Showing papers on "Quantum published in 1984"

Consistent histories and the interpretation of quantum mechanics

Abstract: The usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times, called “consistent histories,” through a criterion which ensures that, within limits which are explicitly defined within the formalism, classical rules for probabilities are satisfied The interpretive scheme which results is applicable to closed (isolated) quantum systems, is explicitly independent of the sense of time (ie, past and future can be interchanged), has no need for wave function “collapse,” makes no reference to processes of measurement (though it can be used to analyze such processes), and can be applied to sequences of microscopic or macroscopic events, or both, as long as the mathematical condition of consistency is satisfied When applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics, though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

Electron Transfer Reactions in Condensed Phases

Abstract: Despite the multitude of formalisms, there is general agreement that the crux of the electron transfer problem is the change in equilibrium nuclear configurations that occurs when a molecule or ion gains or loses an electron. In recent developments attention has been focused on the dynamics of these nuclear configuration changes, and, in addition, on the electronic factors, determining the electron transfer rate. In parallel with these theoretical developments there have been a large number of experimental studies. These studies have not only elucidated the factors determining electron transfer rates, but have in many cases directly tested the theories and suggested modifications to the theories where appropriate. It is impossible in an article such as this to cover the entire area of electron transfer reactions. Instead the authors shall concentrate on those aspects of the problem in which they are particularly interested. Steady-state schemes for the diffusion, activation, and electron transfer steps in bimolecular reactions are discussed first. This is followed by a description in terms of Born-Oppenheimer states and surfaces and a discussion of the classical, semiclassical, and quantum mechanical formalisms. Recent experimental studies bearing on the questions raised are presented in the final section. Throughout the discussion tomore » localized or trapped systems is restricted, specifically to systems in which the electronic interaction of the initial and final states is sufficiently small so that the electron transfer can be described in terms of the electronic properties of the unperturbed reactants and products.« less

Stability of quantum motion in chaotic and regular systems

Abstract: The evolution of a quantum state is altered when a small perturbation is added to the Hamiltonian. As time progresses, the overlap of the perturbed and unperturbed states gives an indication of the stability of quantum motion. It is shown that if a quantum system has a classically chaotic analog, this overlap tends to a very small value, with small fluctuations. On the other hand, if the classical analog is regular, the overlap remains appreciable (on a time average) and its fluctuations are much larger.

Quantum measurements and stochastic processes

Abstract: A nonlinear stochastic process is presented that, for each realization and for large times, reproduces L\"uder's projection postulate. The corresponding density operator undergoes a linear evolution reproducing von Neumann's projection postulate. The violation of the Bell inequality, for instance, is described with the two apparatus acting independently on the composed system.

Quantum network theory

Abstract: A general approach, within the framework of canonical quantization, is described for analyzing the quantum behavior of complicated electronic circuits. This approach is capable of dealing with electrical networks having nonlinear or dissipative elements. The techniques are applied to circuits capable of generating squeezed-state or two-photon coherent-state signals. Circuits capable of performing back-action-evading electrical measurements are also discussed.

Formalism for the quantum Hall effect: Hilbert space of analytic functions

Abstract: We develop a general formulation of quantum mechanics within the lowest Landau level in two dimensions. Making use of Bargmann's Hilbert space of analytic functions we obtain a simple algorithm for the projection of any quantum operator onto the subspace of the lowest Landau level. With this scheme we obtain the Schr\"odinger equation in both real-space and coherent-state representations. A Gaussian interaction among the particles leads to a particularly simple form in which the eigenvalue condition reduces to a purely algebraic property of the polynomial wave function. Finally, we formulate path integration within the lowest Landau level using the coherent-state representation. The techniques developed here should prove to be convenient for the study of the anomalous quantum Hall effect and other phenomena involving electron-electron interactions.

Quantum Limitations for Chaotic Excitation of the Hydrogen Atom in a Monochromatic Field

Abstract: We numerically study the excitation mechanism of the hydrogen atom in a microwave field and show that quantum mechanics imposes limitations to the classical chaotic diffusion. In particular a multiphoton resonance pattern has been found. We suggest that a direct laboratory experimental verification of these phenomena should be possible.

Vibrational energy relaxation in liquids

Abstract: The de-excitation of the vibrational population of small molecules in the liquid state is considered. Experimental techniques applicable to the measurement of relaxation times in dense phases are first described. Theoretical approaches are subsequently developed with special emphasis on the relationship between ab-initio quantum methods and binary interaction models. Finally, a selection of experimental results is analysed in the light of these theories. Special attention is given to the dependence of the relaxation time on experimental parameters such as density, temperature or the concentration of a mixture. The behaviour of the relaxation time across the liquid/solid phase transition is also treated.

The Probabilistic Roots of the Quantum Mechanical Paradoxes

Abstract: The goal of any mathematical investigation on the foundations of a physical theory is to clarify to what extent the mathematical formalism of that theory is uniquely determined by some clearly and explicitely stated physical assumptions. The achievement of that goal is particularly relevant in the case of the quantum theory where the novelty of the formalism, its being far away from any immediate intuition, the substantial failure met, for many years, by any attempt to deduce the quantum formalism from plausible physical assumptions, intersected with the never solved problems concerning the interpretation of the theory. That with quantum theory a new kind of probability theory was. involved, was clear since the very beginnings of quantum mechanics (cf. [28]), even if it was not so clear which of the axioms of classical probability had to be substituted, which physically meaningful statement had to replace it, how and if a physically meaningful statement could justify the apparently strange quantum mechanical formalism. The lack of clear answers to these questions had a tremendous impact on the process of interpretation and misinterpretation of quantum theory.

Quantum creation of a universe with nontrivial topology

Abstract: Quantum creation of a universe with flat comoving 3-space is possible in nontrivial topology. For 3-torus topology, the relative probability of quantum birth of a spatially flat, isotropic world having finite 3-volume during the de Sitter (inflationary) stage is calculated, allowing for the vacuum energy-momentum tensor of massless quantum fields that will result from the nontriviality of the topology.

Quantum-Mechanical Tunnelling in Biological Systems

Abstract: ‘Tunnelling’ is the metaphorical name given to the process, possible in quantum mechanics, but not in classical mechanics, whereby a particle can disappear from one side of a potential-energy barrier and appear on the other side without having enough kinetic energy to mount the barrier. One can think of this as a manifestation of the wave-nature of particles. The wavelength is larger if a particle is lighter. In particular electrons, being very light compared to atoms, have wavelengths as large or larger than atoms at energies found in the valence shells of molecules. Thus, they easily ooze through and around atoms and molecules. We are also concerned with the tunnelling of heavy particles: nuclei, atoms, molecules.

Quantum thermodynamics. A new equation of motion for a single constituent of matter

Abstract: A novel nonlinear equation of motion is proposed for quantum systems consisting of a single elementary constituent of matter. It is satisfied by pure states and by a special class of mixed states evolving unitarily. But, in general, it generates a nonunitary evolution of the state operator. It keeps the energy invariant and causes the entropy to increase with time until the system reaches a state of equilibrium or a limit cycle.

Correlation functions of the one-dimensional Bose gas in the repulsive case

Abstract: The one-dimensional Bose gas model coincides with the quantum version of the nonlinear Schrodinger equation. In the repulsive case the ground state of the system is a Dirac sea with finite density. Correlation functions in this model are calculated using the quantum inverse scattering method.

Reversibility and stability of information processing systems

Abstract: Classical and quantum models of dynamically reversible computers are considered Instabilities in the evolution of the classical 'billiard ball computer' are analyzed and shown to result in a one-bit increase of entropy per step of computation 'Quantum spin computers', on the other hand, are not only microscopically, but also operationally reversible Readoff of the output of quantum computation is shown not to interfere with this reversibility Dissipation, while avoidable in principle, can be used in practice along with redundancy to prevent errors

Non-Recurrent Behaviour in Quantum Dynamics

Abstract: We study the motion of a quantum rotator under an external periodic perturbation. For the resonant case, i.e. when the frequency of driving pulses is rationally connected with the frequencies of the free rotator, the quasi-energy spectrum is known to be continuous. We prove that for a generic choice of the potential there is a non-empty set of non-resonant values of the external frequency such that the quasi-energy spectrum still has a continuous component.

Invertibility of quantum-mechanical control systems

Abstract: This is the first of two papers concerned with the formulation of a continuous-time quantum-mechanical filter. Efforts focus on a quantum system with Hamiltonian of the formH0+u(t)H1, whereH0 is the Hamiltonian of the undisturbed system,H1 is a system observable which couples to an external classical field, andu(t) represents the time-varying signal impressed by this field. An important problem is to determine when and how the signalu(t) can be extracted from the time-development of the measured value of a suitable system observableC (invertibility problem). There exist certain quasiclassical observables such that the expected value and the measured value can be made to coincide. These are called quantum nondemolition observables. The invertibility problem is posed and solved for such observables. Since the physical quantum-mechanical system must be modelled as aninfinite-dimensional bilinear system, the domain issue for the operatorsH0,H1, andC becomes nontrivial. This technical matter is dealt with by invoking the concept of an analytic domain. An additional complication is that the output observableC is in general time-dependent.

Statistical atom: Some quantum improvements

Abstract: The Thomas-Fermi model is improved by simultaneously introducing three different quantum corrections. The first concerns the nonlocality of quantum mechanics; we go beyond the von Weizs\"acker approach by including arbitrary powers of the gradient of the single-particle potential. The second is a special treatment of the strongly bound electrons, which removes the incorrect statistical description of the vicinity of the nucleus. In the third we generalize Dirac's way of handling the exchange interaction by, again, including gradient effects to arbitrary order. All this is done in the framework of a "potential-functional method" and results in a new differential equation for the potential. The comparison of numerical results with both experimental and Hartree-Fock data for the mean-squared distance indicates a superiority of the new statistical theory over the Hartree-Fock theory, at least for the description of the outer reaches of the atom.

Critical non-dissipative current of quantum Hall regime

Abstract: The quantum mechanical description of a spontaneous emission of phonons is presented to derive a critical current, which destroys the non-dissipative current in the regime of the quantum Hall effect.

Fundamentals and mechanisms of quantum localization in multidimensional correlated systems

Abstract: Coupled motion in many degrees of freedom is known to often show in classical mechanics unexpectedly localized quasiperiodic motion that could not have been anticipated from the potential function. Similar phenomena is observed in quantum theory and this article discusses the fundamental physics of such localization. It is argued below that a Born–Oppenheimer type approximation leads to dynamic potentials that make the nonobvious localization obvious. Applications are mentioned for photoselective chemistry, absorption spectroscopy, and chemical mechanisms.

Friction and Particle-Hole Pairs

Abstract: The effect induced by dissipation on quantum phenomena has recently been considered, taking into account as a starting point a phenomenological Hamiltonian in which the environment is simulated by an appropriately chosen set of harmonic oscillators. It is found that this approach should be adequate to describe the low-energy behavior of a wide class of environments. The present investigation is concerned with an analysis of the case in which the environment is a gas (or liquid) of fermions, and the relevant low-energy excitations are particle-hole pairs. A study is conducted regarding the extent to which the quantum results obtained for harmonic oscillators are also valid in the considered situation. Linear-response theory is used to derive an effective action which describes the motion of an external particle coupled to a normal Fermi fluid.