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Showing papers on "Quantum published in 1975"


Journal ArticleDOI
H. Haken1
TL;DR: In this article, a tutorial approach to cooperative phenomena in systems far from thermal equilibrium and in non-physical systems is presented, with particular emphasis on the question of how order and self-organization may arise.
Abstract: This article consists of two parts. The first part presents a tutorial approach to cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems. Particular emphasis is placed on the question of how order and self-organization may arise. The following example is treated among others: the ordered phase of the laser giving rise to both coherently oscillating atomic dipole moments and coherent light emission. A complete analogy of the laser light distribution function to that of the Ginzburg-Landau theory of superconductivity is found mathematically which allows us to interpret the laser threshold as a quasi-second-order phase transition with soft modes, critical slowing down, etc. Similar phenomena, again closely resembling phase transitions, are found in tunnel diodes and in the nonlinear wave interaction which occurs, for example, in nonlinear optics. Remarkable analogies between the instability of the laser and those in hydro-dynamics are elaborated. While these phenomena show pronounced analogies to phase transitions in thermal equilibrium, there are further classes of instabilities and new phases which rather resemble hard excitations known in electrical engineering. Chemical oscillations are particularly important examples. In addition, the first part of this article contains the example of the cooperative behavior of neuron networks and shows the applicability of simple physical concepts, e.g., the Ising model, to the problem of the dynamics of social groups. All these above-mentioned examples demonstrate clearly that rather complex phenomena brought about by the cooperation of many subsystems can be understood and described by a few simple concepts. One of the main concepts is the order parameter; another is the adiabatic elimination of the variables of the subsystems, which is based upon a hierarchy of time constants present in most systems. The second part of this article gives a systematic account of the mathematical tools which allow us to deal with fluctuations. It contains the master equation, the Fokker-Planck equation, the generalized Fokker-Planck equation, and the Langevin equations, and gives several general methods for deriving the stationary and, in certain cases, the nonstationary solutions of master equations and the Fokker-Planck equations. Such general classes comprise those in which detailed balance is present or in which the coupling to the reservoirs is weak. In the quantum mechanical domain, the density matrix and the projection formalism for its reduction are presented. Finally, it is shown how the principle of quantum-classical correspondence allows us to translate quantum statistical problems completely into the classical domain.

815 citations


Journal ArticleDOI
TL;DR: In this article, two types of nonlinear Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time-dependent one and an alternative class of non-linear Hamiltonian.
Abstract: Two types of Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time‐dependent one and an alternative class of nonlinear Hamiltonians. In the latter group we propose a new form. By Ehrenfest’s theorem the expectation values of the operators of physical observables correspond to the classical quantities. For all Schrodinger equations we derive and discuss wavepacket, wave, stationary, and pseudostationary solutions of force free motion, free fall, and harmonic oscillator.

280 citations


Journal ArticleDOI
TL;DR: In this article, a fully quantum-mechanical treatment of resonant light scattering is presented, where the incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation.
Abstract: A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a $c$ number. It is thus proved quite rigorously and generally that the use of a $c$-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.

260 citations


Journal ArticleDOI
TL;DR: In this article, the Lagrangian of the theory contains only one field, but a complete spectrum of particles is manifested, and the quantum corrections are small for small coupling constants and the quasiclassical treatment determines the entire nonanalytic contribution to the physical quantities.
Abstract: We hope that we have succeeded in convincing the reader that this one-dimensional nonlinear model of field theory has a number of attractive properties. Let us list some of them. 1. The Lagrangian of the theory contains only one field, but a complete spectrum of particles is manifested. In the weak interaction approximation the solitons are heavy particles and they interact strongly. 2. The solitons have a quantum number which has a topological nature, and this can be interpreted as a charge. Solitons with the same charge repel each other, while solitons with different charge attract oacl other. 3. In the weak interaction approximation a prescription exists for calculating in perturbation theory. The quantum corrections are small for small coupling constants, and the quasiclassical treatment determines the entire nonanalytic contribution to the physical quantities.

223 citations


Journal ArticleDOI
TL;DR: In this paper, phase transitions for the quantum field interaction λφ4+m02φ2,m02/λ≪1 were established in two dimensional space time.
Abstract: Phase transitions for the quantum field interaction λφ4+m02φ2,m02/λ≪1 are established in two dimensional space time.

162 citations


Journal ArticleDOI
TL;DR: In this paper, the process of vacuum polarization in the field of a "bare" Kerr-Newman geometry is studied and the value of the critical strength of the electromagnetic fields is given together with an analysis of the feedback of the discharge on the geometry.
Abstract: Following the classical approach of Sauter, of Heisenberg and Euler and of Schwinger the process of vacuum polarization in the field of a "bare" Kerr-Newman geometry is studied. The value of the critical strength of the electromagnetic fields is given together with an analysis of the feedback of the discharge on the geometry. The relevance of this analysis for current astrophysical observations is mentioned.

145 citations


Journal ArticleDOI
TL;DR: In this article, the coupling of angular momenta is studied using quantum mechanics in the limit of large quantum numbers (semiclassical limit) and uniform valid semiclassical expressions are derived for the 3j (Wigner) coefficients coupling two angular moments.
Abstract: The coupling of angular momenta is studied using quantum mechanics in the limit of large quantum numbers (semiclassical limit). Uniformly valid semiclassical expressions are derived for the 3j (Wigner) coefficients coupling two angular momenta, and for the 6j (Racah) coefficients coupling three angular momenta. In three limiting cases our new expressions reduce to those conjectured by Ponzano and Regge. The derivation involves solving the recursion relations satisfied by these coefficients, by a discrete analog of the WKB method. Terms of the order of the inverse square of the quantum numbers are neglected in the derivation, so that the results should be increasingly accurate for larger angular momenta. Numerical results confirm this asymptotic convergence. Moreover, the results are of a useful accuracy even at small quantum numbers.

139 citations


Journal ArticleDOI
TL;DR: In this paper, a modified version of Gutzwiller's periodic orbit theory of semiclassical eigenvalues is presented which eliminates some of the principal shortcomings of the original result.
Abstract: A modified version of Gutzwiller’s periodic orbit theory of semiclassical eigenvalues is presented which eliminates some of the principal shortcomings of the original result. In particular, for a nonseparable system with N degrees of freedom the new quantum condition characterizes the eigenvalues by N quantum numbers (rather than just one), and it also reduces to the correct result in the limit that the system is a separable set of harmonic oscillators (whereas the original quantum condition does not). This new periodic orbit quantum condition is seen to bear an interesting relation to Marcus’ recent theory of semiclassical eigenvalues which involves manifolds of quasiperiodic trajectories.

105 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used the classical trajectory equations and an average trajectory to predict the single quantum transitions for the one-dimensional atom-diatom collision problem to within 10-30%.

104 citations


Journal ArticleDOI
TL;DR: In this article, the exact solution for the ground state of the quantum one-dimensional $N$-boson problem with attractive $\ensuremath{\delta}$-function two-body potentials is compared with the (exact) self-consistent solution of the corresponding variational Hartree problem.
Abstract: The exact solution for the ground state of the quantum one-dimensional $N$-boson problem with attractive $\ensuremath{\delta}$-function two-body potentials is compared with the (exact) self-consistent solution of the corresponding variational Hartree problem.

91 citations


Journal ArticleDOI
TL;DR: In this article, examples of bouncing in one dimension and sliding down an incline are proposed for use as conceptual aids in an introductory course, where the examples of one and two dimensions for motion in a uniform gravitational field are considered quantum mechanically.
Abstract: Examples in one and two dimensions for motion in a uniform gravitational field are considered quantum mechanically. The examples of bouncing in one dimension and sliding down an incline are proposed for use as conceptual aids in an introductory course.

Book
01 Jan 1975
TL;DR: In this paper, it was shown that the nonlinear forces associated with the interaction of laser radiation with a solid deuterium plasmas can be modelled as a dielectric nonlinear force.
Abstract: 1. Introduction.- 1.1 Nuclear Fusion.- 1.2 Laser-Produced Nuclear Fusion.- 2. Lasers.- 2.1 Laser Condition.- 2.2 Operation of Lasers.- 2.3 Available Lasers.- 3. Early Measurements and Gas Breakdown.- 3.1 Gas Breakdown.- 3.2 Plasmas Produced from Solids in Vacuum (Linlor Effect).- 4. Microscopic Properties of Plasma.- 4.1 Debye Length.- 4.2 Plasma Frequency.- 4.3 Collisions.- 5. Macroscopic Plasma Physics.- 5.1 Ohm's Law and Electromagnetic Waves.- 5.2 Equation of Motion and Equations of Conservation.- 5.3 Homogeneous Heating.- 6. Refractive Index and Absorption.- 6.1 Linear Properties.- 6.2 Nonlinear Absorption.- 6.3 Relativistic Absorption.- 6.4 Anomalous Absorption and Instabilities.- 7. Dielectric Nonlinear Forces and Dynamic Absorption.- 7.1 Basic Properties of the Dielectric Nonlinear Force.- 7.2 Transferred Momentum and Ion Energies.- 7.3 Predominance of the Nonlinear Force.- 7.4 Self-Focusing of Laser Beams in Plasma.- 7.5 Numerical Examples of Nonlinear Acceleration.- 8. Theory of Laser-Induced Nuclear Fusion.- 8.1 Inertial Confinement.- 8.2 Gas-Dynamic Compression.- 8.3 Direct and More Efficient Transfer of Laser Energy into Mechanical Compression.- 8.4 New Concepts and Nuclear Fission.- 9. Experiments for Laser-Induced Nuclear Fusion.- 9.1 Irradiation of Spherical Targets.- 9.2 Neutron Generation.- 9.3 Anomalous Experimental Results.- 10. Conclusions.- 11. References.- 12. Appendix. List of Reprinted Papers.- "The Conditions of Plasma Heating by the Optical Quantum Generator.".- "Experiments on the Observation of Neutron Emission at the Focus of High-power Laser Radiation on a Lithium Deuteride Surface.".- "Ion Energies Produced by Laser Giant Pulse.".- "The Initial Stage of the Laser-induced Gas Breakdown.".- "Experiments on Self-focusing in Laser-produced Plasmas.".- "Intense Electron Emission from Laser-produced Plasmas.".- "Experimental Result of Free Targets.".- "On the Production of a Plasma by Giant Laser Pulses.".- "Some Results of the Self-similarity Model.".- "Hydrogen Plasma Production by Giant Pulse Lasers.".- "Optical Constants of Fullyionized Hydrogen Plasma for Laser Radiation.".- "Laser-Induced Instabilities and Anomalous Absorption in Dense Plasmas.".- "Nonlinear Confining and Deconfining Forces Associated with the Interaction of Laser Radiation with a Plasma.".- "Ponderomotive Forces on Laser-produced Plasmas.".- "Nonlinear Forces in Laser-produced Plasmas.".- "Physical Mechanisms for Laser-Plasma Parametric Instabilities.".- "Laser-Induced Implosion and Thermonuclear Burn.".- "Exact Steady-state Analogy of Transient Gas Compression by Coalescing Waves.".- "Laser-driven Implosion of Spherical DT Targets to Thermonuclear Burn Conditions.".- "Nuclear Fusion Reactions in Laser-produced Solid Deuterium Plasmas.".- "Heating of Laser Plasmas for Thermonuclear Fusion.".- "Neutron Generation in Spherical Irradiation of a Target by High-power Laser Radiation.".- "Anomalous Heating of a Plasma by Lasers.".- "Neutron Emission from Laser-produced Plasmas.".- "Saturation of Stimulated Back-scattered Radiation in Laser Plasmas.".- "Pair Production by Relativistic Electrons from an Intense Laser Focus.".- 13. Subject Index.

Journal ArticleDOI
TL;DR: In this article, a quantum mechanical analogue of a classical nonlinear system is shown to be exactly solvable and its energy levels and eigenfunctions are obtained completely, and the ordering problem that arises in the quantum mechanical case is overcome.
Abstract: The quantum mechanical analogue of a classical nonlinear system is shown to be exactly solvable and its energy levels and eigenfunctions are obtained completely. The symmetric version (k0=0) of this model is the SU(2)(X)SU(2) chiral invariant Lagrangian in the Gasiorowicz-Geffen coordinates. The radial part of the classical equation of motion (in both the symmetric and non-symmetric cases) admits simple harmonic bounded solutions and the bound state energies of the quantized system show a linear dependence on the coupling parameter lambda . It is shown that the Bohr-Sommerfeld quantization procedure reproduces the form of the correct bound state energy levels while a perturbation theoretic treatment gives the exact energy expressions. The ordering problem that arises in the quantum mechanical case is overcome.

Journal ArticleDOI
TL;DR: In this article, the interaction of a two-level atom with a single mode of the radiation field is considered both in a fully quantized and a semi-classical theory, and the results suggest experimentally verifiable differences between the two theories.
Abstract: The interaction of a two-level atom with a single mode of the radiation field is considered both in a fully quantized and a semi-classical theory. With only the dipole and rotating-wave approximations the Liouville equations are solved to give the exact behaviour of the diagonal elements of the density operator and of their semi-classical analogue. The results suggest experimentally verifiable differences between the two theories.

Journal ArticleDOI
TL;DR: In this article, the authors explore the range of validity of several such correspondence methods for collinear atom-diatom collisions by comparing the results with those from rigorous quantum mechanical calculations.
Abstract: Quantum vibrational transition probabilities may be estimated from single, real classical trajectories by exploiting the approximate correspondence between the classical and quantal motions. In this paper we explore the range of validity of several such correspondence methods for collinear atom–diatom collisions by comparing the results with those from rigorous quantum mechanical calculations. The model systems considered here include: (a) a harmonic oscillator with (1) a repulsive exponential, (2) a Landau–Teller, and (3) a Lennard‐Jones interaction potential, and (b) a Morse oscillator with a repulsive exponential interaction potential. The range of the dimensionless mass parameter M is 0.00628 to 3.737 and the total system energy ranges from 1.55 to 10.0 in units of h/ωe. For both Morse and harmonic oscillator excitation the semiclassical results are generally more accurate for small M and for small initial and final vibrational quantum numbers. Quantitatively, the results are consistently better for a...

Journal ArticleDOI
TL;DR: In this paper, a new method is presented for extracting approximate quantum mechanical state-to-state transition probabilities from the results of classical trajectory calculations, which is capable of treating both classically allowed and classically forbidden processes.

Journal ArticleDOI
TL;DR: Stimulated two-photon emission is proposed as a possible mechanism for the generation of generalized coherent states as discussed by the authors, which have useful quantum properties not available in ordinary coherent states. But this mechanism is not suitable for generalization.


Journal ArticleDOI
TL;DR: In this article, the analog of a quantum kinetic equation for the description of time correlation functions of singled out nonlinear oscillators interacting with a medium (e.g., local or quasi-local vibrations in crystals) is obtained.
Abstract: The analog of a quantum kinetic equation for the description of time correlation functions of singled out nonlinear oscillators interacting with a medium (e.g. local or quasi-local vibrations in crystals) is obtained. Both the frictions, the linear and nonlinear one (the latter is due to decays with participation of two quanta of singled out oscillators), were taken into account. Spectral distributions of the correlation functions of the coordinates are found as well as those of occupation numbers. The essentially non-Lorentzian shape of the spectral distribution and its dependence on interaction parameters and temperature are analysed. [Russian Text Ignored].

Journal ArticleDOI
W.G. Gibson1
TL;DR: In this paper, the authors derived expressions derived in the previous paper for quantum corrections to the properties of a fluid are applied to the hard-sphere fluid and numerical results are given for the first and second-order corrections to free energy and to the pressure.
Abstract: Expressions derived in the previous paper for quantum corrections to the properties of a fluid are applied to the hard-sphere fluid. Numerical results are given for the first- and second-order corrections to the free energy and to the pressure, and for the first-order correction to the radial distribution function. Significant features are the large increase in quantum corrections with increasing density, and the qualitative difference that quantum mechanics makes to the radial distribution function near the hard core.

Journal ArticleDOI
TL;DR: In this paper, a complete description of quantum kinematics on a homogeneous G−space M is presented using imprimitivity systems for G based on M. The quantum system on M is considered (if possible and consistent with this quantization) as kinematic on a G−orbit equivalent to M in some Euclidean space Rn, and a physically justified and mathematically well-defined method of connecting the free Hamiltonian of a quantum system in Rn with an operator proportional to the Laplace−Beltrami operator on M (with the R
Abstract: A complete description of quantum kinematics on a homogeneous G−space M is presented using imprimitivity systems for G based on M. The kinematics on M is considered (if possible and consistent with this quantization) as kinematics on a G−orbit equivalent to M in some Euclidean space Rn. This method gives a physically justified and mathematically well−defined method of connecting the free Hamiltonian of a quantum system in Rn with an operator proportional to the Laplace−Beltrami operator on M (with the Riemannian structure inherited from Rn) which is proposed to be the free Hamiltonian on M.

Journal ArticleDOI
TL;DR: In this article, a semielassical approach derived from Feynman's path integral formulation of quantum mechanics is applied to multiple Coulomb excitation for backward scattering angles, and the limit of sudden collision for η → ∞ (η = Sommerfeld parameter) is evaluated analytically and is in very good agreement with results published for this case.





Journal ArticleDOI
TL;DR: In this paper, an analytical expression for the binding energy of a heavy ion is obtained from the statistical theory, which allows one to find the leading coefficients in Z -1 perturbation theory.

Journal ArticleDOI
TL;DR: In this paper, the liquid-to-gas transition at zero temperature in quantum systems obeying both Bose and Fermi statistics is studied, and the nature of this transition in these quantum systems depends on the statistics in a fundamental way.
Abstract: The liquid-to-gas transition at zero temperature in quantum systems obeying both Bose and Fermi statistics is studied. In contrast to well-known systems, the nature of this transition in these quantum systems depends on the statistics in a fundamental way. For Bose systems there is no coexistence region. For Fermi systems there is a range of masses for which there is a coexistence region and a critical mass below which this region disappears.

Journal ArticleDOI
TL;DR: In this paper, an approximate solution to the set of coupled integro-differential equations discussed previously is considered and the classical limit of the transport coefficients is obtained and a comparison of the results with previous theory is made.
Abstract: An approximate solution to the set of coupled integro‐differential equations discussed previously is considered. The classical limit of the transport coefficients is obtained and a comparison of the results with previous theory is made.

Journal ArticleDOI
TL;DR: In this paper, a simple and tractable quantum expression of the line wings is given when the upper and lower levels of the spectral lines are both perturbed, and this quantum profile converges towards the impact regime at small distances from the line centre and towards the quasistatic limit when the usual semiclassical approximations are made.
Abstract: A simple and tractable quantum expression of the line wings is given when the upper and lower levels of the spectral lines are both perturbed. This quantum profile converges towards the impact regime at small distances from the line centre and towards the quasistatic limit when the usual semiclassical approximations are made. The correspondence between quantum and semiclassical expressions is examined, and the passage from the former to the latter clarifies the implicit assumptions which are always made in any unified semiclassical approach.