Showing papers on "Quantum published in 1974"
532 citations
TL;DR: In this article, a quantum lattice gas with arbitrary statistics was defined for a one-dimensional system with nearest-neighbor interaction, and the ground state energy was obtained for the fermions of spin 1/2.
Abstract: We define a quantum lattice gas with arbitrary statistics. For a one‐dimensional system with nearest‐neighbor interaction, we show that the problem is exactly soluble by use of Bethe's hypothesis when the interaction Δ=±1. The ground state energy is then obtained for the fermions of spin 1/2. Two phases are found in the case Δ=‐1.
219 citations
TL;DR: In this article, exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments) Quantum mechanical streamlines are plotted and found to be smooth and continuous, having continuous first derivatives even through the classical forbidden region, and forming quantized vortices around each of the nodal points.
Abstract: Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments) Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical
168 citations
TL;DR: In this paper, a microscopic theory of the quantum diffusion of light interstitials in a perfect crystal is developed, which allows one to consider the transition from quantum to classical diffusion.
Abstract: A microscopic theory of the quantum diffusion of light interstitials in a perfect crystal is developed. The basic aspects and features of the quantum diffusion and the role of the polaron effects are revealed. The expressions of the coefficients for under-barrier coherent and noncoherent tunnelling diffusion and for over-barrier diffusion, valid at the appropriate temperatures, are derived in a unified way. The basic role of the intra-well scattering for the coherent diffusion in limiting narrow bands is elucidated. The theory permits one to consider the transition from quantum to classical diffusion. It is found that coherent diffusion predominates at the low temperatures, at least in the perfect crystal. The criteria for the observation of the coherent diffusion mechanism are given.
166 citations
TL;DR: In this article, the authors derived exact master equations for two or more systems coupled to each other, perhaps strongly, by using a generalization of the usual projection operator technique to include time-dependent projection operators.
Abstract: In this paper we derive master equations for two or more systems coupled to each other, perhaps strongly, by using a generalization of the usual projection-operator technique to include time-dependent projection operators. The coupled systems may be either similar or dissimilar and classical or quantum mechanical. Whereas the customary approaches to coupled systems are best able to treat situations in which some of the systems are "baths" with a specified density operator or phase-space probability density, our approach allows us to treat situations where it is necessary or convenient to treat the coupled systems on an equal footing. In our scheme the "relevant" part of the full density operator is considered to be the uncorrelated part of the full density operator and is a symmetric functional of the reduced density operators of each of the coupled subsystems. The "irrelevant" part of the density operator is then the part describing correlations between the coupled systems. Our formalism is particularly useful where systems are coupled to one another predominantly in a self-consistent fashion. First, we develop exact master equations for two coupled systems, taking as our prototype the dynamical problem of quantum optics, where a spatially extended collection of two-level atoms interact with a multimode optical field. We then generalize our results to $N$ coupled systems, taking as our prototype the kinetics of a classical nonideal gas interacting through two-body forces, and derive exact master equations for the system. We then consider as examples several approximate theories resulting from our exact equations. In the case of the imperfect gas we investigate the low-density limit and show how Bogoliubov's form of the Boltzmann equation emerges from our formalism, as well as corrections due to Klimontovich. We consider as special cases of our exact quantum-optical equations the equations in the first Born approximation, with and without memory, and show how several existing quantum-optical master equations are contained in our general results. As a second example in quantum optics, we consider the case where the predominant behavior of the system is described by the self-consistent-field or coupled Bloch and Maxwell equations and derive a first-order perturbation description for deviations from self-consistent-field behavior.
128 citations
113 citations
TL;DR: In this article, the mechanism of production of gravitons in the empty, anisotropic, spatially inhomogeneous Gowdy three-torus cosmology is considered and the Hamiltonian methods of Arnowitt, Deser, and Misner are employed to identify the dynamical variables which are to be quantized.
109 citations
01 Jan 1974
TL;DR: In this article, a second look at the essential selfadjointness of the Schrodinger operators is presented, and a remark on the Kochen-Specker theorem is made.
Abstract: I : Art, History and Philosophy.- Science and Art.- Leonard de Vinci et l'hydrodynamique.- Our knowledge of the external world.- Geometrie and Physik.- Quantum physics and process metaphysics.- What happened to our elementary particles? (Variations on a theme of Jauch).- Partons-elementary constituents of the proton?.- Is the zero-point energy real?.- Reflections on "Fundamentality and complexity".- II : Mathematical Physics.- Weights on spaces.- A second look at the essential selfadjointness of the Schrodinger operators.- Some absolutely continuous operators.- A remark on the Kochen-Specker theorem.- Die Heisenberg-Weyl'schen Vertauschungsrelationen: Zum Beweis des von Neumannschen Satzes.- Real versus complex representations and linear-antilinear commutant.- III: Scattering Theory and Field Theory.- Approche algebrique de la theoree non-relativiste de la diffusion a canaux multiples.- Fourier scattering subspaces.- N-Particle scattering rates.- Cross sections in the quantum theory of scattering.- On long-range potentials.- Phenomenological aspects of localizability.- Charge distributions from relativistic form factors.- Charges and currents in the Thirring model.- The nonlocal nature of electromagnetic interactions.- Le modele des champs de jauge unifies.- Is anti-gravitation possible?.- IV : Quantum Theory and Statistical Mechanics.- On a new definition of quantal states.- The minimal K-flow associated to a quantum diffusion process.- Composite particles in many-body theory.- On the quantum analogue of the Levy distribution.- Existence and bounds for critical energies of the Hartree operator.- Long range ordering in one-component Coulomb systems.- A scale group for Bolt zmann-type equations.- Effect of a non-resonant electromagnetic field on the frequencies of a nuclear magnetic moment system.
90 citations
TL;DR: In this paper, an upper bound of transition state form to the quantum rate constant for bimolecular reactions was derived and discussed, and the upper bound was shown to be tight.
89 citations
TL;DR: In this article, a quantum electrodynamic treatment of radiative corrections in atoms is presented, which is patterned after Lorentz's classical work on radiation damping Expressions for both radiative lifetimes and frequency shifts are calculated through second order in the electric charge for a fictitious two-level model atom and for a spinless one-electron atom with an infinite number of arbitrarily spaced energy levels.
Abstract: We present a quantum electrodynamic treatment of radiative corrections in atoms which is patterned after Lorentz's classical work on radiation damping Expressions for both radiative lifetimes and frequency shifts are calculated through second order in the electric charge for a fictitious two-level model atom and for a spinless one-electron atom with an infinite number of arbitrarily spaced energy levels In order to apply the classical ideas of Lorentz to quantum-electrodynamic problems of this kind we work directly with the relevant dynamical variables of the atom and field The calculations are carried out entirely in the Heisenberg picture by recognizing the importance of radiation reaction The quantized-field operator equations are integrated with the aid of a Markov approximation The part of the integrated field that arises from the atomic electron current operator, the radiation-reaction field, is shown to be solely responsible for the atom's linewidths and frequency shifts It is clear that it is unnecessary to invoke vacuum fluctuations at any stage The usual quantum electrodynamic exponential decay law is found to govern the expectation values of the energy and dipole moment of the atom as well as the radiated-field amplitude The theory nevertheless remains unitary The Heisenberg operator commutation relations are shown to be valid at all times, and the Markov approximation is justified for times longer than a reciprocal transition frequency
TL;DR: For quantum spin systems on a lattice of an arbitrary dimension, the KMS condition and the variational principle are shown to be equivalent at an arbitrary temperature for translationally invariant states.
Abstract: For quantum spin systems on a lattice of an arbitrary dimension, theKMS condition and the variational principle are shown to be equivalent at an arbitrary temperature for translationally invariant states.
TL;DR: In this article, a detailed analysis of the large-amplitude temperature-insensitive oscillations in the transverse magnetoresistivity of ultrapure Mg single crystals resulting from the direct interference of electron quantum states is presented.
Abstract: A detailed analysis is presented of the large-amplitude temperature-insensitive oscillations in the transverse magnetoresistivity of ultrapure Mg single crystals resulting from the direct interference of electron quantum states. A calculation of the relative harmonic content of these interference signals based on the transmission characteristics of a magnetic breakdown-generated interferometer is used to quantitatively study certain aspects of the electron states in Mg as well as details of magnetic breakdown. In particular, values of magnetic breakdown parametersH
0are determined without invoking the complexities of transport theory. An absolute lower limit for the electron quantum state lifetime of τ ≳ 0.5 nsec is obtained (forT=1.5° K), although a best fit to the data gives a value an order of magnitude larger, τ∼5 nsec, which corresponds to quantum phase coherence extending over a distance of 3 mm in these crystals. In addition, this work provides direct experimental verification of the π/2 phase difference between transmitted and reflected electron states at a magnetic breakdown junction. Comparison of the results of this experiment with previous work via an existing semiempirical band structure calculation demonstrates the complete consistency of these measurements with previous Fermi surface data.
TL;DR: The equivalence of a Gibbsian equilibrium condition and the KMS condition for one-dimensional quantum lattice systems with a finite range interaction at arbitrary temperature was shown in this paper.
Abstract: The equivalence of a Gibbsian equilibrium condition and the KMS condition is proven for one-dimensional quantum lattice systems with a finite range interaction at arbitrary temperature, and for quantum lattice systems of arbitrary dimension, with a finite body interaction, at high temperature.
TL;DR: Naphthalin addiert Acrylnitril in alkoholischer Losung unter Lichteinwirkung zu den Produkten (I)-(III) as mentioned in this paper.
Abstract: Naphthalin addiert Acrylnitril in alkoholischer Losung unter Lichteinwirkung zu den Produkten (I)-(III).
TL;DR: In this paper, the classical statistical mechanics of an n-dimensional order parameter which exists in one spatial dimension are discussed, and the results for finite n converge toward the n = infinity answer.
Abstract: The classical statistical mechanics of an n-dimensional order parameter which exists in one spatial dimension are discussed. This many-body (field) problem was reduced to a quantum mechanical one-body problem which was solved numerically. It, therefore, provides a convenient testing ground for studying the convergence as well as understanding the nature of approximations used for higher spatial dimensions. It is shown how the results for finite n converge toward the n = infinity answer. In addition, the (l/n) expansion is investigated by computing the first and second order corrections to the n = infinity result. (GRA)
TL;DR: In this article, the inelastic scattering of a gas molecule from a solid surface is treated quantum mechanically and in three dimensions using the close-coupling formalism, where the phonon quantum number is replaced by a continuous variable.
Abstract: The inelastic scattering of a gas molecule from a solid surface is treated quantum mechanically and in three dimensions using the close‐coupling formalism. Energy transfer processes involving internal states of the molecule and one‐phonon states of the solid are included as well as arbitrary diffractions. The phonon quantum number is replaced by a continuous variable. The dependence of the unknown wavefunction on this continuous variable is expressed as an expansion in a complete set of known functions having this continuous quantum number as argument. This substitution results in the continuously infinite set of coupled differential equations being replaced by an infinite set of discrete coupled equations. Truncating this set after a finite number of terms leads to finite sets of coupled equations which are solved by standard techniques. In applying this procedure to a simple example (which, nevertheless, provides a stringent test of the method) reasonably accurate results are obtained with a basis set o...
TL;DR: In this article, it was shown that phase-space tunneling is not only classically forbidden, but also quantum-mechanically forbidden as well, and the existence of this tunneling process is undesirable.
Abstract: By analyzing the simple cosmological model consisting of a real massless Klein-Gordon field with vanishing spatial derivatives in the Friedmann universe, we conclude that this model can be successfully quantized only by using an extrinsic time. If one attempts to quantize using an intrinsic time, one is faced with the problem of either not having a point of maximum expansion, which violates the correspondence principle, or a necessity to devise a new interpretation for a zero-normed quantum mechanics (in addition to the particle-antiparticle interpretation). However, if one uses an extrinsic time, none of these difficulties occur. In analyzing the distinction between these two quantization procedures, we have noted that there are two distinct types of quantum-mechanical tunneling. The first type is the usual quantum-mechanical tunneling which we call "coordinate-space tunneling," where the topology of the classical phase space is usually planar and the phase space has no classically forbidden regions, although for a fixed energy, there can exist certain regions of coordinate space that are classically forbidden. The second type occurs when the phase space has classically forbidden regions, and we call tunneling into these regions "phase-space tunneling." In terms of these two types of tunneling, quantization with an intrinsic time allows "phase-space tunneling" to occur, and it is the presence of this type of tunneling that gives this solution its undesirable features. On the other hand, quantization with a particular choice of extrinsic time absolutely forbids the occurrence of "phase-space tunneling," and it is the lack of this type of tunneling that gives this model its desirable features. Thus, based on this model and other general arguments, we propose that although "coordinate-space tunneling" is quantum-mechanically allowed, the distinctly different tunneling process, "phase-space tunneling," is not only classically forbidden, but also must be considered to be quantum-mechanically forbidden as well.
TL;DR: In this article, a simple model is constructed in which the measuring process is described by a continuous unitary transformation of the state vector of the observed system and the apparatus, and the final state is pure, but appears to be a mixture if we ignore the degrees of freedom of the apparatus.
Abstract: Traditionally, quantum measurements have been associated with irreversible transformations of pure states into mixtures. In this paper we show that this old hypothesis is redundant. A simple model is constructed in which the measuring process is described by a continuous unitary transformation of the state vector of the observed system and the apparatus. The final state is pure, but appears to be a mixture if we ignore the degrees of freedom of the apparatus. This property is most strikingly illustrated by reformulating the problem in the Heisenberg picture: The state vector is fixed, and the dynamical variables are changed by the measurement.
TL;DR: In this paper, a fully quantum treatment of the Rabi flipping was presented, and it was shown that for sufficiently large interaction times, the semi-classical approximation is inadequate even in the case of large field intensities.
TL;DR: In this article, it was shown that there is a proper connection between the classical treatment of Thomas (1927) and the second Born approximation of the forward capture of a light particle.
Abstract: In the high velocity limit there ought to exist a connection between the correct classical and quantum mechanical treatments of the forward capture of a light particle. By means of a semi-classical treatment it is shown that there is a proper connection between the classical treatment of Thomas (1927) and the second Born approximation.
TL;DR: In this article, the problem of finding the ultimate reason for the quanta is solved by deduction of quantum mechanics from three general postulates, those of symmetry, correspondence, and covariance, imposed on a general probabilistic connection between states.
Abstract: Einstein's “quantum riddle” is the almost forgotten problem of finding the ultimate reason for the quanta It is solved here by deduction of quantum mechanics from three general postulates, those of symmetry, correspondence, and covariance, imposed on a general probabilistic connection between states The derivation offers a systematic approach to the quantum mathematics and its teaching by trying to “comprehend the complexity and apparent disorder of Nature in the light of a supreme order” (Einstein)
TL;DR: In this article, the quantum characteristic functions, quasi-distributions and their moments for radiation passing through a random medium are obtained and some useful approximations are derived for the photon counting distribution and its factorial moments.
Abstract: The present paper uses results of the preceding paper (Czech. J. Phys.B 24 (1974), 374) to obtain the quantum characteristic functions, quasi-distributions and their moments for radiation passing through a random medium. It is shown that the quasi-distribution related to normal ordering does not exist as an ordinary function and the time behaviour of the quasi-distribution related to antinormal ordering is discussed. Exact photon counting distribution and its factorial moments are obtained and some useful approximations are derived. General theory is applied to the superposition of coherent and chaotic radiation. Finally some consequences are discussed such as self-radiation effects of the medium, the relation of the present active non-linear quantum description and the previous passive linear quantum description by Tatarski and passive linear quasi-classical description by Diament and Teich and the behaviour of the photon counting distribution for various levels of turbulence.
TL;DR: In this article, the use of non-equilibrium statistical Green's functions for the derivation of kinetic equations is considered, and a number of Boltzmann-like equations are derived for quantum, classical, Markovian and non-Markovian, inhomogeneous systems.
Abstract: The use of non-equilibrium statistical Green's functions for the derivation of kinetic equations is considered. Strong interactions are studied. A number of Boltzmann-like equations are derived for quantum, classical, Markovian and non-Markovian, inhomogeneous systems.
TL;DR: In this paper, a heuristic quantum mechanical path integral formula with paths in phase space is given a precise mathematical meaning, and a quantum quantum path integral model with path integral formulas with path integrals in phase spaces is presented.
01 Jan 1974
TL;DR: In this article, the Copenhagen Interpretation and the Quantum Mechanical Scheme of Quantum Mechanics have been discussed and formal problems in Relativistic Quantum Theory have been identified, and they have been studied in detail.
Abstract: 1. Introduction.- 2. The Copenhagen Interpretation.- 3. Formal Problems of the Quantum Mechanical Scheme.- 3.1. Formal Problems in Nonrelativistic Quantum Theory.- 3.1.1. Superselection Rules.- 3.1.2. Are all Hermitian Operators Observable?.- 3.2. Formal Problems in Relativistic Quantum Theory.- 3.2.1. Instantaneous Nature of Measurements.- 3.2.2. Conflict Between Successive Measurements.- 4. Theory of Measurement and the Equation of Motion.- 4.1. The Formal Scheme of Quantum Mechanics.- 4.2. Quantum Theory as the Theory of Observations.- 4.3. Quantum Theory without Quantum Jumps.- 4.4. Indeterminate State Vector of the Apparatus.- 5. Transition to the Macroscopic World.- 5.1. Complementarity.- 5.2. Statistical Description.- 5.3. Probability in Quantum Physics.- 5.4. Macrophysical Description.- 5.5. Measurement as the Increase of Information.- 5.6. Extension of Von Neumann's View.- 5.7. Microphysics, Macrophysics and Dissipation.- 6. Hidden Variables.- 6.1. Substratum as a Solution of Divergences in Quantum Field Theory.- 6.2. Von Neumann's Proof of the Nonexistence of Hidden Variables.- 6.3. Bell's Local Hidden Variables.- 6.4. The Hidden-Variable Model of Bohm and Bub.- 7. The Notion of 'Reality' and the Epistemology of Quantum Mechanics.- 7.1. Description of Reality.- 7.2. The Complementary Description.- 7.3. The 'Positivistic' Point of View or Two Kinds of Reality.- 7.4. The Collectivistic-Materialistic View.- 7.5. Can a System Be Isolated?.- 8. Quantum Mechanics and the Explanation of Life.- 8.1. The Mind-Body Problem.- 8.2. Complementary Hierarchies.- 8.3. The Totality View of Life.- 8.4. Structure, Dissipation and Life.- 8.5. Are We Machines?.- References and Notes.
TL;DR: In this paper, the effect of the coupling function or form factor on the spontaneous emission of the Wigner-Weisskopf atom in an infinite system limit of various choices of coupling functions or form factors describing the atom's interaction with the spectrum of the radiation field was investigated.
Abstract: An investigation is made of the effect on the dynamics of spontaneous emission of the Wigner‐Weisskopf atom in an infinite‐system limit of various choices of the coupling function or form factor describing the atom's interaction with the spectrum of the radiation field This is carried out both for the exact solution to the problem of spontaneous emission, obtained in the earlier papers in the series, and for some approximate solutions, also previously considered, in particular one based on the Schrodinger equation of the problem and one based on the weak‐coupling Prigogine‐Resibois master equation The details of the form factor are found, by numerical computation of the solutions, to be critical in determining the nonexponential parts of the solutions, and these parts are seen to be capable in some cases of dominating the exponential parts, which are given only by the values of the form factor near the resonance energy The approximate solutions discussed are found to vary widely in their worth, and one, which yields the exact solution for the Wigner‐Weisskopf problem, is singled out as being of probable use in the statistical‐mechanical description of more complicated systems