Showing papers on "Coherent states published in 1973"
TL;DR: In this paper, a system of two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied, and the free energy of the system is calculated exactly in the thermodynamic limit.
Abstract: A system of $N$ two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.
588 citations
TL;DR: In this article, the existence problem for optimal measurements of the mean value is studied and sufficient and necessary conditions for optimality are given. And the general theory is applied to the case of Gaussian (quasifree) states of Bose systems.
536 citations
Journal Article•
TL;DR: In this paper, the largest group of coordinate transformations leaving invariant the Schroedinger equation of the n-dimensional harmonic oscillator is determined and shown to be isomorphic to the corresponding group of the free-particle equation.
Abstract: The largest group of coordinate transformations leaving invariant the Schroedinger equation of the n-dimensional harmonic oscillator is determined and shown to be isomorphic to the corresponding group of the free-particle equation. It can be described as a Galilei group in which the time translations have been replaced by the group SL(2,R) of projective transformations. The relation between the oscillator group and the spectrumgenenating algebra of the harmonic oscillator is investigated. The relevance of the oscillator group and the group SL(2,R) for general quantum systems is discussed. (auth)
236 citations
TL;DR: In this article, the Born-Fock adiabatic theorem is extended to all orders for some quadratic quantum systems with finitely or infinitely degenerate energy spectra.
Abstract: The Born‐Fock adiabatic theorem is extended to all orders for some quadratic quantum systems with finitely or infinitely degenerate energy spectra. A prescription is given for obtaining adiabatic invariants to any order. For any quadratic quantum system with N degrees of freedom there are 2N linear adiabatic invariant series, which correspond to the 2N exact invariants. The exact quantum mechanical solution for any nonstationary quadratic quantum system is also constructed by making use of the coherent‐state representation: The Green's function,coherent states, transition amplitudes and probabilities and their generating functions are obtained explicitly. Two particular systems, the N‐dimensional time‐dependent general oscillator and charged particle motion in a varying and uniform electromagnetic field, are considered in greater detail as examples.
186 citations
TL;DR: In this article, a weak asymptotic limit is proposed for a charged field as an operator on the space of states, leading to a modified Lehmann-Symanzik-Zimmermann reduction formula and a determination of the singularity near the mass shell of the Green's function of a charged particle in the presence of other charged particles.
Abstract: A weak asymptotic limit is proposed for a charged field as an operator on the space of asymptotic states. This leads to a modified Lehmann-Symanzik-Zimmermann reduction formula and a determination of the singularity near the mass shell of the Green's function of a charged particle in the presence of other charged particles. Coherent states of the electromagnetic field are also reduced out. The resultant expression for $S$-matrix elements in terms of vacuum expectation values of time-ordered fields yields a slight elaboration of the Feynman rules which allows a perturbative calculation that is free of infrared and Coulombic divergences order by order. As an application, the amplitude for scattering of a Dirac particle by an external Coulomb potential is calculated to second order in the external potential, with a finite result.
37 citations
23 citations
TL;DR: In this paper, the authors considered group-theoretical aspects of the problem of production of boson pairs in the homogeneous alternating external field and showed that the dynamical symmetry group is the group SU (N, N) (N = 2S + 1, S being the spin of the particle) and the state of the system which arises from the vacuum state in the evolution process, is the generalized coherent state.
Abstract: Group-theoretical aspects of the problem of production of boson pairs in the homogeneous alternating external field are considered It is shown that the dynamical symmetry group of the problem is the group SU (N, N) (N = 2S + 1, S being the spin of the particle) and the state of the system, which arises from the vacuum state in the evolution process, is the generalized coherent state. Probability of the pair production is given by the squared modulus of matrix element of the representation of the dynamical group. (auth)
17 citations
TL;DR: In this paper, it was shown that there exists a large class of semi-coherent states, which represent harmonically oscillating wave packets whose spread or size remains constant, and these states are different from the coherent states in not having the minimum value 1/2 for the uncertainty product Δx·Δp.
Abstract: It is shown that there exists for the quantum harmonic oscillator a large class of « semi-coherent » states, which represent harmonically oscillating wave packets whose « spread » or « size » remains constant. These states are different from the coherent states in not having the minimum value 1/2ħ for the uncertainty product Δx·Δp.
12 citations
TL;DR: In this article, the postulated coherent states of magnetic charges are shown to obey a superselection rule as in the case of the eigenstates of electric charge, an important result for the problem of experimental detection of magnetic monopoles.
TL;DR: In this paper, a survey of the essential concepts, occuring in Landau's excitation model and in the Penrose-Onsager theory of Bose-Einstein condensation in liquid helium is given.
TL;DR: In this paper, a perturbational series expansion with respect to the potential part is obtained for the integral of the density matrix associated with the quantized linear harmonic oscillator, and the correctness of the obtained expansion is verified by summation and comparison with the known formula in closed form.
TL;DR: In this paper, the non-Markoffian effect on superradiance from an assembly of many harmonic oscillators is investigated based on a theory recently developed by Bonifacio, Schwendimann, and Haake.
Abstract: The non-Markoffian effect on superradiance from an assembly of many harmonic oscillators is investigated based on a theory recently developed by Bonifacio, Schwendimann, and Haake. A superradiance master equation is solved exactly by introducing the coherent state basis. It is show how the retardation effect, which takes into account a dynamical role of the photon field played during the radiating processes, modifies the shape and Poissonian statistics of superradiant pulses obtained from the Markoffian approach.
Journal Article•
TL;DR: In this article, a comparison between the approaches of Nelson and of Lewis and Davies to quantum probability, using calculations made on the harmonic oscillator, is made, and the results again differ.
Abstract: A comparison is made between the approaches of Nelson and of Lewis and Davies to quantum probability, using calculations made on the harmonic oscillator. Calculation of the joint distribution of position shows an expected difference in the approaches. The time the particle takes to hit an absorbing counter put in the system is calculated to first order, in both theories, and the results again differ.
TL;DR: In this paper, a general quantum-mechanical method of calculating the high-field magnetoconductivity of nearly free electron metals is discussed, and the results are compared with those recently obtained by Animalu.
TL;DR: In this article, a method of calculation of the density matrix in the Schrödinger picture is given, in terms of the known creation and annihiliation operators a+ and a.
Abstract: In the present paper a method of calculation of the density matrix in the Schrödinger picture is given, in terms of the known creation and annihiliation operators a+ and a. New magnetic operators are given with the help of the coherent states, which depend on two free parameters μ and ν. For the case μ=ν= (e H )/ (2 ħ c), these operators lead to the well-known magnetic operators, as they are given in the current litterature.
01 Jan 1973
TL;DR: In this paper, an expansion of the density matrix ρ in terms of a given complete set of orthogonal operators establishes a one-to-one correspondence between the expanded operator ρ and the quasi-probability phase-space distribution that appears in said expansion.
Abstract: Electromagnetic fields at optical frequencies are excited by indeterministic sources. Their statistical description is usually given by means of the density operator ρ or a phase-space distribution which is, in general, a quasi-probability distribution. Expansions of the density matrix ρ in terms of a given complete set of orthogonal operators establishes a one-to-one correspondence between the expanded operator ρ and the quasi-probability phase-space distribution that appears in said expansion. The time evolution of the field’s statistics are obtained then as a solution of the equation of motion of the density operator ρ or the differential equation of the corresponding phase-space distribution. The latter method has the advantage of being unburdened by problems of commutativity associated with the ρ operator. With the statistical information vested in the phase-space distribution, in lieu of the density matrix ρ the expected value of an observable F is given by an integral of the phase-space distribution multiplied by a weighting function which is representative of the observable F. This is essentially the method first introduced by Wigner[l] and Moyal[2].
01 Jan 1973
TL;DR: In this article, a completely quantum mechanical description of the photodetection mechanism is given, in order to determine the exact relations between electron counting statistics and the incident light, and to obtain the exact relation between the two.
Abstract: We are interested in a completely quantum mechanical description of the photodetection mechanism, in order to determine the exact relations between electron counting statistics and the incident light.
01 Jan 1973
TL;DR: In this article, a number of algebraic techniques have been used to construct and label the symmetrized states describing an ensemble of N identical two-level atoms under a classical driving field.
Abstract: In the preceding work [1] a number of algebraic techniques have been used to construct and label the symmetrized states describing an ensemble of N identical two-level atoms. Under certain physically attainable circumstances, such states evolve into “coherent atomic states” under a classical driving field. The properties of the atomic coherent states were stated and compared with the properties of the field coherent states. The atomic and field coherent states were found to be related by a group contraction process.