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Showing papers on "Coherent states published in 1986"


Book
27 Aug 1986
TL;DR: In this paper, the authors define the notion of generalized coherent states and define a generalization of the Coherent State Representation T?(g) of the Heisenberg-Weyl Group.
Abstract: I Generalized Coherent States for the Simplest Lie Groups.- 1. Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom.- 1.1 The Heisenberg-Weyl Group and Its Representations.- 1.1.1 The Heisenberg-Weyl Group.- 1.1.2 Representations of the Heisenberg-Weyl Group.- 1.1.3 Concrete Realization of the Representation T?(g).- 1.2 Coherent States.- 1.3 The Fock-Bargmann Representation.- 1.4 Completeness of Coherent-State Subsystems.- 1.5 Coherent States and Theta Functions.- 1.6 Operators and Their Symbols.- 1.7 Characteristic Functions.- 2. Coherent States for Arbitrary Lie Groups.- 2.1 Definition of the Generalized Coherent State.- 2.2 General Properties of Coherent-State Systems.- 2.3 Completeness and Expansion in States of the CS System.- 2.4 Selection of Generalized CS Systems with States Closest to Classical.- 3. The Standard System of Coherent States Several Degrees of Freedom.- 3.1 General Properties.- 3.2 Coherent States and Theta Functions for Several Degrees of Freedom.- 4. Coherent States for the Rotation Group of Three-Dimensional Space.- 4.1 Structure of the Groups SO(3) and SU(2).- 4.2 Representations of SU(2).- 4.3 Coherent States.- 5. The Most Elementary Noneompact, Non-Abelian Simple Lie Group: SU(1,1).- 5.1 Group SU(1,1) and Its Representations.- 5.1.1 Fundamental Properties ofU(1,1) 67.- 5.1.2 Discrete Series.- 5.1.3 Principal (Continuous) Series.- 5.2 Coherent States.- 5.2.1 Discrete Series.- 5.2.2 Principal (Continuous) Series.- 6. The Lorentz Group: SO(3,1).- 6.1 Representations of the Lorentz Group.- 6.2 Coherent States.- 7. Coherent States for the SO(n, 1) Group: Class-1 Representations of the Principal Series.- 7.1 Class-I Representations of SO(n,1).- 7.2 Coherent States.- 8. Coherent States for a Bosonic System with Finite Number of Degrees of Freedom.- 8.1 Canonical Transformations.- 8.2 Coherent States.- 8.3 Operators in the Space ?B(+).- 9. Coherent States for a Fermionic System with Finite Number of Degrees of Freedom.- 9.1 Canonical Transformations.- 9.2 Coherent States.- 9.3 Operators in the Space ?F(+).- II General Case.- 10. Coherent States for Nilpotent Lie Groups.- 10.1 Structure of Nilpotent Lie Groups.- 10.2 Orbits of Coadjoint Representation.- 10.3 Orbits of Nilpotent Lie Groups.- 10.4 Representations of Nilpotent Lie Groups.- 10.5 Coherent States.- 11. Coherent States for Compact Semisimple Lie Groups.- 11.1 Elements of the Theory of Compact Semisimple Lie Groups..- 11.2 Representations of Compact Simple Lie Groups.- 11.3 Coherent States.- 12. Discrete Series of Representations: The General Case.- 12.1 Discrete Series.- 12.2 Bounded Domains.- 12.3 Coherent States.- 13. Coherent States for Real Semisimple Lie Groups: Class-I Representations of Principal Series.- 13.1 Class-I Representations.- 13.2 Coherent States.- 13.3 Horocycles in Symmetric Space.- 13.4 Rank-1 Symmetric Spaces.- 13.5 Properties of Rank-1 CS Systems.- 13.6 Complex Homogeneous Bounded Domains.- 13.6.1 Type-I Tube Domains.- 13.6.2 Type-II Tube Domains.- 13.6.3 Type-III Tube Domains.- 13.6.4 Type-IV Domains.- 13.6.5 The Exceptional Domain Dv.- 13.7 Properties of the Coherent States.- 14. Coherent States and Discrete Subgroups: The Case of SU(1,1).- 14.1 Preliminaries.- 14.2 Incompleteness Criterion for CS Subsystems Related to Discrete Subgroups.- 14.3 Growth of a Function Analytical in a Disk Related to the Distribution of Its Zeros.- 14.4 Completeness Criterion for CS Subsystems.- 14.5 Discrete Subgroups of SU(1,1) and Automorphic Forms.- 15. Coherent States for Discrete Series and Discrete Subgroups: General Case.- 15.1 Automorphic Forms.- 15.2 Completeness of Some CS Subsystems.- 16. Coherent States and Berezin's Quantization.- 16.1 Classical Mechanics.- 16.2 Quantization.- 16.3 Quantization on the Lobachevsky Plane.- 16.3.1 Description of Operators.- 16.3.2 The Correspondence Principle.- 16.3.3 Operator Th in Terms of a Laplacian.- 16.3.4 Representation of Group of Motions of the Lobachevsky Plane in Space ?h.- 16.3.5 Quantization by Inversions Analog to Weyl Quantization.- 16.4 Quantization on a Sphere.- 16.5 Quantization on Homogeneous Kahler Manifolds.- III Physical Applications.- 17. Preliminaries.- 18. Quantum Oscillators.- 18.1 Quantum Oscillator Acted on by a Variable External Force..- 18.2 Parametric Excitation of a Quantum Oscillator.- 18.3 Quantum Singular Oscillator.- 18.3.1 The Stationary Case.- 18.3.2 The Nonstationary Case.- 18.3.3 The Case of N Interacting Particles.- 18.4 Oscillator with Variable Frequency Acted on by an External Force.- 19. Particles in External Electromagnetic Fields.- 19.1 Spin Motion in a Variable Magnetic Field.- 19.2 Boson Pair Production in a Variable Homogeneous External Field.- 19.2.1 Dynamical Symmetry for Scalar Particles.- 19.2.2 The Multidimensional Case: Coherent States.- 19.2.3 The Multidimensional Case: Nonstationary Problem..- 19.3 Fermion Pair Production in a Variable Homogeneous External Field.- 19.3.1 Dynamical Symmetry for Spin-1/2 particles.- 19.3.2 Heisenberg Representation.- 19.3.3 The Multidimensional Case: Coherent States.- 20. Generating Function for Clebsch-Gordan Coefficients of the SU(2) group.- 21. Coherent States and the Quasiclassical Limit.- 22. 1/N Expansion for Gross-Neveu Models.- 22.1 Description of the Model.- 22.2 Dimensionality of Space ?N= ?O in the Fermion Case.- 22.3 Quasiclassical Limit.- 23. Relaxation to Thermodynamic Equilibrium.- 23.1 Relaxation of Quantum Oscillator to Thermodynamic Equilibrium.- 23.1.1 Kinetic Equation.- 23.1.2 Characteristic Functions and Quasiprobability Distributions.- 23.1.3 Use of Operator Symbols.- 23.2 Relaxation of a Spinning Particle to Thermodynamic Equilibrium in the Presence of a Magnetic Field.- 24. Landau Diamagnetism.- 25. The Heisenberg-Euler Lagrangian.- 26. Synchrotron Radiation.- 27. Classical and Quantal Entropy.- Appendix A. Proof of Completeness for Certain CS Subsystems.- Appendix B. Matrix Elements of the Operator D(y).- Appendix C. Jacobians of Group Transformations for Classical Domains.- Further Applications of the CS Method.- References.- Subject-Index.- Addendum. Further Applications of the CS Method.- References.- References to Addendum.- Subject-Index.

3,565 citations


Journal ArticleDOI
Bernard Yurke1, David Stoler1
TL;DR: It is pointed out that a coherent state propagating through an amplitude dispersive medium will, under suitable conditions, evolve into a quantum superposition of two coherent states 180\ifmmode^\circ\else\textdegree\fi{} out of phase with each other.
Abstract: It is pointed out here that a coherent state propagating through an amplitude dispersive medium will, under suitable conditions, evolve into a quantum superposition of two coherent states 180\ifmmode^\circ\else\textdegree\fi{} out of phase with each other. The response of a homodyne detector to this superposition of macroscopically distinguishable states is calculated. Signatures which an experimentalist might look for in the homodyne detector's output in order to verify the generation of such states are described.

1,037 citations


Journal ArticleDOI
TL;DR: In this paper, the quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadratures measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier.
Abstract: The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.

340 citations


Journal ArticleDOI
G. Barton1
TL;DR: In this article, it was shown that T ∼ ω −1 log { l ( h mω ) 1 2 } for sojourn in the region | x | l, where l is the resolving power of the detector.

196 citations


Journal ArticleDOI
TL;DR: Strong competition between four-wave mixing and amplified spontaneous emission in resonant two-photon excitations is shown to generate radiation fields with strong squeezing and antibunching.
Abstract: Strong competition between four-wave mixing and amplified spontaneous emission in resonant two-photon excitations is shown to generate radiation fields with strong squeezing and antibunching. The generated fields are in a new type of coherent state which is an eigenstate of the operator corresponding to the simultaneous annihilation of photons in two modes.

195 citations


Journal ArticleDOI
TL;DR: In this article, the Faddeev-Kulish approach of asymptotic dynamics is used to construct the QCD coherent states at the level of leading and first sub-leading infrared singularities.

88 citations


Journal ArticleDOI
TL;DR: In this article, the Kustaanheino-Stiefel transformation is used to transform the Coulomb problem to a four-dimensional isotropic harmonic oscillator with a constraint.
Abstract: The Kustaanheino-Stiefel transformation is used to transform the Coulomb problem to a four-dimensional isotropic harmonic oscillator with a constraint. Ordinary coherent states are introduced over this oscillator and are shown to evolve in a fictitious time. When projected back into the physical space, the states follow the classical Kepler orbits in physical time. The resulting quasiclassical picture is obtained without the Bohr correspondence principle of taking only contributions from high principal quantum numbers.

57 citations


Journal ArticleDOI
TL;DR: It is shown that the Morse oscillator may be viewed as a harmonic oscillator evolving in a fictitious time by using the path integral over these states associated with the SO(2,1) noninvariance group.
Abstract: Coherent states for the Morse oscillator are constructed using generalized coherent states associated with the SO(2,1) noninvariance group for this potential. By using the path integral over these states, it is shown that the Morse oscillator may be viewed as a harmonic oscillator evolving in a fictitious time. To show that this picture is mathematically consistent, we compute the path integral for the Green's function and recover the bound-state spectrum.

54 citations



Journal ArticleDOI
TL;DR: In this article, two different approaches to multiphoton excitation of an anharmonic multilevel system are presented, one involving phase shifting portions of the coherent excitation and the other using sequences of several pulses with selected relative phase and delays.
Abstract: Two different approaches to multiphoton excitation of an anharmonic multilevel system are presented. Both methods result in nearly complete population of the upper state. The first approach involving phase shifting portions of the coherent excitation is treated analytically with square pulses. The second approach uses sequences of several pulses with selected relative phase and delays. Some numerical examples are presented for three‐ and four‐photon excitation of the vibrational level structure of CH3F. This particular molecule is again taken as model to demonstrate four‐photon excitation with a five pulse sequence, taking into account the rotational line structure. The rotational line distribution in the upper state is seen to correspond to a lower temperature than in the ground state.

41 citations


Journal ArticleDOI
TL;DR: In this article, the authors extended the hydrogen-oscillator connection to cover in a systematic (and easily computarizable) way the problem of the expansion of an R3 hydrogen wave function in terms of R4 oscillator wave functions.
Abstract: Recent works on the hydrogen‐oscillator connection are extended to cover in a systematic (and easily computarizable) way the problem of the expansion of an R3 hydrogen wave function in terms of R4 oscillator wave functions. Passage formulas from oscillator to hydrogen wave functions are obtained in six cases resulting from the combination of the following coordinate systems: spherical and parabolic coordinate systems for the hydrogen atom in three dimensions, and Cartesian, double polar, and hyperspherical coordinate systems for the isotropic harmonic oscillator in four dimensions. These coordinate systems are particularly useful in physical applications (e.g., Zeeman and Stark effects for hydrogenlike ions and coherent state approaches to the Coulomb problem).

Journal ArticleDOI
TL;DR: In this article, an algebraic semiclassical approach to the calculation of vibrational transition probabilities in inelastic collisions between molecules is presented, which leads to a set of linear differential equations for the parameters of the coherent state, coupled to the classical Hamilton equations.
Abstract: An algebraic semiclassical approach to the calculation of vibrational transition probabilities in inelastic collisions between molecules is presented. Translational motion is treated classically, while vibrational motion is described quantum mechanically using the generalized coherent state of a proper Lie algebra. This leads to a set of linear differential equations for the parameters of the coherent state, coupled to the classical Hamilton equations. Use is also made of a time dependent canonical transformation to simplify the algebraic structure. Two examples are treated explicitly: colinear collision of an atom and a diatom and a diatom–diatom collision. Good agreement with the exact quantum results is found.

Journal ArticleDOI
TL;DR: In this article, a systematic approach to the use of entropy as a measure of noise and order in quantum optical fields is developed, which is expressed in terms of both the eigenvalues of this operator and the quasidistribution function related to antinormal ordering of the field operators.
Abstract: A systematic approach to the use of entropy as a measure of noise and order in quantum optical fields is developed. The general definition of entropy, adopting the density matrix, is expressed in terms of both the eigenvalues of this operator and the quasidistribution function related to antinormal ordering of the field operators. Special states of optical fields, such as the Fock state, the coherent state, the chaotic state, single-mode and multimode two-photon coherent states, squeezed states and the shifted gaussian state, including the time development under a particular interaction, are considered. The general conclusions reached are illustrated by numerical results.

Journal ArticleDOI
TL;DR: In this paper, a wave packet which travels on an elliptic trajectory is constructed for the hydrogen atom by mapping the Schrodinger equation for hydrogen atoms into the equation for a four-dimensional oscillator with a constraint, which is then shown to have at high average energy the classical limit properties as obtained for planetary motion, to a good approximation.
Abstract: A wave packet which travels on an elliptic trajectory is constructed for the hydrogen atom. This is achieved by mapping the Schrodinger equation for the hydrogen atom into the equation for a four-dimensional oscillator with a constraint. A set of coherent states for the constrained oscillator are then shown to have at high average energy the classical limit properties as obtained for planetary motion, to a good approximation.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the convex set of classical states of the quantum harmonic oscillator is a simplex generated as the closed convex hull of the coherent states in the weak topology of the Banach space of trace class operators.
Abstract: It is shown that the convex set of classical states of the quantum harmonic oscillator is a simplex generated as the closed convex hull of the coherent states in the weak topology of the Banach space of trace class operators.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the properties of the states U2( rho, theta, lambda ) mod A, where U2 is an operator associated with the group SU(1,1), and mod A is a standard coherent state defined in terms of the usual boson creation and destruction operators aDagger and a.
Abstract: The authors study the properties of the states U2( rho , theta , lambda ) mod A) where U2 is an operator associated with the group SU(1,1), and mod A) is a standard (atomic or Glauber) coherent state defined in terms of the usual boson creation and destruction operators aDagger and a. They show how these states may be viewed as ordinary coherent states in terms of the Bogoliubov quasiparticles whose creation and destruction operators bDagger and b are associated with the operators aDagger and a by a Bogoliubov transformation. As an important example of the use of these states, they show that they are the coherent states associated with a uniformly accelerated (Rindler) observer moving through Minkowski space. The previous results then simply show how the Minkowski (inertial) vacuum appears to the Rindler observer as a black-body radiator with a Planckian distribution corresponding to a temperature proportional to the proper acceleration.

Journal ArticleDOI
P Filipowicz1
TL;DR: In this article, the authors obtained an exact integral representation of the sum describing the evolution of the two-level atom in the Jaynes-Cummings model when the field is initially prepared in a coherent state or a state generated by classical sources at non-zero temperature.
Abstract: The author obtains an exact integral representation of the sum describing the evolution of the inversion of the two-level atom in the Jaynes-Cummings model when the field is initially prepared in a coherent state or a state generated by classical sources at non-zero temperature. The author uses the saddle point method to estimate the integrals.

Journal ArticleDOI
TL;DR: In this article, it is shown that when a planar source is spatially band limited in the sense that its cross-spectral density function contains only spatial frequencies smaller than the corresponding wave number, the mode representation has some very simple and useful properties.
Abstract: Some new results are established regarding a recently developed coherent-mode representation of steady-state sources and fields of any state of coherence. It is shown that when a planar source is spatially band limited in the sense that its cross-spectral density function contains only spatial frequencies smaller than the corresponding wave number, the mode representation has some very simple and useful properties. Some potential applications of the results are mentioned.

Journal ArticleDOI
TL;DR: In this article, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations encountered in physical applications, are analyzed in detail with special emphasis on Sp(4,R) and Sp(6,R).
Abstract: In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 〈λd+n/2,...,λ1+n/2〉 encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the unitary‐operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of λ1,...,λd, subject to the conditions λ1≥λ2≥ ⋅ ⋅ ⋅ ≥λd≥0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisf...

Journal ArticleDOI
TL;DR: First-order correlation functions of the electric field and photon-number probabilities in the case of a three-level atom interacting with two-mode radiation field are obtained and it is found that double stimulation will cause the field to approach its initial coherent state and the oscillation of the photon- number probabilities to collapse and revive.
Abstract: First-order correlation functions of the electric field and photon-number probabilities in the case of a three-level atom interacting with two-mode radiation field are obtained to investigate the coherent properties of the stimulated emission under different initial conditions. It is found that double stimulation will cause the field to approach its initial coherent state and the oscillation of the photon-number probabilities to collapse and revive.

Journal ArticleDOI
TL;DR: A method for calculating center-of-mass corrections to hadron properties in soliton models and the method to the soliton bag model is presented and three ''virial theorems'' are used to test the approximate solution.
Abstract: We present a method for calculating center-of-mass corrections to hadron properties in soliton models and we apply the method to the soliton bag model. A coherent state is used to provide a quantum wave function corresponding to the mean-field approximation. This state is projected onto a zero-momentum eigenstate. States of nonzero momentum can be constructed from this with a Lorentz boost operator. Hence center-of-mass corrections can be made in a properly relativistic way. The energy of the projected zero-momentum state is the hadron mass with spurious center-of-mass energy removed. We apply a variational principle to our projected state and use three ``virial theorems'' to test our approximate solution. We also study projection of general one-mode states. Projection reduces the nucleon energy by up to 25%. Variation after projection gives a further reduction of less than 20%. Somewhat larger reductions in the energy are found for meson states.

Book ChapterDOI
01 Jan 1986
TL;DR: In this paper, it was shown that the fluctuations arising from the nonstationarity of an electrically charged particle have a 1/f spectral density and affect the ordered, collective, or translational motion of the current carriers.
Abstract: An electrically charged particle includes the bare particle and its field. The field has been shown in the last two decades to be in a coherent state, which is not an eigenstate of the Hamiltonian. Consequently, the physical particle is not described by an energy eigenstate, and is therefore not in a stationary state. In this paper we show that the fluctuations arising from this non-stationarity have a 1/f spectral density and affect the ordered, collective, or translational motion of the current carriers. This “coherent” quantum 1/f noise should be present along with the familiar quantum 1/f effect of elementary cross sections and process rates introduced ten years ago, just as the magnetic energy of a biased semiconductor sample coexists with the kinetic energy of the individual, randomly moving, current carriers. The amplitude of the quantum 1/f effect is always the difference of the coherent quantum 1/f noise amplitudes in the “out” and “in” states of the process under consideration and dominates in small samples, while large samples should exhibit the larger coherent quantum 1/f noise.

Journal ArticleDOI
TL;DR: In this paper, the dressed molecular Hamiltonian for molecules in strong electromagnetic fields is derived in the Bloch-Nordsieck (BN) and electric field (EF) representations beyond the dipole approximation.
Abstract: The dressed molecular Hamiltonian for molecules in strong electromagnetic fields is derived in the Bloch–Nordsieck (BN) and electric field (EF) representations beyond the dipole approximation. Both representations, which are related by simple unitary transformations generate photon coherent states beyond the dipole approximation. It is shown that applying the dipole approximation to the complete molecule–field equations leaves recoil corrections of order (v/c) which are field dependent. This implies that in the BN representation all Coulomb potentials will be modified at high intensities. In particular, electron–electron repulsions are subject to field dependent photon recoil corrections, which for very intense fields necessitate relativistic corrections as well.

Journal ArticleDOI
TL;DR: In this article, the authors studied the problem of the harmonic oscillator with complex frequency and derived the eigenvalues and eigenfunctions of the squeeze operator in quantum optics.
Abstract: In the present paper we study the problem of the harmonic oscillator with complex frequency. A special case of this problem is the determination of the eigenvalues and eigenfunctions of the squeeze operator in quantum optics. The Hamilton operator of the complex harmonic oscillator is non-Hermitian and its study leads to the Lie-admissible theory. Because of the complex frequency the eigenvalues of the energy are complex numbers and the partition function of Boltzman and the free energy of Helmholtz are complex functions. Especially the imaginary part of the free energy describes the metastable states.

Journal ArticleDOI
TL;DR: In this paper, a new set of phase operators for the electromagnetic field has been defined by an extension of squeezed-state theory, and the expectation values of the phase operators have been found for a squeezed state and were shown to reduce to the expected classical values in the limit of small amounts of squeezing and large field excitation.
Abstract: A new set of phase operators for the electromagnetic field has been defined by an extension of squeezed-state theory. In several cases these operators have similar or the same properties as the previously defined (Susskind–Glogower) operators. However, the new operators also have unique properties of their own. The expectation values of the phase operators have been found for a squeezed state and been shown to reduce to the expected classical values in the limit of small amounts of squeezing and large field excitation.

Journal ArticleDOI
TL;DR: In this article, a quantum Langevin equation in the Schrodinger picture is presented, where the friction term is motivated by a natural generalisation of Wigner's theorem or Dirac's superposition principle.
Abstract: The author presents a quantum Langevin equation in the Schrodinger picture. The friction term is motivated by a natural generalisation of Wigner's theorem or, equivalently, of Dirac's superposition principle. The author applies the model to spin relaxation and to the Brownian motion of the harmonic oscillator. In both cases the state vectors evolve asymptotically to a distribution which has the Gibbs state as corresponding density matrix. It is shown that for any initial state, the harmonic oscillator tends to a coherent state.

Journal ArticleDOI
TL;DR: In this paper, a new approach for studying large-N gauge theories is presented, which directly exploits the classical nature of the N → ∞ limit, and provides a practical algorithm for computing and minimizing the classical hamiltonian which governs N = ∞ dynamics, and allows one to calculate physical quantities such as the mass spectrum or scattering amplitudes of glueballs or mesons.

Journal ArticleDOI
TL;DR: In this paper, the authors used the structure of the leading and first sub-leading infrared singularities for the case of incoming q q pairs to argue that asymptotic colour separation is not allowed.

Journal ArticleDOI
TL;DR: In this article, a noncommutative version of the Cramer theorem is used to show that if two quantum systems are prepared independently, and if their center of mass is found to be in a coherent state, then each of the component systems is also in the coherent state.
Abstract: A noncommutative version of the Cramer theorem is used to show that if two quantum systems are prepared independently, and if their center of mass is found to be in a coherent state, then each of the component systems is also in a coherent state, centered around the position in phase space predicted by the classical theory. Thermal coherent states are also shown to possess properties similar to classical ones.

Book ChapterDOI
01 Jan 1986
TL;DR: In this article, the authors apply the theory of canonical integral transforms built in quantum mechanics to wave optics and translate the treatament of coherent states and other wave packets to lens and pupil systems.
Abstract: Paraxial geometric optics in N dimensions is well known to be described by the inhomogeneous symplectic group I2N ∧ Sp(2N, ℜ). This applies to wave optics when we choose a particular (ray) representation of this group, corresponding to a true representation of its central extension and twofold cover \(\tilde \Gamma _N = W_N ^ \wedge Mp(2N,\Re )\). for wave optics, the representation distinguished by Nature is the oscillator one. There applies the theory of canonical integral transforms built in quantum mechanics. We translate the treatament of coherent states and other wave packets to lens and pupil systems. Some remarks are added on various topics, including a fundamental euclidean algebra and group for metaxial optics.