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Appraisal of practicality of first order perturbation-iteration method /FOPIM/, fast converging perturbation method for solving time independent quantum mechanical problems
A time-independent quantum mechanical approach to the calculation of photodissociation cross sections is developed. The method is based on the use of a discrete variable representation and the application of absorbing boundary conditions. Both total photodissociation cross sections and partial cross sections (hence product state distributions) are obtained using the same basic technique, but the calculation is particularly efficient when only the former quantity is required. The method is applied to the photodissociation of HCl(+) for which accurate potential energy curves and dipole moment functions are available, to the photodissociation of ClCN which is a direct process, involving a single excited electrosonic state, and to the photodissociation of ICN, which involves several strongly coupled excited electronic states.
It is suggested that the Planck h = m(sub k)c Lambda(sub k) and the Boltzmann k = m(sub k)c nu(sub k)Constants have stochastic foundation. It is further suggested that a body of fluid at equilibrium is composed of a spectrum of molecular clusters (energy levels) the size of which are governed by the Maxwell-Boltzmann distribution function. Brownian motions are attributed to equilibrium between suspensions and molecular clusters. Atomic (molecular) transition between different size atomic- (molecular-) clusters (energy levels) is shown to result in emission/absorption of energy in accordance with Bohr's theory of atomic spectra. Physical space is identified as a tachyonic fluid that is Dirac's stochastic ether or de Broglie's hidden thermostat. Compressibility of physical space, in accordance with Planck's compressible ether, is shown to result in the Lorentz-Fitzgerald contraction, thus providing a causal explanation of relativistic effect in accordance with the perceptions of Poincare and Lorentz. The invariant Schrodinger equation is derived from the invariant Bernoulli equation for incompressible potential flow. Following Heisenberg a temporal uncertainty relation is introduced as Delta(nu(sub Beta)) Delta(Rho(sub Beta)) > = k.
The N + N2 exchange rate is calculated using a time-dependent quantum dynamics method on a newly determined ab initio potential energy surface (PES) for the ground A" state. This ab initio PES shows a double barrier feature in the interaction region with the barrier height at 47.2 kcal/mol, and a shallow well between these two barriers, with the minimum at 43.7 kcal/mol. A quantum dynamics wave packet calculation has been carried out using the fitted PES to compute the cumulative reaction probability for the exchange reaction of N + N2(J=O). The J - K shift method is then employed to obtain the rate constant for this reaction. The calculated rate constant is compared with experimental data and a recent quasi-classical calculation using a LEPS PES. Significant differences are found between the present and quasiclassical results. The present rate calculation is the first accurate 3D quantal dynamics study for N + N2 reaction system and the ab initio PES reported here is the first such surface for N3.
Exploration of the Solar System with automated spacecraft that are more than ten astronomical units (1 AU = 149,597,870.691 km) from earth requires very large antennae employing extremely sensitive receivers. A key figure of merit in the specification of the spacecraft-to-earth telecommunications link is the ratio of the antenna gain to operatio nal noise temperature (G/Top) of the system. The Deep Space Network (DSN) receivers are cryogenic, low-noise amplifiers (LNAs) which addres s the need to maintain Top as low as technology permits. Historicall y, the extra-ordinarily sensitive receive systems operated by the DSN have required ctyogenically cooled, ruby masers, operating at a physi cal temperature near the boiling point of helium, as the LNA. Althoug h masers continue to be used today, they are hand crafted at JPL and expensive to manufacture and maintain. Recent advances in the developm ent of indium phosphide (InP) based high electron mobility transistor s (HEMTs) combined with cryogenic cooling near the boiling point of h ydrogen have made this alternate technology comparable with and a fraction of the cost of maser technology. InP HEMT LNA modules are demons trating noise temperatures less than ten times the quantum noise limi t (10hf/k) from 1 to 100 GHz. To date, the lowest noise LNA modules developed for the DSN have demonstrated noise temperatures of 3.5 K and 8.5 K at 8.5 K at 32 GHz, respectively. Front-end receiver packages employing these modules have demonstrated operating system noise temperatures of 17 K at 8.4 GHz (on a 70m antenna at zenith) and 39 K at 3 2 GHz (on a 34m antenna at zenith). The development and demonstration of cryogenic, InP HEMT based front-end amplifiers for the DSN requir es accurate component and module characterization, and modeling from 1 to 100 GHz at physical temperatures down to 12 K. The characterizati on and modeling begins with the HEMT chip, proceeds to the multi-stag e HEMT LNA module, and culminates with the complete front-end cryogenic receiver package for the antenna. This presentation will provide a n overview of this development process. Examples will be shown for de vices, LNA modules, front-end receiver packages, antennae employing these packages and the improvements to the down-link capacity.
The time averaged output power of a Lorenz laser in the self-pulsing and chaotic regime has been numerically examined. The results indicate that the change in average power when unstable behavior occurs are of the order of 1-5 percent. This negligible change could serve as an additional signature of the Lorenz instability in quantum optics.
The argument follows from the viewpoint that quantum mechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantum mechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.
We are studying how biological systems can harness quantum effects of time varying electromagnetic (EM) waves as the time-setting basis for universal biochemical organization via the redox cycle. The effects of extremely weak EM field on the biochemical redox cycle can be monitored through real-time detection of oxidation-induced light emissions of reporter molecules in living cells. It has been shown that EM fields can also induce changes in fluid transport rates through capillaries (approximately 300 microns inner diameter) by generating annular proton gradients. This effect may be relevant to understanding cardiovascular dis-function in spaceflight, beyond the ionosphere. Importantly, we show that these EM effects can be attenuated using an active EM field cancellation device. Central for NASA's Human Research Program is the fact that the absence of ambient EM field in spaceflight can also have a detrimental influence, namely via increased oxidative damage, on DNA replication, which controls heredity.
Nonstationary quantum systems have no energy levels. However, for time-dependent periodical quantum systems, the notion of quasi-energy levels has been introduced. The main point of the quasi-energy concept is to relate quasi-energies to eigenvalues of the Floquet operator or monodromy operators which is equal to the evolution operator of a quantum system taken at the moment coinciding with the period of the system. The purpose of this article is to relate the Floquet operator to integrals of the motion and to introduce a new operator which is the integral of motion and has the same quasi-energy spectrum that the Floquet operator has. We wish to discuss an explicit formula for this new integral of motion.
We demonstrate for the first time that the quantum size effect (QSE) plays a competing role along side the classical thermodynamic effect in the shape relaxation of a small metallic island. Together, these effects transforms a lead(Pb) island grown on Si(111) substrate from its initially flattop faceted morphology to a peculiar ring-shape island, a process catalysed by the tip electric field of a scanning tunnelling microscope (STM). We shall show for the first time how QSE affects the relaxation process dynamically. In particular, it leads to a novel strip-flow growth and double-step growth on selective strips of a plateau inside the ring, defined by the substrate steps more than 60?0?3 below. It appears that atoms diffusing on the plateau can clearly (sub i)(deg)sense(sub i)+/- the quantized energy states inside the island and have preferentially attached to regions that further reduces the surface energy as a result of the QSE, limiting its own growth and stabilizing the ring shape. The mechanism proposed here offers a sound explanation for ring shape metal and semiconductor islands observed in other systems as well.
This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.
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Long coherence times and high fidelity control recently achieved in scalable superconducting circuits paved the way for the growing number of experimental studies of many-qubit quantum coherent phenomena in these devices. Albeit full implementation of quantum error correction and fault tolerant quantum computation remains a challenge the near term pre-error correction devices could allow new fundamental experiments despite inevitable accumulation of errors. One such open question foundational for quantum computing is achieving the so called quantum supremacy, an experimental demonstration of a computational task that takes polynomial time on the quantum computer whereas the best classical algorithm would require exponential time and/or resources. It is possible to formulate such a task for a quantum computer consisting of less than a 100 qubits. The computational task we consider is to provide approximate samples from a non-trivial quantum distribution. This is a generalization for the case of superconducting circuits of ideas behind boson sampling protocol for quantum optics introduced by Arkhipov and Aaronson. In this presentation we discuss a proof-of-principle demonstration of such a sampling task on a 9-qubit chain of superconducting gmon qubits developed by Google. We discuss theoretical analysis of the driven evolution of the device resulting in output approximating samples from a uniform distribution in the Hilbert space, a quantum chaotic state. We analyze quantum chaotic characteristics of the output of the circuit and the time required to generate a sufficiently complex quantum distribution. We demonstrate that the classical simulation of the sampling output requires exponential resources by connecting the task of calculating the output amplitudes to the sign problem of the Quantum Monte Carlo method. We also discuss the detailed theoretical modeling required to achieve high fidelity control and calibration of the multi-qubit unitary evolution in the device. We use a novel cross-entropy statistical metric as a figure of merit to verify the output and calibrate the device controls. Finally, we demonstrate the statistics of the wave function amplitudes generated on the 9-gmon chain and verify the quantum chaotic nature of the generated quantum distribution. This verifies the implementation of the quantum supremacy protocol.
We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.
We report the development and testing of a photon-counting detector for space-borne quantum communication applications with an ultra-low dark count rate (10 counts per second) and low timing jitter (25 ps RMS, 140 ps 1%) at a non-cryogenic temperature of -60°C.
Theory of fundamental particle symmetries derived from basic properties of space-time using principles of quantum mechanics and special relativity
No abstract available
Dynamical decoupling (DD) is a noise-mitigating strategy in which sequences of pulses are applied to single qubits to average out their interaction with the environment. DD has been extensively studied and demonstrated for suppressing single-qubit decoherence and can be tailored for different noise spectrum. We report another important adaptation of DD where crosstalk between qubits are suppressed. We demonstrate the efficiency of this procedure on quantum circuits on superconducting transmon-based quantum devices. We designed a family of syncopated DD sequences that effectively suppress ZZ coupling between qubit pairs, which is the dominating crosstalk form on the device. We insert DD to a quantum circuit whenever single qubits are idle (often during two-qubits gates on other qubits). While standard periodic DD suppress crosstalk between these qubits and their neighbors, the syncopated DD further decouples crosstalk between these qubits. We further designed short sequences that maximize the application of DD without adding time to the quantum circuit execution. Such DD sequences yield significant improvement of the performance of the algorithm on the hardware. The performance is further boosted by combining DD with another mitigation strategy, randomized compilation. Our work demonstrated that syncopated DD is effective and practical way to suppress crosstalk in quantum circuits and serves as a great probe to characterize the crosstalk and inform hardware design.