Showing papers on "Quantum published in 1981"
TL;DR: In this article, the authors proposed a new technique, the squeezed-state technique, that allows one to decrease the photon-counting error while increasing the radiation pressure error, or vice versa.
Abstract: The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave lasers, the sensitivity of currently planned interferometers will be limited by photon-counting error. This paper presents an analysis of the two types of quantum-mechanical noise, and it proposes a new technique---the "squeezed-state" technique---that allows one to decrease the photon-counting error while increasing the radiation-pressure error, or vice versa. The key requirement of the squeezed-state technique is that the state of the light entering the interferometer's normally unused input port must be not the vacuum, as in a standard interferometer, but rather a "squeezed state"---a state whose uncertainties in the two quadrature phases are unequal. Squeezed states can be generated by a variety of nonlinear optical processes, including degenerate parametric amplification.
2,582 citations
TL;DR: In this paper, a variational formulation of classical TST has been proposed, in which the objects of interest are generalized transition states, and a quantum TST that avoids the separability of conventional TST is developed.
Abstract: 1. significant progress with the variational formulation of classical TST, in which the objects of interest are "generalized transition states"; 2. the study of quantum analogues of these generalized transition states, which has led to a practical and reliable rate theory for atom-diatom reactions; 3. the development of a quantum TST that avoids the separability ap proximation of conventional TST; 4. the use of the TST "line of no return" idea as an aid in the calculation of reaction rates from individual initial states; 5. the invention of an interpolating theory to connect the TST rate ex pressions for "direct" and "complex" reactions; 6. the use of variational TST to calculate capture cross sections in ion molecule reactions; 7. the resolution of a few questions concerning transition state symmetry.
484 citations
TL;DR: In this paper, a model consisting of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation, was described.
Abstract: We describe the temporal behavior of the dynamic elements of an exactly soluble quantum model The model consists of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation We give new long-time numerical and closed-form approximate analytic solutions for the expectation values of the atomic dipole moment and the difference in population of the two atomic levels in the rotating wave approximation The atomic dipole-dipole correlation function is calculated All of the results are obtained without semiclassical or decorrelation approximations Unusual features found in the temporal behavior of this lossless model problem are ''collapse,'' ie, episodic nonexponential damping of both the atomic inversion and dipole moment, and two kinds of ''revival'' or partial recorrelation, in the dynamic evolution, during which the initial state is nearly recovered We give analytic formulas for the collapse function, for both of the revival times, and for the envelope of the revival maxima Some remarks are made about the nature of irreversibility in this exactly soluble and loss-free model
469 citations
TL;DR: In this paper, a theory of molecular structure is presented, which demonstrates that the concepts of atoms and bonds may be rigorously defined and given physical expression in terms of the topological properties of the observable distribution of charge for a molecular system.
Abstract: A theory of molecular structure is presented. The theory demonstrates that the concepts of atoms and bonds may be rigorously defined and given physical expression in terms of the topological properties of the observable distribution of charge for a molecular system. As a consequence of these definitions, one in turn obtains a definition of structure and a predictive theory of structural stability. The theory is linked to quantum mechanics by demonstrating that the atoms so defined represent a class of open quantum subsystems with a unique set of variationally defined properties.
445 citations
TL;DR: In this paper, a simple quantum model for a two-level atom interacting with initially coherent radiation is presented, where the mean atomic excitation energy, evaluated in exact closed form, exhibits rapid oscillations which periodically collapse and regenerate.
374 citations
TL;DR: In this article, a review is devoted to an examination of quantum systems possessing stochasticity in the classical limit, and the problem of quantization of systems fulfilling the stochasticallyity condition is connected both with a wide class of problems which are physical in principle (destruction of quantum numbers due to interactions, statistics of the energy spectrum, kinetic description and so on) and with applications (molecular dynamics, interaction of atoms and molecules with a strong radiation field and such on).
269 citations
TL;DR: In this paper, the authors consider the quantization of Regge's discrete description of gravity using functional methods and show that in the weak field limit, the standard continuum theory emerges.
220 citations
TL;DR: The physical basis for valence molecular connectivity was studied and a new way of estimating valence state electronegativity is proposed from a count of exterjacent electrons divided by the quantum number squared for at least the first three quantum levels.
208 citations
TL;DR: In this article, the instantaneity of the state reduction process in relativistic quantum mechanics is studied, and it is argued that the covariance of relativism lies exclusively in the experimental probabilities, and not in the underlying quantum states.
Abstract: We study the instantaneity of the state-reduction process in relativistic quantum mechanics. The conclusion of various authors that this instantaneity will restrict the set of relativistic observables to purely local ones (i.e., that the measurement of any nonlocal property of a system at a well-defined time would give rise to violations of relativistic causality) is found to be erroneous, and experiments (of a kind not encountered before in measurement theory) are described whereby certain nonlocal properties of some simple physical systems can be measured at a well-defined time without violating causality. The attempts of certain authors to reconcile the reduction process with the covariance of the relativistic quantum state are considered and found wanting, and it is argued that the covariance of relativistic quantum theories resides exclusively in the experimental probabilities, and not in the underlying quantum states. The problem of nonlocal measurement is considered in general: distinctions (which are not to be met with in the nonrelativistic case) arise in relativistic quantum mechanics between what can be measured for fermions and what can be measured for bosons, between what can be measured for individual systems and what can be measured for ensembles, and between what kinds of states can be verified by measurement and what kinds of states can be prepared by measurement; and these pose difficult questions about the nature of measurement itself.
183 citations
TL;DR: In this paper, a series of highly exothermic reactions of tris(bipyridyl) complexes involving electronically excited reactants is discussed with regard to the possible importance of quantum effects and of alternate reaction pathways in understanding the failure of the series of reactions to exhibit pronounced "inverted" behavior.
Abstract: Quantum effects in outer-sphere electron transfer reactions in the inverted region are considered. The results of quantum, “semiclassical”, and classical calculations on model systems are presented. A series of highly exothermic reactions of tris(bipyridyl) complexes involving electronically excited reactants is discussed with regard to the possible importance of quantum effects and of alternate reaction pathways in understanding the failure of the series of reactions to exhibit pronounced “inverted” behavior. Electronically excited products or alternate atom-transfer mechanisms provide possible explanations for the large discrepancy.
181 citations
TL;DR: In this article, it was shown that the observed path of a particle in quantum mechanics is a fractal curve with Hausdorff dimension two, which is the same as the path of the particle in this paper.
Abstract: We show that the observed path of a particle in quantum mechanics is a fractal curve with Hausdorff dimension two.
TL;DR: In this article, an equation of the Liouville type is obtained starting with the density matrix equation, and the validity condition and transformation properties of this quantum-classical equation as well as the application of the adiabatic approximation and the perturbation theory within the frame of this equation are discussed.
Abstract: Abstract For a system consisting of a quantum and a classical subsystem, an equation of the Liouville type is obtained starting with the density matrix equation. The validity condition and the transformation properties of this quantum-classical equation as well as the application of the adiabatic approximation and the perturbation theory within the frame of this equation are discussed. Some general expressions are obtained for the probability of the transition between the quasi-equilibrium states of the system. Special attention is given to the electron-nuclei system, as the general formalism was developed first of all in order to obtain a foundation for the theoretical analysis of elementary processes in liquids. An example is given to demonstrate that the quantum-classical approach in the range of its validity gives the same result as the corresponding quantum solution. It is also shown that both the cases of weak and strong interaction (leading to the transition) can be described by the quantum-classical equation in question.
TL;DR: In this paper, the authors analyzed the vacuum fluctuations generated by translation-invariant gauge fields and showed that these fields are unstable unless they are (anti-)self-dual and abelian.
TL;DR: In this paper, a simple special-relativistic derivation of the Sagnac effect is given, which reconciles the earlier general and non-Relativists derivations, and a new group-theoretic derivation is given.
Abstract: A simple special-relativistic derivation of the Sagnac effect, which reconciles the earlier general-relativistic and nonrelativistic derivations, is given. A distinction is made between the "classical Sagnac effect" and the "quantum Sagnac effect." A new group-theoretic derivation of these effects is also given. It is pointed out that there must exist a phase shift due to the Thomas precession in the interference of particles with intrinsic spin. The group-theoretic treatment also elucidates the connection between relativistic and nonrelativistic physics, on a classical and quantum level, with and without gravity. A formulation of the principle of equivalence, which is related to the Sagnac effect, is given in relativistic and nonrelativistic physics in terms of the respective invariance groups. New experiments are proposed to test the Sagnac effect in superfluid helium. The possible use of the general-relativistic Sagnac effect to measure the curvature tensor and in particular to detect gravitational waves is suggested.
TL;DR: In this paper, the quantum probability of the I + HI → IH + I electronically adiabatic exchange reaction was calculated using hyperspherical coordinates, in spite of the small skew angle of 7°.
TL;DR: In this paper, the universal low energy limits of three-body problems with short-range two-body forces were studied, and they were shown that if there are infinitely many spherically symmetric 3-body bound states with energies E n then lim n → ∞ E n / E n + 1 = e 2 λσ, where σ is explicitly computed.
TL;DR: In this article, a two-level geometrical formalism derived from symmetry considerations provides a closed form description of the quantum dynamics for arbitrary N. The quantum formalism demonstrates that efficient polarization transfer is equivalent to population inversion of an ensemble of fictitious spins subjected to different rf field intensities.
Abstract: An analysis of liquid state cross polarization in AXN spin systems is presented. A two‐level geometrical formalism derived from symmetry considerations provides a closed form description of the quantum dynamics for arbitrary N. A parallel discussion using a classical vector model explains the significance of the quantum mechanical solutions and illustrates the nature of the spin–spin correlations accompanying magnetization transfer. General expressions for the J cross polarization A signal with and without X decoupling are given. A discussion of RJCP and PCJCP pulse sequences introduced previously shows how manipulation of Hartmann–Hahn mismatch can advantageously modify cross‐polarization dynamics. The quantum formalism demonstrates that efficient polarization transfer is equivalent to population inversion of an ensemble of fictitious spins subjected to different rf field intensities, and that pulse sequences for cross polarization can be constructed by analogy with conventional spin inversion techniques.
Book•
01 Jan 1981
TL;DR: Leray as discussed by the authors introduced quantum conditions in a purely mathematical way in order to remove the singularities that arise in obtaining approximations to solutions of complex differential equations, and applied lagrangian analysis directly to the Schrodinger, the Klein-Gordon, and the Dirac equations.
Abstract: This work might have been entitled "The Introduction of Planck's Constant into Mathematics, "in that it introduces quantum conditions in a purely mathematical way in order to remove the singularities that arise in obtaining approximations to solutions of complex differential equations.The book's first chapter develops the necessary mathematical apparatus: Fourier transforms, metaplectic and symplectic groups, the Maslov index, and lagrangian varieties. The second chapter orders Maslov's conceptions in a manner that avoids contraditions and creates step by step an essentially new structure-the lagrangian ayalysis.Unexpectedly and strangely the last step requires the datum of a constant, which in applications to quantum mechanics is identified with Planck's constant. The final two chapters apply lagrangian analysis directly to the Schrodinger, the Klein-Gordon, and the Dirac equations. Magnetic field effects and even the Paschen-Back effect are taken into account.Jean Leray-who has been professor at the College de France for the past thirty years-has made fundamental contributions to theoretical hydrodynamics, to the study of elliptic, hyperbolic, and analytic linear and nonlinear equations, and to algebraic topology and its applications to analysis. His motivations always had their origin in physical problems, except during World War II: As a prisoner of war in Germany for five years, he concealed his interest in mathematical applications by making fruitful investigations in the field of pure algebraic topology.
TL;DR: In this article, the quantum regression theorem is shown to result on neglecting a certain term and the properties of this neglected term are briefly discussed, and the master equation approach is used to relate the calculation of correlation functions to the calculation for single-time expectation values.
Abstract: The master equation approach is used to relate the calculation of correlation functions to the calculation of single-time expectation values. The quantum regression theorem is shown to result on neglecting a certain term. The properties of this neglected term are briefly discussed.
TL;DR: In this paper, dynamical invariants are derived for time-dependent systems with nonlinear equations of motion including nonharmonic damped systems, and the concept of dynamical algebra is discussed and its utility for the construction of dynamic invariants for non-harmonic systems is demonstrated.
Abstract: Dynamical invariants are derived for time‐dependent systems with nonlinear equations of motion including nonharmonic damped systems. The concept of a dynamical algebra is discussed and its utility for the construction of dynamical invariants for nonharmonic systems is demonstrated. Finally we show the existence of dynamical invariants for some nonlinear quantum systems.
01 Jan 1981
TL;DR: Starting from the quantum mechanical BBGKY-hierarchy kinetic equations in systems with two particles bound states, the authors in this article considered transport properties in nonideal gases with three particles reactions.
Abstract: Starting from the quantum mechanical BBGKY-hierarchy kinetic equations in systems with two particles bound states are given in this paper. With this equation it is possible to consider transport properties in nonideal gases with three particles reactions.
TL;DR: Miniature end‐plate potentials were recorded from mouse diaphragm and frog cutaneous pectoris muscles and miniature end-plate currents to investigate the proposal that the m.p.e.p.'s is built up of one to thirty subunits.
Abstract: 1. Miniature end-plate potentials (m.e.p.p.s) were recorded from mouse diaphragm and frog cutaneous pectoris muscles and miniature end-plate currents (m.e.p.c.s) were recorded from frog cutaneous pectoris to investigate the proposal that the m.e.p.p. is built up of one to thirty subunits. Evidence for this hypothesis is drawn mainly from the observations that there is a class of m.e.p.p.s smaller than the classical m.e.p.p.s, and that histograms of m.e.p.p. amplitudes display multiple peaks which often appear to be regularly spaced and which extend throughout the histograms; in terms of the subunit hypothesis each successive peak results from an increasing integral number of subunits per m.e.p.p. (Kriebel, Llados & Matteson, 1976; Wernig & Stirner, 1977).
2. Histograms of m.e.p.p. amplitudes and m.e.p.c. areas confirmed the existence of two classes of m.e.p.p.s as reported by Kriebel & Gross (1974): a larger class (well described by a Gaussian curve) which consists of the classical m.e.p.p.s, and a smaller class with amplitudes considerable less than the classical m.e.p.p.s.
3. Histograms of m.e.p.p. amplitudes and m.e.p.c. areas showed multiple peaks that extended throughout the histograms.
4. Autocorrelations of the histograms, an unbiased method used to test for regularity in data, showed that the multiple peaks were not regularly spaced, as required by the subunit hypothesis.
5. A series of computer simulations demonstrated that, for expected levels of base-line noise in the recording system, multiple peaks that extend throughout histograms of m.e.p.p. amplitudes could arise from subunits only if the standard deviation of the subunit amplitude were less than 2-5% of the mean subunit amplitude and the standard deviation of the variability in post-synaptic sensitivity were less than 2% of the mean post-synaptic sensitivity. It seems unlikely that the variability in post-synaptic sensitivity and in proposed subunit amplitude would be as small as this.
6. Taking more realistic estimates for the standard deviation of the subunit amplitude of 12% of the mean subunit amplitude and standard deviation of the variation in post-synaptic sensitivity of 4% of the mean sensitivity, it was found that at most three to four regularly spaced peaks would be apparent in m.e.p.p. amplitude histograms due to subunits.
7. On the basis of these theoretical considerations it seems doubtful that the multiple peaks observed to extend throughout histograms of m.e.p.p. amplitudes could arise from subunits; therefore, the experimental data that have been used to support the subunit hypothesis are unlikely to have arisen from a subunit mechanism.
8. We suggest that there are few, if any, data that directly support the subunit hypothesis. The multiple peaks observed to extend throughout m.e.p.p. amplitude histograms most likely arise from random variation in the data, although additional factors cannot be ruled out.
TL;DR: In this paper, an infinite series representation for the two point correlation function for the quantum nonlinear Schroedinger model was derived using the quantum inverse scattering formalism, and the result of Jimbo, Miwa, Mori and Sato was extended to give an exact expression for the order 1/c correction to the two-point function in terms of a Painleve transcendent of the fifth kind.
Abstract: The two point correlation function for the quantum nonlinear Schroedinger (delta-function gas) model is studied. An infinite series representation for this function is derived using the quantum inverse scattering formalism. For the case of zero temperature, the infinite coupling (c ..-->.. infinity) result of Jimbo, Miwa, Mori and Sato is extended to give an exact expression for the order 1/c correction to the two point function in terms of a Painleve transcendent of the fifth kind.
TL;DR: In this paper, the quantum-mechanical and classical theories of electron transfer in polar media, which involve large inner-shell reorganization energy, were compared, and it was shown that quantum corrections result from nuclear tunneling effects.
Abstract: In this paper we compare the quantum-mechanical and classical theories of electron transfer in polar media, which involve large inner-shell reorganization energy. For symmetrical electron-transfer reactions, quantum corrections result from nuclear tunneling effects. These quantum effects increase the absolute value of the rate of the electron-transfer process for the Co(NH3):+-Co(NH3)2+ exchange at room temperature by less than 1 order of magnitude.
TL;DR: A nonintegrable area-preserving map for a system with one freedom is quantized, and the evolution of Wigner's function W(q,p) illustrated by contour plots of W in the paase plane as mentioned in this paper.
TL;DR: Experiments on human red cells provide evidence for an interaction compatible with the quantum mechanical theory of Frohlich as discussed by the authors, which is the basis for our work. But the experimental results were limited.
TL;DR: In this article, the authors connect the notion of capacity of sets in the theory of symmetric Markov process and Dirichlet forms with tunneling through the boundary of sets.
Abstract: We connect the notion of capacity of sets in the theory of symmetric Markov process and Dirichlet forms with the notion of tunneling through the boundary of sets in quantum mechanics. In particular we show that for diffusion processes the notion appropriate to a boundary without tunneling is more refined than simply capacity zero. We also discuss several examples in ℝd.
TL;DR: In this article, the effect of vibrational excitation of the harmonic degree of freedom on the isomerization rate is investigated as is the extent to which quantum and classical descriptions of this effect differ.
Abstract: We consider the effect of coupling in a model, two mathematical dimension isomerization reaction. The isomerization is described by a symmetric double well potential and the other degree of freedom is a harmonic bond. The time evolution of the reaction is studied in detail by a variety of quantum and classical mechanical methods. We consider first and second order quantum perturbation theory, self‐consistent field theory, self‐consistent field‐configuration interaction theory, and vibrationally adiabatic theory. Classically, we consider exact trajectories and approximate ones based on a quantized vibrationally adiabatic theory. The effect of vibrational excitation of the harmonic degree of freedom on the isomerization rate is investigated as is the extent to which quantum and classical descriptions of this effect differ. We point out two quantum effects in this model system and note that one is due to the coupling between the two degrees of freedom. This effect has not been previously reported; however, it could be a general feature of state selected isomerization reactions.