Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

We have obtained an approximate expression for the impedance function at all frequencies, temperatures, and coupling strengths of an electron coupled to a polar lattice (a system commonly called a polaron). The starting point for the calculation is the quantum mechanical expression for the expected current. The phonon coordinates are eliminated from this expression by well-known field-theory techniques. The resulting exact "influence functional" is then approximated by a corresponding quadratic "influence functional" which, it is hoped, imitates the real polaron. Correction terms are computed to account for the difference between the approximate impedance and the exact polaron impedance in a manner closely analogous to Feynman's treatment of the polaron self-energy. In fact, the analytic evaluation of the expression for the impedance obtained here is carried out using the approximate "influence functional" that was successfully employed in minimizing the binding (and free) energy of the polaron in earlier calculations. However, the accuracy obtained using this approximation, for the impedance calculation, is less satisfactory and its limitations are discussed. Nevertheless, beginning at intermediate coupling strengths, the approximate impedance produces a level structure of increasing complexity and narrowing resonances as the coupling strengthens. This suggests that further refinements may be fruitful. Methods for finding a better quadratic influence functional for use in our impedance expression as well as ways of improving the expression further are suggested. A comparison of our results with those of the Boltzmann equation points up interesting differences which arise from reversing the order of taking limits of zero frequency and coupling.

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Mobility of Slow Electrons in a Polar Crystal

The physical limitations, due to quantum mechanics, on the functioning of computers are analyzed.

Quantum Mechanical Computers

Surely You''re Joking Mr

A generalization of quantum mechanics is given in which the central mathematical concept is the analogue of the action in classical mechanics It is therefore applicable to mechanical systems whose equations of motion cannot be put into Hamiltonian form It is only required that some form of least action principle be available It is shown that if the action is the time integral of a function of velocity and position (that is, if a Lagrangian exists), the generalization reduces to the usual form of quantum mechanics In the classical limit, the quantum equations go over into the corresponding classical ones, with the same action function As a special problem, because of its application to electrodynamics, and because the results serve as a confirmation of the proposed generalization, the interaction of two systems through the agency of an intermediate harmonic oscillator is discussed in detail It is shown that in quantum mechanics, just as in classical mechanics, under certain circumstances the oscillator can be completely eliminated, its place being taken by a direct, but, in general, not instantaneous, interaction between the two systems The work is non-relativistic throughout

The principle of least action in quantum mechanics

Corrections of order e6 to the differential cross section for Compton scattering of unpolarized radiation by electrons are computed. The results for corrections ascribable to virtual photons are finite, relativistically invariant, and valid at all energies, but contain a term which depends logarithmically on an assumed small photon mass λ. A cross section of the same order has also been obtained for double Compton scattering in which one of the emitted photons has an energy small compared to the rest mass of the electron (with the electron initially at rest). This contains a term depending on lnλ which exactly compensates the similar term arising from virtual quanta in all observable cases. Approximations for low and high energies, as well as numerical results, are given. These disagree with results obtained previously by Schafroth.

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Richard Phillips Feynman

Papers

Mobility of Slow Electrons in a Polar Crystal

Quantum Mechanical Computers

Surely You''re Joking Mr

The principle of least action in quantum mechanics

Radiative corrections to Compton scattering