Showing papers on "Quantum published in 1988"

How the result of a measurement of a component of the spin of a spin- 1/2 particle can turn out to be 100

Abstract: We have found that the usual measuring procedure for preselected and postselected ensembles of quantum systems gives unusual results. Under some natural conditions of weakness of the measurement, its result consistently defines a new kind of value for a quantum variable, which we call the weak value. A description of the measurement of the weak value of a component of a spin for an ensemble of preselected and postselected spin-(1/2 particles is presented.

Quantum Many-Particle Systems

Abstract: * Second Quantization and Coherent States * General Formalism at Finite Temperature * Perturbation Theory at Zero Temperature * Order Parameters and Broken Symmetry * Greens Functions * The Landay Theory of Germi Liquids * Further Development of Functional Integrals * Stochastic Methods

Time-dependent quantum-mechanical methods for molecular dynamics

Abstract: The basic framework of time-dependent quantum-mechanical methods for molecular dynamics calculations is described. The central problem addressed by computational methods is a discrete representation of phase space. In classical mechanics, phase space is represented by a set of points whereas in quantum mechanics it is represented by a discrete Hilbert space. The discretization described in this paper is based on collocation. Special cases of this method include the discrete variable representation (DVR) and the Fourier method. The Fourier method is able to represent a system in phase space with the efficiency of one sampling point per unit volume in phase space h, so that, with the proper choice of the initial wave function, exponential convergence is obtained in relation to the number of sampling points. The numerical efficiency of the Fourier method leads to the conclusion that computational effort scales semilinearly with the volume in the phase space occupied by the molecular system. Methods of time propagation are described for time-dependent and time-independent Hamiltonians. The time-independent approaches are based on a polynomial expansion of the evolution operator. Two of these approaches, the Chebychev propagation and the Lanczos recurrence, are also compared. Methods to obtain the Raman spectra directly by using the Chebychev propagation method are shown. For time-dependent problems unitary short-time propagators are described: the second-order differencing and the split operator. Consideration of all these methods has led to scaling laws of computation. The conclusion from such scaling laws is that, for simulations of complex molecular systems, approximation techniques have to be employed which reduce the dimensionality of the problem. The time-dependent self-consistent field (TDSCF) is suggested. Finally, a brief description is presented of current applications of the time-dependent method.

General Setting for Berry's Phase

Abstract: It is shown that Berry's phase appears in a more general context than realized so far. The evolution of the quantum system need be neither unitary nor cyclic and may be interrupted by quantum measurements. A key ingredient in this generalization is the use of some ideas introduced by Pancharatnam in his study of the interference of polarized light, which, when carried over to quantum mechanics, allow a meaningful comparison of the phase between any two nonorthogonal vectors in Hilbert space.

Superconductivity and the quantum hard-core dimer gas.

Abstract: We discuss the short-range resonating-valence-bond system as realized by a quantum hard-core dimer gas of arbitrary density on a two-dimensional square lattice. When the dimers completely cover the lattice, we argue that there is a first-order transition from a dimer crystal to an insulating quantum liquid state which possesses low-energy, neutral, spinless excitations which we call "resonons." For less than close-packed densities, the ground state is a superfluid. In addition to the usual Goldstone mode, there are low-energy, spinless zone-boundary excitations.

Spectral Function of Holes in a Quantum Antiferromagnet

Abstract: By use of an effective Hamiltonian which takes into account the constraints on the motion of a hole in a quantum antiferromagnet, the spectral function of the hole is calculated. For small exchange and away from the antiferromagnetic zone boundary, it is found to be dominated by incoherent multiplespin-wave processes. The dispersion of the quasiparticle part and the possible implications for disordering of the quantum antiferromagnet are discussed.

Quantum Mechanics of a Macroscopic Variable: The Phase Difference of a Josephson Junction

Abstract: Experiments to investigate the quantum behavior of a macroscopic degree of freedom, namely the phase difference across a Josephson tunnel junction, are described. The experiments involve measurements of the escape rate of the junction from its zero voltage state. Low temperature measurements of the escape rate for junctions that are either nearly undamped or moderately damped agree very closely with predictions for macroscopic quantum tunneling, with no adjustable parameters. Microwave spectroscopy reveals quantized energy levels in the potential well of the junction in excellent agreement with quantum-mechanical calculations. The system can be regarded as a "macroscopic nucleus with wires."

Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. I. Physical picture and calculations

Abstract: This is the first of two papers that develop the theory of oscillatory spectra. When an atom is placed in a magnetic field, and the absorption spectrum into states close to the ionization threshold is measured at finite resolution, so that individual energy levels are not resolved, it is found that the absorption as a function of energy is a superposition of sinusoidal oscillations. These papers present a quantitative theory of this phenomenon. In this first paper, we describe the physical ideas underlying the theory in the simplest possible way, and we present our first calculations based upon the theory. In the second paper, the theory is developed in full detail, proofs of all of the assertions are given, and we describe the algorithm that was used to make the calculations.

Quantum Mechanical Computers

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

Study of the Aharonov-Anandan quantum phase by NMR interferometry

Abstract: Aharonov and Anandan have recently reformulated and generalized Berry's phase by showing that a quantum system which evolves through a circuit C in projective Hilbert space acquires a geometrical phase \ensuremath{\beta}(C) related to the topology of the space and the geometry of the circuit. We present NMR interferometry experiments in a three-level system which demonstrate the Aharonov-Anandan phase and its topological invariance for different circuits.

Semiclassical physics and quantum fluctuations.

Abstract: We investigate theories in which classical and quantum-mechanical degrees of freedom interact dynamically. In commonly used semiclassical theories, such as those used to study inflationary-universe models, quantum fluctuations do not affect the dynamics of the classical variables. We construct a new semiclassical theory in which the quantum and classical fluctuations do affect each other; the Wigner probability function turns out to be a special case. Relevance to calculations of perturbations from inflation are discussed.

Classical and quantum pictures of reaction dynamics in condensed matter: resonances, dephasing, and all that

Abstract: A remarkably rich picture of the dynamics of chemical reactions in condensed-phase systems has emerged in recent years. The interplay of friction, electronic nonadiabaticity, and intramolecular energy flow have been elucidated by use of pictures based on classical trajectories. The authors review the qualitative ideas of that picture. There are some significant limitations of that approach to reaction dynamics that arise from quantum interference effects. Using a trajectory picture along with the quantum superposition principle, they give qualitative arguments describing how the transmission coefficient for nonadiabatic barrier crossing can be affected by resonances. They highlight the connections and differences between classical friction and quantum mechanical dephasing effects in barrier crossing. They also discuss the relation of this trajectory-based picture and the traditional language of radiationless processes based on the Golden Rule and master equations.

Quantum Coherence Down the Wormhole

Abstract: It is shown that pure quantum states will appear to decay into mixed states in any theory of quantum gravity that allows the topology of spacetime to be non simply connected. The reason is that the final state may contain little closed universes. There is no way one can detect the existence of these closed universes, or measure their quantum state. This means that the part of the final state that is in asymptotically flat spacetime, appears to be in a mixed state. The loss of quantum coherence in particle collisions is estimated. It comes from a wormhole connecting two asymptotically euclidean regions. The effect would be significant for scalar particles. It would make any scalar field that was not coupled to a Yang-Mills field constant throughout spacetime. It could have an important effect on Higgs particles but the effect would be small for particles of higher spin.

The XY model has long-range order for all spins and all dimensions greater than one.

Abstract: The quantum XY model of interacting spins on a hypercubic lattice has long-range order in the ground state for all values of the spin and all dimensions greater than one. We also show that in the limit of high dimension the spontaneous magnetization converges to the spontaneous magnetization of the Neel state.

Adiabatic quantum transport in multiply connected systems

Abstract: The adiabatic quantum transport in multiply connected systems is examined. The systems considered have several holes, usually three or more, threaded by independent flux tubes, the transport properties of which are described by matrix-valued functions of the fluxes. The main theme is the differential-geometric interpretation of Kubo's formulas as curvatures. Because of this interpretation, and because flux space can be identified with the multitorus, the adiabatic conductances have topological significance, related to the first Chern character. In particular, they have quantized averages. The authors describe various classes of quantum Hamiltonians that describe multiply connected systems and investigate their basic properties. They concentrate on models that reduce to the study of finite-dimensional matrices. In particular, the reduction of the "free-electron" Schr\"odinger operator, on a network of thin wires, to a matrix problem is described in detail. The authors define "loop currents" and investigate their properties and their dependence on the choice of flux tubes. They introduce a method of topological classification of networks according to their transport. This leads to the analysis of level crossings and to the association of "charges" with crossing points. Networks made with three equilateral triangles are investigated and classified, both numerically and analytically. Many of these networks turn out to have nontrivial topological transport properties for both the free-electron and the tight-binding models. The authors conclude with some open problems and questions.

Scaling laws and minimum threshold currents for quantum-confined semiconductor lasers

Abstract: Basic scaling laws are derived for bulk, two‐dimensional (quantum well) and one‐dimensional (quantum wire) semiconductor lasers. Starting from quantum derivation of the optical properties of confined carriers, the dimensional dependencies of the scaling laws are made explicit. Threshold currents of ∼100 and 2–3 μA are predicted for single quantum well and quantum wire lasers, respectively. The basic considerations of this analysis were used recently to obtain ultralow threshold quantum well lasers [P. L. Derry, A. Yariv, K. Lau, N. Bar‐Chaim, K. Lee, and J. Rosenberg, Appl. Phys. Lett. 50, 1773 (1987)].

Ten theorems about quantum mechanical measurements

Abstract: The aim of quantum mechanics is to explain macroscopic, objectively recorded phenomena. Microscopic objects are measured by enabling them to interact with a macroscopic measuring apparatus prepared in a metastable state. Macroscopic objects, such as cats, are not above the laws of quantum mechanics, but owing to their enormously dense level spectrum other aspects than single eigenvalues and eigenfunctions are prominent. These aspects can be described in classical terms, such as probabilities instead of probability amplitudes. The measuring act is fully described by the Schrodinger equation for object system and apparatus together. The collapse of the wave function is a consequence rather than an additional postulate. A model is constructed to demonstrate these statements. It also appears that the entropies of the object system and the apparatus increase by the same amount, namely the entropy difference between the metastable initial state and the stable final state of the apparatus.

Continuously tunable 1.5μm multiple-quantum-well GaInAs/GaInAsP distributed-Bragg-reflector lasers

Abstract: We demonstrate improved performance in tunable distributed-Bragg-reflector lasers using GaInAs/GaInAsP multiple-quantum-well active layers. We observe linewidths as low as 1.9 MHz, differential quantum efficiencies as large as 33%/front facet at 1.5μm, and rapid electronic access to all frequencies throughout a 1000GHz range.

Logical reformulation of quantum mechanics. II. Interferences and the Einstein-Podolsky-Rosen experiment

Abstract: The consistent quantum interpretations of logic that were introduced in a previous paper are applied to four experiments: (1) ordinary interferences, (2) the Badurek-Rauch-Tuppinger neutron interferometry experiment, (3) the Einstein-Podolsky-Rosen experiment, and (4) the detection far away of the origin of a nonrelativistic particle initially near the origin. In the first two cases, the proposition calculus excludes the possibility of observing interferences and of asserting together through which path the particles went. It is used to provide a somewhat complete discussion of the Badurek-Rauch-Tuppinger experiment. The possibility of using logical implication allows a rather complete discussion of the EPR experiment, including the question of causality, although the lack of a relativistic version of the theory does not allow a complete discussion of causality. The last experiment leads to the following result: Detecting the position of a particle at timet sometimes allows one to determine with a finite uncertainty what its momentum was just before the position measurement, even when it is infinitely precise.

Logical reformulation of quantum mechanics. III. Classical limit and irreversibility

Abstract: This paper deals with two questions: (1) It contains a proof of the fact that consistent quantum representations of logic tend to the classical representation of logic when Planck's constant tends to zero. This result is obtained by using the microlocal analysis of partial differential equations and the Weyl calculus, which turn out to be the proper mathematical framework for this type of problems. (2) The analysis of the limitations of this proof turn out to be of physical significance, in particular when one considers quantum systems having for their classical version a KolmogorovK-system. These limitations are used to show the existence of a “best” classical description for such a system leading to an objective definition of entropy. It is shown that in such a description the approach to equilibrium is strictly reduced to a Markov process.

Driven Morse oscillator: Classical chaos, quantum theory, and photodissociation

Abstract: We compare the classical and quantum theories of a Morse oscillator driven by a sinusoidal field, focusing attention on multiple-photon excitation and dissociation. In both the classical and quantum theories the threshold field strength for dissociation may be estimated fairly accurately on the basis of classical resonance overlap, and the classical and quantum results for the threshold are in good agreement except near higher-order classical resonances and quantum multiphoton resonances. We discuss the possibility of ``quantum chaos'' in such driven molecular systems and use the Morse oscillator to test the manifestations of classical resonance overlap suggested semiclassically.

The quantum simulation of hydrogen in metals

Abstract: Realistic quantitative calculations on atomistic models for hydrogen in metals are difficult because quantum effects must be included. We show that quantum simulation based on Feynman's path-integral formulation of quantum mechanics gives a powerful way of making such calculations. After summarizing some essential facts about metal-hydrogen systems, we explain the principles of pathintegral simulation. We present the results of classical molecular-dynamics and quantum path-integral simulations of hydrogen in Pd and Nb based on simple empirical interaction models. Results are given for the probability density ρ(r) of hydrogen as a function of position r in the unit cell, and for a quantity proportional to the diffusion coefficient. We point out that diffraction measurements of ρ(r) would allow an important test of the interaction models. The simulated diffusion coefficient for H in Nb shows the experimentally observed break in Arrhenius slope at ∼250 K, which we argue represents a cross-over from ...

Quantum Effects in Gas Phase Bimolecular Chemical Reactions

Abstract: Although the quantum mechanical underpinnings of chemical reactions have been understood on an abstract theoretical level since the discovery of quantum mechanics, and a variety of simple models of quantum effects such as tunneling have been available for a long time, the quantitative determination of how big quantum effects are and where they show up has only started to appear in the past ten years. Exciting progress of major significance in the experimental observation of several important types of quantum effects in gas-phase chemical reactions has been made during the last two years, so it seems appropriate to write a review that is specifically devoted to this topic. The first half of this review is a rather detailed discussion of what we mean by "quantum effects," with special attention given to the two most extensively studied quantum effects, tunneling and resonances. In the second half of the review, four reactions that show experimentally observable quantum effects are discussed in depth. These are: H + H2, Oep) + H2, Cl + HCl, and H + CO (plus certain deuterated counterparts). The review is "results-oriented" in that I spend little time in discussing either theoretical or experimental methodology, but rather emphasize the results of calculations and measurements. No review with this scope and topic has been written previously, but a number of reviews have touched on parts of what is discussed here. Two recent reviews of tunneling in gas phase reactions are by Schatz (1) and Miller (2). Several reviews on variational transition state theory have been written by Truhlar and co-workers (3-6) and all of these include some discussion of tunneling.

Aspects of chaos in nuclear physics

Abstract: This article addresses the role of such concepts as chaos and predictability in the context of nuclear physics. The topic of this article is closely linked with such diverse areas as random-matrix theory, chaos in classical dynamical systems, statistical mechanics of small quantum systems, and the theory of disordered solids. We present recent information on nuclear data and on their analysis in terms of random-matrix models, a summary of work done on classical chaotic systems, on their quantum analogues, and on special systems like the hydrogen atom in a strong magnetic field. Also, we discuss how random-matrix models can be used to simulate chaotic behaviour in small quantum systems, the role of symmetries (isospin, parity, and time-reversal) in chaotic quantum (nuclear) systems, and how chaos surfaces in experimental and theoretical investigations in molecular physics, in the physics of small clusters, and the analysis of conductance fluctuations in solids. (AIP)