are investigated by using time-dependent relativistic density functional theory,which is based on the newly developed exact two-component Hamiltonian resulting from symmetrized elimination of the small component.The nature of the excited states is analyzed by using the fall molecular symmetry.The calculated results support the previous experimental assignment of the ground and excited states of YbO.%本文用基于精确二分量哈密顿(exact two-component Hamiltonian)的相对论含时密度泛函理论(time-dependent relativistic density functional theory)计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认.
Romaniello, P; de Boeij, P L
2005-04-22
We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation.
Relativistic and non-relativistic geodesic equations
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Time-dependent Dyson orbital theory.
Gritsenko, O V; Baerends, E J
2016-08-21
Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρ(N)(t) of N-electron systems, it also encounters problems in this application. The first problem is the neglect of memory effects stemming from the, in TDDFT virtually unavoidable, adiabatic approximation, the second problem is the reliable evaluation of the probabilities P(n)(t) of multiple photoinduced ionization, while the third problem (which TDDFT shares with other approaches) is the reliable description of continuum states of the electrons ejected in the process of ionization. In this paper time-dependent Dyson orbital theory (TDDOT) is proposed. Exact TDDOT equations of motion (EOMs) for time-dependent Dyson orbitals are derived, which are linear differential equations with just static, feasible potentials of the electron-electron interaction. No adiabatic approximation is used, which formally resolves the first TDDFT problem. TDDOT offers formally exact expressions for the complete evolution in time of the wavefunction of the outgoing electron. This leads to the correlated probability of single ionization P(1)(t) as well as the probabilities of no ionization (P(0)(t)) and multiple ionization of n electrons, P(n)(t), which formally solves the second problem of TDDFT. For two-electron systems a proper description of the required continuum states appears to be rather straightforward, and both P(1)(t) and P(2)(t) can be calculated. Because of the exact formulation, TDDOT is expected to reproduce a notorious memory effect, the "knee structure" of the non-sequential double ionization of the He atom.
Casarin, Maurizio; Finetti, Paola; Vittadini, Andrea; Wang, Fan; Ziegler, Tom
2007-06-21
Time-dependent density functional theory (TDDFT) coupled to the relativistic two-component zeroth-order regular approximation, both available in the last version of the ADF package, have been successfully used to simulate X-ray absorption spectra of TiCl4, Ti(eta5-C5H5)Cl3, and Ti(eta5-C5H5)2Cl2 in terms of their oscillator strength distributions. Besides allowing a first principle assignment of Ti 1s, Cl 1s, and Ti 2p (L2,3 edges) core excitation spectra, theoretical outcomes provide a rationale for deviations from the expected L3/L2 branching ratio.
Ioannidou, Theodora
2016-01-01
An extended version of the BPS Skyrme model that admits time-dependent solutions is discussed. Initially, by introducing a power law at the original potential term of the BPS Skyrme model the existence, stability and structure of the corresponding solutions is investigated. Then, the frequencies and half-lifes of the radial oscillations of the constructed time-dependent solutions are determined.
Guest, G.E.; Dandl, R.A.; Miller, R.L.
1989-01-17
The Plasma Electron Microwave Source (PEMS) concept is a relativistic-electron plasma confined in a magnetic-mirror device. The stored energy is transformed into microwaves through amplification of whistler waves that can be launched externally for amplifier operation or generated spontaneously for oscillator operation. The anisotropy of the hot-electron temperature governs the maximum plasma energy density that can be stored, the amplification rates, and the saturated power level of the unstable whistler waves. This report summarizes the results of theoretical studies of (1) the critical aspects of hot-electron plasmas generated by ECH techniques, such as the Upper Off-Resonant Heating pioneered by Dandl in the ELMO series of experiments; and, (2) the spatial amplification rates of unstable whistler waves in these plasmas. It is shown that a substantial fraction of the energy stored in a hot-electron plasma can be transformed into repetitive pulses of microwave power by employing the PEMS approach, with typical values of gain, about 40db and bandwidth.
Studies of Spuriously Time-dependent Resonances in Time-dependent Density Functional Theory
Luo, Kai; Maitra, Neepa T
2016-01-01
Adiabatic approximations in time-dependent density functional theory (TDDFT) will in general yield unphysical time-dependent shifts in the resonance positions of a system driven far from its ground-state. This spurious time-dependence is rationalized in [J. I. Fuks, K. Luo, E. D. Sandoval and N. T. Maitra, Phys. Rev. Lett. {\\bf 114}, 183002 (2015)] in terms of the violation of an exact condition by the non-equilibrium exchange-correlation kernel of TDDFT. Here we give details on the derivation and discuss reformulations of the exact condition that apply in special cases. In its most general form, the condition states that when a system is left in an arbitrary state, in the absence of time-dependent external fields nor ionic motion, the TDDFT resonance position for a given transition is independent of the state. Special cases include the invariance of TDDFT resonances computed with respect to any reference interacting stationary state of a fixed potential, and with respect to any choice of appropriate stationa...
Relativistic Guiding Center Equations
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
On time dependent Ekman transports
Roed, L.P
1973-01-01
One of the most cited papers in ocean current theories is the paper by Ekman (1905). Here we take his paper as a starting point for computing time dependent solutions for the integrated velocities or the transports.
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution
Relativistic Photoionization Computations with the Time Dependent Dirac Equation
2016-10-12
unlimited. i REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188 3. DATES COVERED (From - To) Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std...REPORT TYPE1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 6. AUTHOR(S) 8. PERFORMING ORGANIZATION REPORT NUMBER 7. PERFORMING ORGANIZATION NAME(S...Graphical Processing Units are utilized in parallel to speed up calculations. 12-10-2016 Interim Naval Research Laboratory 4555 Overlook Avenue, SW
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T.
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it wit...
Quantum-Classical Correspondence of Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2017-04-01
We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Korteweg-de Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of time-dependent parameters. We use the Hamilton-Jacobi theory to define the generalized action. The action is independent of the history of the parameters and is directly related to the adiabatic invariant. The dispersionless KdV hierarchy is obtained from the classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity. This correspondence suggests some relation between the quantum and classical adiabatic theorems.
Relativistic radiative transfer in relativistic spherical flows
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
Time-dependent density functional theory for quantum transport.
Zheng, Xiao; Chen, GuanHua; Mo, Yan; Koo, SiuKong; Tian, Heng; Yam, ChiYung; Yan, YiJing
2010-09-21
Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.
Time dependence of immersion freezing
A. Welti
2012-05-01
Full Text Available The time dependence of immersion freezing was studied for temperatures between 236 K and 243 K. Droplets with single immersed, size-selected 400 nm and 800 nm kaolinite particles were produced at 300 K, cooled down to supercooled temperatures typical for mixed-phase cloud conditions, and the fraction of frozen droplets with increasing residence time was detected. To simulate the conditions of immersion freezing in mixed-phase clouds we used the Zurich Ice Nucleation Chamber (ZINC and its vertical extension, the Immersion Mode Cooling chAmber (IMCA. We observed that the frozen fraction of droplets increased with increasing residence time in the chamber. This suggests that there is a time dependence of immersion freezing and supports the importance of a stochastic component in the ice nucleation process. The rate at which droplets freeze was observed to decrease towards higher temperatures and smaller particle sizes. Comparison of the laboratory data with four different ice nucleation models, three based on classical nucleation theory with different representations of the particle surface properties and one singular, suggest that the classical, stochastic approach combined with a distribution of contact angles is able to reproduce the ice nucleation observed in these experiments most accurately. Using the models to calculate the increase in frozen fraction at typical mixed-phase cloud temperatures over an extended period of time, yields an equivalent effect of −1 K temperature shift and an increase in time scale by a factor of ~10.
Accurate Ground-State Energies of Solids and Molecules from Time-Dependent Density-Functional Theory
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
We demonstrate that ground-state energies approaching chemical accuracy can be obtained by combining the adiabatic-connection fluctuation-dissipation theorem with time-dependent densityfunctional theory. The key ingredient is a renormalization scheme, which eliminates the divergence...
Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential
Campbell, Joel
2009-01-01
The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.
Network-timing-dependent plasticity
Vincent eDelattre
2015-06-01
Full Text Available Bursts of activity in networks of neurons are thought to convey salient information and drive synaptic plasticity. Here we report that network bursts also exert a profound effect on Spike-Timing-Dependent Plasticity (STDP. In acute slices of juvenile rat somatosensory cortex we paired a network burst, which alone induced long-term depression (LTD, with STDP-induced long-term potentiation and depression (LTP and LTD. We observed that STDP-induced LTP was either unaffected, blocked or flipped into LTD by the network burst, and that STDP-induced LTD was either saturated or flipped into LTP, depending on the relative timing of the network burst with respect to spike coincidences of the STDP event. We hypothesized that network bursts flip STDP-induced LTP to LTD by depleting resources needed for LTP and therefore developed a resource-dependent STDP learning rule. In a model neural network under the influence of the proposed resource-dependent STDP rule, we found that excitatory synaptic coupling was homeostatically regulated to produce power law distributed burst amplitudes reflecting self-organized criticality, a state that ensures optimal information coding.
Network-timing-dependent plasticity.
Delattre, Vincent; Keller, Daniel; Perich, Matthew; Markram, Henry; Muller, Eilif B
2015-01-01
Bursts of activity in networks of neurons are thought to convey salient information and drive synaptic plasticity. Here we report that network bursts also exert a profound effect on Spike-Timing-Dependent Plasticity (STDP). In acute slices of juvenile rat somatosensory cortex we paired a network burst, which alone induced long-term depression (LTD), with STDP-induced long-term potentiation (LTP) and LTD. We observed that STDP-induced LTP was either unaffected, blocked or flipped into LTD by the network burst, and that STDP-induced LTD was either saturated or flipped into LTP, depending on the relative timing of the network burst with respect to spike coincidences of the STDP event. We hypothesized that network bursts flip STDP-induced LTP to LTD by depleting resources needed for LTP and therefore developed a resource-dependent STDP learning rule. In a model neural network under the influence of the proposed resource-dependent STDP rule, we found that excitatory synaptic coupling was homeostatically regulated to produce power law distributed burst amplitudes reflecting self-organized criticality, a state that ensures optimal information coding.
Second Quantized Scalar QED in Homogeneous Time-Dependent Electromagnetic Fields
Kim, Sang Pyo
2014-01-01
We formulate the second quantized scalar quantum electrodynamics in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian for a charged scalar field is an infinite system of decoupled time-dependent oscillators for electric fields but of coupled time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator plays the role of the time-dependent annihilation and creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally the quantum state and pair production is discussed when a time-dependent electric field is present in parallel to t...
Effective field theory in time-dependent settings
Collins, Hael; Ross, Andreas
2012-01-01
We use the in-in or Schwinger-Keldysh formalism to explore the construction and interpretation of effective field theories for time-dependent systems evolving out of equilibrium. Starting with a simple model consisting of a heavy and a light scalar field taken to be in their free vacuum states at a finite initial time, we study the effects from the heavy field on the dynamics of the light field by analyzing the equation of motion for the expectation value of the light background field. New terms appear which cannot arise from a local action of an effective field theory in terms of the light field, though they disappear in the adiabatic limit. We discuss the origins of these terms as well as their possible implications for time dependent situations such as inflation.
Nuclear inertia from the time dependent pairing equations
Mirea, M.
2016-10-01
In a dynamical system, the momenta of inertia and the effective masses are not adiabatic quantities, but are dynamical ones that depend on the dissipated energy accumulated during motion. However, these parameters are calculated for adiabatic nuclear systems, leaving no room for dissipated energy. In this work, a formalism is elaborated in order to derive simultaneously the nuclear momenta of inertia and the effective masses by taking into account the appearance of dissipated energy for large amplitude motion of the nuclear system. The expressions that define the inertia are obtained from the variational principle. The same principle manages the time dependent pairing equations, offering estimations of the averaged dissipation energy for large amplitude motions. The model is applied to 232Th fission. The fission barrier was calculated along the least action trajectory. The dissipation energy, effective mass and moment of inertia are determined for different values of the collective velocities. The dissipation increases with the internuclear velocity in binary disintegration processes and modifies the effective mass parameters. We observed that the inertia decreases as long as the collective velocity increases to some moderate values and begins to grow for larger collective velocities. So, a dependence between the cranking mass parameters and the intrinsic excitation energy is evidenced. In order to investigate the overall effect, the half-lives are predicted for adiabatic and dynamics simulations.
Markovian quantum master equation beyond adiabatic regime
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τA(t ) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τA(t ) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Holographic Complexity for Time-Dependent Backgrounds
Momeni, Davood; Bahamonde, Sebastian; Myrzakulov, Ratbay
2016-01-01
In this paper, we will analyse the holographic complexity for time-dependent asymptotically $AdS$ geometries. We will first use a covariant zero mean curvature slicing of the time-dependent bulk geometries, and then use this co-dimension one spacelike slice of the bulk spacetime to define a co-dimension two minimal surface. The time-dependent holographic complexity will be defined using the volume enclosed by this minimal surface. This time-dependent holographic complexity will reduce to the usual holographic complexity for static geometries. We will analyse the time-dependence as a perturbation of the asymptotically $AdS$ geometries. Thus, we will obtain time-dependent asymptotically $AdS$ geometries, and we will calculate the holographic complexity for such a time-dependent geometries.
Fast forward to the classical adiabatic invariant
Jarzynski, Christopher; Patra, Ayoti; Subaşı, Yiğit
2016-01-01
We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of action $I_0$, we construct a "fast-forward" potential energy function $V_{\\rm FF}(q,t)$ that, when added to $H$, guides all trajectories with initial action $I_0$ to end with the same value of action. We use this result to construct a local dynamical invariant $J(q,p,t)$ whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.
Time-dependent density-functional theory for extended systems
Botti, Silvana [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Schindlmayr, Arno [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Del Sole, Rodolfo [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Reining, Lucia [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown)
2007-03-15
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schroedinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schroedinger equations-the Kohn-Sham equations. The complication of the problem is hidden in the-unknown-time-dependent exchange and correlation potential that appears in the Kohn-Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe-Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.
Shortcuts to adiabaticity for quantum annealing
Takahashi, Kazutaka
2017-01-01
We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz, and the Hamiltonian is designed by the inverse engineering. We show that the time dependence of physical quantities such as the magnetization is independent of the speed of the Hamiltonian variation in the infinite-range model. We also show that rotating transverse magnetic fields are useful to achieve the ideal time evolution.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Isothermal and Adiabatic Measurements.
McNairy, William W.
1996-01-01
Describes the working of the Adiabatic Gas Law Apparatus, a useful tool for measuring the pressure, temperature, and volume of a variety of gases undergoing compressions and expansions. Describes the adaptation of this apparatus to perform isothermal measurements and discusses the theory behind the adiabatic and isothermal processes. (JRH)
Preparation of Entangled States of Three Particles by Adiabatic Passage
郭建友
2002-01-01
We propose a novel technique for the creation of entangled states of three particles, based upon an adiabatic passage induced by a suitably crafted time-dependent external field. We derive the corresponding adiabatic and bare conditions for the preparation of entangled states. We obtain the time evolutions of the energy of the system and the populations involving the initial state and target entangled state.
Large blue isocurvature spectral index signals time-dependent mass
Chung, Daniel J. H.
2016-08-01
We show that if a spectator linear isocurvature dark matter field degree of freedom has a constant mass through its entire evolution history, the maximum measurable isocurvature spectral index that is consistent with the current tensor-to-scalar ratio bound of about r ≲0.1 is about nI≲2.4 , even if experiments can be sensitive to a 10-6 contamination of the predominantly adiabatic power spectrum with an isocurvature power spectrum at the shortest observable length scales. Hence, any foreseeable future measurement of a blue isocurvature spectral index larger than ˜2.4 may provide nontrivial evidence for dynamical degrees of freedom with time-dependent masses during inflation. The bound is not sensitive to the details of the reheating scenario and can be made mildly smaller if r is better constrained in the future.
Quantum Computation by Adiabatic Evolution
Farhi, E; Gutmann, S; Sipser, M; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Sipser, Michael
2000-01-01
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on the minimum energy difference between the two lowest states of the interpolating Hamiltonian. We are unable to estimate this gap in general. We give some special symmetric cases of the satisfiability problem where the symmetry allows us to estimate the gap and we show that, in these cases, our algorithm runs in polynomial time.
Bohr Hamiltonian with time-dependent potential
Naderi, L.; Hassanabadi, H.; Sobhani, H.
2016-04-01
In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.
Competing risks and time-dependent covariates
Cortese, Giuliana; Andersen, Per K
2010-01-01
Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates...
Eisenhart lifts and symmetries of time-dependent systems
Cariglia, M.; Duval, C.; Gibbons, G. W.; Horváthy, P. A.
2016-10-01
Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with n degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in n + 2 dimensions, equipped with its covariantly constant null Killing vector field. Reparametrisation of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaître and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.
Adiabatic turbocompound diesel engine
Kamo, R.; Bryzik, W.
1984-02-01
The research and development of an adiabatic turbocompound engine have shown that the concept is feasible. The ability to meet the performance and sociability goals of the future power plants has been demonstrated. Low brake specific fuel consumption, low smoke and particulates, better NO /SUB x/ -BSFC trade-off, excellent multifuel capability, white smoke suppression, and potentially lower maintenance and greater reliability and durability are some of the attributes. The absence of the water cooling system adds to its attractiveness because of lower installed weight, cost, and reduction in parasitic losses. The operating environment of an adiabatic engine is shown as the basis for analysis and designing of adiabatic components. The types of material which can satisfy the needs of an adiabatic engine are presented. These materials include high temperature metals, high performance ceramics, and glass ceramics. The use of a turbocompound system to utilize the increased exhaust energy of an adiabatic engine is covered. A minimum fuel consumption of 0.285 lb/bhp-hr was achieved at 200 psi BMEP. Although the technical feasibility and viability of an adiabatic engine was demonstrated, the adiabatic diesel engine has problems which must be solved before it becomes a commercially viable product. These problem areas where more work is required are discussed.
Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation
WANG Fei; QIAN Shang-Wu; FU Li-Ping; WANG Jing-Shan; GUO Ke-Tao
2008-01-01
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A genera/ equation for obtaining gauge-invariant transition probability amplitudes is derived.
Quantum adiabatic machine learning
Pudenz, Kristen L
2011-01-01
We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. We apply and illustrate this approach in detail to the problem of software verification and validation.
Diabatic constrained relativistic mean field approach
L"u, H F; Meng, J
2005-01-01
A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. The potential energy surfaces of $^{208}$Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. The diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to define the single particle orbits at very deformed region by their quantum numbers, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.
Non-adiabatic effects in near-adiabatic mixed-field orientation and alignment
Maan, Anjali; Ahlawat, Dharamvir Singh; Prasad, Vinod
2016-11-01
We present a theoretical study of the impact of a pair of moderate electric fields tilted an angle with respect to one another on a molecule. As a prototype, we consider a molecule with large rotational constant (with corresponding small rotational period) and moderate dipole moment. Within rigid-rotor approximation, the time-dependent Schrodinger equation is solved using fourth-order Runge-Kutta method. We have analysed that lower rotational states are significantly influenced by variation in pulse durations, the tilt angle between the fields and also on the electric field strengths. We also suggest a control scheme of how the rotational dynamics, orientation and alignment of a molecule can be enhanced by a combination of near-adiabatic pulses in comparision to non-adiabatic or adiabatic pulses.
Oreshkov, Ognyan; Calsamiglia, John
2010-07-30
We propose a theory of adiabaticity in quantum markovian dynamics based on a decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As two applications of our theory, we propose a general framework for decoherence-assisted computation in noiseless codes and a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by nondissipative means.
ALCHEMIC: Advanced time-dependent chemical kinetics
Semenov, Dmitry A.
2017-08-01
ALCHEMIC solves chemical kinetics problems, including gas-grain interactions, surface reactions, deuterium fractionization, and transport phenomena and can model the time-dependent chemical evolution of molecular clouds, hot cores, corinos, and protoplanetary disks.
Lobe, Elisabeth; Stollenwerk, Tobias; Tröltzsch, Anke
2015-01-01
In the recent years, the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. These machines are suited to solve discrete optimisation problems which are typically very hard to solve on a classical computer. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. We explain the basic principles of adiabatic ...
Magnetic circular dichroism in real-time time-dependent density functional theory
Lee, K -M; Bertsch, G F
2010-01-01
We apply the adiabatic time-dependent density functional theory to magnetic ci the real-space, real-time computational method. The standard formulas for the MCD response and its A and B terms are derived from the observables in the time-dependent wave function. We find the real time method is well suited for calculating the overall spectrum, particularly at higher excitation energies where individual excited states are numerous and overlapping. The MCD sum rules are derived and interpreted in the real-time formalism; we find that they are very useful for normalization purposes and assessing the accuracy of the theory. The method is applied to MCD spectrum of C-60 using the adiabatic energy functional from the local density approximation. The theory correctly predicts the signs of the A and B terms for the lowest allowed excitations. However, the magnitudes of the terms only show qualitative agreement with experiment.
Adiabatic quantum computation along quasienergies
Tanaka, Atushi
2009-01-01
The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy is recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [Tanaka and Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of...
Rüger, Robert; Niehaus, Thomas; van Lenthe, Erik; Heine, Thomas; Visscher, Lucas
2016-01-01
We report a time-dependent density functional based tight-binding (TD-DFTB) scheme for the calculation of UV/Vis spectra, explicitly taking into account the excitation of nuclear vibrations via the adiabatic Hessian Franck-Condon (AH|FC) method with a harmonic approximation for the nuclear wavefunction. The theory of vibrationally resolved UV/Vis spectroscopy is first summarized from the viewpoint of TD-DFTB. The method is benchmarked against time-dependent density functional theory (TD-DFT) ...
Giesbertz, K J H; Pernal, K; Gritsenko, O V; Baerends, E J
2009-03-21
Time-dependent density functional theory in its current adiabatic implementations exhibits three striking failures: (a) Totally wrong behavior of the excited state surface along a bond-breaking coordinate, (b) lack of doubly excited configurations, affecting again excited state surfaces, and (c) much too low charge transfer excitation energies. We address these problems with time-dependent density matrix functional theory (TDDMFT). For two-electron systems the exact exchange-correlation functional is known in DMFT, hence exact response equations can be formulated. This affords a study of the performance of TDDMFT in the TDDFT failure cases mentioned (which are all strikingly exhibited by prototype two-electron systems such as dissociating H(2) and HeH(+)). At the same time, adiabatic approximations, which will eventually be necessary, can be tested without being obscured by approximations in the functional. We find the following: (a) In the fully nonadiabatic (omega-dependent, exact) formulation of linear response TDDMFT, it can be shown that linear response (LR)-TDDMFT is able to provide exact excitation energies, in particular, the first order (linear response) formulation does not prohibit the correct representation of doubly excited states; (b) within previously formulated simple adiabatic approximations the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (c) an adiabatic approximation is formulated in which also the double excitations are fully accounted for.
Time-dependent density functional theory for strong-field ionization by circularly polarized pulses
Chirilă, Ciprian C.; Lein, Manfred
2017-03-01
By applying time-dependent density functional theory to a two-dimensional multielectron atom subject to strong circularly polarized light pulses, we confirm that the ionization of p orbitals with defined angular momentum depends on the sense of rotation of the applied field. A simple ad-hoc modification of the adiabatic local-density exchange-correlation functional is proposed to remedy its unphysical behavior under orbital depletion.
Dzyaloshinskii-Moriya interactions and adiabatic magnetization dynamics in molecular magnets
De Raedt, H; Miyashita, S; Michielsen, K; Machida, M
A microscopic model of the molecular magnet V-15 is used to study mechanisms for the adiabatic change of the magnetization in time-dependent magnetic fields. The effects of the Dzyaloshinskii-Moriya interaction, the most plausible source for the energy-level repulsions that lead to adiabatic changes
Time-Dependent Transport in Nanoscale Devices
CHEN Zhi-Dong; ZHANG Jin-Yu; YU Zhi-Ping
2009-01-01
A method for simulating ballistic time-dependent device transport,which solves the time-dependent SchrSdinger equation using the finite difference time domain (FDTD) method together with Poisson's equation,is described in detail The effective mass SchrSdinger equation is solved. The continuous energy spectrum of the system is discretized using adaptive mesh,resulting in energy levels that sample the density-of-states.By calculating time evolution of wavefunctions at sampled energies,time-dependent transport characteristics such as current and charge density distributions are obtained.Simulation results in a uanowire and a coaxially gated carbon nanotube field-effect transistor (CNTFET) are presented.Transient effects,e.g.,finite rising time,are investigated in these devices.
Pulsar braking: Time dependent moment of inertia?
Urbanec, Martin
2017-08-01
Pulsars rotate with extremely stable rotational frequency enabling one to measure its first and second time derivatives. These observed values can be combined to the so-called braking index. However observed values of braking index differ from the theoretical value of 3 corresponding to braking by magnetic dipole radiation being the dominant theoretical model. Such a difference can be explained by contribution of other mechanism like pulsar wind or quadrupole radiation, or by time dependency of magnetic field or moment of inertia. In this presentation we focus on influence of time dependent moment of inertia on the braking index. We will also discuss possible physical models for time-dependence of moment of inertia.
Investigations of Low Temperature Time Dependent Cracking
Van der Sluys, W A; Robitz, E S; Young, B A; Bloom, J
2002-09-30
The objective of this project was to investigate metallurgical and mechanical phenomena associated with time dependent cracking of cold bent carbon steel piping at temperatures between 327 C and 360 C. Boiler piping failures have demonstrated that understanding the fundamental metallurgical and mechanical parameters controlling these failures is insufficient to eliminate it from the field. The results of the project consisted of the development of a testing methodology to reproduce low temperature time dependent cracking in laboratory specimens. This methodology was used to evaluate the cracking resistance of candidate heats in order to identify the factors that enhance cracking sensitivity. The resultant data was integrated into current available life prediction tools.
The Bloch wave operator: generalizations and applications: II. The time-dependent case
Jolicard, Georges [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France); Killingbeck, John P [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France); Mathematics Department, University of Hull, Hull HU6 7RX (United Kingdom)
2003-10-10
Part II of the review shows how the stationary Bloch wave operator of part I can be suitably modified to give a time-dependent wave operator. This operator makes it possible to use a relatively small active space in order to describe the dynamical processes which occur in quantum mechanical systems which have a time-dependent Hamiltonian. A close study is made of the links between the time-dependent and time-independent wave operators at the adiabatic limit; the analysis clarifies the way in which the wave operator formalism allows the time evolution of a system or a wave packet to be described in terms of a fast evolution inside the active space together with weak transitions out of this space which can be treated by perturbation methods. Two alternative wave operator equations of motion are derived and analysed. The first one is a non-linear differential equation in the usual Hilbert space; the second one is a differential equation in an extended Hilbert space with an extra time variable added and becomes equivalent to the usual Bloch equation when the Floquet Hamiltonian is taken in place of the ordinary Hamiltonian. A study is made of the close relationships between the time-dependent wave operator formalism, the Floquet theory and the (t, t') theory. Some original methods of solution of the two forms of wave operator equation are proposed and lead to new techniques of integration for the time-dependent Schroedinger equation (e.g., the generalized Green equation procedure). Mixed procedures involving both the time-independent and time-dependent wave operators are shown to be applicable to the internal eigenstate problem for large complex matrices. A detailed account is given of the description of inelastic and photoreactive processes by means of the time-dependent wave operator formalism, with particular attention to laser-molecule interactions. The emphasis is on projection operator techniques, with special attention being given to the method of selection
Second quantized scalar QED in homogeneous time-dependent electromagnetic fields
Kim, Sang Pyo
2014-12-01
We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.
Differential Geometry of Time-Dependent Mechanics
Giachetta, G; Sardanashvily, G
1997-01-01
The usual formulations of time-dependent mechanics start from a given splitting $Y=R\\times M$ of the coordinate bundle $Y\\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical transformations. Our goal is to formulate time-dependent mechanics in gauge-invariant form, i.e., independently of any reference frame. The main ingredient in this formulation is a connection on the bundle $Y\\to R$ which describes an arbitrary reference frame. We emphasize the following peculiarities of this approach to time-dependent mechanics. A phase space does not admit any canonical contact or presymplectic structure which would be preserved under reference frame transformations, whereas the canonical Poisson structure is degenerate. A Hamiltonian fails to be a function on a phase space. In particular, it can not participate in a Poisson bracket so that the evolution equation is not reduced...
Quantum work statistics of charged Dirac particles in time-dependent fields.
Deffner, Sebastian; Saxena, Avadh
2015-09-01
The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.
On the General Class of Models of Adiabatic Evolution
Sun, Jie; Lu, Songfeng; Liu, Fang
2016-10-01
The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown [8] that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
Komissarov, S S; Lyutikov, M
2015-01-01
In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with v~c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialized code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres a...
Time-dependent species sensitivity distributions.
Fox, David R; Billoir, Elise
2013-02-01
Time is a central component of toxicity assessments. However, current ecotoxicological practice marginalizes time in concentration-response (C-R) modeling and species sensitivity distribution (SSD) analyses. For C-R models, time is invariably fixed, and toxicity measures are estimated from a function fitted to the data at that time. The estimated toxicity measures are used as inputs to the SSD modeling phase, which similarly avoids explicit recognition of the temporal component. The present study extends some commonly employed probability models for SSDs to derive theoretical results that characterize the time-dependent nature of hazardous concentration (HCx) values. The authors' results show that even from very simple assumptions, more complex patterns in the SSD time dependency can be revealed.
Time-Dependent Erosion of Ion Optics
Wirz, Richard E.; Anderson, John R.; Katz, Ira; Goebel, Dan M.
2008-01-01
The accurate prediction of thruster life requires time-dependent erosion estimates for the ion optics assembly. Such information is critical to end-of-life mechanisms such as electron backstreaming. CEX2D was recently modified to handle time-dependent erosion, double ions, and multiple throttle conditions in a single run. The modified code is called "CEX2D-t". Comparisons of CEX2D-t results with LDT and ELT post-tests results show good agreement for both screen and accel grid erosion including important erosion features such as chamfering of the downstream end of the accel grid and reduced rate of accel grid aperture enlargement with time.
Time-dependent problems and difference methods
Gustafsson, Bertil; Oliger, Joseph
2013-01-01
Praise for the First Edition "". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations."" -SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-de
Coasting cosmologies with time dependent cosmological constant
Pimentel, L O; Pimentel, Luis O.
1999-01-01
The effect of a time dependent cosmological constant is considered in a family of scalar tensor theories. Friedmann-Robertson-Walker cosmological models for vacumm and perfect fluid matter are found. They have a linear expansion factor, the so called coasting cosmology, the gravitational "constant" decreace inversely with time; this model satisfy the Dirac hipotesis. The cosmological "constant" decreace inversely with the square of time, therefore we can have a very small value for it at present time.
Transformation of time dependence to linear algebra
Menšík, Miroslav
2005-10-01
Reduced density matrix and memory function in the Nakajima-Zwanzig equation are expanded in properly chosen basis of special functions. This trick completely transforms time dependence to linear algebra. Then, the master equation for memory function is constructed and expanded in the same basis functions. For the model of a simple harmonic oscillator it is shown that this trick introduces infinite partial summation of the memory function in the system-bath interaction.
Quantum fluctuations in the time-dependent BCS-BEC crossover.
Breid, B M; Anglin, J R
2008-08-28
We describe the time-dependent formation of a molecular Bose-Einstein condensate from a BCS state of fermionic atoms as a result of slow sweeping through a Feshbach resonance. We apply a path integral approach for the molecules, and use two-body adiabatic approximations to solve the atomic evolution in the presence of the classical molecular fields, obtaining an effective action for the molecules. In the narrow resonance limit, the problem becomes semiclassical, and we discuss the growth of the molecular condensate in the saddle point approximation. Considering this time-dependent process as an analogue of the cosmological Zurek scenario, we compare the way condensate growth is driven in this rigorous theory with its phenomenological description via time-dependent Ginzburg-Landau theory.
The Time Dependent CP Violation in Charm
Inguglia, Gianluca
2012-01-01
A model which describes the time-dependent CP formalism in $D^0$ decays has recently been proposed. There it has been highlighted a possible measurement of the angle $\\beta_c$, in the charm unitarity triangle, using the decays $D^0\\to K^+ K^-$ and $D^0\\to \\pi^+ \\pi^-$, and a measurement of the mixing phase $\\phi_{MIX}$. The same method can be used to measure the value of the parameter $x$, one of the two parameters defining charm mixing. We numerically evaluate the impact of a time-dependent analysis in terms of the possible outcomes from present and future experiments. We consider the scenarios of correlated $D^0$ mesons production at the center of mass energy of the $\\Psi(3770)$ at Super$B$, uncorrelated production at the center of mass energy of the $\\Upsilon(4S)$ at Super$B$ and Belle II, and LHCb. Recently a hint of direct CP violation in charm decays was reported by the LHCb collaboration, we estimate the rate of time-dependent asymmetry that could be achieved using their available data, and we generali...
Dissipative time-dependent quantum transport theory.
Zhang, Yu; Yam, Chi Yung; Chen, GuanHua
2013-04-28
A dissipative time-dependent quantum transport theory is developed to treat the transient current through molecular or nanoscopic devices in presence of electron-phonon interaction. The dissipation via phonon is taken into account by introducing a self-energy for the electron-phonon coupling in addition to the self-energy caused by the electrodes. Based on this, a numerical method is proposed. For practical implementation, the lowest order expansion is employed for the weak electron-phonon coupling case and the wide-band limit approximation is adopted for device and electrodes coupling. The corresponding hierarchical equation of motion is derived, which leads to an efficient and accurate time-dependent treatment of inelastic effect on transport for the weak electron-phonon interaction. The resulting method is applied to a one-level model system and a gold wire described by tight-binding model to demonstrate its validity and the importance of electron-phonon interaction for the quantum transport. As it is based on the effective single-electron model, the method can be readily extended to time-dependent density functional theory.
Time dependent modelisation of TeV blazars by a stratified jet model
Boutelier, Timothé; Petrucci, Pierre-Olivier
2008-01-01
We present a new time-dependent inhomogeneous jet model of non-thermal blazar emission. Ultra-relativistic leptons are injected at the base of a jet and propagate along it. We assume continuous reacceleration and cooling, producing a relativistic quasi-maxwellian (or "pile-up") particle energy distribution. The synchrotron and Synchrotron-Self Compton jet emissivity are computed at each altitude. Klein-Nishina effects as well as intrinsic gamma-gamma absorption are included in the computation. Due to the pair production optical depth, considerable particle density enhancement can occur, particularly during flaring states.Time-dependent jet emission can be computed by varying the particle injection, but due to the sensitivity of pair production process, only small variations of the injected density are required during the flares. The stratification of the jet emission, together with a pile-up distribution, allows significantly lower bulk Lorentz factors, compared to one-zone models. Applying this model to the ...
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
Hadasz, L; Rocek, M; Von Unge, R; Hadasz, Leszek; Lindstrom, Ulf; Rocek, Martin; Unge, Rikard von
2003-01-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case it is not possible to find the dynamics of the solitons using traditional moduli space techniques. To do better we have found exact time dependent one soliton solutions to the full equations of motion. They represent solitons moving in straight lines with constant velocity. Surprisingly we find that the set of allowed velocities is quantized! The allowed velocities are proportional to the square root of an integer. In the relativistic case we find the metric on the two soliton moduli space and using techinques developed in the nonrelativistic case we also find exact time dependent one-soliton solutions. Again the allowed velocities are quantized, though in a slightly more complicated fashion.
Pernal, Katarzyna; Giesbertz, Klaas J H
2016-01-01
Recent advances in reduced density matrix functional theory (RDMFT) and linear response time-dependent reduced density matrix functional theory (TD-RDMFT) are reviewed. In particular, we present various approaches to develop approximate density matrix functionals which have been employed in RDMFT. We discuss the properties and performance of most available density matrix functionals. Progress in the development of functionals has been paralleled by formulation of novel RDMFT-based methods for predicting properties of molecular systems and solids. We give an overview of these methods. The time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting practical and generally useful functionals which would work within the adiabatic approximation. In this chapter we concentrate on the formulation of TD-RDMFT response equations and various adiabatic approximations. None of the adiabatic approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals (PINOs). We focus on applications of the linear response formulations to two-electron systems, for which the (almost) exact functional is known.
Kinetic and potential components of the exact time-dependent correlation potential
Luo, Kai; Sandoval, Ernesto D; Elliott, Peter; Maitra, Neepa T
2013-01-01
The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction potential components, and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional (1D) two-electron systems. We find that often, but not always, the kinetic contri- bution is mostly responsible for these features, that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the potential contribution, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. These observations also held in non-equilibrium cases we studied where there are large features in the correlation po- tential although no step ...
Semiconductor adiabatic qubits
Carroll, Malcolm S.; Witzel, Wayne; Jacobson, Noah Tobias; Ganti, Anand; Landahl, Andrew J.; Lilly, Michael; Nguyen, Khoi Thi; Bishop, Nathaniel; Carr, Stephen M.; Bussmann, Ezra; Nielsen, Erik; Levy, James Ewers; Blume-Kohout, Robin J.; Rahman, Rajib
2016-12-27
A quantum computing device that includes a plurality of semiconductor adiabatic qubits is described herein. The qubits are programmed with local biases and coupling terms between qubits that represent a problem of interest. The qubits are initialized by way of a tuneable parameter, a local tunnel coupling within each qubit, such that the qubits remain in a ground energy state, and that initial state is represented by the qubits being in a superposition of |0> and |1> states. The parameter is altered over time adiabatically or such that relaxation mechanisms maintain a large fraction of ground state occupation through decreasing the tunnel coupling barrier within each qubit with the appropriate schedule. The final state when tunnel coupling is effectively zero represents the solution state to the problem represented in the |0> and |1> basis, which can be accurately read at each qubit location.
Biamonte, J D; Whitfield, J D; Fitzsimons, J; Aspuru-Guzik, A
2010-01-01
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be error resistant, easily controllable, and built using existing technology. Moving away from gate-model and projective measurement based implementations of quantum computing may offer a less resource-intensive, and consequently a more feasible solution. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-body interaction terms, using sparse Hamiltonians with at most three-body interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes...
The time-dependent Gutzwiller approximation
Fabrizio, Michele
2015-03-01
The time-dependent Gutzwiller Approximation (t-GA) is shown to be capable of tracking the off-equilibrium evolution both of coherent quasiparticles and of incoherent Hubbard bands. The method is used to demonstrate that the sharp dynamical crossover observed by time-dependent DMFT in the quench-dynamics of a half-filled Hubbard model can be identified within the t-GA as a genuine dynamical transition separating two distinct physical phases. This result, strictly variational for lattices of infinite coordination number, is intriguing as it actually questions the occurrence of thermalization. Next, we shall present how t-GA works in a multi-band model for V2O3 that displays a first-order Mott transition. We shall show that a physically accessible excitation pathway is able to collapse the Mott gap down and drive off-equilibrium the insulator into a metastable metal phase. Work supported by the European Union, Seventh Framework Programme, under the project GO FAST, Grant Agreement No. 280555.
Time-dependent secular evolution in galaxies
Weinberg, M D
2004-01-01
Lynden-Bell & Kalnajs (1972) presented a useful formula for computing the long-range torque between spiral arms and the disk at large. The derivation uses second-order perturbation theory and assumes that the perturbation slowly grows over a very long time: the time-asymptotic limit. This formula has been widely used to predict the angular momentum transport between spiral arms and stellar bars between disks and dark-matter halos. However, this paper shows that the LBK time-asymptotic limit is not appropriate because the characteristic evolution time for galaxies is too close to the relevant dynamical times. We demonstrate that transients, not present in the time-asymptotic formula, can play a major role in the evolution for realistic astronomical time scales. A generalisation for arbitrary time dependence is presented and illustrated by the bar--halo and satellite--halo interaction. The natural time dependence in bar-driven halo evolution causes quantitative differences in the overall torque and qualitat...
Fission dynamics within time-dependent Hartree-Fock: deformation-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide $^{240}$Pu as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate non-adiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data. Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behaviour. Those beginning just beyond the ...
Time-dependence of the holographic spectral function: Diverse routes to thermalisation
Banerjee, Souvik; Joshi, Lata Kh; Mukhopadhyay, Ayan; Ramadevi, P
2016-01-01
We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quench duration, the spectral function indeed follows the thermal form at the instantaneous effective temperature adiabatically, although with a slight initial time delay and a bit premature thermalisation. At shorter quench durations, several new non-adiabatic features appear: (i) time-dependence of the spectral function is seen much before than that in the effective temperature (advanced time-dependence), (ii) a big transfe...
Time-dependence of the holographic spectral function: diverse routes to thermalisation
Banerjee, Souvik; Ishii, Takaaki; Joshi, Lata Kh; Mukhopadhyay, Ayan; Ramadevi, P.
2016-08-01
We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quench duration, the spectral function indeed follows the thermal form at the instantaneous effective temperature adiabatically, although with a slight initial time delay and a bit premature thermalisation. At shorter quench durations, several new non-adiabatic features appear: (i) time-dependence of the spectral function is seen much before than that in the effective temperature (advanced time-dependence), (ii) a big transfer of spectral weight to frequencies greater than the initial temperature occurs at an intermediate time (kink formation) and (iii) new peaks with decreasing amplitudes but in greater numbers appear even after the effective temperature has stabilised (persistent oscillations). We find four broad routes to thermalisation for lower values of spatial momenta. At higher values of spatial momenta, kink formations and persistent oscillations are suppressed, and thermalisation time decreases. The general thermalisation pattern is globally top-down, but a closer look reveals complexities.
Constitutive model with time-dependent deformations
Krogsbøll, Anette
1998-01-01
are common in time as well as size. This problem is adressed by means of a new constitutive model for soils. It is able to describe the behavior of soils at different deformation rates. The model defines time-dependent and stress-related deformations separately. They are related to each other and they occur......In many geological and Engineering problems it is necessary to transform information from one scale to another. Data collected at laboratory scale are often used to evaluate field problems on a much larger scale. This is certainly true for geological problems where extreme scale differences...... simultanelously. The model is based on concepts from elasticity and viscoplasticity theories. In addition to Hooke's law for the elastic behavior, the framework for the viscoplastic behavior consists, in the general case (two-dimensional or three-dimensional), of a yield surface, an associated flow rule...
Time-dependent Cooling in Photoionized Plasma
Gnat, Orly
2017-02-01
I explore the thermal evolution and ionization states in gas cooling from an initially hot state in the presence of external photoionizing radiation. I compute the equilibrium and nonequilibrium cooling efficiencies, heating rates, and ion fractions for low-density gas cooling while exposed to the ionizing metagalactic background radiation at various redshifts (z = 0 ‑ 3), for a range of temperatures (108–104 K), densities (10‑7–103 cm‑3), and metallicities (10‑3–2 times solar). The results indicate the existence of a threshold ionization parameter, above which the cooling efficiencies are very close to those in photoionization equilibrium (so that departures from equilibrium may be neglected), and below which the cooling efficiencies resemble those in collisional time-dependent gas cooling with no external radiation (and are thus independent of density).
Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.
Clumps in large scale relativistic jets
Tavecchio, F; Celotti, A
2003-01-01
The relatively intense X-ray emission from large scale (tens to hundreds kpc) jets discovered with Chandra likely implies that jets (at least in powerful quasars) are still relativistic at that distances from the active nucleus. In this case the emission is due to Compton scattering off seed photons provided by the Cosmic Microwave Background, and this on one hand permits to have magnetic fields close to equipartition with the emitting particles, and on the other hand minimizes the requirements about the total power carried by the jet. The emission comes from compact (kpc scale) knots, and we here investigate what we can predict about the possible emission between the bright knots. This is motivated by the fact that bulk relativistic motion makes Compton scattering off the CMB photons efficient even when electrons are cold or mildly relativistic in the comoving frame. This implies relatively long cooling times, dominated by adiabatic losses. Therefore the relativistically moving plasma can emit, by Compton sc...
Amendt, Peter; Wilks, Scott
2012-01-01
The plasma analog of an adiabatic lapse rate (or temperature variation with height) in atmospheric physics is obtained. A new source of plasma temperature gradient in a binary ion species mixture is found that is proportional to the concentration gradient and difference in average ionization states . Application to inertial-confinement-fusion implosions indicates a potentially strong effect in plastic (CH) ablators that is not modeled with mainline (single-fluid) simulations. An associated plasma thermodiffusion coefficient is derived, and charge-state diffusion in a single-species plasma is also predicted.
Nonresonance adiabatic photon trap
Popov, S S; Burdakov, A V; Ushkova, M Yu
2016-01-01
Concept of high efficiency photon storage based on adiabatic confinement between concave mirrors is presented and experimentally investigated. The approach is insensitive to typical for Fabri-Perot cells requirements on quality of accumulated radiation, tolerance of resonator elements and their stability. Experiments have been carried out with the trap, which consists from opposed concave cylindrical mirrors and conjugated with them spherical mirrors. In result, high efficiency for accumulation of radiation with large angular spread and spectrum width has been confirmed. As radiation source a commercial fiber laser has been used.
Gavnholt, Jeppe; Rubio, Angel; Olsen, Thomas;
2009-01-01
Using time-evolution time-dependent density functional theory (TDDFT) within the adiabatic local-density approximation, we study the interactions between single electrons and molecular resonances at surfaces. Our system is a nitrogen molecule adsorbed on a ruthenium surface. The surface is modeled...... resonance and the lowering of the resonance energy due to an image charge effect. Finally we apply the TDDFT procedure to only consider the decay of molecular excitations and find that it agrees quite well with the width of the projected density of Kohn-Sham states....
Application of Time-Dependent Density-Functional Theory to C6
ZHOU Xiao-Lin; BAI Yu-Lin; CHEN Xiang-Rong; YANG Xiang-Dong
2004-01-01
@@ We employ a real-space pseudopotential method to determine the ground state structure of the carbon cluster C6 via simulated annealing and the corresponding optical absorption spectra from the adiabatic time-dependent density-functional theory (TDDFT) and the local density approximation (TDLDA). It is found that the ground state structure of the carbon cluster C6 belongs to a monocyclic D3h structure and the calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations.
Multi-configuration time-dependent density-functional theory based on range separation
Fromager, E.; Knecht, S.; Jensen, Hans Jørgen Aagaard
2013-01-01
Multi-configuration range-separated density-functional theory is extended to the time-dependent regime. An exact variational formulation is derived. The approximation, which consists in combining a long-range Multi-Configuration- Self-Consistent Field (MCSCF) treatment with an adiabatic short...... in Be and the 11u+ state in the stretched H molecule are improved, although the latter is still significantly underestimated. Exploratory TD-MC-srDFT/GGA calculations for ferrocene yield in general excitation energies at least as good as TD-DFT using the Coulomb attenuated method based on the three-parameter Becke...
Time dependent friction in a free gas
Fanelli, Cristiano; Sisti, Francesco; Stagno, Gabriele V.
2016-03-01
We consider a body moving in a perfect gas, described by the mean-field approximation and interacting elastically with the body, we study the friction exerted by the gas on the body fixed at constant velocities. The time evolution of the body in this setting was studied in Caprino et al. [Math. Phys. 264, 167-189 (2006)], Caprino et al. [Math. Models Methods Appl. Sci. 17, 1369-1403 (2007)], and Cavallaro [Rend. Mat. Appl. 27, 123-145 (2007)] for object with simple shape; the first study where a simple kind of concavity was considered was in Sisti and Ricciuti [SIAM J. Math. Anal. 46, 3759-3611 (2014)], showing new features in the dynamic but not in the friction term. The case of more general shape of the body was left out for further difficulties, and we believe indeed that there are actually non-trivial issues to be faced for these more general cases. To show this and in the spirit of getting a more realistic perspective in the study of friction problems, in this paper, we focused our attention on the friction term itself, studying its behavior on a body with a more general kind of concavity and fixed at constant velocities. We derive the expression of the friction term for constant velocities, we show how it is time dependent, and we give its exact estimate in time. Finally, we use this result to show the absence of a constant velocity in the actual dynamic of such a body.
Time-dependent Backgrounds Of String Theory
Maloney, A D
2003-01-01
This thesis is devoted to the study of time-dependent backgrounds in string theory. The first chapter contains a brief, non-technical introduction to the subject. In the second chapter quantum field theory in d-dimensional de Sitter space is studied, with an emphasis on the dS/CFT correspondence. We study a one-parameter family of dS-invariant vacua; this bulk vacuum dependence is dual to a deformation of the boundary CFT by a marginal operator. In odd spacetime dimensions the state with no particles on I- has no particles on I+ , implying the absence of particle production. In Kerr-dS, a thermal density matrix is found by tracing over causally inaccessible modes. Assuming Cardy's formula, the microscopic entropy of such a thermal state in the boundary CFT precisely equals the Bekenstein-Hawking value. Next, we construct de Sitter vacua of supercritical string theories in D > 10 dimensions. Compactifying D − 4 of these dimensions on a carefully constructed asymmetric orientifold projects out t...
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
Time Dependence of Hawking Radiation Entropy
Page, Don N
2013-01-01
If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4 pi M_0^2, or about 7.509 M_0^2 \\approx 6.268\\times 10^{76}(M_0/M_\\odot)^2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the...
Time-dependent correlations in electricity markets
Alvarez-Ramirez, Jose; Escarela-Perez, Rafael [Departamento de Energia, Universidad Autonoma Metropolitana, Mexico DF, 09340 (Mexico)
2010-03-15
In the last years, many electricity markets were subjected to deregulated operation where prices are set by the action of market participants. In this form, producers and consumers rely on demand and price forecasts to decide their bidding strategies, allocate assets, negotiate bilateral contracts, hedge risks, and plan facility investments. A basic feature of efficient market hypothesis is the absence of correlations between price increments over any time scale leading to random walk-type behavior of prices, so arbitrage is not possible. However, recent studies have suggested that this is not the case and correlations are present in the behavior of diverse electricity markets. In this paper, a temporal quantification of electricity market correlations is made by means of detrended fluctuation and Allan analyses. The approach is applied to two Canadian electricity markets, Ontario and Alberta. The results show the existence of correlations in both demand and prices, exhibiting complex time-dependent behavior with lower correlations in winter while higher in summer. Relatively steady annual cycles in demand but unstable cycles in prices are detected. On the other hand, the more significant nonlinear effects (measured in terms of a multifractality index) are found for winter months, while the converse behavior is displayed during the summer period. In terms of forecasting models, our results suggest that nonlinear recursive models (e.g., feedback NNs) should be used for accurate day-ahead price estimation. In contrast, linear models can suffice for demand forecasting purposes. (author)
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.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
Rüger, Robert; Niehaus, Thomas; van Lenthe, Erik; Heine, Thomas; Visscher, Lucas
2016-11-01
We report a time-dependent density functional based tight-binding (TD-DFTB) scheme for the calculation of UV/Vis spectra, explicitly taking into account the excitation of nuclear vibrations via the adiabatic Hessian Franck-Condon method with a harmonic approximation for the nuclear wavefunction. The theory of vibrationally resolved UV/Vis spectroscopy is first summarized from the viewpoint of TD-DFTB. The method is benchmarked against time-dependent density functional theory (TD-DFT) calculations for strongly dipole allowed excitations in various aromatic and polar molecules. Using the recent 3ob:freq parameter set of Elstner's group, very good agreement with TD-DFT calculations using local functionals was achieved.
Rüger, Robert; Niehaus, Thomas; van Lenthe, Erik; Heine, Thomas; Visscher, Lucas
2016-11-14
We report a time-dependent density functional based tight-binding (TD-DFTB) scheme for the calculation of UV/Vis spectra, explicitly taking into account the excitation of nuclear vibrations via the adiabatic Hessian Franck-Condon method with a harmonic approximation for the nuclear wavefunction. The theory of vibrationally resolved UV/Vis spectroscopy is first summarized from the viewpoint of TD-DFTB. The method is benchmarked against time-dependent density functional theory (TD-DFT) calculations for strongly dipole allowed excitations in various aromatic and polar molecules. Using the recent 3ob:freq parameter set of Elstner's group, very good agreement with TD-DFT calculations using local functionals was achieved.
A theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels
Muller, Peter Barkholt
2015-01-01
Based on first- and second-order perturbation theory, we present a numerical study of the temporal build-up and decay of unsteady acoustic fields and acoustic streaming flows actuated by vibrating walls in the transverse cross-sectional plane of a long straight microchannel under adiabatic conditions and assuming temperature-independent material parameters. The unsteady streaming flow is obtained by averaging the time-dependent velocity field over one oscillation period, and as time increases, it is shown to converge towards the well-known steady time-averaged solution calculated in the frequency domain. Scaling analysis reveals that the acoustic resonance builds up much faster than the acoustic streaming, implying that the radiation force may dominate over the drag force from streaming even for small particles. However, our numerical time-dependent analysis indicates that pulsed actuation does not reduce streaming significantly due to its slow decay. Our analysis also shows that for an acoustic resonance wit...
Theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels
Muller, Peter Barkholt; Bruus, Henrik
2015-01-01
Based on first- and second-order perturbation theory, we present a numerical study of the temporal buildup and decay of unsteady acoustic fields and acoustic streaming flows actuated by vibrating walls in the transverse cross-sectional plane of a long straight microchannel under adiabatic...... conditions and assuming temperature-independent material parameters. The unsteady streaming flow is obtained by averaging the time-dependent velocity field over one oscillation period, and as time increases, it is shown to converge towards the well-known steady time-averaged solution calculated...... in the frequency domain. Scaling analysis reveals that the acoustic resonance builds up much faster than the acoustic streaming, implying that the radiation force may dominate over the drag force from streaming even for small particles. However, our numerical time-dependent analysis indicates that pulsed actuation...
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Time-dependence in mixture toxicity prediction.
Dawson, Douglas A; Allen, Erin M G; Allen, Joshua L; Baumann, Hannah J; Bensinger, Heather M; Genco, Nicole; Guinn, Daphne; Hull, Michael W; Il'Giovine, Zachary J; Kaminski, Chelsea M; Peyton, Jennifer R; Schultz, T Wayne; Pöch, Gerald
2014-12-04
The value of time-dependent toxicity (TDT) data in predicting mixture toxicity was examined. Single chemical (A and B) and mixture (A+B) toxicity tests using Microtox(®) were conducted with inhibition of bioluminescence (Vibrio fischeri) being quantified after 15, 30 and 45-min of exposure. Single chemical and mixture tests for 25 sham (A1:A2) and 125 true (A:B) combinations had a minimum of seven duplicated concentrations with a duplicated control treatment for each test. Concentration/response (x/y) data were fitted to sigmoid curves using the five-parameter logistic minus one parameter (5PL-1P) function, from which slope, EC25, EC50, EC75, asymmetry, maximum effect, and r(2) values were obtained for each chemical and mixture at each exposure duration. Toxicity data were used to calculate percentage-based TDT values for each individual chemical and mixture of each combination. Predicted TDT values for each mixture were calculated by averaging the TDT values of the individual components and regressed against the observed TDT values obtained in testing, resulting in strong correlations for both sham (r(2)=0.989, n=25) and true mixtures (r(2)=0.944, n=125). Additionally, regression analyses confirmed that observed mixture TDT values calculated for the 50% effect level were somewhat better correlated with predicted mixture TDT values than at the 25 and 75% effect levels. Single chemical and mixture TDT values were classified into five levels in order to discern trends. The results suggested that the ability to predict mixture TDT by averaging the TDT of the single agents was modestly reduced when one agent of the combination had a positive TDT value and the other had a minimal or negative TDT value. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Time dependence of Hawking radiation entropy
Page, Don N.
2013-09-01
If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM02, or about 7.509M02 ≈ 6.268 × 1076(M0/Msolar)2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M02 ≈ 1.254 × 1077(M0/Msolar)2, and then decreases back down to 4πM02 = 1.049 × 1077(M0/Msolar)2.
Adiabatic paths and pseudoholomorphic curves
Armen; G.; Sergeev
2005-01-01
We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show that the Taubes correspondence may be considered as a (2+2)-dimensional analogue of the adiabatic limit construction.
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Pinski, Sebastian D
2011-01-01
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small problems were solved; although the explanations that journalists and critics received were minimal and very little was divulged in the question and answer session. This 'unconvincing' demonstration has caused physicists and computer scientists to hit back at D-Wave. The aim of this project is to give an introduction to the historic advances in classical and quantum computing and to explore the methods of AQC. Through numerical simulations an algorithm for the Max Independent Set problem is empirically obtained.
Radiative transfer in ultra-relativistic outflows
Beloborodov, Andrei M.
2010-01-01
Analytical and numerical solutions are obtained for the equation of radiative transfer in ultra-relativistic opaque jets. The solution describes the initial trapping of radiation, its adiabatic cooling, and the transition to transparency. Two opposite regimes are examined: (1) Matter-dominated outflow. Surprisingly, radiation develops enormous anisotropy in the fluid frame before decoupling from the fluid. The radiation is strongly polarized. (2) Radiation-dominated outflow. The transfer occu...
Perveaux, A; Lasorne, B; Gatti, F; Robb, M A; Halász, G J; Vibók, Á
2014-01-01
A nonadiabatic scheme for the description of the coupled electron and nuclear motions in the ozone molecule was proposed recently. An initial coherent nonstationary state was prepared as a superposition of the ground state and the excited Hartley band. In this situation neither the electrons nor the nuclei are in a stationary state. The multiconfiguration time dependent Hartree method was used to solve the coupled nuclear quantum dynamics in the framework of the adiabatic separation of the time-dependent Schr\\"odinger equation. The resulting wave packet shows an oscillation of the electron density between the two chemical bonds. As a first step for probing the electronic motion we computed the time-dependent molecular dipole and the Dyson orbitals. The latter play an important role in the explanation of the photoelectron angular distribution. Calculations of the Dyson orbitals are presented both for the time-independent as well as the time-dependent situations. We limited our description of the electronic mot...
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Pernal, Katarzyna
2012-05-14
Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other
The Relativistic Transformation for an Electromagnetic Plane Wave with General Time Dependence
Smith, Glenn S.
2012-01-01
In special relativity, the transformation between inertial frames for an electromagnetic plane wave is usually derived for the time-harmonic case (the field is a sinusoid of infinite duration), even though all practical waves are of finite duration and may not even contain a dominant sinusoid. This paper presents an alternative derivation in which…
Dark Energy and Dark Matter from an additional adiabatic fluid
Dunsby, Peter K S; Reverberi, Lorenzo
2016-01-01
The Dark Sector is described by an additional barotropic fluid which evolves adiabatically during the universe's history and whose adiabatic exponent $\\gamma$ is derived from the standard definitions of specific heats. Although in general $\\gamma$ is a function of the redshift, the Hubble parameter and its derivatives, we find that our assumptions lead necessarily to solutions with $\\gamma = $ constant in a FLRW universe. The adiabatic fluid acts effectively as the sum of two distinct components, one evolving like non-relativistic matter and the other depending on the value of the adiabatic index. This makes the model particularly interesting as a way of simultaneously explaining the nature of both Dark Energy and Dark Matter, at least at the level of the background cosmology. The $\\Lambda$CDM model is included in this family of theories when $\\gamma = 0$. We fit our model to SNIa, $H(z)$ and BAO data, discussing the model selection criteria. The implications for the early-universe and the growth of small per...
Time-dependent constrained Hamiltonian systems and Dirac brackets
Leon, Manuel de [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Madrid (Spain); Marrero, Juan C. [Departamento de Matematica Fundamental, Facultad de Matematicas, Universidad de La Laguna, La Laguna, Tenerife, Canary Islands (Spain); Martin de Diego, David [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, Madrid (Spain)
1996-11-07
In this paper the canonical Dirac formalism for time-dependent constrained Hamiltonian systems is globalized. A time-dependent Dirac bracket which reduces to the usual one for time-independent systems is introduced. (author)
Time dependent deformation of Kilauea Volcano, Hawaii
Montgomery-Brown, Emily Kvietka Desmarais
to a decollement structure 8 km under the south flank, and the locations of the microearthquakes suggest that both occur on the same structure. In 2007, Episode 56 of the Pu'u 'O'o-Kupianaha eruption occurred. This episode was exciting both because it was the largest intrusion in the last decade, and because it occurred concurrently with a flank slow-slip event. The intrusion started on Father's day (June 17th), 2007 with increased seismicity and abrupt tilts at the summit and rift zones. Quasi-static models of the total deformation determined from GPS, tilt, and InSAR indicate that the intrusion occurred on two en echelon dike segments in the upper East Rift Zone along with deformation consistent with slow-slip in the same areas of previous events. The ˜ 2 m maximum opening occurred on the eastern segment near Makaopui crater. Unlike previous intrusions in 1997, 1999, and 2000, the dike model was not sufficient to explain deformation on the western flank. Additionally, a coastal tiltmeter installed in anticipation of a slow-slip event recorded tilts consistent with those observed during the 2005 slow-slip event. These observations led to the conclusion that a concurrent slow-slip event occurred. Geodetic models indicate a similar amount of decollement slip occurred as in previous slow-slip events. Sub-daily GPS positions were used to study the spatio-temporal distribution of the dike intrusion. The time-dependent intrusion model shows that the intrusion began on the western en echelon segment before jumping to the eastern segment, which accumulated the majority of the 2 m of opening. Sub-daily GPS positions limit the number of stations available since there are very few continuous stations north of the East Rift Zone, where coverage is critical for separating the intrusion from the slow-slip. However, an ENVISAT interferogram at 08:22 on June 18, 2007 provides additional spatial coverage of deformation up to that point. Combining this image with the GPS and tilt
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Performance analysis of adiabatic engine
Sudhakar, V.
1984-01-01
As the development of the adiabatic diesel engine continues with a goal of 65% reduction in net in-cylinder heat transfer over a cooled engine, several uncooled engines with intermediate levels of reduced heat transfer were studied. Some aspects and results of the adiabatic diesel engine cycle simulation are discussed. Performance test data and simulation results are compared for a conventionally cooled and uncooled Cummins NH-450 turbocompound engines. Exhaust emissions were also measured and compared.
Real time propagation of the exact two component time-dependent density functional theory
Goings, Joshua J.; Kasper, Joseph M.; Egidi, Franco; Sun, Shichao; Li, Xiaosong
2016-09-01
We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. We apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.
Introduction to numerical methods for time dependent differential equations
Kreiss, Heinz-Otto
2014-01-01
Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t
Response of a quantum system to a time-dependent external field and dynamical symmetry of the system
Wang, S J; Weiguny, A; Wiese, H
1998-01-01
The response of a quantum system to a time-dependent periodic external field is investigated in connection with the dynamical symmetry breaking and level dynamics of the adiabatic states of the system. The main results are as follows. (A) When the periodic external field preserves the dynamical symmetry of the system, its response is like that of elastic matter. (B) When the periodic external field breaks the dynamical symmetry, several cases may occur: (a) in the adiabatic limit, the system still responds elastically; (b) if the initial state is an eigenstate of the evolution operator U(T) for one period T of the external field, the system evolves in time cyclically and responds quasi-elastically; (c) if the initial state is not an eigenstate of the evolution operator U(T), the system evolves in time non-cyclically and responds non-elastically. The detailed non-elastic behaviour depends on the statistical nature of the adiabatic eigenstates of the system. If the adiabatic spectrum is chaotic, the non-elastic...
Random Time Dependent Resistance Analysis on Reinforced Concrete Structures
GUAN Chang-sheng; WU Ling
2002-01-01
The analysis method on random time dependence of reinforced concrete material is introduced,the effect mechanism on reinforced concrete are discussed, and the random time dependence resistance of reinforced concrete is studied. Furthermore, the corrosion of steel bar in reinforced concrete structures is analyzed. A practical statistical method of evaluating the random time dependent resistance, which includes material, structural size and calculation influence, is also established. In addition, an example of predicting random time dependent resistance of reinforced concrete structural element is given.
Fission dynamics within time-dependent Hartree-Fock: boost-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide $^{240}$Pu as an example. Methods: Quadrupole constrained Hartree-Fock calculations are used to create a potential energy surface. An isomeric state and a state beyond the second barrier peak are excited by means of instantaneous as well as temporally extended gauge boosts with quadrupole shapes. The subsequent deexcitation is studied in a time-dependent Hartree-Fock simulation, with emphasis on fissioned final states. The corresponding fission fragment mass numbers are studied. Results: In general, the energy deposited by the quadrupole boost is quickl...
Large Blue Spectral Isocurvature Spectral Index Signals Time-Dependent Mass
Chung, Daniel J H
2015-01-01
We show that if a spectator linear isocurvature dark matter field degree of freedom has a constant mass through its entire evolution history, the maximum measurable isocurvature spectral index that is consistent with the current tensor-to-scalar ratio bound is about 2.4, even if experiments can be sensitive to a $10^{-6}$ contamination of the predominantly adiabatic power spectrum with an isocurvature power spectrum at the shortest observable length scales. Hence, any foreseeable future measurement of a blue isocurvature spectral index larger than about 2.4 may provide nontrivial evidence for dynamical degrees of freedom with time-dependent masses during inflation. The bound is not sensitive to the details of the reheating scenario and can be made mildly smaller if the tensor-to-scalar ratio is better constrained in the future.
Omiste, Juan J
2016-01-01
We present a theoretical study of the mixed-field-orientation of asymmetric top molecules in tilted static electric field and non-resonant linearly polarized laser pulse by solving the time-dependent Schr\\"odinger equation. Within this framework, we compute the mixed-field orientation of a state selected molecular beam of benzonitrile (C$_7$H$_5$N) and compare with the experimental observations [J. L. Hansen et al., Phys. Rev. A 83, 023406 (2011)], and with our previous time-independent descriptions [J. J. Omiste et al., Phys. Chem. Chem. Phys. 13, 18815 (2011)]. For an excited rotational state, we investigate the field-dressed dynamics for several field configurations as those used in the mixed-field experiments. The non-adiabatic phenomena and their consequences on the rotational dynamics are analyzed in detail.
Time-dependent density functional studies of nuclear quantum dynamics in large amplitudes
Wen, Kai; Fang, Ni; Nakatsukasa, Takashi
2015-01-01
The time-dependent density functional theory (TDDFT) provides a unified description of the structure and reaction. The linear approximation leads to the random-phase approximation (RPA) which is capable of describing a variety of collective motion in a harmonic regime. Beyond the linear regime, we present applications of the TDDFT to nuclear fusion and fission reaction. In particular, the extraction of the internuclear potential and the inertial mass parameter is performed using two different methods. A fusion hindrance mechanism for heavy systems is investigated from the microscopic point of view. The canonical collective variables are determined by the adiabatic self-consistent collective coordinate method. Preliminary results of the spontaneous fission path, the potential, and the collective mass parameter are shown for 8Be --> alpha+alpha.
Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations
Alberto Nocera
2016-03-01
Full Text Available Background: Soft nanosystems are electronic nanodevices, such as suspended carbon nanotubes or molecular junctions, whose transport properties are modulated by soft internal degrees of freedom, for example slow vibrational modes. Effects of the electron–vibration coupling on the charge and heat transport of soft nanoscopic systems are theoretically investigated in the presence of time-dependent perturbations, such as a forcing antenna or pumping terms between the leads and the nanosystem. A well-established approach valid for non-equilibrium adiabatic regimes is generalized to the case where external time-dependent perturbations are present. Then, a number of relevant applications of the method are reviewed for systems composed by a quantum dot (or molecule described by a single electronic level coupled to a vibrational mode.Results: Before introducing time-dependent perturbations, the range of validity of the adiabatic approach is discussed showing that a very good agreement with the results of an exact quantum calculation is obtained in the limit of low level occupation. Then, we show that the interplay between the low frequency vibrational modes and the electronic degrees of freedom affects the thermoelectric properties within the linear response regime finding out that the phonon thermal conductance provides an important contribution to the figure of merit at room temperature. Our work has been stimulated by recent experimental results on carbon nanotube electromechanical devices working in the semiclassical regime (resonator frequencies in the megahertz range compared to an electronic hopping frequency of the order of tens of gigahertz with extremely high quality factors. The nonlinear vibrational regime induced by the external antenna in such systems has been discussed within the non-perturbative adiabatic approach reproducing quantitatively the characteristic asymmetric shape of the current–frequency curves. Within the same set-up, we
How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?
Yarman, T.; L. Kholmetskii, A.
2011-10-01
We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3 = Constant, where P is the pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al. 2010 Int. J. Phys. Sci. 5 1524). We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.
How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?
T. Yarman; A. L. Kholmetskii
2011-01-01
We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3 =Constant,where P is the pressure and V is the volume,and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al.2010 Int.J.Phys.Sci.5 1524).We explicitly determine the constant for the general parallelepiped geometry of a container.We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation.Physical implications of the results obtained are discussed.
Non-adiabatic primordial fluctuations
Noller, Johannes; Magueijo, Joao, E-mail: johannes.noller08@imperial.ac.uk [Theoretical Physics Group, Imperial College, London SW7 2BZ (United Kingdom)
2011-05-21
We consider general mixtures of isocurvature and adiabatic cosmological perturbations. With a minimal assumption set consisting of the linearized Einstein equations and a primordial perfect fluid we derive the second-order action and its curvature variables. We also allow for varying equation of state and speed of sound profiles. The derivation is therefore carried out at the same level of generality that has been achieved for adiabatic modes before. As a result we find a new conserved super-horizon quantity and relate it to the adiabatically conserved curvature perturbation. Finally we demonstrate how the formalism can be applied by considering a Chaplygin gas-like primordial matter model, finding two scale-invariant solutions for structure formation.
Analysis of Adiabatic Batch Reactor
Erald Gjonaj
2016-05-01
Full Text Available A mixture of acetic anhydride is reacted with excess water in an adiabatic batch reactor to form an exothermic reaction. The concentration of acetic anhydride and the temperature inside the adiabatic batch reactor are calculated with an initial temperature of 20°C, an initial temperature of 30°C, and with a cooling jacket maintaining the temperature at a constant of 20°C. The graphs of the three different scenarios show that the highest temperatures will cause the reaction to occur faster.
Adiabatic theory for the bipolaron
Lakhno, V.D. (Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino Moscow Region, 142292 (Russian Federation))
1995-02-01
A translation-invariant adiabatic theory is constructed for the bipolaron. It is shown that motions in the bipolaron are divided: the relative electron coordinates describe fast electron oscillations in the induced polarization well and the center of mass coordinates represent slow electron movement followed by polarization. Nonlinear differential bipolaron equations are derived which are asymptotically exact in the adiabatic limit. Particlelike solutions of these equations correspond to the bipolaron bound state. The exact solution yields the value of the ion critical parameter [eta]=0.31 for which the bipolaron state is stable, where [eta]=[epsilon][sub [infinity
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
Evaluation of Time-Dependent Behavior of Soils
Augustesen, Anders; Liingaard, Morten; Lade, Poul V.
2004-01-01
The time-dependent behavior of soils has been investigated extensively through one-dimensional and triaxial test conditions. Most of the observations in literature have focused on the determination of the time-dependent behavior of clayey soils, whereas the reported experimental studies of granul...
K shortest paths in stochastic time-dependent networks
Nielsen, Lars Relund; Pretolani, Daniele; Andersen, Kim Allan
2004-01-01
A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...
Non-adiabatic oscillations of compact stars in general relativity
Gualtieri, L; Miniutti, G
2004-01-01
We have developed a formalism to study non-adiabatic, non-radial oscillations of compact stars in the frequency domain including the effects of thermal diffusion in a general relativistic framework. When a general equation of state depending on temperature is used, the perturbations of the fluid result in heat flux which is coupled with the spacetime geometry through the Einstein field equations. Our results show that the frequency of the first pressure (p) and gravity (g) oscillation modes is significantly affected by thermal diffusion, while that of the fundamental (f) mode is basically unaltered due to the global nature of that oscillation. The damping time of the oscillations is generally much smaller than in the adiabatic case (more than two orders of magnitude for the p- and g-modes) reflecting the effect of thermal dissipation. Both the isothermal and adiabatic limits are recovered in our treatment and we study in more detail the intermediate regime. Our formalism finds its natural astrophysical applic...
Adiabatic invariants in stellar dynamics. 2: Gravitational shocking
Weinberg, Martin D.
1994-01-01
A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.
Non-adiabatic study of the Kepler subgiant KIC 6442183
Grosjean M.
2015-01-01
Full Text Available Thanks to the precision of Kepler observations, [3] were able to measure the linewidth and amplitude of individual modes (including mixed modes in several subgiant power spectra. We perform a forward modelling of a Kepler subgiant based on surface properties and observed frequencies. Non-adiabatic computations including a time- dependent treatment of convection give the lifetimes of radial and non-radial modes. Next, combining the lifetimes and inertias with a stochastic excitation model gives the amplitudes of the modes. We can now directly compare theoretical and observed linewidths and amplitudes of mixed-modes to obtain new constraints on our theoretical models.
A Many Particle Adiabatic Invariant
Hjorth, Poul G.
1999-01-01
For a system of N charged particles moving in a homogeneous, sufficiently strong magnetic field, a many-particle adiabatic invariant constrains the collisional exchange of energy between the degrees of freedom perpendicular to and parallel to the magnetic field. A description of the phenomenon...
Elementary examples of adiabatic invariance
Crawford, F.S. (Physics Department, University of California, Berkeley, CA (USA) Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 (USA))
1990-04-01
Simple classical one-dimensional systems subject to adiabatic (gradual) perturbations are examined. The first examples are well known: the adiabatic invariance of the product {ital E}{tau} of energy {ital E} and period {tau} for the simple pendulum and for the simple harmonic oscillator. Next, the adiabatic invariants of the vertical bouncer are found---a ball bouncing elastically from the floor of a rising elevator having slowly varying velocity and acceleration. These examples lead to consideration of adiabatic invariance for one-dimensional systems with potentials of the form {ital V}={ital ax}{sup {ital n}}, with {ital a}={ital a}({ital t}) slowly varying in time. Then, the horizontal bouncer is considered---a mass sliding on a smooth floor, bouncing back and forth between two impenetrable walls, one of which is slowly moving. This example is generalized to a particle in a bound state of a general potential with one slowly moving turning point.'' Finally, circular motion of a charged particle in a magnetic field slowly varying in time under three different configurations is considered: (a) a free particle in a uniform field; (b) a free particle in a nonuniform betatron'' field; and (c) a particle constrained to a circular orbit in a uniform field.
Relativistic like structure of classical thermodynamics
Quevedo, Hernando; Sánchez, Alberto; Vázquez, Alejandro
2015-04-01
We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state of equilibrium, so that the resulting curve represents a quasi-static process. A rigorous geometric structure is derived in which the thermodynamic geodesics at a given point split the equilibrium space into two disconnected regions separated by adiabatic geodesics. This resembles the causal structure of special relativity, which we use to introduce the concept of adiabatic cone for thermodynamic systems. This result might be interpreted as an alternative indication of the inter-relationship between relativistic physics and classical thermodynamics.
Digital Waveguide Adiabatic Passage Part 1: Theory
Vaitkus, Jesse A; Greentree, Andrew D
2016-01-01
Spatial adiabatic passage represents a new way to design integrated photonic devices. In conventional adiabatic passage designs require smoothly varying waveguide separations. Here we show modelling of adiabatic passage devices where the waveguide separation is varied digitally. Despite digitisation, our designs show robustness against variations in the input wavelength and refractive index contrast of the waveguides relative to the cladding. This approach to spatial adiabatic passage opens new design strategies and hence the potential for new photonics devices.
Diabatic and Adiabatic Collective Motion in a Model Pairing System
Nakatsukasa, T; Nakatsukasa, Takashi; Walet, Niels R.
1998-01-01
Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field theory or a direct parametrisation of the time-dependent Schrödinger equation. A modified local harmonic equation is formulated to take account of the Nambu-Goldstone mode. It turns out that in some cases the system selects a diabatic path. Requantizing the collective Hamiltonian, a reasonable agreement with an exact calculation for the low-lying levels are obtained for both weak and strong pairing force. This improves on results of the conventional Born-Oppenheimer approximation.
Konecny, Lukas; Kadek, Marius; Komorovsky, Stanislav; Malkina, Olga L; Ruud, Kenneth; Repisky, Michal
2016-12-13
The Liouville-von Neumann equation based on the four-component matrix Dirac-Kohn-Sham Hamiltonian is transformed to a quasirelativistic exact two-component (X2C) form and then used to solve the time evolution of the electronic states only. By this means, a significant acceleration by a factor of 7 or more has been achieved. The transformation of the original four-component equation of motion is formulated entirely in matrix algebra, following closely the X2C decoupling procedure of Ilias and Saue [ J. Chem. Phys. 2007 , 126 , 064102 ] proposed earlier for a static (time-independent) case. In a dynamic (time-dependent) regime, however, an adiabatic approximation must in addition be introduced in order to preserve the block-diagonal form of the time-dependent Dirac-Fock operator during the time evolution. The resulting X2C Liouville-von Neumann electron dynamics (X2C-LvNED) is easy to implement as it does not require an explicit form of the picture-change transformed operators responsible for the (higher-order) relativistic corrections and/or interactions with external fields. To illustrate the accuracy and performance of the method, numerical results and computational timings for nonlinear optical properties are presented. All of the time domain X2C-LvNED results show excellent agreement with the reference four-component calculations as well as with the results obtained from frequency domain response theory.
Quantum mechanics in strong time dependent external fields
Pomeau, Y.
1986-01-01
In quantum mechanics, time dependent Hamiltonians are most often studied by perturbation methods, the amplitude of the unsteady force being assumed to be small. On two examples (two level system with a large time dependent coupling, and atoms in large external unsteady field). I show that the opposite limit (large time dependent field) can be analyzed in some details too. For a particle in a central potential and submitted to a large periodic external field, one is led to make a Kapitza averaging because the intrinsic frequency tends to zero when the external field diverges. In that way one has to introduce a steady effective potential with singular turning points.
Jet-Ricci Geometry of Time-Dependent Human Biomechanics
Ivancevic, Tijana T
2009-01-01
We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exhaustion of biochemical resources) is closely related to the Ricci flow on the biomechanical configuration manifold. Keywords: Time-dependent biomechanics, extended configuration manifold, configuration bundle, jet manifolds, Ricci flow diffusion
A Time Dependent Leptonic Model for Microquasar Jets: Application to LSI 61 303
Gupta, S; Gupta, Swati; Boettcher, Markus
2006-01-01
he Galactic high-mass X-ray binary and jet source (microquasar) LSI +61 303 has recently been detected at TeV gamma-ray energies by the MAGIC telescope. We have applied a time-dependent leptonic jet model to the broadband spectral energy distribution and orbital modulation of the very high energy gamma-ray emission of this source. Our model takes into account time dependent electron injection and acceleration, and the adiabatic and radiative cooling of non-thermal electrons. It includes synchrotron, inverse Compton (with seed photons from the companion star and the accretion disk), and synchrotron self-Compton emission, as well as gamma-gamma absorption of gamma-rays by starlight photons. The model can successfully reproduce the available multiwavelength observational data. Our best fit to the SED indicates that a magnetic field of B_0 ~ 5 X 10^3 G at ~ 10^3 R_g is required, and electrons need to be accelerated out to TeV energies (gamma_2 = 10^6) with a nonthermal injection spectrum with a spectral index of ...
Theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels.
Muller, Peter Barkholt; Bruus, Henrik
2015-12-01
Based on first- and second-order perturbation theory, we present a numerical study of the temporal buildup and decay of unsteady acoustic fields and acoustic streaming flows actuated by vibrating walls in the transverse cross-sectional plane of a long straight microchannel under adiabatic conditions and assuming temperature-independent material parameters. The unsteady streaming flow is obtained by averaging the time-dependent velocity field over one oscillation period, and as time increases, it is shown to converge towards the well-known steady time-averaged solution calculated in the frequency domain. Scaling analysis reveals that the acoustic resonance builds up much faster than the acoustic streaming, implying that the radiation force may dominate over the drag force from streaming even for small particles. However, our numerical time-dependent analysis indicates that pulsed actuation does not reduce streaming significantly due to its slow decay. Our analysis also shows that for an acoustic resonance with a quality factor Q, the amplitude of the oscillating second-order velocity component is Q times larger than the usual second-order steady time-averaged velocity component. Consequently, the well-known criterion v(1)≪c(s) for the validity of the perturbation expansion is replaced by the more restrictive criterion v(1)≪c(s)/Q. Our numerical model is available as supplemental material in the form of comsol model files and matlab scripts.
Time dependent two phase flows in Magnetohydrodynamics: A ...
Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT Subscription or Fee Access. Time dependent two phase flows in Magnetohydrodynamics: A Greens function approach. BK Jha, HM Jibril ...
Time-dependent rheological behaviour of bacterial cellulose hydrogel.
Gao, Xing; Shi, Zhijun; Kuśmierczyk, Piotr; Liu, Changqing; Yang, Guang; Sevostianov, Igor; Silberschmidt, Vadim V
2016-01-01
This work focuses on time-dependent rheological behaviour of bacterial cellulose (BC) hydrogel. Due to its ideal biocompatibility, BC hydrogel could be employed in biomedical applications. Considering the complexity of loading conditions in human body environment, time-dependent behaviour under relevant conditions should be understood. BC specimens are produced by Gluconacetobacter xylinus ATCC 53582 at static-culture conditions. Time-dependent behaviour of specimens at several stress levels is experimentally determined by uniaxial tensile creep tests. We use fraction-exponential operators to model the rheological behaviour. Such a representation allows combination of good accuracy in analytical description of viscoelastic behaviour of real materials and simplicity in solving boundary value problems. The obtained material parameters allow us to identify time-dependent behaviour of BC hydrogel at high stress level with sufficient accuracy.
Entanglement Entropy for time dependent two dimensional holographic superconductor
Mazhari, N S; Myrzakulov, Kairat; Myrzakulov, R
2016-01-01
We studied entanglement entropy for a time dependent two dimensional holographic superconductor. We showed that the conserved charge of the system plays the role of the critical parameter to have condensation.
Skinner-Rusk approach to time-dependent mechanics
Cortés, Jorge; Martínez, Sonia; Cantrijn, Frans
2002-01-01
The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by Skinner and Rusk, is extended to the time-dependent framework.
Time-Dependent Modulation of Cosmic Rays in the Heliosphere
Manuel, Rex; Potgieter, Marius
2013-01-01
The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a time-dependent modulation model. By introducing recent theoretical advances in the transport coefficients in the model, computed intensities are compared with Voyager 1, International Monitoring Platform (IMP) 8, and Ulysses proton observations in search of compatibility. The effect of different modulation parameters on computed intensities is also illustrated. It is shown that this approach produces, on a global scale, realistic cosmic-ray proton intensities along the Voyager 1 spacecraft trajectory and at Earth upto ~2004, whereafter the computed intensities recovers much slower towards solar minimum than observed in the inner heliosphere. A modified time dependence in the diffusion coefficients is proposed to improve compatibility with the observations at Earth after ~2004. This modified time dependence led to an improved compatibility between computed intensities and the observations along ...
Optimization of a relativistic quantum mechanical engine
Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.
2016-08-01
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
The adiabatic electron affinities (EAs) for the heteroatomic molecule SO 4: An MP2/CBS study
Zheng, Wenxu; Lau, Kai-Chung; Wong, Ning-Bew; Li, Wai-Kee
2009-01-01
An MP2/CBS approach has been proposed to calculate the adiabatic electron affinities (EAs) for the heteroatomic molecule SO 4. The method involves the approximation to the complete basis set (CBS) limit at the MP2 level. The zero-point vibrational energy correction, the diagonal Born-Oppenheimer correction, and the scalar relativistic effect correction have been also made in the calculations. The present MP2/CBS predictions are found to be in good accord with the available experimental values.
K-shell ionization in relativistic ion-atom collisions
Mehler, G.; Soff, G.; Rumrich, K.; Greiner, W.
1989-08-01
We present calculations of K-shell ionization probabilities in asymmetric ion-atom collisions at relativistic velocities of the projectile. The time-dependent Dirac equation is represented as a system of coupled differential equations. The transition probabilities are determined using the coordinate space method. This necessitates an extension of the angular momentum coupling compared with nonrelativistic collision systems. Effects of the relativistic projectile motion on the coupling matrix elements and their consequences on K-shell ionization are discussed. (orig.).
K-shell ionization in relativistic ion-atom collisions
Mehler, G.; Rumrich, K.; Greiner, W.; Soff, G.
1989-02-01
We present calculations of K-shell ionization probabilities in asymmetric ion-atom collisions at relativistic velocities of the projectile. The time-dependent Dirac equation is represented as a system of coupled differential equations. The transition probabilities are determined using the coordinate space method. This necessitates an extension of the angular momentum coupling compared with nonrelativistic collision systems. Effects of the relativistic projectile motion on the coupling matrix elements and their consequences on K-shell ionization are discussed.
Jet-Ricci Geometry of Time-Dependent Human Biomechanics
Ivancevic, Tijana T.
2009-01-01
We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exh...
One Dimensional Time-Dependent Tunnelling of Excitons
Kilcullen, Patrick; Salayka-Ladouceur, Logan; Malmgren, Kevin; Reid, Matthew; Shegelski, Mark R. A.
2017-03-01
We study the time-dependent tunnelling of excitons in one dimension using numerical integration based on the Crank-Nicholson method. A complete development of the time-dependent simulator is provided. External barriers studied include single and double delta barriers. We find that the appearance of transmission resonances depends strongly on the dielectric constant, relative effective masses, and initial spatial spread of the wavefunction. A discussion regarding applications to realistic systems is provided.
Solving the transport without transit quantum paradox of the spatial adiabatic passage technique
Benseny, Albert; Oriols, Xavier; Mompart, Jordi
2011-01-01
We discuss and solve the transport without transit quantum paradox recently introduced in the context of the adiabatic transport of a single particle or a Bose--Einstein condensate between the two extreme traps of a triple-well potential. To this aim, we address the corresponding quantum dynamics in terms of Bohmian trajectories and show that transport always implies transit through the middle well, in full agreement with the quantum continuity equation. This adiabatic quantum transport presents a very counterintuitive effect: by slowing down the total time duration of the transport process, ultra-high Bohmian velocities are achieved such that, in the limit of perfect adiabaticity, relativistic corrections are needed to properly address the transfer process while avoiding superluminal matter wave propagation.
Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua
2011-08-28
We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.
Modeling multiband emissions from two young SNRs with a time-dependent magnetic field
Yun-Yong Tang; Zu-Cheng Dai; Li Zhang
2013-01-01
The nonthermal components in hard X-rays have been detected in two young supernova remnants (SNRs):SN 1006 and Kepler's SNR.Various theoretical models showed that the amplification of the magnetic field was crucial to explain their multiband emission properties.We investigate the evolution of the magnetic field and model the multiband emissions from these two young SNRs with a time-dependent injection model.The results indicate that (1) the radio and X-ray emissions are reproduced by synchrotron radiation of the injected electrons,while the γ-rays can be explained as inverse Compton scattering of the relativistic electrons and proton-proton interaction of the high-energy protons; and (2) the amplification of the magnetic field spontaneously happens with reasonable parameters.
Towards time-dependent current-density-functional theory in the non-linear regime.
Escartín, J M; Vincendon, M; Romaniello, P; Dinh, P M; Reinhard, P-G; Suraud, E
2015-02-28
Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.
Linear-response time-dependent density-functional theory with pairing fields.
Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao
2014-05-14
Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.
Instability of Extremal Relativistic Charged Spheres
Anninos, P; Anninos, Peter; Rothman, Tony
2002-01-01
With the question, ``Can relativistic charged spheres form extremal black holes?" in mind, we investigate the properties of such spheres from a classical point of view. The investigation is carried out numerically by integrating the Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding interior Reissner-Nordstr\\"om solutions for these objects. We consider both constant density and adiabatic equations of state, as well as several possible charge distributions, and examine stability by both a normal mode and an energy analysis. In all cases, the stability limit for these spheres lies between the extremal ($Q = M$) limit and the black hole limit ($R = R_+$). That is, we find that charged spheres undergo gravitational collapse before they reach $Q = M$, suggesting that extremal Reissner-Nordtr\\"om black holes produced by collapse are ruled out. A general proof of this statement would support a strong form of the cosmic censorship hypothesis, excluding not only stable naked singularities, ...
Non-Adiabatic Molecular Dynamics Methods for Materials Discovery
Furche, Filipp [Univ. of California, Irvine, CA (United States); Parker, Shane M. [Univ. of California, Irvine, CA (United States); Muuronen, Mikko J. [Univ. of California, Irvine, CA (United States); Roy, Saswata [Univ. of California, Irvine, CA (United States)
2017-04-04
The flow of radiative energy in light-driven materials such as photosensitizer dyes or photocatalysts is governed by non-adiabatic transitions between electronic states and cannot be described within the Born-Oppenheimer approximation commonly used in electronic structure theory. The non-adiabatic molecular dynamics (NAMD) methods based on Tully surface hopping and time-dependent density functional theory developed in this project have greatly extended the range of molecular materials that can be tackled by NAMD simulations. New algorithms to compute molecular excited state and response properties efficiently were developed. Fundamental limitations of common non-linear response methods were discovered and characterized. Methods for accurate computations of vibronic spectra of materials such as black absorbers were developed and applied. It was shown that open-shell TDDFT methods capture bond breaking in NAMD simulations, a longstanding challenge for single-reference molecular dynamics simulations. The methods developed in this project were applied to study the photodissociation of acetaldehyde and revealed that non-adiabatic effects are experimentally observable in fragment kinetic energy distributions. Finally, the project enabled the first detailed NAMD simulations of photocatalytic water oxidation by titania nanoclusters, uncovering the mechanism of this fundamentally important reaction for fuel generation and storage.
Brics, M
2013-01-01
Favorably scaling numerical time-dependent many-electron techniques such as time-dependent density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We propose a method based on natural orbitals, i.e., the eigenfunctions of the one-body reduced density matrix, that is almost as inexpensive numerically as adiabatic TDDFT, but which is capable of describing correlated phenomena such as doubly excited states, autoionization, Fano profiles in the photoelectron spectra, and strong-field ionization in general. Equations of motion (EOM) for natural orbitals and their occupation numbers have been derived earlier. We show that by using renormalized natural orbitals (RNO) both can be combined into one equation governed by a hermitian effective Hamiltonian. We specialize on the two-electron spin-singlet system, known as being a "worst case" testing ground for TDDFT, and employ the widely used, numerically exactly solvable, one-dimens...
Peng, Weng Kung; Takeda, Kazuyuki
2007-10-01
In this work, we propose a new and efficient heteronuclear cross polarization scheme, in which adiabatic frequency sweeps from far off-resonance toward on-resonance are applied simultaneously on both the source and target spins. This technique, which we call as Simultaneous ADIabatic Spin-locking Cross Polarization (SADIS CP), is capable of efficiently locking both the source and target spins with moderate power even in the presence of large spectral distribution and fast relaxation. It is shown that by keeping the time-dependent Hartmann-Hahn mismatch minimal throughout the mixing period, polarization transfer can be accelerated. Experiments are demonstrated in a powder sample of L-alanine.
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.
Baksic, Alexandre; Belyansky, Ron; Ribeiro, Hugo; Clerk, Aashish A.
2017-08-01
We present a method for accelerating adiabatic protocols for systems involving a coupling to a continuum, one that cancels both nonadiabatic errors as well as errors due to dissipation. We focus on applications to a generic quantum state transfer problem, where the goal is to transfer a state between a single level or mode, and a propagating temporal mode in a waveguide or transmission line. Our approach enables perfect adiabatic transfer protocols in this setup, despite a finite protocol speed and a finite waveguide coupling. Our approach even works in highly constrained settings, where there is only a single time-dependent control field available.
Li, Dafa
2016-05-01
The adiabatic theorem was proposed about 90 years ago and has played an important role in quantum physics. The quantitative adiabatic condition constructed from eigenstates and eigenvalues of a Hamiltonian is a traditional tool to estimate adiabaticity and has proven to be the necessary and sufficient condition for adiabaticity. However, recently the condition has become a controversial subject. In this paper, we list some expressions to estimate the validity of the adiabatic approximation. We show that the quantitative adiabatic condition is invalid for the adiabatic approximation via the Euclidean distance between the adiabatic state and the evolution state. Furthermore, we deduce general necessary and sufficient conditions for the validity of the adiabatic approximation by different definitions.
A 3D radiative transfer framework. IX. Time dependence
Jack, D.; Hauschildt, P. H.; Baron, E.
2012-10-01
Context. Time-dependent, 3D radiation transfer calculations are important for the modeling of a variety of objects, from supernovae and novae to simulations of stellar variability and activity. Furthermore, time-dependent calculations can be used to obtain a 3D radiative equilibrium model structure via relaxation in time. Aims: We extend our 3D radiative transfer framework to include direct time dependence of the radiation field; i.e., the ∂I/∂t terms are fully considered in the solution of radiative transfer problems. Methods: We build on the framework that we have described in previous papers in this series and develop a subvoxel method for the ∂I/∂t terms. Results: We test the implementation by comparing the 3D results to our well tested 1D time dependent radiative transfer code in spherical symmetry. A simple 3D test model is also presented. Conclusions: The 3D time dependent radiative transfer method is now included in our 3D RT framework and in PHOENIX/3D.
A 3D radiative transfer framework IX. Time dependence
Jack, D; Baron, E
2012-01-01
Context. Time-dependent, 3D radiation transfer calculations are important for the modeling of a variety of objects, from supernovae and novae to simulations of stellar variability and activity. Furthermore, time-dependent calculations can be used to obtain a 3D radiative equilibrium model structure via relaxation in time. Aims. We extend our 3D radiative transfer framework to include direct time dependence of the radiation field; i.e., the $\\partial I/ \\partial t$ terms are fully considered in the solution of radiative transfer problems. Methods. We build on the framework that we have described in previous papers in this series and develop a subvoxel method for the $\\partial I/\\partial t$ terms. Results. We test the implementation by comparing the 3D results to our well tested 1D time dependent radiative transfer code in spherical symmetry. A simple 3D test model is also presented. Conclusions. The 3D time dependent radiative transfer method is now included in our 3D RT framework and in PHOENIX/3D.
Particle in a box with a time-dependent δ -function potential
Baek, Seung Ki; Yi, Su Do; Kim, Minjae
2016-11-01
In quantum information processing, one often considers inserting a barrier into a box containing a particle to generate one bit of Shannon entropy. We formulate this problem as a one-dimensional Schrödinger equation with a time-dependent δ -function potential. It is a natural generalization of the particle in a box, a canonical example of quantum mechanics, and we present analytic and numerical investigations on this problem. After deriving an exact Volterra-type integral equation, composed of an infinite sum of modes, we show that approximate formulas with the lowest-frequency modes correctly capture the qualitative behavior of the wave function. If we take into account hundreds of modes, our numerical calculation shows that the quantum adiabatic theorem actually gives a very good approximation even if the barrier height diverges within finite time, as long as it is sufficiently longer than the characteristic time scale of the particle. In particular, if the barrier is slowly inserted at an asymmetric position, the particle is localized by the insertion itself, in accordance with a prediction of the adiabatic theorem. On the other hand, when the barrier is inserted quickly, the wave function becomes rugged after the insertion because of the energy transfer to the particle. Regardless of the position of the barrier, the fast insertion leaves the particle unlocalized so that we can obtain meaningful information by a which-side measurement. Our numerical procedure provides a precise way to calculate the wave function throughout the process, from which one can estimate the amount of this information for an arbitrary insertion protocol.
Reversible and Irreversible Time-Dependent Behavior of GRCop-84
Lerch, Bradley A.; Arnold, Steven M.; Ellis, David L.
2017-01-01
A series of mechanical tests were conducted on a high-conductivity copper alloy, GRCop-84, in order to understand the time dependent response of this material. Tensile, creep, and stress relaxation tests were performed over a wide range of temperatures, strain rates, and stress levels to excite various amounts of time-dependent behavior. At low applied stresses the deformation behavior was found to be fully reversible. Above a certain stress, termed the viscoelastic threshold, irreversible deformation was observed. At these higher stresses the deformation was observed to be viscoplastic. Both reversible and irreversible regions contained time dependent deformation. These experimental data are documented to enable characterization of constitutive models to aid in design of high temperature components.
Time-dependent massless Dirac fermions in graphene
Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)
2015-10-30
Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.
Time-dependent stabilization in AdS/CFT
Auzzi, Roberto; Gudnason, Sven Bjarke; Rabinovici, Eliezer
2012-01-01
We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We first study a free field theory on a torus with a time-dependent mass term, finding that the stability regions are described in terms of the phase diagram of the Mathieu equation. Using number theory we have found a compactification scheme such as to avoid resonances for all momentum modes in the theory. We further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities; we study when such singularities can be cured by dynamical stabilization. We numerically solve the Einstein-scalar equations of motion in the case of a time-dependent doubletrace deformation and find that for sufficiently high freque...
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Eigenstates of the time-dependent density-matrix theory
Tohyama, M. [Kyorin University School of Medicine, 181-8611, Mitaka, Tokyo (Japan); Schuck, P. [Institut de Physique Nucleaire, IN2P3-CNRS, Universite Paris-Sud, F-91406, Orsay Cedex (France)
2004-02-01
An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying 2{sup +} states in {sup 24}O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the 2{sup +} states has physically reasonable behavior and that the strength function is practically positive definite though the non-Hermitian Hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an Extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the Hermitian Extended RPA theory. (orig.)
Jet Methods in Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associat...
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Röken, Christian; Schöneberg, Sebastian; Schuppan, Florian
2016-01-01
A leptonic one-zone model accounting for the radiation emission of blazars is presented. This model describes multiple successive injections of mono-energetic, ultra-relativistic, interacting electron populations, which are subjected to synchrotron and synchrotron-self Compton radiative losses. The electron number density is computed analytically by solving a time-dependent, relativistic transport equation. Moreover, the synchrotron and synchrotron-self Compton intensities as well as the corresponding total fluences are explicitly calculated. The lightcurves and fluences are plotted for realistic parameter values, showing that the model can simultaneously explain both the specific short-time variability in the flaring of blazars and the characteristic broad-band fluence behavior.
Time-Dependent Collective Neutrino Oscillations in Supernovae
Abbar, Sajad; Duan, Huaiyu
2015-10-01
Neutrinos can experience self-induced flavor conversion in core-collapse supernovae due to neutrino-neutrino forward scattering. Previously a stationary supernova model, the so called ``neutrino bulb model,'' was used exclusively to study collective neutrino oscillations in the core-collapse supernova. We show that even a small time-dependent perturbation in neutrino fluxes on the surface of the proto-neutron star can lead to fast varying collective oscillations at large radii. This result calls for time-dependent supernova models for the study of collective neutrino oscillations. This work was supported by DOE EPSCoR Grant DE-SC0008142 at UNM.
Vacuum radiation induced by time dependent electric field
Bo Zhang
2017-04-01
Full Text Available Many predictions of new phenomena given by strong field quantum electrodynamics (SFQED will be tested on next generation multi-petawatt laser facilities in the near future. These new phenomena are basis to understand physics in extremely strong electromagnetic fields therefore have attracted wide research interest. Here we discuss a new SFQED phenomenon that is named as vacuum radiation. In vacuum radiation, a virtual electron loop obtain energy from time dependent external electric field and radiate an entangled photon pair. Features of vacuum radiation in a locally time dependent electric field including spectrum, characteristic temperature, production rate and power are given.
Exact response functions within the time-dependent Gutzwiller approach
Bünemann, J.; Wasner, S.; Oelsen, E. v.; Seibold, G.
2015-02-01
We investigate the applicability of the two existing versions of a time-dependent Gutzwiller approach (TDGA) beyond the frequently used limit of infinite spatial dimensions. To this end, we study the two-particle response functions of a two-site Hubbard model where we can compare the exact results and those derived from the TDGA. It turns out that only the more recently introduced version of the TDGA can be combined with a diagrammatic approach which allows for the evaluation of Gutzwiller wave functions in finite dimensions. For this TDGA method, we derive the time-dependent Lagrangian for general single-band Hubbard models.
Time-dependent perturbation theory for inelastic scattering
Cross, R. J.
1982-08-01
We show by numerical integration that the first-order, time-dependent, Magnus approximation agrees with the first-order, exponential, distorted-wave approximation to within a few percent, provided that the trajectory used for the time-dependent calculation is characterized by the arithmetic mean of the initial and final velocities and the arithmetic mean of the initial and final orbital angular momenta. Calculations are done for rotational energy transfer from an exponentially repulsive potential characteristic of He+H2 and for a Lennard-Jones potential characteristic of Ar+N2.
Vacuum radiation induced by time dependent electric field
Zhang, Bo; Zhang, Zhi-meng; Hong, Wei; He, Shu-Kai; Teng, Jian; Gu, Yu-qiu
2017-04-01
Many predictions of new phenomena given by strong field quantum electrodynamics (SFQED) will be tested on next generation multi-petawatt laser facilities in the near future. These new phenomena are basis to understand physics in extremely strong electromagnetic fields therefore have attracted wide research interest. Here we discuss a new SFQED phenomenon that is named as vacuum radiation. In vacuum radiation, a virtual electron loop obtain energy from time dependent external electric field and radiate an entangled photon pair. Features of vacuum radiation in a locally time dependent electric field including spectrum, characteristic temperature, production rate and power are given.
Direct imaging of small scatterers using reduced time dependent data
Cakoni, Fioralba; Rezac, Jacob D.
2017-06-01
We introduce qualitative methods for locating small objects using time dependent acoustic near field waves. These methods have reduced data collection requirements compared to typical qualitative imaging techniques. In particular, we only collect scattered field data in a small region surrounding the location from which an incident field was transmitted. The new methods are partially theoretically justified and numerical simulations demonstrate their efficacy. We show that these reduced data techniques give comparable results to methods which require full multistatic data and that these time dependent methods require less scattered field data than their time harmonic analogs.
Appel, H.
2007-05-15
In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f{sub xc} from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the
Effective Maxwell Equations from Time-dependent Density Functional Theory
Weinan E; Jianfeng LU; Xu YANG
2011-01-01
The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.
Classical and quantum time dependent solutions in string theory
Mart'inez-Prieto, C; Socorro, J
2004-01-01
Using the ontological interpretation of quantum mechanics in a particular sense, we obtain the classical behaviour of the scale factor and two scalar fields, derived from a string effective action for the FRW time dependent model. Besides, the Wheeler-DeWitt equation is solved exactly. We speculate that the same procedure could also be applied to S-branes.
PRODUCT FORMULA METHODS FOR TIME-DEPENDENT SCHRODINGER PROBLEMS
HUYGHEBAERT, J; DERAEDT, H
1990-01-01
This paper introduces a family of explicit and unconditionally stable algorithms for solving linear differential equations which contain a time-dependent Hermitian operator. Rigorous upper bounds are derived for two different `time-ordered' approximation schemes and for errors resulting from approxi
Simulation of time-dependent Heisenberg models in one dimension
Volosniev, A. G.; Hammer, H. -W.; Zinner, N. T.
2016-01-01
In this Letter, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling...
Characterization of Models for Time-Dependent Behavior of Soils
Liingaard, Morten; Augustesen, Anders; Lade, Poul V.
2004-01-01
Different classes of constitutive models have been developed to capture the time-dependent viscous phenomena ~ creep, stress relaxation, and rate effects ! observed in soils. Models based on empirical, rheological, and general stress-strain-time concepts have been studied. The first part is a r...
Dynamic structure evolution of time-dependent network
Zhang, Beibei; Zhou, Yadong; Xu, Xiaoyan; Wang, Dai; Guan, Xiaohong
2016-08-01
In this paper, we research the long-voided problem of formulating the time-dependent network structure evolution scheme, it focus not only on finding new emerging vertices in evolving communities and new emerging communities over the specified time range but also formulating the complex network structure evolution schematic. Previous approaches basically applied to community detection on time static networks and thus failed to consider the potentially crucial and useful information latently embedded in the dynamic structure evolution process of time-dependent network. To address these problems and to tackle the network non-scalability dilemma, we propose the dynamic hierarchical method for detecting and revealing structure evolution schematic of the time-dependent network. In practice and specificity, we propose an explicit hierarchical network evolution uncovering algorithm framework originated from and widely expanded from time-dependent and dynamic spectral optimization theory. Our method yields preferable results compared with previous approaches on a vast variety of test network data, including both real on-line networks and computer generated complex networks.
Time-dependent exact solutions of the nonlinear Kompaneets equation
Ibragimov, N H, E-mail: nib@bth.s [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2010-12-17
Time-dependent exact solutions of the Kompaneets photon diffusion equation are obtained for several approximations of this equation. One of the approximations describes the case when the induced scattering is dominant. In this case, the Kompaneets equation has an additional symmetry which is used for constructing some exact solutions as group invariant solutions. (fast track communication)
Introduction to quantum mechanics a time-dependent perspective
Tannor, David J
2007-01-01
"Introduction to Quantum Mechanics" covers quantum mechanics from a time-dependent perspective in a unified way from beginning to end. Intended for upper-level undergraduate and graduate courses this text will change the way people think about and teach quantum mechanics in chemistry and physics departments.
Stability on time-dependent domains: convective and dilution effects
Krechetnikov, R.; Knobloch, E.
2017-03-01
We explore near-critical behavior of spatially extended systems on time-dependent spatial domains with convective and dilution effects due to domain flow. As a paradigm, we use the Swift-Hohenberg equation, which is the simplest nonlinear model with a non-zero critical wavenumber, to study dynamic pattern formation on time-dependent domains. A universal amplitude equation governing weakly nonlinear evolution of patterns on time-dependent domains is derived and proves to be a generalization of the standard Ginzburg-Landau equation. Its key solutions identified here demonstrate a substantial variety-spatially periodic states with a time-dependent wavenumber, steady spatially non-periodic states, and pulse-train solutions-in contrast to extended systems on time-fixed domains. The effects of domain flow, such as bifurcation delay due to domain growth and destabilization due to oscillatory domain flow, on the Eckhaus instability responsible for phase slips in spatially periodic states are analyzed with the help of both local and global stability analyses. A nonlinear phase equation describing the approach to a phase-slip event is derived. Detailed analysis of a phase slip using multiple time scale methods demonstrates different mechanisms governing the wavelength changing process at different stages.
Time-dependent effects of cardiovascular exercise on memory
Roig, Marc; Thomas, Richard; Mang, Cameron S
2016-01-01
We present new evidence supporting the hypothesis that the effects of cardiovascular exercise on memory can be regulated in a time-dependent manner. When the exercise stimulus is temporally coupled with specific phases of the memory formation process, a single bout of cardiovascular exercise may ...
Multicomponent density-functional theory for time-dependent systems
Butriy, O.; Ebadi, H.; de Boeij, P. L.; van Leeuwen, R.; Gross, E. K. U.
2007-01-01
We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried ou
Time dependent solution for acceleration of tau-leaping
Fu, Jin, E-mail: iamfujin@hotmail.com [Department of Computer Science, University of California, Santa Barbara (United States); Wu, Sheng, E-mail: sheng@cs.ucsb.edu [Department of Computer Science, University of California, Santa Barbara (United States); Petzold, Linda R., E-mail: petzold@cs.ucsb.edu [Department of Computer Science, University of California, Santa Barbara (United States)
2013-02-15
The tau-leaping method is often effective for speeding up discrete stochastic simulation of chemically reacting systems. However, when fast reactions are involved, the speed-up for this method can be quite limited. One way to address this is to apply a stochastic quasi-steady state assumption. However we must be careful when using this assumption. If the fast subsystem cannot reach a steady distribution fast enough, the quasi-steady-state assumption will propagate error into the simulation. To avoid these errors, we propose to use the time dependent solution rather than the quasi-steady-state. Generally speaking, the time dependent solution is not easy to derive for an arbitrary network. However, for some common motifs we do have time dependent solutions. We derive the time dependent solutions for these motifs, and then show how they can be used with tau-leaping to achieve substantial speed-ups, including for a realistic model of blood coagulation. Although the method is complicated, we have automated it.
Noncommutative quantum mechanics in a time-dependent background
Dey, Sanjib; Fring, Andreas
2014-10-01
We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional canonical variables. We employ the Lewis-Riesenfeld method of invariants to construct explicit analytical solutions for the corresponding time-dependent Schrödinger equation. The eigenfunctions are expressed in terms of the solutions of variants of the nonlinear Ermakov-Pinney equation and discussed in detail for various types of background fields. We utilize the solutions to verify a generalized version of Heisenberg's uncertainty relations for which the lower bound becomes a time-dependent function of the background fields. We study the variance for various states, including standard Glauber coherent states with their squeezed versions and Gaussian Klauder coherent states resembling a quasiclassical behavior. No type of coherent state appears to be optimal in general with regard to achieving minimal uncertainties, as this feature turns out to be background field dependent.
Time dependent solution for acceleration of tau-leaping
Fu, Jin; Wu, Sheng; Petzold, Linda R.
2013-02-01
The tau-leaping method is often effective for speeding up discrete stochastic simulation of chemically reacting systems. However, when fast reactions are involved, the speed-up for this method can be quite limited. One way to address this is to apply a stochastic quasi-steady state assumption. However we must be careful when using this assumption. If the fast subsystem cannot reach a steady distribution fast enough, the quasi-steady-state assumption will propagate error into the simulation. To avoid these errors, we propose to use the time dependent solution rather than the quasi-steady-state. Generally speaking, the time dependent solution is not easy to derive for an arbitrary network. However, for some common motifs we do have time dependent solutions. We derive the time dependent solutions for these motifs, and then show how they can be used with tau-leaping to achieve substantial speed-ups, including for a realistic model of blood coagulation. Although the method is complicated, we have automated it.
Student Understanding of Time Dependence in Quantum Mechanics
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-01-01
The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
Time dependent behavior of cores from the Pleasant Bayou wells
Thompson, T.W.; Jogi, P.N.; Gray, K.E.; Richardson, J.; Bebout, D.G.; Bachman, A.L. (eds.)
1981-01-01
Results of constant-load creep tests on sands from the Pleasant Bayou wells are reported. Significant time dependent behavior under both hydrostatic and non-hydrostatic states of stress have been fit to linear rheological models. The data and models are reported.
Student Understanding of Time Dependence in Quantum Mechanics
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-01-01
The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
Linear-response thermal time-dependent density functional theory
Pribram-Jones, Aurora; Burke, Kieron
2015-01-01
The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation (XC) approximations.
Numerical analysis of time-dependent Boussinesq models
Houwen, P.J. van der; Mooiman, J.; Wubs, F.W.
1991-01-01
In this paper we analyse numerical models for time-dependent Boussinesq equations. These equations arise when so-called Boussinesq terms are introduced into the shallow water equations. We use the Boussinesq terms proposed by Katapodes and Dingemans. These terms generalize the constant depth terms g
Adiabatic Wankel type rotary engine
Kamo, R.; Badgley, P.; Doup, D.
1988-01-01
This SBIR Phase program accomplished the objective of advancing the technology of the Wankel type rotary engine for aircraft applications through the use of adiabatic engine technology. Based on the results of this program, technology is in place to provide a rotor and side and intermediate housings with thermal barrier coatings. A detailed cycle analysis of the NASA 1007R Direct Injection Stratified Charge (DISC) rotary engine was performed which concluded that applying thermal barrier coatings to the rotor should be successful and that it was unlikely that the rotor housing could be successfully run with thermal barrier coatings as the thermal stresses were extensive.
Theory of Adiabatic Fountain Resonance
Williams, Gary A.
2017-01-01
The theory of "Adiabatic Fountain Resonance" with superfluid ^4{He} is clarified. In this geometry a film region between two silicon wafers bonded at their outer edge opens up to a central region with a free surface. We find that the resonance in this system is not a Helmholtz resonance as claimed by Gasparini et al., but in fact is a fourth sound resonance. We postulate that it occurs at relatively low frequency because the thin silicon wafers flex appreciably from the pressure oscillations of the sound wave.
Adiabatic mixed-field orientation of ground-state-selected carbonyl sulfide molecules
Kienitz, Jens S; Mullins, Terry; Długołęcki, Karol; González-Férez, Rosario; Küpper, Jochen
2016-01-01
We experimentally demonstrated strong adiabatic mixed-field orientation of carbonyl sulfide molecules (OCS) in their absolute ground state of $\\text{N}_{\\text{up}}/\\text{N}_{\\text{tot}}=0.882$. OCS was oriented in combined non-resonant laser and static electric fields inside a two-plate velocity map imaging spectrometer. The transition from non-adiabatic to adiabatic orientation for the rotational ground state was studied by varying the applied laser and static electric field. Above static electric field strengths of 10~kV/cm and laser intensities of $10^{11} \\text{W/cm}^2$ the observed degree of orientation reached a plateau. These results are in good agreement with computational solutions of the time-dependent Schr\\"odinger equation.
On the topology of adiabatic passage
Yatsenko, L P; Jauslin, H R
2002-01-01
We examine the topology of eigenenergy surfaces characterizing the population transfer processes based on adiabatic passage. We show that this topology is the essential feature for the analysis of the population transfers and the prediction of its final result. We reinterpret diverse known processes, such as stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic passage and Stark-chirped rapid adiabatic passage (SCRAP). Moreover, using this picture, we display new related possibilities of transfer. In particular, we show that we can selectively control the level which will be populated in STIRAP process in Lambda or V systems by the choice of the peak amplitudes or the pulse sequence.
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.
Time-dependent magnetohydrodynamic simulations of the inner heliosphere
Merkin, V. G.; Lyon, J. G.; Lario, D.; Arge, C. N.; Henney, C. J.
2016-04-01
This paper presents results from a simulation study exploring heliospheric consequences of time-dependent changes at the Sun. We selected a 2 month period in the beginning of year 2008 that was characterized by very low solar activity. The heliosphere in the equatorial region was dominated by two coronal holes whose changing structure created temporal variations distorting the classical steady state picture of the heliosphere. We used the Air Force Data Assimilate Photospheric Flux Transport (ADAPT) model to obtain daily updated photospheric magnetograms and drive the Wang-Sheeley-Arge (WSA) model of the corona. This leads to a formulation of a time-dependent boundary condition for our three-dimensional (3-D) magnetohydrodynamic (MHD) model, LFM-helio, which is the heliospheric adaptation of the Lyon-Fedder-Mobarry MHD simulation code. The time-dependent coronal conditions were propagated throughout the inner heliosphere, and the simulation results were compared with the spacecraft located near 1 astronomical unit (AU) heliocentric distance: Advanced Composition Explorer (ACE), Solar Terrestrial Relations Observatory (STEREO-A and STEREO-B), and the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft that was in cruise phase measuring the heliospheric magnetic field between 0.35 and 0.6 AU. In addition, during the selected interval MESSENGER and ACE aligned radially allowing minimization of the effects of temporal variation at the Sun versus radial evolution of structures. Our simulations show that time-dependent simulationsreproduce the gross-scale structure of the heliosphere with higher fidelity, while on smaller spatial and faster time scales (e.g., 1 day) they provide important insights for interpretation of the data. The simulations suggest that moving boundaries of slow-fast wind transitions at 0.1 AU may result in the formation of inverted magnetic fields near pseudostreamers which is an intrinsically time-dependent process
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Multiple chiral doublet candidate nucleus $^{105}$Rh in a relativistic mean-field approach
Li, Jian; Meng, J; 10.1103/PhysRevC.83.037301
2011-01-01
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\\chi$D) phenomenon. The existence of M$\\chi$D phenomenon in $^{105}$Rh is highly expected.
Time-Dependent Warping and Non-Singular Bouncing Cosmologies
Balasubramanian, Koushik
2014-01-01
In this note, we construct a family of non-singular time-dependent solutions of a six-dimensional gravitational theory that are warped products of a four dimensional bouncing cosmological solution and a two dimensional internal manifold. The warp factor is time-dependent and breaks translation invariance along one of the internal directions. When the warp factor is periodic in time, the non-compact part of the geometry bounces periodically. The six dimensional geometry is supported by matter that does not violate the null energy condition. We show that this 6D geometry does not admit a closed trapped surface and hence the Hawking-Penrose singularity theorems do not apply to these solutions. We also present examples of singular solutions where the topology of the internal manifold changes dynamically.
Scintillation time dependence and pulse shape discrimination in liquid argon
Lippincott, W H; Gastler, D; Hime, A; Kearns, E; McKinsey, D N; Nikkel, J A; Stonehill, L C
2008-01-01
Using a single-phase liquid argon detector with a signal yield of 4.85 photoelectrons per keV of electronic-equivalent recoil energy (keVee), we measure the scintillation time dependence of both electronic and nuclear recoils in liquid argon down to 5 keVee. We develop two methods of pulse shape discrimination to distinguish between electronic and nuclear recoils. Using one of these methods, we measure a background and statistics-limited level of electronic recoil contamination to be $7.6\\times10^{-7}$ between 60 and 128 keV of nuclear recoil energy (keVr) for a nuclear recoil acceptance of 50% with no nuclear recoil-like events above 72 keVr. Finally, we develop a maximum likelihood method of pulse shape discrimination using the measured scintillation time dependence and predict the sensitivity to WIMP-nucleon scattering in three configurations of a liquid argon dark matter detector.
Eisenhart lifts and symmetries of time-dependent systems
Cariglia, M; Gibbons, G W; Horvathy, P A
2016-01-01
Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in $n+2$ dimensions, equipped with its covariantly constant null Killing vector field. Reparametrization of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schr\\"odinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space...
A test of time-dependent theories of stellar convection
Gastine, T
2011-01-01
Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variabilit...
Tokamak power reactor ignition and time dependent fractional power operation
Vold, E.L.; Mau, T.K.; Conn, R.W.
1986-06-01
A flexible time-dependent and zero-dimensional plasma burn code with radial profiles was developed and employed to study the fractional power operation and the thermal burn control options for an INTOR-sized tokamak reactor. The code includes alpha thermalization and a time-dependent transport loss which can be represented by any one of several currently popular scaling laws for energy confinement time. Ignition parameters were found to vary widely in density-temperature (n-T) space for the range of scaling laws examined. Critical ignition issues were found to include the extent of confinement time degradation by alpha heating, the ratio of ion to electron transport power loss, and effect of auxiliary heating on confinement. Feedback control of the auxiliary power and ion fuel sources are shown to provide thermal stability near the ignition curve.
Generating time dependent conformally coupled Einstein-scalar solutions
Sultana, Joseph
2015-07-01
Using the correspondence between a minimally coupled scalar field and an effective stiff perfect fluid with or without a cosmological constant, we present a simple method for generating time dependent Einstein-scalar solutions with a conformally coupled scalar field that has vanishing or non-vanishing potential. This is done by using Bekenstein's transformation on Einstein-scalar solutions with minimally coupled massless scalar fields, and its later generalization by Abreu et al. to massive fields. In particular we obtain two new spherically symmetric time dependent solutions to the coupled system of Einstein's and the conformal scalar field equations, with one of the solutions having a Higgs' type potential for the scalar field, and we study their properties.
Time-dependent phase error correction using digital waveform synthesis
Doerry, Armin W.; Buskirk, Stephen
2017-10-10
The various technologies presented herein relate to correcting a time-dependent phase error generated as part of the formation of a radar waveform. A waveform can be pre-distorted to facilitate correction of an error induced into the waveform by a downstream operation/component in a radar system. For example, amplifier power droop effect can engender a time-dependent phase error in a waveform as part of a radar signal generating operation. The error can be quantified and an according complimentary distortion can be applied to the waveform to facilitate negation of the error during the subsequent processing of the waveform. A time domain correction can be applied by a phase error correction look up table incorporated into a waveform phase generator.
Time-dependent density functional theory: Causality and other problems
Ruggenthaler, Michael; Bauer, Dieter [Max-Planck-Inst. fuer Kernphysik, Heidelberg (Germany)
2007-07-01
Time-dependent density functional theory (TDDFT) is a reformulation of the time dependent many-body problem in quantum mechanics which is capable of reducing the computational cost to calculate, e.g., strongly driven many-electron systems enormously. Recent developments were able to overcome fundamental problems associated with ionization processes. Still vital issues have to be clarified. Besides the construction of the underlying functionals we investigate the causality problem of TDDFT by general considerations and by studying a exactly solvable system of two correlated electrons in an intense laser-pulse. For the latter system, the two alternative approaches to the construction of the action functional or a constrained functional derivative by van Leeuwen and Gal, respectively, are explored.
Time-dependent viscoelastic behavior of an LDPE melt
Shuxin Huang; Chuanjing Lu; Yurun Fan
2006-01-01
Two differential constitutive equations,i.e.Giesekus model and Johnson-Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. Johnson-Segalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the-melt at high shear rate.
Student understanding of time dependence in quantum mechanics
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-12-01
[This paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantum mechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.
Time-Dependent Synchrotron and Compton Spectra from Jets of Microquasars
Gupta, S; Dermer, C D; Boettcher, Markus; Dermer, Charles D.; Gupta, Swati
2006-01-01
Jet models for the high-energy emission of Galactic X-ray binary sources have regained significant interest with detailed spectral and timing studies of the X-ray emission from microquasars, the recent detection by the HESS collaboration of very-high-energy gamma-rays from the microquasar LS~5039, and the earlier suggestion of jet models for ultraluminous X-ray sources observed in many nearby galaxies. Here we study the synchrotron and Compton signatures of time-dependent electron injection and acceleration, adiabatic and radiative cooling, and different jet geometries in the jets of Galactic microquasars. Synchrotron, synchrotron-self-Compton, and external-Compton radiation processes with soft photons provided by the companion star and the accretion disk are treated. An analytical solution is presented to the electron kinetic equation for general power-law geometries of the jets for Compton scattering in the Thomson regime. We pay particular attention to predictions concerning the rapid flux and spectral var...
Stability Analysis of Strange-Modes in Hot Massive Stars with Time-Dependent Convection
Sonoi, Takafumi
2014-01-01
We carry out a nonadiabatic analysis of strange-modes in hot massive stars with time-dependent convection (TDC). In envelopes of such stars, convective luminosity is not so dominant as that in envelopes of stars in the redder side of the classical instability strip. Around the Fe opacity bump, however, convection non-negligibly contributes to energy transfer. Indeed, instability of modes excited at the Fe bump is likely to be suppressed with TDC compared with the case of adopting the frozen-in convection approximation. But we make sure that unstable strange-modes certainly appear in hot massive stars even by taking into account TDC. We also examine properties of the strange-mode instability, which is related to destabilization of strange-modes without adiabatic counterparts. In this type of instability, the phase lag between density and pressure varies from 0 to $180^{\\circ}$ in an excitation zone unlike the case of the $\\kappa$-mechanism. In addition, we confirm by comparing models with $Z=0$ and $Z=0.02$ th...
Time-dependent density functional theory of open quantum systems in the linear-response regime.
Tempel, David G; Watson, Mark A; Olivares-Amaya, Roberto; Aspuru-Guzik, Alán
2011-02-21
Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Görling-Levy perturbation theory is calculated.
The role of exchange and correlation in time-dependent density-functional theory for photoionization
Stener, M.; Decleva, P.; Görling, A.
2001-05-01
Atomic photoionization cross sections are calculated by time-dependent density-functional (TDDF) methods using different exchange-correlation potentials including the exact one. The exchange-correlation kernel is treated in the adiabatic local density approximation (ALDA). Results for the exact full and the exact exchange-only Kohn-Sham (KS) potential are very similar, the calculated photo cross section agree very well with experimental data. Thus the exact correlation potential seems to have no influence on photoionization and the ALDA for the exchange-correlation kernel seems to be sufficient for most features of the cross sections. The TDDF method employing the exact exchange-only KS potential in combination with the ALDA exchange-correlation kernel therefore is a promising approach to describe photoionization. Deviations from experiment are observed for the widths and shape of the autoionization resonances and have to be attributed to deficiencies of the ALDA exchange-correlation kernel. The calculation of widths and shapes of autoionization resonances therefore may serve as a severe test for new approximate exchange-correlation density-functionals. The asymptotically exact exchange-correlation potential of van Leeuwen and Baerends also leads to quite good photo cross section, which, however, shows deficiencies close to the ionization threshold and in the energetic position of the autoionization resonances. Supplementation of the exact exchange potential with the LDA correlation potential leads to a worsening of the photo cross section because the LDA correlation potential is too attractive.
Time-Dependent Density Functional Theory Beyond Kohn-Sham Slater Determinants
Fuks, Johanna I; Ruggenthaler, Michael; Maitra, Neepa T
2016-01-01
When running time-dependent density functional theory (TDDFT) calculations for real-time simulations of non-equilibrium dynamics, the user has a choice of initial Kohn-Sham state, and typically a Slater determinant is used. We explore the impact of this choice on the exchange-correlation potential when the physical system begins in a 50:50 superposition of the ground and first-excited state of the system. We investigate the possibility of judiciously choosing a Kohn-Sham initial state that minimizes errors when adiabatic functionals are used. We find that if the Kohn-Sham state is chosen to have a configuration matching the one that dominates the interacting state, this can be achieved for a finite time duration for some but not all such choices. When the Kohn-Sham system does not begin in a Slater determinant, we further argue that the conventional splitting of the exchange-correlation potential into exchange and correlation parts has limited value, and instead propose a decomposition into a "single-particle...
Single electron relativistic clock interferometer
Bushev, P. A.; Cole, J. H.; Sholokhov, D.; Kukharchyk, N.; Zych, M.
2016-09-01
Although time is one of the fundamental notions in physics, it does not have a unique description. In quantum theory time is a parameter ordering the succession of the probability amplitudes of a quantum system, while according to relativity theory each system experiences in general a different proper time, depending on the system's world line, due to time dilation. It is therefore of fundamental interest to test the notion of time in the regime where both quantum and relativistic effects play a role, for example, when different amplitudes of a single quantum clock experience different magnitudes of time dilation. Here we propose a realization of such an experiment with a single electron in a Penning trap. The clock can be implemented in the electronic spin precession and its time dilation then depends on the radial (cyclotron) state of the electron. We show that coherent manipulation and detection of the electron can be achieved already with present day technology. A single electron in a Penning trap is a technologically ready platform where the notion of time can be probed in a hitherto untested regime, where it requires a relativistic as well as quantum description.
A time-dependent measuring system for welding deformation
蔡志鹏; 赵海燕; 鹿安理; 史清宇; 施光凯
2002-01-01
In this paper the establishment and application of a time-dependent measuring system for welding deformation are presented which is established with high quality sensors shielded from strong welding interference. By using this system, vertical and horizontal displacements of the high temperature area are surveyed at the same time. And this system is also used for monitoring and controlling the deformation of real welded structures.
Thermal state of the general time-dependent harmonic oscillator
Jeong-Ryeol Choi
2003-07-01
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator satisfying Leouville–von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola–Kanai oscillator.
Time dependent density functional calculation of plasmon response in clusters
Wang Feng(王锋); Zhang Feng-Shou(张丰收); Eric Suraud
2003-01-01
We have introduced a theoretical scheme for the efficient description of the optical response of a cluster based on the time-dependent density functional theory. The practical implementation is done by means of the fully fledged timedependent local density approximation scheme, which is solved directly in the time domain without any linearization.As an example we consider the simple Na2 cluster and compute its surface plasmon photoabsorption cross section, which is in good agreement with the experiments.
ARTICLES: Time-Dependent Stokes Shift from Solvent Dielectric Relaxation
Xu, Jing; Wang, Quan-de; Zhu, Quan; Fu, Ke-xiang; He, Fu-cheng; Li, Xiang-yuan
2010-06-01
The Stokes shift response function, which is related to the time dependent solvation energy, is calculated with the dielectric response function and a novel expression of nonequilibrium solvation energy. In the derivation, relationship between the polarization and the dielectric response function is used. With the dipole-in-a-sphere model applied to the system coumarin 343 and water as the solvent, encouraging agreement with the experimental data from Jimenez et al. is obtained [Nature 369, 471 (1994)].
Spectral methods for time dependent partial differential equations
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
Time dependence of the pH of rain
John A. Kadlecek; Volkar A. Mohnen
1976-01-01
Standard procedures for determining the pH of rain samples usually involve substantial delays from the time of rainfall to the time of analysis. This assumes that no change in pH occurs during the storage period. We have found that this is not always true. We have determined that individual rain water samples possess a time dependent pH which can be correlated with the...
Time-dependent HF approach to SHE dynamics
Umar, A. S.; Oberacker, V. E.
2015-12-01
We employ the time-dependent Hartree-Fock (TDHF) method to study various aspects of the reactions utilized in searches for superheavy elements. These include capture cross-sections, quasifission, prediction of PCN, and other interesting dynamical quantities. We show that the microscopic TDHF approach provides an important tool to shed some light on the nuclear dynamics leading to the formation of superheavy elements.
Dose and time dependence of box jellyfish antivenom
2014-01-01
Background The effectiveness of the currently available box jellyfish (Chironex fleckeri) antivenom has been subject of debate for many years. To assess whether the box jellyfish antivenom has the ability to attenuate venom-induced damage at cellular level, the present study analyzed the dose and time dependence of the antivenom in a cell-based assay. Methods Different doses of antivenom were added to venom and subsequently administered to cells and the cell index was measured using xCelligen...
Relating Time-Dependent Acceleration and Height Using an Elevator
Kinser, Jason M.
2015-01-01
A simple experiment in relating a time-dependent linear acceleration function to height is explored through the use of a smartphone and an elevator. Given acceleration as a function of time, a(t), the velocity function and position functions are determined through integration as in v(t)=? a(t) dt (1) and x(t)=? v(t) dt. Mobile devices such as…
Tiny graviton matrix theory on time-dependent background
Chen Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 (China)], E-mail: bchen01@pku.edu.cn; Liu Xiao [Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 (China)], E-mail: liuxiaoerty@pku.edu.cn
2009-04-11
In this article we construct a tiny graviton matrix model for type IIB string theory on a plane-wave background with null dilaton. For the linear null dilaton case, we analyze its vacuum and the excitation spectrum around the vacuum, and discuss the time-dependent fuzzy three-sphere solutions and their evolution. It turns out that at very late time the non-Abelian fuzzy degrees of freedom disappear, which indicates the appearance of perturbative strings.
Exact Invariants for a Time-Dependent Hamiltonian System
LUO Xiao-Bing
2009-01-01
We have a classical look for a quantum system which is exactly solvable. We construct the invariant manifolds analytically, and then apply the semiclassical quantization rules in a final step to compute the quasienergies. The invariant is obtained by performing a canonical transformation of the initially time-dependent Hamiltonian to a time-independent one. The correspondence between classical and quantum mechanics is elucidated.
Unique Measure for Time-Dependent Random Dynamical Systems
Varner, Gregory
2016-01-01
This paper proves the uniqueness of measure for the two-dimensional Navier-Stokes equations under a random kick-force and a time-dependent deterministic force. By extending a result for uniqueness of measure for time-homogeneous Markov processes to the time-inhomogeneous case, it is shown that the measures are exponentially mixing for the 2D Navier-Stokes equations on the sphere.
Rosenberger, Martina
1997-05-15
Method development of the time-dependent numerical MCSCF and CI method for atoms, without and with inclusion of an oscillating electric field, linearly polarized (electric dipole approximation for light). In the CI method, the numerical orbitals are kept fixed (not time-dependent), and only the CI coefficients are propagated, whereas in the MCSCF method both the CI coefficients and the numerical orbitals in the CSFs are propagated. The basis for this work were the non-relativistic numerical atomic structure codes for free atoms and for atoms in a static electric field developed at Bielefeld. (orig.)
Behaviour of time-dependent materials exposed to periodical loading
Zupancic B.
2010-06-01
Full Text Available Paper presents methodology for analyzing behaviour of time-dependent (viscoelastic materials when exposed to periodical (cyclic loading. Within each loading cycle time-dependent material undergoes a combination of the creep and retardation process. At certain conditions the retardation process between two loading cycles cannot be fully completed to a strain free state. Consequently, strain starts to accumulate, which leads to hardening of the material and ultimately to the failure of polymeric product. Critical frequency of the applied periodical loading depends on the material retardation time (location of mechanical spectrum, while the magnitude of accumulated strain on the strength of corresponding discrete spectrum lines. The shape of mechanical spectrum defines the intensity and the magnitude of accumulated strain. Thus, the mechanical spectrum of time-dependent material is the most important function for predicting durability of dynamically loaded polymeric products. In continuation we present mathematical methodology for predicting durability of periodically loaded polymeric components of drive belt. Methodology includes numerical calculations of accumulated strain as a function of the number of loading cycles and function of loading angular velocity. Based on these calculations we can determine the critical angular velocity area of periodical loading where the strain accumulation is the most intensive.
Neutrino flavor instabilities in a time-dependent supernova model
Sajad Abbar
2015-12-01
Full Text Available A dense neutrino medium such as that inside a core-collapse supernova can experience collective flavor conversion or oscillations because of the neutral-current weak interaction among the neutrinos. This phenomenon has been studied in a restricted, stationary supernova model which possesses the (spatial spherical symmetry about the center of the supernova and the (directional axial symmetry around the radial direction. Recently it has been shown that these spatial and directional symmetries can be broken spontaneously by collective neutrino oscillations. In this letter we analyze the neutrino flavor instabilities in a time-dependent supernova model. Our results show that collective neutrino oscillations start at approximately the same radius in both the stationary and time-dependent supernova models unless there exist very rapid variations in local physical conditions on timescales of a few microseconds or shorter. Our results also suggest that collective neutrino oscillations can vary rapidly with time in the regimes where they do occur which need to be studied in time-dependent supernova models.
Relativistic hadrons and the origin of relativistic outflows in active galactic nuclei
Contopoulos, John; Kazanas, D.
1995-01-01
We examine the hydrodynamic origin of relativistic outflows in active galactic nuclei (AGN). Specifically, we propose that the presence of a population of relativistic hadrons in the AGN 'central engine' and the associated neutron production suffices to produce outflows which under rather general conditions could be relativistic. The main such condition is that the size of the neutron production region be larger than the neutron flight path tau(sub n) approximately 3 x 10(exp 13) cm. This condition guarantees that the mean energy per particle in the proton fluid, resulting from the decay of the neutrons outside their production region, be greater than the proton rest mass. The expansion of this fluid can then lead naturally to a relativistic outflow by conversion of its internal energy to directed motion. We follow the development of such flows by solving the mass, energy as well as the kinetic equation for the proton gas in steady state, taking into account the source terms due to compute accurately the adiabatic index of the expanding gas, and in conjunction with Bernoulli's equation the detailed evolution of the bulk Lorentz factor. We further examine the role of large-scale magnetic fields in confining these outflows to produce the jets observed at larger scales.
(Hybrid) Baryons Quantum Numbers and Adiabatic Potentials
Page, P R
1999-01-01
We construct (hybrid) baryons in the flux-tube model of Isgur and Paton. In the limit of adiabatic quark motion, we build proper eigenstates of orbital angular momentum and indicate the flavour, spin, chirality and J^P of (hybrid) baryons. The adiabatic potential is calculated as a function of the quark positions.
Cummins/Tacom advanced adiabatic engine
Kamo, R.; Bryzik, W.
1984-01-01
Cummins Engine Company, Inc. and the U.S. Army have been jointly developing an adiabatic turbocompound engine during the last nine years. Although progress in the early years was slow, recent developments in the field of advanced ceramics have made it possible to make steady progress. It is now possible to reconsider the temperature limitation imposed on current heat engines and its subsequent influence on higher engine efficiency when using an exhaust energy utilization system. This paper presents an adiabatic turbocompound diesel engine concept in which high-performance ceramics are used in its design. The adiabatic turbocompound engine will enable higher operating temperatures, reduced heat loss, and higher exhaust energy recovery, resulting in higher thermal engine efficiency. This paper indicates that the careful selection of ceramics in engine design is essential. Adiabatic engine materials requirements are defined and the possible ceramic materials which will satisfy these requirements are identified. Examples in design considerations of engine components are illustrated. In addition to these important points, the use of ceramic coatings in the design of engine components. The first generation adiabatic engine with ceramic coatings is described. The advanced adiabatic engine with minimum friction features utilizaing ceramics is also presented. The advanced ceramic turbocharger turbine rotor as well as the oilless ceramic bearing design is described. Finally, the current status of the advanced adiabatic engine program culminating in the AA750 V-8 adiabatic engine is presented.
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Solvable time-dependent models in quantum mechanics
Cordero-Soto, Ricardo J.
In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrodinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrodinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrodinger equation in Rn with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrodinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models
Progress Report on Alloy 617 Time Dependent Allowables
Wright, Julie Knibloe [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-06-01
Time dependent allowable stresses are required in the ASME Boiler and Pressure Vessel Code for design of components in the temperature range where time dependent deformation (i.e., creep) is expected to become significant. There are time dependent allowable stresses in Section IID of the Code for use in the non-nuclear construction codes, however, there are additional criteria that must be considered in developing time dependent allowables for nuclear components. These criteria are specified in Section III NH. St is defined as the lesser of three quantities: 100% of the average stress required to obtain a total (elastic, plastic, primary and secondary creep) strain of 1%; 67% of the minimum stress to cause rupture; and 80% of the minimum stress to cause the initiation of tertiary creep. The values are reported for a range of temperatures and for time increments up to 100,000 hours. These values are determined from uniaxial creep tests, which involve the elevated temperature application of a constant load which is relatively small, resulting in deformation over a long time period prior to rupture. The stress which is the minimum resulting from these criteria is the time dependent allowable stress St. In this report data from a large number of creep and creep-rupture tests on Alloy 617 are analyzed using the ASME Section III NH criteria. Data which are used in the analysis are from the ongoing DOE sponsored high temperature materials program, form Korea Atomic Energy Institute through the Generation IV VHTR Materials Program and historical data from previous HTR research and vendor data generated in developing the alloy. It is found that the tertiary creep criterion determines St at highest temperatures, while the stress to cause 1% total strain controls at low temperatures. The ASME Section III Working Group on Allowable Stress Criteria has recommended that the uncertainties associated with determining the onset of tertiary creep and the lack of significant
On a Nonlinear Model in Adiabatic Evolutions
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
PIPER Continuous Adiabatic Demagnetization Refrigerator
Kimball, Mark O.; Shirron, Peter J.; Canavan, Edgar R.; James, Bryan L.; Sampson, Michael A.; Letmate, Richard V.
2017-01-01
We report upon the development and testing of a 4-stage adiabatic demagnetization refrigerator (ADR) capable of continuous cooling at 0.100 Kelvin. This cooler is being built to cool the detector array aboard NASA's Primordial Inflation Polarization Explorer (PIPER) observatory. The goal of this balloon mission is to measure the primordial gravitational waves that should exist if the theory of cosmological inflation is correct. At altitude, the ADR will hold the array of transition-edge sensors at 100 mK continuously while periodically rejecting heat to a 1.2 K pumped helium bath. During testing on ground, the array is held at the same temperature but heat is rejected to a 4.2 K helium bath indicating the flexibility in this coolers design.
Quenching in coupled adiabatic coils
Williams, J.E.C.
1985-03-01
The prediction of the effects of a quench on stress and temperature is an important aspect of the design of superconducting magnets. Of particular interest, and the exclusive topic of this study, is the prediction of the effects of quenching in coupled adiabatic coils, such as the multi-section windings of a high field NMR spectrometer magnet. The predictive methods used here are based on the measurement of the time of propagation of quench between turns. From this measurement an approximate algorithum for the propagation time is used in a code which solves the linear differential equations for the coil currents and calculates the movement of normal zone boundaries and hence the associated winding resistance.
ZHANG Peng-Fei; RUAN Tu-Nan
2001-01-01
A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.
Relativistic Linear Restoring Force
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
Nikitin, N. V., E-mail: nnikit@mail.cern.ch; Sotnikov, V.P., E-mail: sotnikov@physics.msu.ru [Moscow State University, Faculty of Physics (Russian Federation); Toms, K. S., E-mail: ktoms@mail.cern.ch [The University of New Mexico, Department of Physics and Astronomy (United States)
2015-10-15
A radically new class of Bell inequalities in Wigner’s form was obtained on the basis of Kolmorov’s axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner’s form). By using these inequalities, one can propose a means for experimentally testing Bohr’ complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion–antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett–Garg approach, for example.
Resonant enhancement of relativistic electron fluxes during geomagnetically active periods
I. Roth
Full Text Available The strong increase in the flux of relativistic electrons during the recovery phase of magnetic storms and during other active periods is investigated with the help of Hamiltonian formalism and simulations of test electrons which interact with whistler waves. The intensity of the whistler waves is enhanced significantly due to injection of 10-100 keV electrons during the substorm. Electrons which drift in the gradient and curvature of the magnetic field generate the rising tones of VLF whistler chorus. The seed population of relativistic electrons which bounce along the inhomogeneous magnetic field, interacts resonantly with the whistler waves. Whistler wave propagating obliquely to the magnetic field can interact with energetic electrons through Landau, cyclotron, and higher harmonic resonant interactions when the Doppler-shifted wave frequency equals any (positive or negative integer multiple of the local relativistic gyrofrequency. Because the gyroradius of a relativistic electron may be the order of or greater than the perpendicular wavelength, numerous cyclotron, harmonics can contribute to the resonant interaction which breaks down the adiabatic invariant. A similar process diffuses the pitch angle leading to electron precipitation. The irreversible changes in the adiabatic invariant depend on the relative phase between the wave and the electron, and successive resonant interactions result in electrons undergoing a random walk in energy and pitch angle. This resonant process may contribute to the 10-100 fold increase of the relativistic electron flux in the outer radiation belt, and constitute an interesting relation between substorm-generated waves and enhancements in fluxes of relativistic electrons during geomagnetic storms and other active periods.
Key words. Magnetospheric physics (energetic particles · trapped; plasma waves and instabilities; storms and substorms
MALFLIET, R
1993-01-01
We discuss the present status of relativistic transport theory. Special emphasis is put on problems of topical interest: hadronic features, thermodynamical consistent approximations and spectral properties.
Adiabatic quantum pump in a zigzag graphene nanoribbon junction
张林
2015-01-01
The adiabatic electron transport is theoretically studied in a zigzag graphene nanoribbon (ZGNR) junction with two time-dependent pumping electric fields. By modeling a ZGNR p–n junction and applying the Keldysh Green’s function method, we find that a pumped charge current is flowing in the device at a zero external bias, which mainly comes from the photon-assisted tunneling process and the valley selection rule in an even-chain ZGNR junction. The pumped charge current and its ON and OFF states can be efficiently modulated by changing the system parameters such as the pumping frequency, the pumping phase difference, and the Fermi level. A ferromagnetic ZGNR device is also studied to generate a pure spin current and a fully polarized spin current due to the combined spin pump effect and the valley valve effect. Our finding might pave the way to manipulate the degree of freedom of electrons in a graphene-based electronic device.
Adiabatic Dynamics of Edge Waves in Photonic Graphene
Ablowitz, M J; Ma, Y -P
2014-01-01
The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying dynamics. Depending on parameters, edge states can exist over an entire period or only part of a period; in the latter case an edge mode can effectively disintegrate and scatter into the bulk. In the presence of nonlinearity, a `time'-dependent one-dimensional nonlinear Schr\\"odinger (NLS) equation describes the envelope dynamics of edge modes. When the average of the `time varying' coefficients yields a focusing NLS equation, soliton propagation is exhibited. For both linear and nonlinear systems, certain long lived traveling modes with minimal backscattering are found; they exhibit properties of topologically protected states.
Effect of Poisson noise on adiabatic quantum control
Kiely, A.; Muga, J. G.; Ruschhaupt, A.
2017-01-01
We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and provide approximations for the different noise strength regimes. We show that using the eigenstates of the noise superoperator as a basis can be a useful way of expressing the master equation. Using this, we simulate various settings to illustrate different effects of Poisson noise. In particular, we show a dip in the fidelity as a function of noise strength where high fidelity can occur in the strong-noise regime for some cases. We also investigate recent claims [J. Jing et al., Phys. Rev. A 89, 032110 (2014), 10.1103/PhysRevA.89.032110] that this type of noise may improve rather than destroy adiabaticity.
Filtering of matter wave vibrational states via spatial adiabatic passage
Loiko, Yu; Corbalán, R; Birkl, G; Mompart, J; 10.1103/PhysRevA.83.033629
2011-01-01
We discuss the filtering of the vibrational states of a cold atom in an optical trap, by chaining this trap with two empty ones and controlling adiabatically the tunneling. Matter wave filtering is performed by selectively transferring the population of the highest populated vibrational state to the most distant trap while the population of the rest of the states remains in the initial trap. Analytical conditions for two-state filtering are derived and then applied to an arbitrary number of populated bound states. Realistic numerical simulations close to state-of-the-art experimental arrangements are performed by modeling the triple well with time dependent P\\"oschl-Teller potentials. In addition to filtering of vibrational states, we discuss applications for quantum tomography of the initial population distribution and engineering of atomic Fock states that, eventually, could be used for tunneling assisted evaporative cooling.
Lima, Frederico A; Bjornsson, Ragnar; Weyhermüller, Thomas; Chandrasekaran, Perumalreddy; Glatzel, Pieter; Neese, Frank; DeBeer, Serena
2013-12-28
X-ray absorption spectroscopy (XAS) is a widely used experimental technique capable of selectively probing the local structure around an absorbing atomic species in molecules and materials. When applied to heavy elements, however, the quantitative interpretation can be challenging due to the intrinsic spectral broadening arising from the decrease in the core-hole lifetime. In this work we have used high-energy resolution fluorescence detected XAS (HERFD-XAS) to investigate a series of molybdenum complexes. The sharper spectral features obtained by HERFD-XAS measurements enable a clear assignment of the features present in the pre-edge region. Time-dependent density functional theory (TDDFT) has been previously shown to predict K-pre-edge XAS spectra of first row transition metal compounds with a reasonable degree of accuracy. Here we extend this approach to molybdenum K-edge HERFD-XAS and present the necessary calibration. Modern pure and hybrid functionals are utilized and relativistic effects are accounted for using either the Zeroth Order Regular Approximation (ZORA) or the second order Douglas-Kroll-Hess (DKH2) scalar relativistic approximations. We have found that both the predicted energies and intensities are in excellent agreement with experiment, independent of the functional used. The model chosen to account for relativistic effects also has little impact on the calculated spectra. This study provides an important calibration set for future applications of molybdenum HERFD-XAS to complex catalytic systems.
Characterizing time-dependent mechanics in metallic MEMS
Geers M.G.D.
2010-06-01
Full Text Available Experiments for characterization of time-dependent material properties in free-standing metallic microelectromechanical system (MEMS pose challenges: e.g. fabrication and handling (sub-μm sized specimens, control and measurement of sub-μN loads and sub-μm displacements over long periods and various temperatures [1]. A variety of experimental setups have been reported each having their pros and cons. One example is a micro-tensile tester with an ingenious electro-static specimen gripping system [2] aiding simple specimen design giving good results at μN and sub-μm levels, but without in-situ full-field observations. Other progressive examples assimilate the specimen, MEMS actuators and load cells on a single chip [3,4] yielding significant results at nN and nm levels with in-situ TEM/SEM observability, though not without complications: complex load actuator/sensor calibration per chip, measures to reduce fabrication failure and unfeasible cofabrication on wafers with commercial metallic MEMS. This work aims to overcome these drawbacks by developing experimental methods with high sensitivity, precision and in-situ full-field observation capabilities. Moreover, these should be applicable to simple free-standing metallic MEMS that can be co-fabricated with commercial devices. These methods will then serve in systematic studies into size-effects in time-dependent material properties. First a numeric-experimental method is developed. It characterizes bending deformation of onwafer μm-sized aluminum cantilevers. A specially designed micro-clamp is used to mechanically apply a constant precise deflection of the beam (zres <50 nm for a prolonged period, see fig. 1. After this period, the deflection by the micro-clamp is removed. Full-field height maps with the ensuing deformation are measured over time with confocal optical profilometry (COP. This yields the tip deflection as function of time with ~3 nm precision, see fig.2. To extract material
Time-Dependent Neutron and Photon Dose-Field Analysis
Wooten, Hasani Omar [Georgia Inst. of Technology, Atlanta, GA (United States)
2005-08-01
A unique tool is developed that allows the user to model physical representations of complicated glovebox facilities in two dimensions and determine neutral-particle flux and ambient dose-equivalent fields throughout that geometry. The Pandemonium code, originally designed to determine flux and dose-rates only, is improved to include realistic glovebox geometries, time-dependent source and detector positions, time-dependent shielding thickness calculations, time-integrated doses, a representative criticality accident scenario based on time-dependent reactor kinetics, and more rigorous photon treatment. A primary benefit of this work has been an extensive analysis and improvement of the photon model that is not limited to the application described in this thesis. The photon model has been extended in energy range to 10 MeV to include photons from fission and new photon buildup factors have been included that account for the effects of photon buildup at slant-path thicknesses as a function of angle, where the mean free path thickness has been preserved. The overall system of codes is user-friendly and it is directly applicable to facilities such as the plutonium facility at Los Alamos National Laboratory, where high-intensity neutron and photon emitters are regularly used. The codes may be used to determine a priori doses for given work scenarios in an effort to supply dose information to process models which will in turn assist decision makers on ensuring as low as reasonably achievable (ALARA) compliance. In addition, coupling the computational results of these tools with the process model visualization tools will help to increase worker safety and radiological safety awareness.
Time-dependent tomographic reconstruction of the solar corona
Vibert, D.; Peillon, C.; Lamy, P.; Frazin, R. A.; Wojak, J.
2016-10-01
Solar rotational tomography (SRT) applied to white-light coronal images observed at multiple aspect angles has been the preferred approach for determining the three-dimensional (3D) electron density structure of the solar corona. However, it is seriously hampered by the restrictive assumption that the corona is time-invariant which introduces significant errors in the reconstruction. We first explore several methods to mitigate the temporal variation of the corona by decoupling the "fast-varying" inner corona from the "slow-moving" outer corona using multiple masking (either by juxtaposition or recursive combination) and radial weighting. Weighting with a radial exponential profile provides some improvement over a classical reconstruction but only beyond ≈ 3R⊙. We next consider a full time-dependent tomographic reconstruction involving spatio-temporal regularization and further introduce a co-rotating regularization aimed at preventing concentration of reconstructed density in the plane of the sky. Crucial to testing our procedure and properly tuning the regularization parameters is the introduction of a time-dependent MHD model of the corona based on observed magnetograms to build a time-series of synthetic images of the corona. Our procedure, which successfully reproduces the time-varying model corona, is finally applied to a set of 53 LASCO-C2 pB images roughly evenly spaced in time from 15 to 29 March 2009. Our procedure paves the way to a time-dependent tomographic reconstruction of the coronal electron density to the whole set of LASCO-C2 images presently spanning 20 years.
The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
Pedlosky, J.; Flierl, G. R.
2006-12-01
The nonlinear dynamics of baroclinically unstable waves in a time dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear we have detected a symmetry breaking in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasi-geostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded the inviscid, linear problem is formally stable. However, our calculations show that a small degree of nonlinearity is enough to destabilize the flow leading to large amplitude
Perspective: Fundamental aspects of time-dependent density functional theory
Maitra, Neepa T.
2016-06-01
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Density-functional perturbation theory goes time-dependent
Gebauer, Ralph; Rocca, Dario; Baroni, Stefano
2009-01-01
The scope of time-dependent density-functional theory (TDDFT) is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most). In the static regime, density-functional perturbation theory (DFPT) allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix e...
Time-dependent models of dense PDRs with complex molecules
Morata, O.; Herbst, E.
2008-01-01
We present a study of the chemistry of a dense photon-dominated region (PDR) using a time-dependent chemical model. Our major interest is to study the spatial distribution of complex molecules such as hydrocarbons and cyanopolyynes in the cool dense material bordering regions where star formation has taken place. Our standard model uses a homogeneous cloud of density 2x10e4 cm-3 and temperature T=40 K, which is irradiated by a far-ultraviolet radiation field of intermediate intensity, given b...
Time-dependent coupled-cluster method for atomic nuclei
Pigg, D A; Nam, H; Papenbrock, T
2012-01-01
We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate the capabilities of the method.
Quantifying Time Dependent Moisture Storage and Transport Properties
Peuhkuri, Ruut H
2003-01-01
This paper describes an experimental and numerical approach to quantify the time dependence of sorption mechanisms for some hygroscopic building - mostly insulation - materials. Some investigations of retarded sorption and non-Fickian phenomena, mostly on wood, have given inspiration to the present...... analysis on these other materials. The true moisture capacity of a material can not be described by the slope of the sorption isotherms alone, when the material is exposed to dynamic changes in the moisture conditions. Still, the assumption of an immediate equilibrium is well accepted in the simulation...
Time-dependant cosmological interpretation of quantum mechanics
Moulay, Emmanuel
2015-01-01
The aim of this article is to define a time-dependant cosmological interpretation of quantum mechanics in the context of a multiverse coming from eternal inflation. A common notion of time is defined for observers in similar observable universes by using the holographic principle. It is the time elapsed since the post-inflationary epoch. With this improvement, the cosmological interpretation of quantum mechanics becomes a full interpretation of quantum mechanics where the unitary evolution of quantum states is preserved. Moreover, it is well suited for eternal inflation .
Time-dependent Integrated Predictive Modeling of ITER Plasmas
R.V. Budny
2007-01-01
@@ Introduction Modeling burning plasmas is important for speeding progress toward practical Tokamak energy production. Examples of issues that can be elucidated by modelinginclude requirements for heating, fueling, torque, and current drive systems, design of diagnostics, and estimates of the plasma performance (e.g., fusion power production) in various plasma scenarios. The modeling should be time-dependent to demonstrate that burning plasmas can be created, maintained (controlled), and terminated successfully. The modeling also should be integrated to treat self-consistently the nonlinearities and strong coupling between the plasma, heating, current drive, confinement, and control systems.
Evaluation of Time-Dependent Behavior of Soils
Augustesen, Anders; Liingaard, Morten; Lade, Poul V.
2004-01-01
materials are few. This paper presents an up-to-date review of the various observed time- and rate-dependent phenomena that are known to exist for both clay and sand. The description is carried out separately for creep, stress relaxation, rate dependency, and structuration in laboratory experiments. All...... of the above-mentioned phenomena are present in both sand and clay. The time-dependent phenomena are more pronounced in clay than sand. However, sand exhibits relatively large deformations at high confining pressures because of grain crushing. Furthermore, the review revealed an essential characteristic...
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Time-dependent density-functional theory concepts and applications
Ullrich, Carsten A
2011-01-01
Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s
Efficient auxiliary-mode approach for time-dependent nanoelectronics
Popescu, Bogdan Stefan; Croy, Alexander
2016-09-01
A new scheme for numerically solving the equations arising in the time-dependent non-equilibrium Green's function formalism is developed. It is based on an auxiliary-mode expansion of the self-energies which convert the complicated set of integro-differential equations into a set of ordinary differential equations. In the new scheme all auxiliary matrices are replaced by vectors or scalars. This drastically reduces the computational effort and memory requirements of the method, rendering it applicable to topical problems in electron quantum optics and molecular electronics. As an illustrative example we consider the dynamics of a Leviton wave-packet in a 1D wire.
Optimal moving grids for time-dependent partial differential equations
Wathen, A. J.
1992-01-01
Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.
Time-dependent asymmetries in Bs decays at LHCb
Blouw, Johan
2007-01-01
The LHCb experiment will search for New Physics in Bs mixing. The Bs mixing phase will be extracted from the measurement of the time-dependent CP asymmetry in exclusive Bs decays governed by the $b \\to c\\bar{c}s$ quark level transition. Large New Physics effects can be discovered or excluded with the data collected during the very first physics run of LHC. Based on Monte Carlo simulations of the LHCb detector, the expected sensitivity with 2 fb$^{-1}$ on the CP-violation parameter $\\phi_s$, is $\\sigma(\\phi_s)$ = 0.022.
The time-dependent prize-collecting arc routing problem
Black, Dan; Eglese, Richard; Wøhlk, Sanne
2013-01-01
A new problem is introduced named the Time-Dependent Prize-Collecting Arc Routing Problem (TD-PARP). It is particularly relevant to situations where a transport manager has to choose between a number of full truck load pick-ups and deliveries on a road network where travel times change...... with the time of day. Two metaheuristic algorithms, one based on Variable Neighborhood Search and one based on Tabu Search, are proposed and tested for a set of benchmark problems, generated from real road networks and travel time information. Both algorithms are capable of finding good solutions, though...
Quasi-adiabatic transport in Mercury's magnetotail
Delcourt, Dominique; Malova, Helmi; Zelenyi, Lev
2017-04-01
MESSENGER observations have revealed that the magnetotail of Mercury is fairly dynamical, possibly subjected to series of magnetic field line dipolarization on time scales of a few seconds. Because of the sharp reversal of the magnetic field, ions may not travel adiabatically in this region of space, and their behavior can be organized according to different categories. Among these categories, quasi-adiabatic (Speiser) ions are such that they experience negligible net change of magnetic moment upon crossing of the field reversal and can thus travel back to low altitudes. We examine the robustness of this quasi-adiabatic behavior during magnetic field line dipolarization where ions are subjected to a large induced electric field. We demonstrate that, although this surging electric field possibly yields substantial nonadiabatic heating, quasi-adiabaticity is robust for ions with velocities larger than the peak ExB drift speed, a behavior that we refer to as "strong" quasi-adiabaticity (as opposed to "weak" quasi-adiabaticity that is violated during dipolarization). We show that the impulsive energization of such quasi-adiabatic ions during dipolarization events can lead to prominent energy-time dispersion structures at low altitudes.
Partial evolution based local adiabatic quantum search
Sun Jie; Lu Song-Feng; Liu Fang; Yang Li-Ping
2012-01-01
Recently,Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution,which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one.Later,they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database.In the present paper,following the idea of Roland and Cerf [Roland J and Cerf N J 2002Phys.Rev.A 65 042308],if within the small symmetric evolution interval defined by Zhang et al.,a local adiabatic evolution is performed instead of the original “global” one,this “new” algorithm exhibits slightly better performance,although they are progressively equivalent with M increasing.In addition,the proof of the optimality for this partial evolution based local adiabatic search when M =1 is also presented.Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search,which are found to have the same phenomenon above,are also discussed.
Trans-Relativistic Particle Acceleration in Astrophysical Plasmas
Becker, Peter A.; Subramanian, P.
2014-01-01
Trans-relativistic particle acceleration due to Fermi interactions between charged particles and MHD waves helps to power the observed high-energy emission in AGN transients and solar flares. The trans-relativistic acceleration process is challenging to treat analytically due to the complicated momentum dependence of the momentum diffusion coefficient. For this reason, most existing analytical treatments of particle acceleration assume that the injected seed particles are already relativistic, and therefore they are not suited to study trans-relativistic acceleration. The lack of an analytical model has forced workers to rely on numerical simulations to obtain particle spectra describing the trans-relativistic case. In this work we present the first analytical solution to the global, trans-relativistic problem describing the acceleration of seed particles due to hard-sphere collisions with MHD waves. The new results include the exact solution for the steady-state Green's function resulting from the continual injection of monoenergetic seed particles with an arbitrary energy. We also introduce an approximate treatment of the trans-relativistic acceleration process based on a hybrid form for the momentum diffusion coefficient, given by the sum of the two asymptotic forms. We refer to this process as "quasi hard-sphere scattering." The main advantage of the hybrid approximation is that it allows the extension of the physical model to include (i) the effects of synchrotron and inverse-Compton losses and (ii) time dependence. The new analytical results can be used to model the trans-relativistic acceleration of particles in AGN and solar environments, and can also be used to compute the spectra of the associated synchrotron and inverse-Compton emission. Applications of both types are discussed. We highlight (i) relativistic ion acceleration in black hole accretion coronae, and (ii) the production of gyrosynchrotron microwave emission due to relativistic electron
Relativistic quantum mechanics; Mecanique quantique relativiste
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
Time-dependent strains and stresses in a pumpkin balloon
Gerngross, T.; Xu, Y.; Pellegrino, S.
This paper presents a study of pumpkin-shaped superpressure balloons consisting of gores made from a thin polymeric film attached to high stiffness meridional tendons This type of design is being used for the NASA ULDB balloons The gore film shows considerable time-dependent stress relaxation whereas the behaviour of the tendons is essentially time-independent Upon inflation and pressurization the instantaneous i e linear-elastic strain and stress distributions in the film show significantly higher values in the meridional direction However over time and due to the biaxial visco-elastic stress relaxation of the the gore material the em hoop strains increase and the em meridional stresses decrease whereas the em remaining strain and stress components remain substantially unchanged These results are important for a correct assessment of the structural integrity of a pumpkin balloon in a long-duration mission both in terms of the material performance and the overall stability of the shape of the balloon An experimental investigation of the time dependence of the biaxial strain distribution in the film of a 4 m diameter 48 gore pumpkin balloon is presented The inflated shape of selected gores has been measured using photogrammetry and the time variation in strain components at some particular points of these gores has been measured under constant pressure and temperature The results show good correlation with a numerical study using the ABAQUS finite-element package that includes a widely used model of
Solar Magnetic Flux Tube Simulations with Time-Dependent Ionization
Fawzy, Diaa E; Rammacher, Wolfgang
2012-01-01
In the present work we expand the study of time-dependent ionization previously identified to be of pivotal importance for acoustic waves in solar magnetic flux tube simulations. We focus on longitudinal tube waves (LTW) known to be an important heating agent of solar magnetic regions. Our models also consider new results of wave energy generation as well as an updated determination of the mixing length of convection now identified as 1.8 scale heights in the upper solar convective layers. We present 1-D wave simulations for the solar chromosphere by studying tubes of different spreading as function of height aimed at representing tubes in environments of different magnetic filling factors. Multi-level radiative transfer has been applied to correctly represent the total chromospheric emission function. The effects of time-dependent ionization are significant in all models studied. They are most pronounced behind strong shocks and in low density regions, i.e., the middle and high chromosphere. Concerning our m...
A collisional extension of time-dependent Hartree-Fock
Lacombe, L.; Reinhard, P.-G.; Dinh, P. M.; Suraud, E.
2016-12-01
We propose a collisional extension of time-dependent mean-field theories on the basis of a recently proposed stochastic extension of mean-field dynamics (stochastic time-dependent Hartree-Fock, STDHF). The latter theory is unfortunately too involved to envision practical applications in realistic systems in the near future and is thus bound to model systems. It is also hard to explore moderate to low energies with STDHF, because of vanishing transition probabilities that are impossible to sample properly. For such moderately excited situations covering small fluctuations, we compactify sampling by employing the same average mean field for all STDHF trajectories. The new approach, coined average STDHF (ASTDHF), ignores the fluctuations of the mean field but still accounts correctly for the collisional correlations responsible for dissipative features on top of mean-field dynamics. We detail the main features of the new approach in relation to existing equations, in particular quantum kinetic theories. The new theory is directly connected to STDHF, both formally and practically. We thus discuss in detail how the two approaches are related to each other. We apply the new scheme to illustrative examples taking as benchmark STDHF dynamics in 1D. ASTDHF provides results that are in remarkable agreement with the more elaborate STDHF. It makes it a promising approach to deal with dissipative dynamics in finite quantum systems, because of its moderate cost allowing applications in realistic systems and the possibility of exploring any excitation energy range where collisional correlations are expected to play a role.
Characterization of time-dependent anelastic microbeam bending mechanics
Bergers, L. I. J. C.; Hoefnagels, J. P. M.; Geers, M. G. D.
2014-09-01
This paper presents an accurate yet straightforward methodology for characterizing time-dependent anelastic mechanics of thin metal films employed in metalic microelectromechanical systems (MEMS). The deflection of microbeams is controlled with a mechanical micro-clamp, measured with digital holographic microscopy and processed with global digital image correlation (GDIC). The GDIC processing directly incorporates kinematics into the three-dimensional correlation problem, describing drift-induced rigid body motion and the beam deflection. This yields beam curvature measurements with a resolution of <1.5 × 10-6 µm-1, or for films thinner than 5 µm, a strain resolution of <4 μɛ. Using a simple experimental sequence, these curvature measurements are then combined with a linear multi-mode time-dependent anelastic model and a priori knowledge of the Young's modulus. This allows the characterization of the material behaviour in the absence of an additional explicit force measurement, which simplifies the experimental setup. Using this methodology we characterize the anelasticity of 5 µm-thick Al(1 wt%)-Cu microbeams of varying microstructures over relevant timescales of 1 to 1 × 105 s and adequately predict the time and amplitude response of experiments performed for various loading conditions. This demonstrates the validity of the methodology and the suitability for thin film mechanics research for MEMS development.
Time Circular Birefringence in Time-Dependent Magnetoelectric Media
Zhang, Ruo-Yang; Lin, Shi-Rong; Zhao, Qing; Wen, Weijia; Ge, Mo-Lin
2015-01-01
Light traveling in time-dependent media has many extraordinary properties which can be utilized to convert frequency, achieve temporal cloaking, and simulate cosmological phenomena. In this paper, we focus on time-dependent axion-type magnetoelectric (ME) media, and prove that light in these media always has two degenerate modes with opposite circular polarizations corresponding to one wave vector $\\mathbf{k}$, and name this effect "time circular birefringence" (TCB). By interchanging the status of space and time, the pair of TCB modes can appear simultaneously via "time refraction" and "time reflection" of a linear polarized incident wave at a time interface of ME media. The superposition of the two TCB modes causes the "time Faraday effect", namely the globally unified polarization axes rotate with time. A circularly polarized Gaussian pulse traversing a time interface is also studied. If the wave-vector spectrum of a pulse mainly concentrates in the non-traveling-wave band, the pulse will be trapped with n...
Towards relativistic quantum geometry
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Adiabatic theorems for generators of contracting evolutions
Avron, J E; Graf, G M; Grech, P
2011-01-01
We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.
Digital Waveguide Adiabatic Passage Part 2: Experiment
Ng, Vincent; Chaboyer, Zachary J; Nguyen, Thach; Dawes, Judith M; Withford, Michael J; Greentree, Andrew D; Steel, M J
2016-01-01
Using a femtosecond laser writing technique, we fabricate and characterise three-waveguide digital adiabatic passage devices, with the central waveguide digitised into five discrete waveguidelets. Strongly asymmetric behaviour was observed, devices operated with high fidelity in the counter-intuitive scheme while strongly suppressing transmission in the intuitive. The low differential loss of the digital adiabatic passage designs potentially offers additional functionality for adiabatic passage based devices. These devices operate with a high contrast ($>\\!90\\%$) over a 60~nm bandwidth, centered at $\\sim 823$~nm.
Energy consumption for shortcuts to adiabaticity
Torrontegui, E.; Lizuain, I.; González-Resines, S.; Tobalina, A.; Ruschhaupt, A.; Kosloff, R.; Muga, J. G.
2017-08-01
Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the "energy cost" of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking.
Reiche, S.; Rosenzweig, J.B.; Anderson, S.; Frigola, P.; Hogan, M.; Murokh, A.; Pellegrini, C.; Serafini, L.; Travish, G.; Tremaine, A. [Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California 90095-1547 (United States)
1997-09-01
The measurement of the transverse phase-space map, or transport matrix, of a relativistic electron in a high-gradient, radio-frequency linear accelerator (rf linac) at the UCLA photoinjector is reported. This matrix, which indicates the effects of acceleration (adiabatic damping), first-order transient focusing, and ponderomotive second-order focusing, is measured as a function of both rf field amplitude and phase in the linac. The elements of the matrix, determined by observation of centroid motion at a set of downstream diagnostics due to deflections induced by a set of upstream steering magnets, compare well with previously developed analytical theory [J. Rosenzweig and L. Serafini, Phys. Rev. E {bold 49}, 1599 (1994)]. The determinant of the matrix is obtained, yielding a direct confirmation of trace space adiabatic damping. Implications of these results on beam optics at moderate energy in high-gradient linear accelerators such as rf photoinjectors are discussed. {copyright} {ital 1997} {ital The American Physical Society}
Sharma, P; Quataert, E; Parrish, I J
2009-01-01
Using a linear stability analysis and two and three-dimensional nonlinear simulations, we study the physics of buoyancy instabilities in a combined thermal and relativistic (cosmic ray) plasma, motivated by the application to clusters of galaxies. We argue that cosmic ray diffusion is likely to be slow compared to the buoyancy time on large length scales, so that cosmic rays are effectively adiabatic. If the cosmic ray pressure $p_{cr}$ is $\\gtrsim 25 %$ of the thermal pressure, and the cosmic ray entropy ($p_{\\rm cr}/\\rho^{4/3}$; $\\rho$ is the thermal plasma density) decreases outwards, cosmic rays drive an adiabatic convective instability analogous to Schwarzschild convection in stars. Global simulations of galaxy cluster cores show that this instability saturates by reducing the cosmic ray entropy gradient and driving efficient convection and turbulent mixing. At larger radii in cluster cores, the thermal plasma is unstable to the heat flux-driven buoyancy instability (HBI), a convective instability genera...
Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan; Medeiros, Lia; Özel, Feryal; Psaltis, Dimitrios
2016-12-01
The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.
Becker, P A; Le, T
2006-01-01
Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) plasma waves is the dominant process leading to the formation of the high-energy electron and ion distributions in a variety of astrophysical systems. Collisions with the waves influence both the energization and the spatial transport of the particles, and therefore it is important to treat these two aspects of the problem in a self-consistent manner. We solve the representative Fokker-Planck equation to obtain a new, closed-form solution for the time-dependent Green's function describing the acceleration and escape of relativistic ions interacting with Alfven or fast-mode waves characterized by momentum diffusion coefficient $D(p)\\propto p^q$ and mean particle escape timescale $t_esc(p) \\propto p^{q-2}$, where $p$ is the particle momentum and $q$ is the power-law index of the MHD wave spectrum. In particular, we obtain solutions for the momentum distribution of the ions in the plasma and also for the momentum dist...
Kim, Kyung-Chan; Shprits, Yuri; Subbotin, Dmitriy; Ni, Binbin
2012-08-01
Understanding the dynamics of relativistic electron acceleration, loss, and transport in the Earth's radiation belt during magnetic storms is a challenging task. The U.S. National Science Foundation's Geospace Environment Modeling (GEM) has identified five magnetic storms for in-depth study that occurred during the second half of the Combined Release and Radiation Effects Satellite (CRRES) mission in the year 1991. In this study, we show the responses of relativistic radiation belt electrons to the magnetic storms by comparing the time-dependent 3-D Versatile Electron Radiation Belt (VERB) simulations with the CRRES MEA 1 MeV electron observations in order to investigate the relative roles of the competing effects of previously proposed scattering mechanisms at different storm phases, as well as to examine the extent to which the simulations can reproduce observations. The major scattering processes in our model are radial transport due to Ultra Low Frequency (ULF) electromagnetic fluctuations, pitch angle and energy diffusion including mixed diffusion by whistler mode chorus waves outside the plasmasphere, and pitch angle scattering by plasmaspheric hiss inside the plasmasphere. The 3-D VERB simulations show that during the storm main phase and early recovery phase the estimated plasmapause is located deep in the inner region, indicating that pitch angle scattering by chorus waves can be a dominant loss process in the outer belt. We have also confirmed the important role played by mixed energy-pitch angle diffusion by chorus waves, which tends to reduce the fluxes enhanced by local acceleration, resulting in comparable levels of computed and measured fluxes. However, we cannot reproduce the more pronounced flux dropout near the boundary of our simulations during the main phase, which indicates that non-adiabatic losses may extend toL-shells lower than our simulation boundary. We also provide a detailed description of simulations for each of the GEM storm events.
Thermoelectric Effects under Adiabatic Conditions
George Levy
2013-10-01
Full Text Available This paper investigates not fully explained voltage offsets observed by several researchers during the measurement of the Seebeck coefficient of high Z materials. These offsets, traditionally attributed to faulty laboratory procedures, have proven to have an irreducible component that cannot be fully eliminated in spite of careful laboratory procedures. In fact, these offsets are commonly observed and routinely subtracted out of commercially available Seebeck measurement systems. This paper offers a possible explanation based on the spontaneous formation of an adiabatic temperature gradient in the presence of a force field. The diffusion-diffusion heat transport mechanism is formulated and applied to predict two new thermoelectric effects. The first is the existence of a temperature gradient across a potential barrier in a semiconductor and the second is the Onsager reciprocal of the first, that is, the presence of a measureable voltage that arises across a junction when the temperature gradient is forced to zero by a thermal clamp. Suggested future research includes strategies for utilizing the new thermoelectric effects.
Fuzzy economic production quantity model with time dependent demand rate
Susanta Kumar Indrajitsingha
2016-09-01
Full Text Available Background: In this paper, an economic production quantity model is considered under a fuzzy environment. Both the demand cost and holding cost are considered using fuzzy pentagonal numbers. The Signed Distance Method is used to defuzzify the total cost function. Methods: The results obtained by these methods are compared with the help of a numerical example. Sensitivity analysis is also carried out to explore the effect of changes in the values of some of the system parameters. Results and conclusions: The fuzzy EPQ model with time dependent demand rate was presented together with the possible implementation. The behavior of changes in parameters was analyzed. The possible extension of the implementation of this method was presented.
Time-dependent particle acceleration in a Fermi reservoir
Litvinenko, Y. E.
2012-08-01
Context. A steady model was presented by Burn, in which energy conservation is used to constrain the parameters of stochastic Fermi acceleration. A steady model, however, is unlikely to be adequate for particle acceleration in impulsive solar flares. Aims: This paper describes a time-dependent model for particle acceleration in a Fermi reservoir Methods: The calculation is based on the original formulation of stochastic acceleration by Fermi, with additional physically motivated assumptions about the turbulent and particle energy densities within the reservoir, that are similar to those of the steady analysis. The problem is reduced to an integro-differential equation that possesses an analytical solution. Results: The model predicts the formation of a power-law differential energy spectrum N(E) ~ E-2, that is observable outside the reservoir. The predicted spectral index is independent of the parameters of the model. The results may help in understanding particle acceleration in solar flares and other astrophysical applications.
Effects of Temperature on Time Dependent Rheological Characteristics of Koumiss
Serdal Sabancı
2016-04-01
Full Text Available The rheological properties of koumiss were investigated at different temperatures (4, 10, and 20°C. Experimental shear stress–shear rate data were fitted to different rheological models. The consistency of koumiss was predicted by using the power-law model since it described the consistency of koumiss best with highest regression coefficient and lowest errors (root mean square error and chi-square. Koumiss exhibited shear thinning behavior (n<1. The flow activation energy for temperature dependency of consistency was 25.532 kJ/mol, and the frequency constant was 2.18×10-7Pa.sn. As the temperature increased the time dependent thixotropic characteristics of koumiss decreased.
Time-dependent calculations in Potassium mid-infrared wavelengths
Maragakis, P; Lambropoulos, P
1999-01-01
We study the dynamics of the Potassium atom in the mid-infrared, high intensity, short laser pulse regime. We ascertain our numerical convergence by comparing the results of two different propagation methods of the time-dependent Schroedinger equation. We present ionization curves in the 12-, 13-, and 14-photon ionization range for Potassium. The ionization curve of a scaled system, namely Hydrogen starting from the 2s, is compared to the 12-photon results. In the 13-photon regime, a dynamic resonance is observed and analyzed in more detail. The results for all wavelengths and intensities, including the case of Hydrogen, display a clear plateau formation in the peak-heights of the low energy part of the Above Threshold Ionization (ATI) spectrum, which scales with the ponderomotive energy Up, and extends to (2.8 +- 0.5) Up.
Time-dependent interactions between iboga agents and cocaine.
Maisonneuve, I M; Visker, K E; Mann, G L; Bandarage, U K; Kuehne, M E; Glick, S D
1997-10-08
The purpose of this study was to clarify the effects of iboga agents on cocaine-induced hyperactivity. Both inhibition and enhancement of cocaine-induced activity by ibogaine have been reported. In the present study, rats were treated with either ibogaine (40 mg/kg, i.p.), noribogaine (40 mg/kg, i.p.), 18-methoxycoronaridine (40 mg/kg, i.p.), or saline, 1 or 19 h prior to the administration of cocaine (20 mg/kg, i.p.) or saline. Motor activity was monitored thereafter for 3 h. All three iboga agents had acute inhibitory effects and delayed potentiating effects on cocaine-induced hyperactivity. These time-dependent effects, which could not be attributed to the motor activity induced by the iboga agents alone, account for divergent results reported in the literature.
Timing intervals using population synchrony and spike timing dependent plasticity
Wei Xu
2016-12-01
Full Text Available We present a computational model by which ensembles of regularly spiking neurons can encode different time intervals through synchronous firing. We show that a neuron responding to a large population of convergent inputs has the potential to learn to produce an appropriately-timed output via spike-time dependent plasticity. We explain why temporal variability of this population synchrony increases with increasing time intervals. We also show that the scalar property of timing and its violation at short intervals can be explained by the spike-wise accumulation of jitter in the inter-spike intervals of timing neurons. We explore how the challenge of encoding longer time intervals can be overcome and conclude that this may involve a switch to a different population of neurons with lower firing rate, with the added effect of producing an earlier bias in response. Experimental data on human timing performance show features in agreement with the model’s output.
Time-Dependent Tomographic Reconstruction of the Solar Corona
Vibert, Didier; Lamy, Philippe; Frazin, Richard A; Wojak, Julien
2016-01-01
Solar rotational tomography (SRT) applied to white-light coronal images observed at multiple aspect angles has been the preferred approach for determining the three-dimensional (3D) electron density structure of the solar corona. However, it is seriously hampered by the restrictive assumption that the corona is time-invariant which introduces significant errors in the reconstruction. We first explore several methods to mitigate the temporal variation of the corona by decoupling the "fast-varying" inner corona from the "slow-moving" outer corona using multiple masking (either by juxtaposition or recursive combination) and radial weighting. Weighting with a radial exponential profile provides some improvement over a classical reconstruction but only beyond 3 Rsun. We next consider a full time-dependent tomographic reconstruction involving spatio-temporal regularization and further introduce a co-rotating regularization aimed at preventing concentration of reconstructed density in the plane of the sky. Crucial t...
On a time-dependent extra spatial dimension
Kuhfittig, P K F
2006-01-01
In the usual brane-world scenario matter fields are confined to the four-dimensional spacetime, called a 3-brane, embedded in a higher-dimensional space, usually referred to as the bulk spacetime. In this paper we assume that the 3-brane a de Sitter space; there is only one extra spatial dimension, assumed to be time dependent. By using the form of the brane-world energy-momentum tensor suggested by Shiromizu et al. in the five-dimensional Einstein equations, it is shown that whenever the bulk cosmological constant \\Lambda is negative, the extra spatial dimension rapidly shrinks during the inflation of the brane. When \\Lambda>0, on the other hand, the extra spatial dimension either completely follows the cosmological expansion of the brane or completely ignores it. This behavior resembles the all-or-nothing behavior of ordinary systems in an expanding universe, as recently demonstrated by R.H. Price.
Spin-orbit torque induced spike-timing dependent plasticity
Sengupta, Abhronil, E-mail: asengup@purdue.edu; Al Azim, Zubair; Fong, Xuanyao; Roy, Kaushik [School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States)
2015-03-02
Nanoelectronic devices that mimic the functionality of synapses are a crucial requirement for performing cortical simulations of the brain. In this work, we propose a ferromagnet-heavy metal heterostructure that employs spin-orbit torque to implement spike-timing dependent plasticity. The proposed device offers the advantage of decoupled spike transmission and programming current paths, thereby leading to reliable operation during online learning. Possible arrangement of such devices in a crosspoint architecture can pave the way for ultra-dense neural networks. Simulation studies indicate that the device has the potential of achieving pico-Joule level energy consumption (maximum 2 pJ per synaptic event) which is comparable to the energy consumption for synaptic events in biological synapses.
Hamiltonian formulation of time-dependent plausible inference
Davis, Sergio
2014-01-01
Maximization of the path information entropy is a clear prescription for performing time-dependent plausible inference. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the Second Law of Thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the Second Law is a fundamental property of ...
A gauge invariant theory for time dependent heat current
Chen, Jian; ShangGuan, Minhui; Wang, Jian
2015-05-01
In this work, we develop a general gauge-invariant theory for AC heat current through multi-probe systems. Using the non-equilibrium Green’s function, a general expression for time-dependent electrothermal admittance is obtained where we include the internal potential due to the Coulomb interaction explicitly. We show that the gauge-invariant condition is satisfied for heat current if the self-consistent Coulomb interaction is considered. It is known that the Onsager relation holds for dynamic charge conductance. We show in this work that the Onsager relation for electrothermal admittance is violated, except for a special case of a quantum dot system with a single energy level. We apply our theory to a nano capacitor where the Coulomb interaction plays an essential role. We find that, to the first order in frequency, the heat current is related to the electrochemical capacitance as well as the phase accumulated in the scattering event.
Goal Directed Relative Skyline Queries in Time Dependent Road Networks
Iyer, K B Priya
2012-01-01
The Wireless GIS technology is progressing rapidly in the area of mobile communications. Location-based spatial queries are becoming an integral part of many new mobile applications. The Skyline queries are latest apps under Location-based services. In this paper we introduce Goal Directed Relative Skyline queries on Time dependent (GD-RST) road networks. The algorithm uses travel time as a metric in finding the data object by considering multiple query points (multi-source skyline) relative to user location and in the user direction of travelling. We design an efficient algorithm based on Filter phase, Heap phase and Refine Skyline phases. At the end, we propose a dynamic skyline caching (DSC) mechanism which helps to reduce the computation cost for future skyline queries. The experimental evaluation reflects the performance of GD-RST algorithm over the traditional branch and bound algorithm for skyline queries in real road networks.
Time-dependent density-functional description of nuclear dynamics
Nakatsukasa, Takashi; Matsuo, Masayuki; Yabana, Kazuhiro
2016-01-01
We present the basic concepts and recent developments in the time-dependent density functional theory (TDDFT) for describing nuclear dynamics at low energy. The symmetry breaking is inherent in nuclear energy density functionals (EDFs), which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, we treat the quantum fluctuations associated with slow collective motions assuming that time evolution of...
Measuring time-dependent diffusion in polymer matrix composites
Pilli, Siva Prasad; Smith, Lloyd V.; Shutthanandan, V.
2014-11-01
Moisture plays a significant role in influencing the mechanical behavior and long-term durability of polymer matrix composites (PMC’s). The common methods used to determine the moisture diffusion coefficients of PMCs are based on the solution of Fickian diffusion in the one-dimensional domain. Fick’s Law assumes that equilibrium between the material surface and the external vapor is established instantaneously. A time dependent boundary condition has been shown to improve correlation with some bulk diffusion measurements, but has not been validated experimentally. The surface moisture content in a Toray 800S/3900-2B toughened quasi-isotropic laminate system, [0/±60]s, was analyzed experimentally using Nuclear Reaction Analysis (NRA). It was found that the surface moisture content showed a rapid increase to an intermediate concentration C0, followed by a slow linear increase to the saturation level.
Time-dependent Corotation Resonance in Barred Galaxies
Wu, Yu-Ting; Pfenniger, Daniel; Taam, Ronald E.
2016-10-01
The effective potential neighboring the corotation resonance region in barred galaxies is shown to be strongly time-dependent in any rotating frame, due to the competition of nearby perturbations of similar strengths with differing rotation speeds. Contrary to the generally adopted assumption that in the bar rotating frame the corotation region should possess four stationary equilibrium points (Lagrange points), with high quality N-body simulations, we localize the instantaneous equilibrium points (EPs) and find that they circulate or oscillate broadly in azimuth with respect to the pattern speeds of the inner or outer perturbations. This implies that at the particle level the Jacobi integral is not well conserved around the corotation radius. That is, angular momentum exchanges decouple from energy exchanges, enhancing the chaotic diffusion of stars through the corotation region.
The time-dependent Aharonov–Casher effect
Douglas Singleton
2016-02-01
Full Text Available In this paper we give a covariant expression for Aharonov–Casher phase. This expression is a combination of the canonical electric field, Aharonov–Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov–Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the time dependent electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic fields lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.
The time-dependent Aharonov-Casher effect
Singleton, Douglas
2015-01-01
In this paper we give a covariant expression for Aharonov-Casher phase. This expression is a combination of the canonical electric field, Aharonov-Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov-Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the {\\it time dependent} electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic field lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.
The time-dependent Aharonov–Casher effect
Singleton, Douglas, E-mail: dougs@csufresno.edu [Department of Physics, California State University Fresno, Fresno, CA 93740-8031 (United States); ICTP South American Institute for Fundamental Research, UNESP – Univ. Estadual Paulista, Rua Dr. Bento T. Ferraz 271, 01140-070, São Paulo, SP (Brazil); Ulbricht, Jaryd, E-mail: julbrich@ucsc.edu [Physics Department, University of California Santa Cruz, Santa Cruz, CA 95064 (United States); Department of Physics, California State University Fresno, Fresno, CA 93740-8031 (United States)
2016-02-10
In this paper we give a covariant expression for Aharonov–Casher phase. This expression is a combination of the canonical electric field, Aharonov–Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov–Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the time dependent electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic fields lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.
The time-dependent Aharonov-Casher effect
Singleton, Douglas; Ulbricht, Jaryd
2016-02-01
In this paper we give a covariant expression for Aharonov-Casher phase. This expression is a combination of the canonical electric field, Aharonov-Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov-Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the time dependent electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic fields lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.
Painleve V and time-dependent Jacobi polynomials
Basor, Estelle [American Institute of Mathematics, Palo Alto, CA 94306 (United States); Chen Yang [Department of Mathematics, Imperial College London, 180 Queen' s Gates, London SW7 2BZ (United Kingdom); Ehrhardt, Torsten [Department of Mathematics, University of California, Santa Cruz, CA 95064 (United States)], E-mail: ebasor@aimath.org, E-mail: ychen@imperial.ac.uk, E-mail: ehrhardt@math.ucsc.edu
2010-01-08
In this paper we study the simplest deformation on a sequence of orthogonal polynomials. This in turn induces a deformation on the moment matrix of the polynomials and associated Hankel determinant. We replace the original (or reference) weight w{sub 0}(x) (supported on R or subsets of R) by w{sub 0}(x) e{sup -tx}. It is a well-known fact that under such a deformation the recurrence coefficients denoted as {alpha}{sub n} and {beta}{sub n} evolve in t according to the Toda equations, giving rise to the time-dependent orthogonal polynomials and time-dependent determinants, using Sogo's terminology. If w{sub 0} is the normal density e{sup -x{sup 2}}, x element of R, or the gamma density x{sup {alpha}} e{sup -x}, x element of R{sub +}, {alpha} > -1, then the initial value problem of the Toda equations can be trivially solved. This is because under elementary scaling and translation the orthogonality relations reduce to the original ones. However, if w{sub 0} is the beta density (1 - x){sup {alpha}}(1 + x){sup {beta}}, x in [ - 1, 1], {alpha}, {beta} > -1, the resulting 'time-dependent' Jacobi polynomials will again satisfy a linear second-order ode, but no longer in the Sturm-Liouville form, which is to be expected. This deformation induces an irregular singular point at infinity in addition to three regular singular points of the hypergeometric equation satisfied by the Jacobi polynomials. We will show that the coefficients of this ode, as well as the Hankel determinant, are intimately related to a particular Painleve V. In particular we show that p{sub 1}(n,t), where p{sub 1}(n,t) is the coefficient of z{sup n-1} of the monic orthogonal polynomials associated with the 'time-dependent' Jacobi weight, satisfies, up to a translation in t, the Jimbo-Miwa {sigma}-form of the same P{sub V}; while a recurrence coefficient {alpha}{sub n}(t) is up to a translation in t and a linear fractional transformation P{sub V}({alpha}{sup 2}/2, - {beta}{sup 2
Histogram bin width selection for time-dependent Poisson processes
Koyama, Shinsuke; Shinomoto, Shigeru [Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502 (Japan)
2004-07-23
In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.
Histogram bin width selection for time-dependent Poisson processes
Koyama, Shinsuke; Shinomoto, Shigeru
2004-07-01
In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.
Origin of the spike-timing-dependent plasticity rule
Cho, Myoung Won; Choi, M. Y.
2016-08-01
A biological synapse changes its efficacy depending on the difference between pre- and post-synaptic spike timings. Formulating spike-timing-dependent interactions in terms of the path integral, we establish a neural-network model, which makes it possible to predict relevant quantities rigorously by means of standard methods in statistical mechanics and field theory. In particular, the biological synaptic plasticity rule is shown to emerge as the optimal form for minimizing the free energy. It is further revealed that maximization of the entropy of neural activities gives rise to the competitive behavior of biological learning. This demonstrates that statistical mechanics helps to understand rigorously key characteristic behaviors of a neural network, thus providing the possibility of physics serving as a useful and relevant framework for probing life.
Characterization of Models for Time-Dependent Behavior of Soils
Liingaard, Morten; Augustesen, Anders; Lade, Poul V.
2004-01-01
Different classes of constitutive models have been developed to capture the time-dependent viscous phenomena ~ creep, stress relaxation, and rate effects ! observed in soils. Models based on empirical, rheological, and general stress-strain-time concepts have been studied. The first part...... is a review of the empirical relations, which apply only to problems of specific boundary conditions and frequently involve natural time alone. The second part deals with different rheological models used for describing the viscous effects in the field of solid mechanics. The rheological models are typically...... developed for metals and steel but are, to some extent, used to characterize time effects in geomaterials. The third part is a review of constitutive laws that describe not only viscous effects but also the inviscid ( rate-independent) behavior of soils, in principle, under any possible loading condition...
Time-dependent Corotation Resonance in Barred Galaxies
Wu, Yu-Ting; Taam, Ronald E
2016-01-01
The effective potential neighboring the corotation resonance region in barred galaxies is shown to be strongly time-dependent in any rotating frame because of the competition of nearby perturbations of similar strengths with differing rotation speeds. Contrary to the generally adopted assumption, that in the bar rotating frame the corotation region should possess four stationary equilibrium points (Lagrange points), with high quality N-body simulations we localize the instantaneous equilibrium points and find that they circulate or oscillate broadly in azimuth with respect to the pattern speeds of the inner or outer perturbations. This implies that at the particle level the Jacobi integral is not well conserved around the corotation radius. That is, angular momentum exchanges decouple from energy exchanges, enhancing the chaotic diffusion of stars through the corotation region.
Study of Time-Dependent Properties of Thermoplastics
Bolchoun A.
2010-06-01
Full Text Available Simple tests carried out with a common tension/compression testing machine are used to obtain timedependent properties of non-reinforced thermoplastics. These tests include ramp loadings as well as relaxation and creep tests. Two materials (PBT Celanex 2002-2 and POM Hostaform C9021, Ticona GmbH, Kelsterbach were taken for the experiments. The experiments show that an adequate description of the long-term material properties can be obtained from the short-time tests, namely from tests with constant traverse speed $L^.$. Below a model for the time-dependent mechanical behavior is presented and fitted to the obtained measured data. For the evaluation of the fitting quality long-term tests are used. Especially creep and relaxation tests with ”jumps”, i.e. rapid change of loading, are important for this purpose.
Time-dependent reliability analysis and condition assessment of structures
Ellingwood, B.R. [Johns Hopkins Univ., Baltimore, MD (United States)
1997-01-01
Structures generally play a passive role in assurance of safety in nuclear plant operation, but are important if the plant is to withstand the effect of extreme environmental or abnormal events. Relative to mechanical and electrical components, structural systems and components would be difficult and costly to replace. While the performance of steel or reinforced concrete structures in service generally has been very good, their strengths may deteriorate during an extended service life as a result of changes brought on by an aggressive environment, excessive loading, or accidental loading. Quantitative tools for condition assessment of aging structures can be developed using time-dependent structural reliability analysis methods. Such methods provide a framework for addressing the uncertainties attendant to aging in the decision process.
Exponential time-dependent perturbation theory in rotationally inelastic scattering
Cross, R. J.
1983-08-01
An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error.
On the time dependence of the $h$-index
Mannella, Riccardo
2012-01-01
The time dependence of the $h$-index is analyzed by considering the average behaviour of $h$ as a function of the academic age $A_A$ for about 1400 Italian physicists, with career lengths spanning from 3 to 46 years. The individual $h$-index is strongly correlated with the square root of the total citations $N_C$: $h \\approx 0.53 \\sqrt{N_C}$. For academic ages ranging from 12 to 24 years, the distribution of the time scaled index $h/\\sqrt{A_A}$ is approximately time-independent and it is well described by the Gompertz function. The time scaled index $h/\\sqrt{A_A}$ has an average approximately equal to 3.8 and a standard deviation approximately equal to 1.6. Finally, the time scaled index $h/\\sqrt{A_A}$ appears to be strongly correlated with the contemporary $h$-index $h_c$.
SYMTRAN - A Time-dependent Symmetric Tandem Mirror Transport Code
Hua, D; Fowler, T
2004-06-15
A time-dependent version of the steady-state radial transport model in symmetric tandem mirrors in Ref. [1] has been coded up and first tests performed. Our code, named SYMTRAN, is an adaptation of the earlier SPHERE code for spheromaks, now modified for tandem mirror physics. Motivated by Post's new concept of kinetic stabilization of symmetric mirrors, it is an extension of the earlier TAMRAC rate-equation code omitting radial transport [2], which successfully accounted for experimental results in TMX. The SYMTRAN code differs from the earlier tandem mirror radial transport code TMT in that our code is focused on axisymmetric tandem mirrors and classical diffusion, whereas TMT emphasized non-ambipolar transport in TMX and MFTF-B due to yin-yang plugs and non-symmetric transitions between the plugs and axisymmetric center cell. Both codes exhibit interesting but different non-linear behavior.
Multiaxial Temperature- and Time-Dependent Failure Model
Richardson, David; McLennan, Michael; Anderson, Gregory; Macon, David; Batista-Rodriquez, Alicia
2003-01-01
A temperature- and time-dependent mathematical model predicts the conditions for failure of a material subjected to multiaxial stress. The model was initially applied to a filled epoxy below its glass-transition temperature, and is expected to be applicable to other materials, at least below their glass-transition temperatures. The model is justified simply by the fact that it closely approximates the experimentally observed failure behavior of this material: The multiaxiality of the model has been confirmed (see figure) and the model has been shown to be applicable at temperatures from -20 to 115 F (-29 to 46 C) and to predict tensile failures of constant-load and constant-load-rate specimens with failure times ranging from minutes to months..
Relating Time-Dependent Acceleration and Height Using an Elevator
Kinser, Jason M.
2015-04-01
A simple experiment in relating a time-dependent linear acceleration function to height is explored through the use of a smartphone and an elevator. Given acceleration as a function of time1, a(t), the velocity function and position functions are determined through integration as in v (t ) =∫ a (t ) d t (1) and x (t ) =∫ v (t ) dt. Mobile devices such as smartphones or tablets have accelerometers that capture slowly evolving acceleration with respect to time and can deliver those measurements as a CSV file. A recent example measured the oscillations of the elevator as it starts its motion.2 In the application presented here the mobile device is used to estimate the height of the elevator ride. By estimating the functional form of the acceleration of an elevator ride, it is possible to estimate the height of the ride through Eqs. (1) and (2).
Translation invariant time-dependent solutions to massive gravity
Mourad, J.; Steer, D.A., E-mail: mourad@apc.univ-paris7.fr, E-mail: steer@apc.univ-paris7.fr [AstroParticule and Cosmologie (UMR 7164 - APC, Univ Paris Diderot, CNRS/IN2P3, CEA/lrfu, Obs de Paris, Sorbonne Paris Cité, France), 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13 (France)
2013-12-01
Homogeneous time-dependent solutions of massive gravity generalise the plane wave solutions of the linearised Fierz-Pauli equations for a massive spin-two particle, as well as the Kasner solutions of General Relativity. We show that they also allow a clear counting of the degrees of freedom and represent a simplified framework to work out the constraints, the equations of motion and the initial value formulation. We work in the vielbein formulation of massive gravity, find the phase space resulting from the constraints and show that several disconnected sectors of solutions exist some of which are unstable. The initial values determine the sector to which a solution belongs. Classically, the theory is not pathological but quantum mechanically the theory may suffer from instabilities. The latter are not due to an extra ghost-like degree of freedom.
Time-dependent resonant magneto-optical rotation
Dziczek, Dariusz
2015-01-01
Results of a fairly straightforward experiment on resonant magneto-optical rotation by rubidium-87 atoms revealed strong time-dependence of the polarization plane of light emerging from atomic vapors following a sudden irradiation with a laser beam. The rotation of the plane appears as a not direct consequence of the influence of the magnetic field on atoms. Reported measurements conducted using a vapor cell without any buffer gas or an anti-relaxation wall coating show that transmitted light has initially the same (linear) polarization as the incident one. Rotation of the polarization plane caused by an axial magnetic field develops in time scales similar to the pace of establishing the optical pumping/relaxation equilibrium in the atomic ensemble. The traditional passive Faraday rotation picture providing working description for the resonant magneto-optical effects in steady-state conditions does not explain the observed sequence of evolution of the polarization. The picture has to be augmented with analysi...
Translation invariant time-dependent solutions to massive gravity
Mourad, J
2013-01-01
Homogeneous time-dependent solutions of massive gravity generalise the plane wave solutions of the linearised Fierz-Pauli equations for a massive spin-two particle, as well as the Kasner solutions of General Relativity. We show that they also allow a clear counting of the degrees of freedom and represent a simplified framework to work out the constraints, the equations of motion and the initial value formulation. We work in the vielbein formulation of massive gravity, find the phase space resulting from the constraints and show that several disconnected sectors of solutions exist some of which are unstable. The initial values determine the sector to which a solution belongs. Classically, the theory is not pathological but quantum mechanically the theory may suffer from instabilities. The latter are not due to an extra ghost-like degree of freedom.
Adiabatic Quantum Search in Open Systems.
Wild, Dominik S; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y; Lukin, Mikhail D
2016-10-07
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Adiabatic hydrodynamics: The eightfold way to dissipation
Haehl, Felix M; Rangamani, Mukund
2015-01-01
We provide a complete solution to hydrodynamic transport at all orders in the gradient expansion compatible with the second law constraint. The key new ingredient we introduce is the notion of adiabaticity, which allows us to take hydrodynamics off-shell. Adiabatic fluids are such that off-shell dynamics of the fluid compensates for entropy production. The space of adiabatic fluids is quite rich, and admits a decomposition into seven distinct classes. Together with the dissipative class this establishes the eightfold way of hydrodynamic transport. Furthermore, recent results guarantee that dissipative terms beyond leading order in the gradient expansion are agnostic of the second law. While this completes a transport taxonomy, we go on to argue for a new symmetry principle, an Abelian gauge invariance that guarantees adiabaticity in hydrodynamics. We suggest that this symmetry is the macroscopic manifestation of the microscopic KMS invariance. We demonstrate its utility by explicitly constructing effective ac...
Adiabatic quantum gates and Boolean functions
Andrecut, M; Ali, M K [Department of Physics, University of Lethbridge, Lethbridge, AB, T1K 3M4 (Canada)
2004-06-25
We discuss the logical implementation of quantum gates and Boolean functions in the framework of quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language. (letter to the editor)
Adiabatic Quantum Search in Open Systems
Wild, Dominik S.; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y.; Lukin, Mikhail D.
2016-10-01
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Spike-timing dependent plasticity in the striatum
Elodie Fino
2010-06-01
Full Text Available The striatum is the major input nucleus of basal ganglia, an ensemble of interconnected sub-cortical nuclei associated with fundamental processes of action-selection and procedural learning and memory. The striatum receives afferents from the cerebral cortex and the thalamus. In turn, it relays the integrated information towards the basal ganglia output nuclei through which it operates a selected activation of behavioral effectors. The striatal output neurons, the GABAergic medium-sized spiny neurons (MSNs, are in charge of the detection and integration of behaviorally relevant information. This property confers to the striatum the ability to extract relevant information from the background noise and select cognitive-motor sequences adapted to environmental stimuli. As long-term synaptic efficacy changes are believed to underlie learning and memory, the corticostriatal long-term plasticity provides a fundamental mechanism for the function of the basal ganglia in procedural learning. Here, we reviewed the different forms of spike-timing dependent plasticity (STDP occurring at corticostriatal synapses. Most of the studies have focused on MSNs and their ability to develop long-term plasticity. Nevertheless, the striatal interneurons (the fast-spiking GABAergic, the NO synthase and cholinergic interneurons also receive monosynaptic afferents from the cortex and tightly regulated corticostriatal information processing. Therefore, it is important to take into account the variety of striatal neurons to fully understand the ability of striatum to develop long-term plasticity. Corticostriatal STDP with various spike-timing dependence have been observed depending on the neuronal sub-populations and experimental conditions. This complexity highlights the extraordinary potentiality in term of plasticity of the corticostriatal pathway.
New applications with time-dependent thermochemical simulation
Koukkari, P. [VTT Chemical Technology, Espoo (Finland); Laukkanen, L. [VTT Automation, Espoo (Finland); Penttilae, K. [Kemira Engineering Oy, Helsinki (Finland)
1996-12-31
A new method (RATEMIX) to calculate multicomponent chemical reaction mixtures as a series of sequential thermochemical states was recently introduced. The procedure combines multicomponent thermodynamics with chemical kinetics and may be used to simulate the multicomponent reactors as a thermochemical natural process. The method combines the desired reaction rates sequentially with constrained Gibbs energy minimization. The reactant concentrations are determined by the experimental (Arrhenius) rate laws. During the course of the given reaction the subsequent side reactions are supposed to occur reversibly. At every sequential stage of the given reaction the temperature and composition of the reaction mixture are calculated by a thermodynamic subroutine, which minimizes the Gibbs energy of the system and takes into account the heat transfer between the system and its surroundings. The extents of reaction are included as algorithmic constraints in the Gibbs energy minimization procedure. Initially, the reactants are introduced to the system as inert copies to match both the mass and energy balance of the reactive system. During the calculation the copies are sequentially interchanged to the actual reactants which allows one to simulate the time-dependent reaction route by using the thermochemical procedure. For each intermediate stage, the temperature and composition are calculated and as well numerical estimates of the thermodynamic functions are obtained. The method is applicable in processes where the core thermodynamic and kinetic data of the system are known and the time-dependent heat transfer data can either be measured or estimated by calculation. The method has been used to simulate e.g. high temperature flame reactions, zinc vapour oxidation and a counter-current rotary drum with chemical reactions. The procedure has today been tested with SOLGASMIX, CHEMSAGE and HSC programs. (author)
Time-dependent compaction band formation in sandstone
Heap, Michael J.; Brantut, Nicolas; Baud, Patrick; Meredith, Philip G.
2015-07-01
Compaction bands in sandstone are laterally extensive planar deformation features that are characterized by lower porosity and permeability than the surrounding host rock. As a result, this form of localization has important implications for both strain partitioning and fluid flow in the Earth's upper crust. To better understand the time dependency of compaction band growth, we performed triaxial deformation experiments on water-saturated Bleurswiller sandstone (initial porosity = 0.24) under constant stress (creep) conditions in the compactant regime. Our experiments show that inelastic strain accumulates at a constant stress in the compactant regime, manifest as compaction bands. While creep in the dilatant regime is characterized by an increase in porosity and, ultimately, an acceleration in axial strain rate to shear failure, compaction creep is characterized by a reduction in porosity and a gradual deceleration in axial strain rate. The global decrease in the rates of axial strain, acoustic emission energy, and porosity change during creep compaction is punctuated at intervals by higher rate excursions, interpreted as the formation of compaction bands. The growth rate of compaction bands formed during creep is lower as the applied differential stress, and hence, background creep strain rate, is decreased. However, the inelastic strain associated with the growth of a compaction band remains constant over strain rates spanning several orders of magnitude (from 10-8 to 10-5 s-1). We find that despite the large differences in strain rate and growth rate (from both creep and constant strain rate experiments), the characteristics (geometry and thickness) of the compaction bands remain essentially the same. Several lines of evidence, notably the similarity between the differential stress dependence of creep strain rate in the dilatant and compactant regimes, suggest that as for dilatant creep, subcritical stress corrosion cracking is the mechanism responsible for
Time-dependent changes in altruistic punishment following stress.
Vinkers, Christiaan H; Zorn, Jelle V; Cornelisse, Sandra; Koot, Susanne; Houtepen, Lotte C; Olivier, Berend; Verster, Joris C; Kahn, René S; Boks, Marco P M; Kalenscher, Tobias; Joëls, Marian
2013-09-01
Decisions are rarely made in social isolation. One phenomenon often observed in social interactions is altruistic punishment, i.e. the punishment of unfair behavior by others at a personal cost. The tendency for altruistic punishment is altered by affective states including those induced by stress exposure. Stress is thought to exert bi-directional effects on behavior: immediately after stress, reflex-like and habitual behavior is promoted while later on more far-sighted, flexible and goal-directed behavior is enhanced. We hypothesized that such time-dependent effects of stress would also be present in the context of altruistic punishment behavior. Healthy male participants (N=80) were exposed to either a grouped stress test or a control condition. Participants were tested in prosocial decision making tasks either directly after stress or 75 min later. Altruistic punishment was assessed using the Ultimatum Game. General altruism was assessed with a one-shot version of the Dictator Game in which an anonymous donation could be offered to a charitable organization. We found that stress caused a bi-directional effect on altruistic punishment, with decreased rejection rates in the late aftermath of stress in response to ambiguous 30% offers. In the Dictator Game, stressed participants were less generous than controls, but no time-dependent effect was observed, indicating that the general reward sensitivity remained unchanged at various time-points after stress. Overall, during the late aftermath after acute stress exposure (i.e. 75 min later), participants acted more consistent with their own material self-interest, and had a lower propensity for altruistic punishment, possibly through upregulation of cognitive self-control mechanisms. Thus, our findings underscore the importance of time as a factor in simple, real-life economic decisions in a stressful social context.
Faster computation of adiabatic EMRIs using resonances
Grossman, Rebecca; Perez-Giz, Gabe
2011-01-01
Motivated by the prohibitive computational cost of producing adiabatic extreme mass ratio inspirals, we explain how a judicious use of resonant orbits can dramatically expedite both that calculation and the generation of snapshot gravitational waves from geodesic sources. In the course of our argument, we clarify the resolution of a lingering debate on the appropriate adiabatic averaging prescription in favor of torus averaging over time averaging.
Quantum Adiabatic Evolution Algorithms versus Simulated Annealing
Farhi, E; Gutmann, S; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function depends only on the Hamming weight of the n bits. We also give two examples, closely related to these, where the similarity breaks down in that the quantum adiabatic algorithm succeeds in polynomial time whereas simulated annealing requires exponential time.
The best of both Reps—Diabatized Gaussians on adiabatic surfaces
Meek, Garrett A.; Levine, Benjamin G.
2016-11-01
When simulating nonadiabatic molecular dynamics, choosing an electronic representation requires consideration of well-known trade-offs. The uniqueness and spatially local couplings of the adiabatic representation come at the expense of an electronic wave function that changes discontinuously with nuclear motion and associated singularities in the nonadiabatic coupling matrix elements. The quasi-diabatic representation offers a smoothly varying wave function and finite couplings, but identification of a globally well-behaved quasi-diabatic representation is a system-specific challenge. In this work, we introduce the diabatized Gaussians on adiabatic surfaces (DGAS) approximation, a variant of the ab initio multiple spawning (AIMS) method that preserves the advantages of both electronic representations while avoiding their respective pitfalls. The DGAS wave function is expanded in a basis of vibronic functions that are continuous in both electronic and nuclear coordinates, but potentially discontinuous in time. Because the time-dependent Schrödinger equation contains only first-order derivatives with respect to time, singularities in the second-derivative nonadiabatic coupling terms (i.e., diagonal Born-Oppenheimer correction; DBOC) at conical intersections are rigorously absent, though singular time-derivative couplings remain. Interpolation of the electronic wave function allows the accurate prediction of population transfer probabilities even in the presence of the remaining singularities. We compare DGAS calculations of the dynamics of photoexcited ethene to AIMS calculations performed in the adiabatic representation, including the DBOC. The 28 fs excited state lifetime observed in DGAS simulations is considerably shorter than the 50 fs lifetime observed in the adiabatic simulations. The slower decay in the adiabatic representation is attributable to the large, repulsive DBOC in the neighborhood of conical intersections. These repulsive DBOC terms are artifacts
Hierarchical theory of quantum adiabatic evolution
Zhang, Qi; Gong, Jiangbin; Wu, Biao
2014-12-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.
Non-Adiabatic Dynamics around a Conical Intersection with Surface-Hopping Coupled Coherent States
Humeniuk, Alexander
2016-01-01
An extension of the CCS-method [Chem. Phys. 2004, 304, p. 103-120] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schr\\"{o}dinger 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 intereference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution i...
Zhang, Yiran; Liu, Siming; Yuan, Qiang
2017-07-01
Recent precise measurements of cosmic-ray (CR) spectra show that the energy distribution of protons is softer than those of heavier nuclei, and there are spectral hardenings for all nuclear compositions above ∼200 GV. Models proposed for these anomalies generally assume steady-state solutions of the particle acceleration process. We show that if the diffusion coefficient has a weak dependence on the particle rigidity near shock fronts of supernova remnants (SNRs), time-dependent solutions of the linear diffusive shock acceleration at two stages of SNR evolution can naturally account for these anomalies. The high-energy component of CRs is dominated by acceleration in the free expansion and adiabatic phases with enriched heavy elements and a high shock speed. The low-energy component may be attributed to acceleration by slow shocks propagating in dense molecular clouds with low metallicity in the radiative phase. Instead of a single power-law distribution, the spectra of time-dependent solutions soften gradually with the increase of energy, which may be responsible for the “knee” of CRs.
Pipolo, Silvio; Corni, Stefano; Cammi, Roberto
2017-02-01
The dynamics of the electrons for a molecule in solution is coupled to the dynamics of its polarizable environment, i.e., the solvent. To theoretically investigate such electronic dynamics, we have recently developed equations of motion (EOM) for the apparent solvent polarization charges that generate the reaction field in the Polarizable Continuum Model (PCM) for solvation and we have coupled them to a real-time time-dependent density functional theory (RT TDDFT) description of the solute [S. Corni et al., J. Phys. Chem. A 119, 5405 (2014)]. Here we present an extension of the EOM-PCM approach to a Time-Dependent Configuration Interaction (TD CI) description of the solute dynamics, which is free from the qualitative artifacts of RT TDDFT in the adiabatic approximation. As tests of the developed approach, we investigate the solvent Debye relaxation after an electronic excitation of the solute obtained either by a π pulse of light or by assuming the idealized sudden promotion to the excited state. Moreover, we present EOM for the Onsager solvation model and we compare the results with PCM. The developed approach provides qualitatively correct real-time evolutions and is promising as a general tool to investigate the electron dynamics elicited by external electromagnetic fields for molecules in solution.
Albareda, Guillermo; Abedi, Ali; Tavernelli, Ivano; Rubio, Angel
2016-12-01
It was recently shown [G. Albareda et al., Phys. Rev. Lett. 113, 083003 (2014)], 10.1103/PhysRevLett.113.083003 that within the conditional decomposition approach to the coupled electron-nuclear dynamics, the electron-nuclear wave function can be exactly decomposed into an ensemble of nuclear wave packets effectively governed by nuclear conditional time-dependent potential-energy surfaces (C-TDPESs). Employing a one-dimensional model system, we show that for strong nonadiabatic couplings the nuclear C-TDPESs exhibit steps that bridge piecewise adiabatic Born-Oppenheimer potential-energy surfaces. The nature of these steps is identified as an effect of electron-nuclear correlation. Furthermore, a direct comparison with similar discontinuities recently reported in the context of the exact factorization framework allows us to draw conclusions about the universality of these discontinuities, viz., they are inherent to all nonadiabatic nuclear dynamics approaches based on (exact) time-dependent potential-energy surfaces.
Relativistic spherical plasma waves
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Relativistic GLONASS and geodesy
Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.
2016-12-01
GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.
Bliokh, Konstantin Y
2011-01-01
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, mechanical flywheel, and discuss various fundamental aspects of the phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.
Time Dependent Couplings as Observables in de Sitter Space
Kitamoto, Hiroyuki
2014-01-01
We summarize and expand our investigations concerning the soft graviton effects on microscopic matter dynamics in de Sitter space. The physical couplings receive IR logarithmic corrections which are sensitive to the IR cut-off at the one-loop level. The scale invariant spectrum in the gravitational propagator at the super-horizon scale is the source of the de Sitter symmetry breaking. The quartic scalar, Yukawa and gauge couplings become time dependent and diminish with time. In contrast, the Newton's constant increases with time. We clarify the physical mechanism behind these effects in terms of the conformal mode dynamics in analogy with 2d quantum gravity. We show that they are the inevitable consequence of the general covariance and lead to gauge invariant predictions. We construct a simple model in which the cosmological constant is self-tuned to vanish due to UV-IR mixing effect. We also discuss phenomenological implications such as decaying Dark Energy and SUSY breaking at the Inflation era. The quantu...
Time Dependent Hadronic Modeling of Flat Spectrum Radio Quasars
Diltz, Christopher; Fossati, Giovanni
2015-01-01
We introduce a new time-dependent lepto-hadronic model for blazar emission that takes into account the radiation emitted by secondary particles, such as pions and muons, from photo hadronic interactions. Starting from a baseline parameter set guided by a fit to the spectral energy distribution of the blazar 3C 279, we perform a parameter study to investigate the effects of perturbations of the input parameters to mimic different flaring events to study the resulting lightcurves in the optical, X-ray, high energy (HE: E > 100 MeV) and very-high-energy (VHE: E > 100 GeV) gamma-rays as well as the neutrino emission associated with charged-pion and muon decay. We find that flaring events from an increase in the efficiency of Fermi II acceleration will produce a positive correlation between all bandpasses and a marked plateau in the HE gamma-ray lightcurve. We also predict a distinctive dip in the HE lightcurve for perturbations caused by a change in the proton injection spectral index. These plateaus / dips could...
Density-functional perturbation theory goes time-dependent
Gebauer, Ralph
2008-05-01
Full Text Available The scope of time-dependent density-functional theory (TDDFT is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most. In the static regime, density-functional perturbation theory (DFPT allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix element of the resolvent of the Kohn-Sham Liouvillian super-operator. A DFPT representation of response functions allows one to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is finally conveniently evaluated using a newly developed non-symmetric Lanczos technique, which allows for the calculation of the entire spectrum with a single Lanczos recursion chain. Each step of the chain essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian or, for that matter, as a single time step of a Car-Parrinello molecular dynamics run. The method will be illustrated with a few case molecular applications.
Time-dependent models of dense PDRs with complex molecules
Morata, O
2008-01-01
We present a study of the chemistry of a dense photon-dominated region (PDR) using a time-dependent chemical model. Our major interest is to study the spatial distribution of complex molecules such as hydrocarbons and cyanopolyynes in the cool dense material bordering regions where star formation has taken place. Our standard model uses a homogeneous cloud of density 2x10e4 cm-3 and temperature T=40 K, which is irradiated by a far-ultraviolet radiation field of intermediate intensity, given by X=100. We find that over a range of times unsaturated hydrocarbons (e.g., C2H, C4H, C3H2) have relatively high fractional abundances in the more external layers of the PDR, whereas their abundances in the innermost layers are several orders of magnitudes lower. On the other hand, molecules that are typical of late-time chemistry are usually more abundant in the inner parts of the PDR. We also present results for models with different density, temperature, intensity of the radiation field and initial fractional abundance...
Hot Jupiter Breezes: Time-dependent Outflows from Extrasolar Planets
Owen, James E
2015-01-01
We explore the dynamics of magnetically controlled outflows from Hot Jupiters, where these flows are driven by UV heating from the central star. In these systems, some of the open field lines do not allow the flow to pass smoothly through the sonic point, so that steady-state solutions do not exist in general. This paper focuses on this type of magnetic field configuration, where the resulting flow becomes manifestly time-dependent. We consider the case of both steady heating and time-variable heating, and find the time scales for the corresponding time variations of the outflow. Because the flow cannot pass through the sonic transition, it remains subsonic and leads to so-called breeze solutions. One manifestation of the time variability is that the flow samples a collection of different breeze solutions over time, and the mass outflow rate varies in quasi-periodic fashion. Because the flow is subsonic, information can propagate inward from the outer boundary, which determines, in part, the time scale of the...
Time-dependent cavitation in a viscous fluid
Shneidman, Vitaly A.
2016-12-01
Kinetics of nucleation and growth of empty bubbles in a nonvolatile incompressible fluid under negative pressure is considered within the generalized Zeldovich framework. The transient matched asymptotic solution obtained earlier for predominantly viscous nucleation is used to evaluate the distribution of growing cavities over sizes. Inertial effects described by the Rayleigh-Plesset equation are further included. The distributions are used to estimate the volume occupied by cavities, which leads to increase of pressure and eventual self-quenching of nucleation. Numerical solutions are obtained and compared with analytics. Due to rapid expansion of cavities the conventional separation of the nucleation and the growth time scales can be less distinct, which increases the role of transient effects. In particular, in the case of dominant viscosity a typical power-law tail of the quasistationary distribution is replaced by a time-dependent exponential tail. For fluids of the glycerin type such distributions can extend into the micrometer region, while in low-viscosity liquids (water, mercury) exponential distributions are short lived and are restricted to nanometer scales due to inertial effects.
Time-dependent effect in green synthesis of silver nanoparticles
Darroudi M
2011-04-01
Full Text Available Majid Darroudi1,2, Mansor Bin Ahmad3, Reza Zamiri4, AK Zak5, Abdul Halim Abdullah1,3, Nor Azowa Ibrahim31Advanced Materials and Nanotechnology Laboratory, Institute of Advanced Technology (ITMA, Universiti Putra Malaysia, Selangor, Malaysia; 2Department of Chemistry, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran; 3Department of Chemistry, 4Department of Physics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia; 5Low Dimensional Materials Research Center, Department of Physics, Faculty of Science, University of Malaya, Kuala Lumpur, MalaysiaAbstract: The application of “green” chemistry rules to nanoscience and nanotechnology is very important in the preparation of various nanomaterials. In this work, we successfully developed an eco-friendly chemistry method for preparing silver nanoparticles (Ag-NPs in natural polymeric media. The colloidal Ag-NPs were synthesized in an aqueous solution using silver nitrate, gelatin, and glucose as a silver precursor, stabilizer, and reducing agent, respectively. The properties of synthesized colloidal Ag-NPs were studied at different reaction times. The ultraviolet-visible (UV-vis spectra were in excellent agreement with the obtained nanostructure studies performed by transmission electron microscopy (TEM and their size distributions. The prepared samples were also characterized by X-ray diffraction (XRD and atomic force microscopy (AFM. The use of eco-friendly reagents, such as gelatin and glucose, provides green and economic attributes to this work.Keywords: silver nanoparticles, gelatin, green chemistry, time-dependent effect, ultraviolet-visible spectra
Time-dependent radiation dose simulations during interplanetary space flights
Dobynde, Mikhail; Shprits, Yuri; Drozdov, Alexander; Hoffman, Jeffrey; Li, Ju
2016-07-01
Space radiation is one of the main concerns in planning long-term interplanetary human space missions. There are two main types of hazardous radiation - Solar Energetic Particles (SEP) and Galactic Cosmic Rays (GCR). Their intensities and evolution depend on the solar activity. GCR activity is most enhanced during solar minimum, while the most intense SEPs usually occur during the solar maximum. SEPs are better shielded with thick shields, while GCR dose is less behind think shields. Time and thickness dependences of the intensity of these two components encourage looking for a time window of flight, when radiation intensity and dose of SEP and GCR would be minimized. In this study we combine state-of-the-art space environment models with GEANT4 simulations to determine the optimal shielding, geometry of the spacecraft, and launch time with respect to the phase of the solar cycle. The radiation environment was described by the time-dependent GCR model, and the SEP spectra that were measured during the period from 1990 to 2010. We included gamma rays, electrons, neutrons and 27 fully ionized elements from hydrogen to nickel. We calculated the astronaut's radiation doses during interplanetary flights using the Monte-Carlo code that accounts for the primary and the secondary radiation. We also performed sensitivity simulations for the assumed spacecraft size and thickness to find an optimal shielding. In conclusion, we present the dependences of the radiation dose as a function of launch date from 1990 to 2010, for flight durations of up to 3 years.
Time-dependent histamine release from stored human blood products
Nielsen, Hans Jørgen; Edvardsen, L; Vangsgaard, K;
1996-01-01
storage. Whole blood (six units), plasma-reduced whole blood (six units), and plasma- and buffy coat-reduced (saline-adenine-glucose-mannitol) (SAGM) blood (six units) from unpaid healthy donors were stored in the blood bank for 35 days at 4 degrees C. Plasma histamine and total cell-bound histamine......Perioperative transfusion of whole blood has been shown to amplify trauma-induced immunosuppression, which could be attenuated by perioperative administration of histamine2 receptor antagonists. Supernatants from different blood products were, therefore, analysed for histamine content during.......0 (range 176.0-910.0) nmol/l in whole blood and 475.0 (range 360.0-1560.0) nmol/l in plasma-reduced whole blood, while it was undetectable in SAGM blood. Spontaneous histamine release increased in a time-dependent manner from a median of 6.7 (range 2.2-17.4) nmol/l at the time of storage to 175.0 (range 33...
Experimental quantum cosmology in time-dependent optical media
Westerberg, N; Belgiorno, F; Piazza, F Dalla; Faccio, D
2014-01-01
It is possible to construct artificial spacetime geometries for light by using intense laser pulses that modify the spatiotemporal properties of an optical medium. Here we theoretically investigate experimental possibilities for studying spacetime metrics of the form $\\textrm{d}s^2=c^2\\textrm{d}t^2-\\eta(t)^2\\textrm{d}x^2$. By tailoring the laser pulse shape and medium properties, it is possible to create a refractive index variation $n=n(t)$ that can be identified with $\\eta(t)$. Starting from a perturbative solution to a generalised Hopfield model for the medium described by an $n=n(t)$ we provide estimates for the number of photons generated by the time-dependent spacetime. The simplest example is that of a uniformly varying $\\eta(t)$ that therefore describes the Robertson-Walker metric, i.e. a cosmological expansion. The number of photon pairs generated in experimentally feasible conditions appears to be extremely small. However, large photon production can be obtained by periodically modulating the medium...
Recovery of time-dependent volatility in option pricing model
Deng, Zui-Cha; Hon, Y. C.; Isakov, V.
2016-11-01
In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).
Time-dependence of non-planar accretion discs
Papaloizou, J.C.B. (Queen Mary Coll., London (UK). Dept. of Applied Mathematics); Pringle, J.E. (Amsterdam Univ. (Netherlands). Astronomical Inst.)
1983-03-01
Equations are derived which describe the time-dependence of a viscous, tilted accretion disc subject to external torques. A full hydrodynamical treatment is used and the equations linearized in terms of a small tilt. It is shown that previous attempts at deriving these equations are inadequate due to the inconsistency of some of the assumptions made. The behaviour of a tilted viscous disc is not simple to describe. Viscous forces tend to flatten the disc, but they also produce torques within the disc which induce local precession of disc elements. The main complication is that the horizontal motions induced in the disc by the tilt are resonantly driven so that their magnitude and phase are governed by the viscosity. This leads to the disc being smoothed on a time-scale faster than the usual viscous one. In order to obtain a simple diffusion equation governing the tilt angle ..beta.., it is necessary in a Keplerian disc that the viscosity parameter ..cap alpha.. be greater than the opening angle of the disc (H/R). If this condition is not satisfied consideration must be given to the proper dynamical modes of the disc, and the simple approach to the problem adopted here is inadequate.
Charge transfer in time-dependent density functional theory
Maitra, Neepa T.
2017-10-01
Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.
A time-dependent model for improved biogalvanic tissue characterisation.
Chandler, J H; Culmer, P R; Jayne, D G; Neville, A
2015-10-01
Measurement of the passive electrical resistance of biological tissues through biogalvanic characterisation has been proposed as a simple means of distinguishing healthy from diseased tissue. This method has the potential to provide valuable real-time information when integrated into surgical tools. Characterised tissue resistance values have been shown to be particularly sensitive to external load switching direction and rate, bringing into question the stability and efficacy of the technique. These errors are due to transient variations observed in measurement data that are not accounted for in current electrical models. The presented research proposes the addition of a time-dependent element to the characterisation model to account for losses associated with this transient behaviour. Influence of switching rate has been examined, with the inclusion of transient elements improving the repeatability of the characterised tissue resistance. Application of this model to repeat biogalvanic measurements on a single ex vivo human colon tissue sample with healthy and cancerous (adenocarcinoma) regions showed a statistically significant difference (p 0.05) between tissue types was found when measurements were subjected to the current model, suggesting that the proposed model may allow for improved biogalvanic tissue characterisation. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
Stochastic Time-Dependent Current-Density Functional Theory
D'Agosta, Roberto
2008-03-01
Static and dynamical density functional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current Density Functional theory (S-TDCDFT) [1]: starting from a suitable description of the system dynamics via a stochastic Schrödinger equation [2], we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.[1] M. Di Ventra and R. D'Agosta, Physical Review Letters 98, 226403 (2007)[2] N.G. van Kampen, Stochastic processes in Physics and Chemistry, (North Holland, 2001), 2nd ed.
Gap vortex streets and turbulence in time-dependent streams
Duong, Dan; Tavoularis, Stavros
2016-11-01
Gap vortex streets form in axial flows in highly eccentric annular channels, tightly packed rod bundles and other channels having narrow gap regions flanked by wider ones. The characteristics of these vortices and the flow and turbulence distributions in some of these channels have in the past documented for steady streams; in particular, the vortex generation frequency was found to be proportional to the bulk Reynolds number. The present study extends these findings to both accelerating and decelerating air flows in a large-scale rod bundle, configured as a wind tunnel with a by-pass branch equipped with a controlled movable flap just downstream of the blower. Time-dependent statistical properties in a gap and a subchannel centre were determined by phase-averaging velocity measurements collected with hot-wire anemometers and the time history of the phase-averaged vortex street frequency was determined with the use of a wavelet transform. Contrary to expectations, the results show that deviations of the vortex frequency and other flow characteristics from the corresponding values in steady flows at the same bulk Reynolds number were significant during acceleration and much less so during deceleration. Supported by the Natural Sciences and Engineering Research Council of Canada and the Canadian Nuclear Laboratories.
Translation invariant time-dependent solutions to massive gravity II
Mourad, J.; Steer, D.A., E-mail: mourad@apc.univ-paris7.fr, E-mail: steer@apc.univ-paris7.fr [AstroParticule and Cosmologie, UMR 7164-CNRS, Université Denis Diderot-Paris 7, CEA, Observatoire de Paris, F-75205 Paris Cedex 13 (France)
2014-06-01
This paper is a sequel to JCAP 12 (2013) 004 and is also devoted to translation-invariant solutions of ghost-free massive gravity in its moving frame formulation. Here we consider a mass term which is linear in the vielbein (corresponding to a β{sub 3} term in the 4D metric formulation) in addition to the cosmological constant. We determine explicitly the constraints, and from the initial value formulation show that the time-dependent solutions can have singularities at a finite time. Although the constraints give, as in the β{sub 1} case, the correct number of degrees of freedom for a massive spin two field, we show that the lapse function can change sign at a finite time causing a singular time evolution. This is very different to the β{sub 1} case where time evolution is always well defined. We conclude that the β{sub 3} mass term can be pathological and should be treated with care.
Translation invariant time-dependent solutions to massive gravity II
Mourad, J
2014-01-01
This paper is a sequel to arXiv:1310.6560 [hep-th] and is also devoted to translation-invariant solutions of ghost-free massive gravity in its moving frame formulation. Here we consider a mass term which is linear in the vielbein (corresponding to a $\\beta_3$ term in the 4D metric formulation) in addition to the cosmological constant. We determine explicitly the constraints, and from the initial value formulation show that the time-dependent solutions can have singularities at a finite time. Although the constraints give, as in the $\\beta_1$ case, the correct number of degrees of freedom for a massive spin two field, we show that the lapse function can change sign at a finite time causing a singular time evolution. This is very different to the $\\beta_1$ case where time evolution is always well defined. We conclude that the $\\beta_3$ mass term can be pathological and should be treated with care.
Simple preconditioning for time-dependent density functional perturbation theory
Lehtovaara, Lauri; Marques, Miguel A. L.
2011-07-01
By far, the most common use of time-dependent density functional theory is in the linear-reponse regime, where it provides information about electronic excitations. Ideally, the linear-response equations should be solved by a method that avoids the use of the unoccupied Kohn-Sham states — such as the Sternheimer method — as this reduces the complexity and increases the precision of the calculation. However, the Sternheimer equation becomes ill-conditioned near and indefinite above the first resonant frequency, seriously hindering the use of efficient iterative solution methods. To overcome this serious limitation, and to improve the general convergence properties of the iterative techniques, we propose a simple preconditioning strategy. In our method, the Sternheimer equation is solved directly as a linear equation using an iterative Krylov subspace method, i.e., no self-consistent cycle is required. Furthermore, the preconditioner uses the information of just a few unoccupied states and requires simple and minimal modifications to existing implementations. In this way, convergence can be reached faster and in a considerably wider frequency range than the traditional approach.
Distributed energy storage: Time-dependent tree flow design
Bejan, A.; Ziaei, S.; Lorente, S.
2016-05-01
This article proposes "distributed energy storage" as a basic design problem of distributing energy storage material on an area. The energy flows by fluid flow from a concentrated source to points (users) distributed equidistantly on the area. The flow is time-dependent. Several scenarios are analyzed: sensible-heat storage, latent-heat storage, exergy storage vs energy storage, and the distribution of a finite supply of heat transfer surface between the source fluid and the distributed storage material. The chief conclusion is that the finite amount of storage material should be distributed proportionally with the distribution of the flow rate of heating agent arriving on the area. The total time needed by the source stream to "invade" the area is cumulative (the sum of the storage times required at each storage site) and depends on the energy distribution paths and the sequence in which the users are served by the source stream. Directions for future designs of distributed storage and retrieval are outlined in the concluding section.
Modeling of time dependent subsidence for coal and ore deposits
Ryszard Hejmanowski
2015-01-01
Coal and ore underground mining generates subsidence and deformation of the land surface. Those defor-mations may cause damage to buildings and infrastructures. The environmental impact of subsidence will not be accepted in the future by the society in many countries. Especially there, where the mining regions are densely urbanized, the acceptance of the ground deformations decreases every year. The only solution is to limit the subsidence or its impact on the infrastructure. The first is not rentable for the mining industry, the second depends on the precise subsidence prediction and good preventing management involved in the mining areas. The precision of the subsidence prediction depends strictly on the mathematical model of the deformation phenomenon and on the uncertainty of the input data. The subsidence prediction in the geological conditions of the raw materials used to be made on the basis of numerical modeling or the stochastic models. A modified solution of the stochastic model by Knothe will be presented in the paper. The author focuses on the precise description of the deposit shape and on the time dependent displacements of the rock mass. A two parameters’ time function has been introduced in the algorithm.
Exact Relativistic 'Antigravity' Propulsion
Felber, F S
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Relativistic quantum revivals.
Strange, P
2010-03-26
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
Assessment of total efficiency in adiabatic engines
Mitianiec, W.
2016-09-01
The paper presents influence of ceramic coating in all surfaces of the combustion chamber of SI four-stroke engine on working parameters mainly on heat balance and total efficiency. Three cases of engine were considered: standard without ceramic coating, fully adiabatic combustion chamber and engine with different thickness of ceramic coating. Consideration of adiabatic or semi-adiabatic engine was connected with mathematical modelling of heat transfer from the cylinder gas to the cooling medium. This model takes into account changeable convection coefficient based on the experimental formulas of Woschni, heat conductivity of multi-layer walls and also small effect of radiation in SI engines. The simulation model was elaborated with full heat transfer to the cooling medium and unsteady gas flow in the engine intake and exhaust systems. The computer program taking into account 0D model of engine processes in the cylinder and 1D model of gas flow was elaborated for determination of many basic engine thermodynamic parameters for Suzuki DR-Z400S 400 cc SI engine. The paper presents calculation results of influence of the ceramic coating thickness on indicated pressure, specific fuel consumption, cooling and exhaust heat losses. Next it were presented comparisons of effective power, heat losses in the cooling and exhaust systems, total efficiency in function of engine rotational speed and also comparison of temperature inside the cylinder for standard, semi-adiabatic and full adiabatic engine. On the basis of the achieved results it was found higher total efficiency of adiabatic engines at 2500 rpm from 27% for standard engine to 37% for full adiabatic engine.
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
On criterion of modal adiabaticity
WANG; Ning(
2001-01-01
［1］Pierce, A. D., Extension of the method of normal modes to sound propagation in an almost-stratified medium, J. Acoust.Soc. Am., 1965, 37: 19－27.［2］Wang, D. Z. , Shang, E. C., Underwater Acoustics (in Chinese), Beijing: Science Press, 1981.［3］Zhang Renhe, Li Fenghua, Beam-displacement rya-mode theory of sound propagation in shallow water, Science in China, Ser.A, 1999, 42(7): 739－749.［4］Zhou Jixun, Zhang Xuezhen, Rogers P., Resonance interaction of sound waves with internal solitons in coastal zone, J.Acoust. Soc. Am., 1991, 90: 2042－2054.［5］Shang, E. C., Wang, Y. Y., The impact of mesoscale oceanic structure on global-scale acoustic propagation, in Theoretical and Computational Acoustics (ed. Ding Lee et al. ), Singapore: World Scientific Publishing Co. , 1996, 409－431.［6］Milder, D. M., Ray and wave invariants for SOFAR channel propagation, J. Acoust. Soc. Am., 1969, 46: 1259－1263.［7］Nag l, A., Milder, D. M., Adiabatic mode theory of underwater sound propagation in a range-dependent environment, J.Acoust. Soc. Am., 1978, 63: 739－749.［8］Brekhovskikh, L. M., Waves in Layered Media, 2nd ed., New York: Academic Press Inc., 1973.［9］Brekhovskikh, L. M., Lysanov, Yu., Fundamental of Ocean Acoustics, Ch. 7, Sec. 7.2, Berlin: Springer-Verlag, 1982.［10］Evans, R. B., A coupled mode solution for acoustic propagation in a wave-guide with stepwise depth variations of a penerable bottom, J. Acoust. Soc. A.m., 1983, 74: 188－195.［11］Jensen, F. B., Kuperman, W. A., Porter, M. B. et al., Computational Ocean Acoustics, New York: Springer-Verlag,1992.［12］Wang Ning, Inverse scattering problem for the coupled second order ODE, Journal of The Physical Society of Japan, 1995, 64(12): 4907－4915.
Photoabsorption spectra of (Mo/W)@Au12Si60 clusters from time-dependent DFT calculations
Mokkath, Junais Habeeb
2013-11-14
The electronic structure and photoabsorption spectrum of encapsulated (Mo/W)@Au12Si60 clusters are theoretically investigated via static and time-dependent density functional theory. The photoabsorption spectrum is calculated both at the scalar relativistic and spin-orbit coupling levels. The encapsulated (Mo/W)@Au12 clusters interact with the Si and thus stabilize the Si60 cage. The spin-orbit coupling strongly affects the optical properties of (Mo/W)@Au12 clusters as it leads to a splitting of spectral lines together with an intensity redistribution, whereas the spectra of (Mo/W)@Au12Si60 clusters show hardly any difference. The nanoscale properties thus can be tuned by choosing the endohedral metal atom, while keeping the optical properties unaffected. © 2013 American Chemical Society.
Relativistic gravitational collapse in comoving coordinates: The post-quasistatic approximation
Herrera, L
2010-01-01
A general iterative method proposed some years ago for the description of relativistic collapse, is presented here in comoving coordinates. For doing that we redefine the basic concepts required for the implementation of the method for comoving coordinates. In particular the definition of the post-quasistatic approximation in comoving coordinates is given. We write the field equations, the boundary conditions and a set of ordinary differential equations (the surface equations) which play a fundamental role in the algorithm. As an illustration of the method, we show how to build up a model inspired in the well known Schwarzschild interior solution. Both, the adiabatic and non adiabatic, cases are considered.
Prandtl-Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities
Al Janaideh, M.; Krejčí, P
2012-01-01
We introduce a new class of time dependent hysteresis models by combining the time dependent Prandtl–Ishlinskii model with functional nonlinearities. This combination improves the capability of the time dependent Prandtl–Ishlinskii model to characterize a class of complex time dependent hysteresis nonlinearities in smart actuators. The analytical inversion for the proposed time dependent hysteresis model is also presented in order to extend the inversion algorithm of the inverse time dependen...
Spike-timing dependent plasticity and the cognitive map
Daniel eBush
2010-10-01
Full Text Available Since the discovery of place cells – single pyramidal neurons that encode spatial location – it has been hypothesised that the hippocampus may act as a cognitive map of known environments. This putative function has been extensively modelled using auto-associative networks, which utilise rate-coded synaptic plasticity rules in order to generate strong bi-directional connections between concurrently active place cells that encode for neighbouring place fields. However, empirical studies using hippocampal cultures have demonstrated that the magnitude and direction of changes in synaptic strength can also be dictated by the relative timing of pre- and post- synaptic firing according to a spike-timing dependent plasticity (STDP rule. Furthermore, electrophysiology studies have identified persistent ‘theta-coded’ temporal correlations in place cell activity in vivo, characterised by phase precession of firing as the corresponding place field is traversed. It is not yet clear if STDP and theta-coded neural dynamics are compatible with cognitive map theory and previous rate-coded models of spatial learning in the hippocampus. Here, we demonstrate that an STDP rule based on empirical data obtained from the hippocampus can mediate rate-coded Hebbian learning when pre- and post- synaptic activity is stochastic and has no persistent sequence bias. We subsequently demonstrate that a spiking recurrent neural network that utilises this STDP rule, alongside theta-coded neural activity, allows the rapid development of a cognitive map during directed or random exploration of an environment of overlapping place fields. Hence, we establish that STDP and phase precession are compatible with rate-coded models of cognitive map development.
Time-dependent cortical activation in voluntary muscle contraction.
Yang, Qi; Wang, Xiaofeng; Fang, Yin; Siemionow, Vlodek; Yao, Wanxiang; Yue, Guang H
2011-01-01
This study was to characterize dynamic source strength changes estimated from high-density scalp electroencephalogram (EEG) at different phases of a submaximal voluntary muscle contraction. Eight healthy volunteers performed isometric handgrip contractions of the right arm at 20% maximal intensity. Signals of the handgrip force, electromyography (EMG) from the finger flexor and extensor muscles and 64-channel EEG were acquired simultaneously. Sources of the EEG were analyzed at 19 time points across preparation, execution and sustaining phases of the handgrip. A 3-layer boundary element model (BEM) based on the MNI (Montréal Neurological Institute) brain MRI was used to overlay the sources. A distributed current density model, LORETA L1 norm method was applied to the data that had been processed by independent component analysis (ICA). Statistical analysis based on a mixed-effects polynomial regression model showed a significant and consistent time-dependent non-linear source strength change pattern in different phases of the handgrip. The source strength increased at the preparation phase, peaked at the force onset time and decreased in the sustaining phase. There was no significant difference in the changing pattern of the source strength among Brodmann's areas 1, 2, 3, 4, and 6. These results show, for the first time, a high time resolution increasing-and-decreasing pattern of activation among the sensorimotor regions with the highest activity occurs at the muscle activity onset. The similarity in the source strength time courses among the cortical centers examined suggests a synchronized parallel function in controlling the motor activity.
Solving the time dependent vehicle routing problem by metaheuristic algorithms
Johar, Farhana; Potts, Chris; Bennell, Julia
2015-02-01
The problem we consider in this study is Time Dependent Vehicle Routing Problem (TDVRP) which has been categorized as non-classical VRP. It is motivated by the fact that multinational companies are currently not only manufacturing the demanded products but also distributing them to the customer location. This implies an efficient synchronization of production and distribution activities. Hence, this study will look into the routing of vehicles which departs from the depot at varies time due to the variation in manufacturing process. We consider a single production line where demanded products are being process one at a time once orders have been received from the customers. It is assumed that order released from the production line will be loaded into scheduled vehicle which ready to be delivered. However, the delivery could only be done once all orders scheduled in the vehicle have been released from the production line. Therefore, there could be lateness on the delivery process from awaiting all customers' order of the route to be released. Our objective is to determine a schedule for vehicle routing that minimizes the solution cost including the travelling and tardiness cost. A mathematical formulation is developed to represent the problem and will be solved by two metaheuristics; Variable Neighborhood Search (VNS) and Tabu Search (TS). These algorithms will be coded in C ++ programming and run using 56's Solomon instances with some modification. The outcome of this experiment can be interpreted as the quality criteria of the different approximation methods. The comparison done shown that VNS gave the better results while consuming reasonable computational efforts.
Time-dependent viscoelastic properties along rat small intestine
James B Smith; Jing-Bo Zhao; Yan-Ling Dou; Hans Gregersen
2005-01-01
AIM: To measure the time-dependent (viscoelastic)behavior in the change of the small intestinal opening angle and to test how well the behavior could be described by the Kelvin model for a standard linear solid.METHODS: Segments from the duodenum, jejunum, and ileum were harvested from 10 female Wistar rats and the luminal diameter, wall thickness, and opening angleover time (θ(t)) were measured from rings cut from thesesegments.RESULTS: Morphometric variations were found along thesmall intestine with an increase in luminal area and adecrease in wall thickness from the duodenum to theileum. The opening angle obtained after 60 min washighest in the duodenum (220.8±12.9°) and decreasedalong the length of the intestine to 143.9±8.9° in the jejunum and 151.4±9.4° in the ileum. The change ofopening angle as a function of time, fitted well to theKelvin model using the equation θ(t)/θo = [1-ηexp (-λt)]after the ring was cut. The computed creep rate λ did notdiffer between the segments. Compared to constantcalculated from pig aorta and coronary artery, it showedthat α agreed well (within 5%), η was three times largerthan that for vascular tissue, and λ ranged ±40% from the value of the pig coronary artery and was a third of the value of pig aorta.CONCLUSION: The change of opening angle over timefor all the small intestine segments fits well to the standardlinear spring-dashpot model. This viscoelastic constantof the rat small intestine is fairly homogenous along itslength. The data obtained from this study add to a baseset of biomechanical data on the small intestine andprovide a reference state for comparison to other tissues,diseased intestinal tissue or intestinal tissue exposed todrugs or chemicals.
A history of spike-timing-dependent plasticity
Henry eMarkram
2011-08-01
Full Text Available How learning and memory is achieved in the brain is a central question in neuroscience research. Key to today’s research into information storage in the brain is the concept of synaptic plasticity, a notion that has been heavily influenced by Donald Hebb’s 1949 postulate. Hebb conjectured that repeatedly and persistently coactive cells should increase connective strength among populations of interconnected neurons as a means of storing a memory trace, also known as an engram. Hebb certainly was not the first to make such a conjecture, as we show in this history. Nevertheless, literally thousands of studies into the classical frequency-dependent paradigm of cellular learning rules were directly inspired by the Hebbian postulate. But in more recent years, a novel concept in cellular learning has emerged, where temporal order instead of frequency is emphasized. This new learning paradigm — known as Spike-Timing-Dependent Plasticity, or STDP — has rapidly gained tremendous interest, perhaps because of its combination of elegant simplicity, biological plausibility, and computational power. But what are the roots of today’s STDP concept? Here, we discuss several centuries of diverse thinking, beginning with philosophers such as Aristotle, Locke and Ribot, traversing e.g. Lugaro’s plasticità and Rosenblatt’s Perceptron, and culminating with the discovery of STDP. We highlight interactions between theoretical and experimental fields, showing how discoveries sometimes occurred in parallel, seemingly without much knowledge of the other field, and sometimes via concrete back-and-forth communication. We point out where the future directions may lie, which includes interneuron STDP, the functional impact of STDP, its mechanisms and its neuromodulatory regulation, and the linking of STDP to the developmental formation and continuous plasticity of neuronal networks.
Time-dependent CP violation in B decays at Belle
Santelj, Luka
2013-01-01
Using the full data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we present three recent measurements of time-dependent CP violation in $B$ decays, and a measurement of branching fraction of the $B^0\\to\\rho^0\\rho^0$ decay. We studied $B\\to\\omega K$ decays and measured the values of CP violation parameters in $B^0\\to\\omega K^0_S$ to be $A_{\\omega K^0_S} =-0.36\\pm 0.19(stat)\\pm 0.05(syst)$ and $S_{\\omega K^0_S}= +0.91\\pm 0.32 \\pm 0.05 $, which gives the first evidence of CP violation in this decay. In addition, we measured the direct CP violation in $B^+\\to\\omega K^+$ to be $A_{CP} (B^+ \\to \\omega K^+)=-0.03\\pm 0.04 \\pm 0.01$, and two branching fractions $B(B^0 \\to \\omega K^0)=(4.5\\pm 0.4\\pm 0.3) \\times 10^{-6}$ and $B(B^+ \\to \\omega K^+)=(6.8\\pm 0.4 \\pm 0.4) \\times 10^{-6}$ (preliminary). From the measurement of CP violation parameters in the $B^0\\to\\eta'K^0$ decay we obtain $S_{\\eta'K^0} = 0.68 \\pm 0.07\\pm 0.03$ and $A_{\\eta'K^0} = +0.03 \\pm 0.05\\pm 0.04$ (prelimin...
Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes
Agostini, Federica; Gross, E K U
2015-01-01
In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schroedinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics.
The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems
Ausländer, O M; Auslaender, Ophir M.; Fishman, Shmuel
1999-01-01
The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time ...
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.
Zamstein, Noa; Tannor, David J
2012-12-14
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.
Relativistic and quantum electrodynamics effects in the helium pair potential.
Przybytek, M; Cencek, W; Komasa, J; Łach, G; Jeziorski, B; Szalewicz, K
2010-05-01
The helium pair potential was computed including relativistic and quantum electrodynamics contributions as well as improved accuracy adiabatic ones. Accurate asymptotic expansions were used for large distances R. Error estimates show that the present potential is more accurate than any published to date. The computed dissociation energy and the average R for the (4)He(2) bound state are 1.62+/-0.03 mK and 47.1+/-0.5 A. These values can be compared with the measured ones: 1.1(-0.2)(+0.3) mK and 52+/-4 A [R. E. Grisenti, Phys. Rev. Lett. 85, 2284 (2000)].
A Signed Particle Formulation of Non-Relativistic Quantum Mechanics
Sellier, Jean Michel
2015-01-01
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schroedinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the val...
Wigner phase space distribution via classical adiabatic switching
Bose, Amartya [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Makri, Nancy [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801 (United States)
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
Rapid adiabatic passage without level crossing
Rangelov, A A; Shore, B W
2009-01-01
We present a method for achieving complete population transfer in a two-state quantum system via adiabatic time evolution in which, contrary to conventional rapid adiabatic passage produced by chirped pulses, there occurs no crossing of diabatic energy curves: there is no sign change of the detuning. Instead, we use structured pulses, in which, in addition to satisfying conditions for adiabatic evolution, there occurs a sign change of the Rabi frequency when the detuning is zero. We present simulations that offer simple geometrical interpretation of the two-dimensional motion of the Bloch vector for this system, illustrating how both complete population inversion and complete population return occur for different choices of structured pulses.
Adiabatic optimization versus diffusion Monte Carlo methods
Jarret, Michael; Jordan, Stephen P.; Lackey, Brad
2016-10-01
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k -SAT at k =2 ,3 ,4 .
Nonadiabatic exchange dynamics during adiabatic frequency sweeps.
Barbara, Thomas M
2016-04-01
A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging.
Energy efficiency of adiabatic superconductor logic
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-01-01
Adiabatic superconductor logic (ASL), including adiabatic quantum-flux-parametron (AQFP) logic, exhibits high energy efficiency because its bit energy can be decreased below the thermal energy through adiabatic switching operations. In the present paper, we present the general scaling laws of ASL and compare the energy efficiency of ASL with those of other energy-efficient logics. Also, we discuss the minimum energy-delay product (EDP) of ASL at finite temperature. Our study shows that there is a maximum temperature at which the EDP can reach the quantum limit given by ħ/2, which is dependent on the superconductor material and the Josephson junction quality, and that it is reasonable to operate ASL at cryogenic temperatures in order to achieve an EDP that approaches ħ/2.
Quantum Drude friction for time-dependent density functional theory
Neuhauser, Daniel; Lopata, Kenneth
2008-10-01
way to very simple finite grid description of scattering and multistage conductance using time-dependent density functional theory away from the linear regime, just as absorbing potentials and self-energies are useful for noninteracting systems and leads.
Complexity of the Quantum Adiabatic Algorithm
Hen, Itay
2013-01-01
The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.
Adiabatic Quantum Computation: Coherent Control Back Action
Goswami, Debabrata
2013-01-01
Though attractive from scalability aspects, optical approaches to quantum computing are highly prone to decoherence and rapid population loss due to nonradiative processes such as vibrational redistribution. We show that such effects can be reduced by adiabatic coherent control, in which quantum interference between multiple excitation pathways is used to cancel coupling to the unwanted, non-radiative channels. We focus on experimentally demonstrated adiabatic controlled population transfer experiments wherein the details on the coherence aspects are yet to be explored theoretically but are important for quantum computation. Such quantum computing schemes also form a back-action connection to coherent control developments. PMID:23788822
Adiabatic hyperspherical analysis of realistic nuclear potentials
Daily, K M; Greene, Chris H
2015-01-01
Using the hyperspherical adiabatic method with the realistic nuclear potentials Argonne V14, Argonne V18, and Argonne V18 with the Urbana IX three-body potential, we calculate the adiabatic potentials and the triton bound state energies. We find that a discrete variable representation with the slow variable discretization method along the hyperradial degree of freedom results in energies consistent with the literature. However, using a Laguerre basis results in missing energy, even when extrapolated to an infinite number of basis functions and channels. We do not include the isospin $T=3/2$ contribution in our analysis.
On adiabatic invariant in generalized Galileon theories
Ema, Yohei; Mukaida, Kyohei; Nakayama, Kazunori
2015-01-01
We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is useful in estimating the expansion law of the universe and also the particle production rate due to the oscillation of the Hubble parameter.
Quench propagation analysis in adiabatic superconducting windings
Ishiyama, A.; Matsumura, H.; Takita, W. (Dept. of Electrical Engineering, Waseda Univ., Tokyo (JP)); Iwasa, Y (Massachusetts Inst. of Tech., Cambridge, MA (United States). Francis Bitter National Magnet Lab.)
1991-03-01
This paper reports the basic postulate of the author's quench simulation code, developed to analyze normal-zone propagation in adiabatic magnets which is the code's computation may be immensely simplified without sacrifice in accuracy by aggregating all thermal properties of the winding affecting normal-zone propagation into a single parameter of the transverse quench velocity. In order to verify this postulate, a finite element method (FEM) analysis has been applied to solve the temporal and spatial evolution of temperature within a section of an adiabatic magnet winding.
Pueyo, Adrián Gómez; Castro, Alberto
2016-01-01
We present an implementation of optimal control theory for the first-principles non-adiabatic Ehrenfest Molecular Dynamics model, which describes a condensed matter system by considering classical point-particle nuclei, and quantum electrons, handled in our case with time-dependent density-functional theory. The scheme is demonstrated by optimizing the Coulomb explosion of small Sodium clusters: the algorithm is set to find the optimal femtosecond laser pulses that disintegrate the clusters, for a given total pulse duration, fluence, and cut-off frequency. We describe the numerical details and difficulties of the methodology.
An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances
Faraj, A; Nier, F
2010-01-01
This paper is concerned with a linearized version of the transport problem where the Schr\\"{o}dinger-Poisson operator is replaced by a non-autonomous Hamiltonian, slowly varying in time. We consider an explicitly solvable model where a semiclassical island is described by a flat potential barrier, while a time dependent 'delta' interaction is used as a model for a single quantum well. Introducing, in addition to the complex deformation, a further modification formed by artificial interface conditions, we give a reduced equation for the adiabatic evolution of the sheet density of charges accumulating around the interaction point.
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
Relativistic Quantum Communication
Hosler, Dominic
2013-01-01
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tend...
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Handbook of relativistic quantum chemistry
Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering
2017-03-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.
Relativistic electronic dressing
Attaourti, Y
2002-01-01
We study the effects of the relativistic electronic dressing in laser-assisted electron-hydrogen atom elastic collisions. We begin by considering the case when no radiation is present. This is necessary in order to check the consistency of our calculations and we then carry out the calculations using the relativistic Dirac-Volkov states. It turns out that a simple formal analogy links the analytical expressions of the differential cross section without laser and the differential cross section in presence of a laser field.
Fabian, A C; Parker, M L
2014-01-01
Broad emission lines, particularly broad iron-K lines, are now commonly seen in the X-ray spectra of luminous AGN and Galactic black hole binaries. Sensitive NuSTAR spectra over the energy range of 3-78 keV and high frequency reverberation spectra now confirm that these are relativistic disc lines produced by coronal irradiation of the innermost accretion flow around rapidly spinning black holes. General relativistic effects are essential in explaining the observations. Recent results are briefly reviewed here.
Relativistic Rotating Vector Model
Lyutikov, Maxim
2016-01-01
The direction of polarization produced by a moving source rotates with the respect to the rest frame. We show that this effect, induced by pulsar rotation, leads to an important correction to polarization swings within the framework of rotating vector model (RVM); this effect has been missed by previous works. We construct relativistic RVM taking into account finite heights of the emission region that lead to aberration, time-of-travel effects and relativistic rotation of polarization. Polarizations swings at different frequencies can be used, within the assumption of the radius-to-frequency mapping, to infer emission radii and geometry of pulsars.
Moulopoulos, Konstantinos, E-mail: cos@ucy.ac.c [University of Cyprus, Department of Physics, 1678 Nicosia (Cyprus)
2010-09-03
We show that the standard Dirac phase factor is not the only solution of the usual gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac phases (spatial or temporal integrals over potentials), also contains terms of classical fields that act nonlocally (in spacetime) on the local solutions of the time-dependent Schroedinger equation. As a result, the phases of wavefunctions in the Schroedinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in specific ways that are fully explored. These contributions go beyond the usual Aharonov-Bohm effects (magnetic or electric). (i) Application to cases of particles passing through full static magnetic or electric fields leads to cancellations of Aharonov-Bohm phases at the observation point; these cancellations are linked to behaviors at the semiclassical level (i.e. the old Werner and Brill experimental observations, or their 'electric analogs'-or to more recent reports of Batelaan and Tonomura) but are shown to be far more general (true not only for narrow wavepackets but also for completely delocalized (spread-out) quantum states). By using these cancellations, certain previously unnoticed sign-errors in the literature are corrected. (ii) Application to time-dependent situations provides a remedy for erroneous results in the literature (concerning an uncritical use of Dirac phase factors) and leads to phases that contain an Aharonov-Bohm part and a field-nonlocal part: their competition is shown to recover relativistic causality in earlier 'paradoxes' (such as the van Kampen thought-experiment), while a more general consideration indicates that the temporal nonlocalities found here demonstrate in part a causal propagation of phases of quantum mechanical wavefunctions in the Schroedinger picture. This may open a new and direct way to
The special relativistic shock tube
Thompson, Kevin W.
1986-01-01
The shock-tube problem has served as a popular test for numerical hydrodynamics codes. The development of relativistic hydrodynamics codes has created a need for a similar test problem in relativistic hydrodynamics. The analytical solution to the special relativistic shock-tube problem is presented here. The relativistic shock-jump conditions and rarefaction solution which make up the shock tube are derived. The Newtonian limit of the calculations is given throughout.
Improving the positive feedback adiabatic logic familiy
J. Fischer
2004-01-01
Full Text Available Positive Feedback Adiabatic Logic (PFAL shows the lowest energy dissipation among adiabatic logic families based on cross-coupled transistors, due to the reduction of both adiabatic and non-adiabatic losses. The dissipation primarily depends on the resistance of the charging path, which consists of a single p-channel MOSFET during the recovery phase. In this paper, a new logic family called Improved PFAL (IPFAL is proposed, where all n- and pchannel devices are swapped so that the charge can be recovered through an n-channel MOSFET. This allows to decrease the resistance of the charging path up to a factor of 2, and it enables a significant reduction of the energy dissipation. Simulations based on a 0.13µm CMOS process confirm the improvements in terms of power consumption over a large frequency range. However, the same simple design rule, which enables in PFAL an additional reduction of the dissipation by optimal transistor sizing, does not apply to IPFAL. Therefore, the influence of several sources of dissipation for a generic IPFAL gate is illustrated and discussed, in order to lower the power consumption and achieve better performance.
Semi adiabatic theory of seasonal Markov processes
Talkner, P. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1999-08-01
The dynamics of many natural and technical systems are essentially influenced by a periodic forcing. Analytic solutions of the equations of motion for periodically driven systems are generally not known. Simulations, numerical solutions or in some limiting cases approximate analytic solutions represent the known approaches to study the dynamics of such systems. Besides the regime of weak periodic forces where linear response theory works, the limit of a slow driving force can often be treated analytically using an adiabatic approximation. For this approximation to hold all intrinsic processes must be fast on the time-scale of a period of the external driving force. We developed a perturbation theory for periodically driven Markovian systems that covers the adiabatic regime but also works if the system has a single slow mode that may even be slower than the driving force. We call it the semi adiabatic approximation. Some results of this approximation for a system exhibiting stochastic resonance which usually takes place within the semi adiabatic regime are indicated. (author) 1 fig., 8 refs.
Startup of an industrial adiabatic tubular reactor
Verwijs, J.W.; Berg, van den H.; Westerterp, K.R.
1992-01-01
The dynamic behaviour of an adiabatic tubular plant reactor during the startup is demonstrated, together with the impact of a feed-pump failure of one of the reactants. A dynamic model of the reactor system is presented, and the system response is calculated as a function of experimentally-determine
A Diffusion Equation for Quantum Adiabatic Systems
Jain, S R
1998-01-01
For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion.
Quantum Pumping and Adiabatic Transport in Nanostructures
Wakker, G.M.M.
2011-01-01
This thesis consists of a theoretical exploration of quantum transport phenomena and quantum dynamics in nanostructures. Specifically, we investigate adiabatic quantum pumping of charge in several novel types of nanostructures involving open quantum dots or graphene. For a bilayer of graphene we fin
Xue, Yuting; Mishra, Brijes; Gao, Danqing
2017-09-01
Field observations have demonstrated that roof failure occurs spatially in a mine from the time of excavation. It is suspected that time-dependent deformation propagates failure in the rock mass. In this paper, the relaxation test is used to study variation in the time-dependent property of rock and the consequent effect on time-dependent roof failure. This investigation uses a numerical simulation in 3DEC. The relaxation equation is developed from Burgers model. Variations in the time-dependent property in the post-failure region show negligible variation and, therefore, are averaged to represent the time-dependent property of the failed rock. Finally, these parameters are used in the numerical simulation of underground excavations. Two groups of parameters are used to represent the time-dependent property for pre- and post-failure conditions. FISH functions within 3DEC are used to monitor the state of each zone. Once failure is detected, the parameters are changed to the values corresponding to failed rock. The results show that the new relaxation model accurately predicts the time-dependent propagation of the failure zone. The variation of the time-dependent parameters significantly affects the rock mass behavior and roof convergence.
Adiabatic limits,vanishing theorems and the noncommutative residue
无
2009-01-01
In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity
HUANG Bo-Wen; GU Zhi-Yu; QIAN Shang-Wu
2003-01-01
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity isobtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
Adiabatic and Non-adiabatic quenches in a Spin-1 Bose Einstein Condensate
Boguslawski, Matthew; Hebbe Madhusudhana, Bharath; Anquez, Martin; Robbins, Bryce; Barrios, Maryrose; Hoang, Thai; Chapman, Michael
2016-05-01
A quantum phase transition (QPT) is observed in a wide range of phenomena. We have studied the dynamics of a spin-1 ferromagnetic Bose-Einstein condensate for both adiabatic and non-adiabatic quenches through a QPT. At the quantum critical point (QCP), finite size effects lead to a non-zero gap, which makes an adiabatic quench possible through the QPT. We experimentally demonstrate such a quench, which is forbidden at the mean field level. For faster quenches through the QCP, the vanishing energy gap causes the reaction timescale of the system to diverge, preventing the system from adiabatically following the ground state. We measure the temporal evolution of the spin populations for different quench speeds and determine the exponents characterizing the scaling of the onset of excitations, which are in good agreement with the predictions of Kibble-Zurek mechanism.
Description of $^{178}$Hf$^{m2}$ in the constrained relativistic mean field theory
Wei, Zhang; Shuang-Quan, Zhang
2009-01-01
The properties of the ground state of $^{178}$Hf and the isomeric state $^{178}$Hf$^{m2}$ are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of $^{178}$Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with $K^\\pi=16^+$ is found to be $\
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.
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
A trapped ion with time-dependent frequency interaction with a laser field
MartInez, J M Vargas; Moya-Cessa, H [INAOE, Apartado Postal 51 y 216, 72000 Puebla (Mexico)
2004-06-01
We analyse the problem of a trapped ion with time-dependent frequency interacting with a laser field. By using a set of unitary time-dependent transformations we show that this system is equivalent to the interaction between a quantized field and a double level with time-dependent interaction parameters. In passing, we show that in the on-resonance case different vibrational transitions may be achieved by using time-dependent parameters.
Exact solution of a quantum forced time-dependent harmonic oscillator
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Non-Hermitian Swanson model with a time-dependent metric
Fring, Andreas; Moussa, Miled H. Y.
2016-10-01
We provide further nontrivial solutions to the recently proposed time-dependent Dyson and quasi-Hermiticity relation. Here, we solve them for the generalized version of the non-Hermitian Swanson Hamiltonian with time-dependent coefficients. We construct time-dependent solutions by employing the Lewis-Riesenfeld method of invariants and discuss concrete physical applications of our results.
Exact solutions of Feinberg–Horodecki equation for time-dependent anharmonic oscillator
P K Bera; Tapas Sil
2013-01-01
In this work, an alternative treatment known as Nikiforov–Uvarov (NU) method is proposed to find the exact solutions of the Feinberg–Horodecki equation for the time-dependent potentials. The present procedure is illustrated with two examples: (1) time-dependent Wei Hua oscillator, (2) time-dependent Manning–Rosen potential.
Hojman Exact Invariants and Adiabatic Invariants of Hamilton System
无
2007-01-01
The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higherorder adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of the results.
Non-adiabatic geometrical quantum gates in semiconductor quantum dots
Solinas, P; Zanghì, N; Rossi, F; Solinas, Paolo; Zanardi, Paolo; Zanghì, Nino; Rossi, Fausto
2003-01-01
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implemented
Relativistic cosmology; Cosmologia Relativista
Bastero-Gil, M.
2015-07-01
Relativistic cosmology is nothing but the study of the evolution of our universe expanding from the General Theory of Relativity, which describes the gravitational interaction at any scale and given its character far-reaching is the force that dominate the evolution of the universe. (Author)
Relativistic impulse dynamics.
Swanson, Stanley M
2011-08-01
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.
Antippa, Adel F.
2009-01-01
We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…
Relativistic length agony continued
Redžić D.V.
2014-01-01
Full Text Available We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redžić 2008b, we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the ‘pole in a barn’ paradox. [Projekat Ministarstva nauke Republike Srbije, br. 171028
Frontiers in Relativistic Celestial Mechanics, Vol. 1. Theory
Kopeikin, Sergei
2014-10-01
Relativistic celestial mechanics - investigating the motion celestial bodies under the influence of general relativity - is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics - starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This first volume of a two-volume series is concerned with theoretical foundations such as post-Newtonian solutions to the two-body problem, light propagation through time-dependent gravitational fields, as well as cosmological effects on the movement of bodies in the solar systems. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg - one of the pioneers in modern relativistic celestial mechanics. Contributions include: M. Soffel: On the DSX-framework T. Damour: The general relativistic two body problem G. Schaefer: Hamiltonian dynamics of spinning compact binaries through high post-Newtonian approximations A. Petrov and S. Kopeikin: Post-Newtonian approximations in cosmology T. Futamase: On the backreaction problem in cosmology Y. Xie and S. Kopeikin: Covariant theory of the post-Newtonian equations of motion of extended bodies S. Kopeikin and P. Korobkov: General relativistic theory of light propagation in multipolar gravitational fields
Strong-field relativistic processes in highly charged ions
Postavaru, Octavian
2010-12-08
In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part, we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic phenomena and nuclear effects by applying coherent light with x-ray frequencies. Atomic dipole or multipole moments may be determined to unprecedented accuracy by measuring the interference-narrowed fluorescence spectrum. Furthermore, we investigate the level structure of heavy hydrogenlike ions in laser beams. Interaction with the light field leads to dynamic shifts of the electronic energy levels, which is relevant for spectroscopic experiments. We apply a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the dipole approximation and takes into account non-dipole effects of retardation and interaction with the magnetic field components of the laser beam. We predicted cross sections for the inter-shell trielectronic recombination (TR) and quadruelectronic recombination processes which have been experimentally confirmed in electron beam ion trap measurements, mainly for C-like ions, of Ar, Fe and Kr. For Kr{sup 30}+, inter-shell TR contributions of nearly 6% to the total resonant photorecombination rate were found. (orig.)
Calculating excitation energies by extrapolation along adiabatic connections
Rebolini, Elisa; Teale, Andrew M; Helgaker, Trygve; Savin, Andreas
2015-01-01
In this paper, an alternative method to range-separated linear-response time-dependent density-functional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially interacting system around the physical system, we use an extrapolation scheme to improve the estimation of the energies of the physical system at an intermediate point of the range-separated or linear adiabatic connection where either the electron--electron interaction is scaled or only the long-range part of the Coulomb interaction is included. The extrapolation scheme is first applied to the range-separated energies of the helium and beryllium atoms and of the hydrogen molecule at its equilibrium and stretched geometries. It improves significantly the convergence rate of the energies toward their exact limit with respect to the range-separation parameter. The range...
Bhargava, Kapilesh, E-mail: kapil_66@barc.gov.i [Architecture and Civil Engineering Division, Bhabha Atomic Research Center, Trombay, Mumbai 400 085 (India); Mori, Yasuhiro [Graduate School of Environmental Studies, Nagoya University, Nagoya 464-8603 (Japan); Ghosh, A.K. [Reactor Safety Division, Bhabha Atomic Research Center, Trombay, Mumbai 400 085 (India)
2011-05-15
This paper forms the third part of a study which addresses time-dependent reliability analyses of reinforced concrete (RC) beams affected by reinforcement corrosion. Parts 1 and 2 of the reliability study are presented in companion papers. Part 1 of the reliability study presents evaluation of probabilistic descriptions for time-dependent strengths of a typical simply supported corrosion-affected RC beam. These probabilistic descriptions, i.e., mean and coefficient of variation (c.o.v.) for the time-dependent strengths are presented for two limit states: (a) flexural failure; and (b) shear failure. Part 2 of the reliability study presents evaluation of time-dependent failure probability for the considered RC beam by utilizing the information on probabilistic descriptions for time-dependent strengths available in Part 1. Evaluation of time-dependent failure probability considering the variability in time-dependent strengths and/or time-dependent degradation functions is also presented. This paper investigates the effects of time to corrosion initiation and its variability on failure probability of the same RC beam presented in companion papers. By considering variability in the identified variables that could affect the expected time of first corrosion, simple estimations are presented for mean time to corrosion initiation and variability associated with time to corrosion initiation. Evaluation of time-dependent failure probability for the beam is presented by considering estimated probabilistic descriptions, i.e., mean and c.o.v. for time to corrosion initiation. Parametric analyses show that failure probability for the beam is sensitive to the mode of strength degradation and time to corrosion initiation.
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Non-adiabatic perturbations in multi-component perfect fluids
Koshelev, N.A., E-mail: koshna71@inbox.ru [Ulyanovsk State University, Leo Tolstoy str 42, 432970 (Russian Federation)
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Scaling-up quantum heat engines efficiently via shortcuts to adiabaticity
Beau, M; del Campo, A
2016-01-01
The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inv...
Scaling-Up Quantum Heat Engines Efficiently via Shortcuts to Adiabaticity
Mathieu Beau
2016-04-01
Full Text Available The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction, and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions that includes non-interacting and hard-core bosons as limiting cases.
Adiabatic quantum simulation of quantum chemistry.
Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-10-13
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
Adiabatic Quantum Optimization for Associative Memory Recall
Hadayat eSeddiqi
2014-12-01
Full Text Available Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO. Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.