Showing papers on "Quantum published in 1989"

Rigorous formulation of quantum transition state theory and its dynamical corrections

Abstract: We describe a procedure for computing the thermal rate constants for infrequent events that occur in complicated quantum mechanical systems. Following the ideas of Gillan, the procedure focuses on the equilibrium statistics of the centroids for the imaginary time quantum paths. We argue that the imaginary time statistics can be used to efficiently bias Monte Carlo sampling of the real time reaction dynamics. Consideration of imaginary time paths or equilibrium statistics alone leads to a quantum transition state theory. Analytical versions of this transition state theory are developed with the aid of a variational principle. Numerical applications of the quantum transition state theory are given for the one‐dimensional Eckart barrier problem and for the nonseparable two‐dimensional collinear H2+H reaction. Remarkably accurate results are obtained. The quantum transition state theory we describe provides a rigorous basis and generalizes algorithms recently employed to treat electron transfer and also ionization in polar media.

The physical basis of the direction of time

Abstract: The physical asymmetry of nature under time reversal is analysed in this essay. The author investigates the most important classes of phenomena that characterize a direction of time: radiation, thermodynamics, quantum phenomena, and the structure of spacetime. Their relations and the search for a cosmological common root of these "arrows of time" and of the traditional concept of causality are discussed. Particular emphasis is placed on quantum indeterminism. It is argued that a common root may be found in the properties of the time-independent wave function of the universe that arises from the quantization of general relativity. This requires that the physical concept of time is reduced to a correlation between physical states, including those characterizing clocks and observers. The description of irreversible phenomena is shown to be fundamentally "observer-related" in a way that can be formalized following Zwanzig. The book is aimed mainly at the student or scientist seeking an overview of the whole issue. Compared to the German version the book has been widely revised and extended.

Quantum Mechanics in the Light of Quantum Cosmology

Abstract: We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An observer (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its initial condition, and a study of the problem of quasiclassical domains.

Unimodular theory of canonical quantum gravity.

Abstract: Einstein's theory of gravity is reformulated so that the cosmological constant becomes an integration constant of the theory, rather than a "coupling" constant. However, in the Hamiltonian form of the theory, the Hamiltonian constraint is missing, while the usual momentum constraints are still present. Replacing the Hamiltonian constraint is a secondary constraint, which introduces the cosmological constant. The quantum version has a normal "Schr\"odinger" form of time development, and the wave function does not obey the usual "Wheeler-DeWitt" equation, making the interpretation of the theory much simpler. The small value of the cosmological constant in the Universe at present becomes a genuine question of initial conditions, rather than a question of why one of the coupling constants has a particular value. The key "weakness" of this formulation is that one must introduce a nondynamic background spacetime volume element.

Quantum Mechanics in the Light of Quantum Cosmology

Abstract: We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An observer (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its initial condition, and a study of the problem of quasiclassical domains.

Periodic-orbit quantization of chaotic systems.

Abstract: We demonstrate the utility of the periodic-orbit description of chaotic motion by computing from a few periodic orbits highly accurate estimates of a large number of quantum resonances for the classically chaotic three-disk scattering problem. The symmetry decompositions of the eigenspectra are the same for the classical and the quantum problem, and good agreement between the periodic-orbit estimates and the exact quantum poles is observed

Dispersed polaron simulations of electron transfer in photosynthetic reaction centers

Abstract: A microscopic method for simulating quantum mechanical, nuclear tunneling effects in biological electron transfer reactions is presented and applied to several electron transfer steps in photosynthetic bacterial reaction centers. In this "dispersed polaron" method the fluctuations of the protein and the electron carriers are projected as effective normal modes onto an appropriate reaction coordinate and used to evaluate the quantum mechanical rate constant. The simulations, based on the crystallographic structure of the reaction center from Rhodopseudomonas viridis, focus on electron transfer from a bacteriopheophytin to a quinone and the subsequent back-reaction. The rates of both of these reactions are almost independent of temperature or even increase with decreasing temperature. The simulations reproduce this unusual temperature dependence in a qualitative way, without the use of adjustable parameters for the protein's Franck-Condon factors. The observed dependence of the back-reaction on the free energy of the reaction also is reproduced, including the special behavior in the "inverted region."

Introduction to Quantum Mechanics

Abstract: Part 1 Origins of quantum theory: the Compton effect the Stern-Gerlach experiment De Broglie's hypothesis. Part 2 The wave function and the Heisenberg uncertainty principle. Part 3 The Schrodinger equation and the Ehrenfest theorem. Part 4 One-dimensional examples. Part 5 The formalism of quantum mechanics. Part 6 Angular momentum. Part 7 The Schrodinger equation in three dimensions. Part 8 Approximation methods for stationary problems. Part 9 Approximation methods for time-dependent problems. Part 10 Several and many particle systems. Part 11 The interaction of quantum systems with radiation. Part 12 The interaction of quantum systems with external electrical and magnetic fields. Part 13 Quantum collision theory. Part 14 Quantum statistics. Part 15 Further applications of quantum mechanics: the van der Waals interaction. Part 16 Measurement and interpretation: the Einstein Rosen Podolsky paradox Bell's theorem. Appendix: Fourier integrals and the Dirac delta function WKB connection formulae.

Quantum theory of solitons in optical fibers. I: Time-dependent Hartree approximation

Abstract: This paper is the first part of a two-part study on the quantum nonlinear Schr\"odinger equation [the second paper follows: Lai and Haus, Phys. Rev. A 39, 854 (1989)]. The quantum nonlinear Schr\"odinger equation is solved analytically and is shown to have bound-state solutions. These bound-state solutions are closely related to the soliton phenomenon. This fact has not been pursued in the literature. In this paper we use the time-dependent Hartree approximation to construct approximate bound states and then superimpose these bound states to construct soliton states. This construction enables us to study the quantum effects of soliton propagation and soliton collisions.

Quantum theory of solitons in optical fibers. II. Exact solution.

Abstract: In the preceding paper [paper I of a two-part study; Lai and Haus, Phys. Rev. A 40, 844 (1989)] we have used the time-dependent Hartree approximation to solve the quantum nonlinear Schr\"odinger equation. In the present paper, the eigenstates of the Hamiltonian are constructed exactly by Bethe's ansatz method and are superimposed to construct exact soliton states. Both fundamental and higher-order soliton states are constructed and their mean fields are calculated. The quantum effects of soliton propagation and soliton collisions are studied in the framework of this construction. It is shown that a soliton experiences dispersion as well as phase spreading. The magnitude of this dispersion is estimated and is shown to be very small when the average photon number of the soliton is much larger than unity. The phase and position shifts due to a collision and the uncertainty of these shifts are also calculated.

Anomalous integer quantum Hall effect in the ballistic regime with quantum point contacts.

Abstract: The Hall conductance of a wide two-dimensional electron gas has been measured in a geometry in which two quantum point contacts form controllable current and voltage probes, separated by less than the transport mean free path. Adjustable barriers in the point contacts allow selective population and detection of Landau levels. The quantization of the Hall conductance is determined by the number of quantum channels in the point contacts and is independent of the number of occupied bulk Landau levels. A theoretical description based on the Landauer-B\"uttiker formalism is given.

Zeeman bifurcation of quantum-dot spectra.

Abstract: We observe the magnetic-field-induced bifurcation of quantum levels into surface states and bulklike Landau States. The disruption of the electric field quantization by a magnetic field is most dramatic for electrons bound in two dimensions perpendicular to the magnetic field. The interplay between competing spatial and magnetic quantization mechanisms results in a pronounced and complex level splitting. The observed splitting of zero-dimensional energy levels depends critically on the size of the quantum dots, and can be explained with a calculated single-particle energy spectrum.

Nonlinear conductance of quantum point contacts

Abstract: The conductance of ballistic quantum constrictions in a two-dimensional electron gas has been studied experimentally as a function of the applied voltage. Large nonlinearities are found in the current-voltage characteristics. We give a simple model, which explains the main features of the nonlinear conductance. Breakdown of the conductance quantization occurs when the number of occupied one-dimensional sub bands becomes unequal for the two velocity directions. A critical voltage is found for the breakdown, which is equal to the subband separation at the Fermi level.

Is minisuperspace quantization valid?: Taub in mixmaster

Abstract: The paper addresses quantitatively the question of the validity of physical predictions based on minisuperspace quantization of Einstein's theory of gravitation. It studies a homogeneous, anisotropic cosmological model of higher symmetry (the Taub model) embedded in one of lesser symmetry (the mixmaster model). The comparison of the physical behavior of these two models is based on the construction of a non-negative probability density and the associated conserved inner product which allow a consistent probabilistic interpretation of the state function of the Universe in the interesting regime of deep channel penetration. It is shown that the respective behavior is widely different. A program is set for investigating a hierarchy of models with higher symmetry embedded in models of lesser symmetry to spell out the criteria under which minisuperspace quantum results can be expected to make meaningful predictions about full quantum gravity.

Differential calculus on quantum spheres

Abstract: Three-dimensional differential calculus on quantum spheres S infμc sup2 ,μ∈]−1, 1[∖{0}, c∈[0, ∞], is introduced and investigated. Spectra of generalized Laplacians are found. These operators are expressed by generalized directional derivatives. Classical limits of these objects are obtained and a simple approach to quantum mechanics on a quantum sphere is presented.

Quantum Paradoxes and Physical Reality

Abstract: 1 / Quantum Theorists and the Physical World.- 1.1. Three Central Questions about Physics.- 1.2. The Older Generation.- 1.3. The Middle Generation.- 1.4. The Younger Generation.- 1.5. Conclusions.- 2 / Is Quantum Mechanics a Complete Theory?.- 2.1. The Problem of Completeness and of Hidden Variables.- 2.2. De Broglie's Paradox.- 2.3. The Spin-1/2 System in Quantum Mechanics.- 2.4. A Simple Proof of von Neumann's Theorem.- 2.5. The Theorem is not General Enough.- 2.6. Von Neumann's Theorem: Assumptions, Definitions, and Results.- 2.7. General Proof of von Neumann's Theorem.- 2.8. Jauch and Piron's Theorem.- 2.9. The Debate on Impossibility Proofs.- 3 / The Wave-Particle Duality.- 3.1. Duality for Photons.- 3.2. Duality for Neutrons.- 3.3. Einstein's Discovery of Duality.- 3.4. De Broglie's Duality.- 3.5. Schrodinger's Waves.- 3.6. Bohr's Complementarity.- 3.7. Fock's Relativity with Respect to the Means of Observation.- 3.8. Heisenberg Beyond Complementarity.- 3.9. The Consciousness Interpretation.- 3.10. Delayed Choices.- 3.11. How to do what Complementarity Forbids.- 4 / Properties of Quantum Waves.- 4.1. Quantum Waves and Quantum Potential.- 4.2. Experiments on the Nature of Duality.- 4.3. Stimulated Emission.- 4.4. Quantitative Empty Wave Amplification.- 4.5. Two Further Experimental Proposals.- 4.6. Triple-Slit Experiments.- 4.7. The Bohm-Aharonov Effect.- 4.8. Further Ideas about Wave-Particle Duality.- 5 / The Einstein-Podolsky-Rosen Paradox.- 5.1. The Original Formulation.- 5.2. Bohr's Answer.- 5.3. Two Types of State Vectors.- 5.4. Spin States for Two Particles.- 5.5. Reality and Separability.- 5.6. The EPR Paradox: Quantum Mechanics Complete.- 5.7. The EPR Paradox: Quantum Mechanics not Complete.- 5.8. From Theory to Practice.- 5.9. The Experimental Information.- 5.10. Solution 1: Modifying the Past.- 5.11. Solution 2: Superluminal Connections.- 5.12. Solution 3: New Definitions of Probability.- 5.13. Solution 4: Modifications of Quantum Theory.- 6 / The EPR Paradox in the Real World.- 6.1. Criticisms of Einstein Locality.- 6.2. Probabilistic Einstein Locality.- 6.3. New Proof of Bell's Inequality.- 6.4. Probabilities for Pairs of Correlated Systems.- 6.5. A New Factorizability Condition.- 6.6. All the Inequalities of Einstein Locality.- 6.7. Tests of the EPR Paradox in Particle Physics.- 6.8. On the Possibility of New Experiments.- 6.9. Variable Probabilities.- 7 / Perspectives of Physical Realism.- 7.1. Objectivity of Scientific Knowledge.- 7.2. Mathematics and Reality.- 7.3. The Role of History of Physics.- 7.4. Fragmentation of Modern Physics.- 7.5. Niels Bohr and Philosophy.- 7.6. Quantum Physics and Biological Sciences.- 7.7. Forms of Physical Realism.

Quantum optical test of observation and complementarity in quantum mechanics.

Abstract: We propose and analyze experiments designed to probe the way in which the measurement process (the presence of a detector) influences the investigated system. These experiments are based on the fact that number states of the radiation field can be generated by the use of the micromaser and cavity quantum electrodynamics. It is shown that ``which-path'' (particle) information rules out interference (wave) effects due to the system-detector correlations and not due to a randomization of phase. Specific experiments based on neutron interferometry and quantum-beat techniques taken together with the micromaser are suggested and analyzed.

Localization of classically chaotic diffusion for hydrogen atoms in microwave fields.

Abstract: New experimental results are presented for short-pulse microwave ionization of highly excited hydrogen atoms. A comparison of these results with quantum numerical computations and analytical predictions provides for the first time experimentally grounded evidence of the localization phenomenon that leads to the suppression of the quantum version of the chaotic diffusion in action space occurring in the classical limit.

Harmonic oscillator driven by a quantum current.

Abstract: We show that under certain circumstances a simple quantum harmonic oscillator driven by a quantum current evolves to unique pure states even if started as a mixed state. In various limits, these states exhibit nonclassical properties such as sub-Poissonian statistics, or more interestingly resemble macroscopic superpositions.

On quantum integrable models related to nonlinear quantum optics. An algebraic Bethe ansatz approach

Abstract: A unified approach based on Bethe ansatz in a large variety of integrable models in quantum optics is given. Second harmonics generation, three‐boson interaction, the Dicke model, and some cases of four‐boson interaction as special cases of su(2)⊕su(1,1)‐Gaudin models are included.

Quantum measurements with postselection

Abstract: A Comment on the Letter by Yakir Aharonov, David Z Albert, and Lev Vaidman, Phys Rev Lett 60, 1351 (1988)

Intermediate statistics of the quasi-energy spectrum and quantum localisation of classical chaos

Abstract: The statistical properties of the quasi-energy spectrum in a simple quantum model are investigated for the case when the corresponding classical system is fully chaotic while quantum chaos is restricted by the localisation effects. It is shown that the level spacing distribution depends effectively on some parameter which is the ratio of the dimension of the eigenfunctions (mean localisation length) to the total number of the quasi-energy levels. Numerical data for a wide range of parameters of the system are given.

Steady-state quantum kinetic equation.

Abstract: Starting from the Dyson equation in the Keldysh formulation, we derive a kinetic equation for steady-state quantum transport under the simplifying assumption that the inelastic scattering is caused by uncorrelated point scatterers, such as impurities with internal degrees of freedom. This assumption allows us to write a transport equation that involves only the electron density and not the spatial correlations of the wave function. Assuming local thermodynamic equilibrium we then simplify the transport equation to a form which resembles the B\"uttiker-Landauer formula extended to include a continuous distribution of probes.