Showing papers on "Quantum state published in 1985"
TL;DR: The dependence of macroscopic systems upon their environment under the assumption that quantum theory is universally valid is studied in this paper, where scattering of photons and molecules turns out to be essential even in intergalactic space in restricting the observable properties by locally destroying the corresponding phase relations.
Abstract: The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to be essential even in intergalactic space in restricting the observable properties by locally destroying the corresponding phase relations. The remaining coherence determines the ‘classical’ properties of the macroscopic systems. In this way local classical properties have their origin in the nonlocal character of quantum states.
1,204 citations
01 May 1985
TL;DR: A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states.
Abstract: A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
539 citations
TL;DR: In this paper, the mathematical foundation for the two-mode formalism is provided, and the fundamental unitary operators of the formalism are described and their properties examined; particular attention is paid to the twomode squeeze operator.
Abstract: This paper provides the mathematical foundation for the two-mode formalism introduced in the preceding paper. A vector notation is introduced; it allows two-mode properties to be written as compactly as the comparable properties for a single mode. The fundamental unitary operators of the formalism are described and their properties are examined; particular attention is paid to the two-mode squeeze operator. Special quantum states associated with the formalism are considered, with emphasis on the two-mode squeezed states.
444 citations
TL;DR: In this paper, the photodissociation of a single rotational state in an excited vibrational state was investigated using a tunable IR laser, and it was shown that the process is possible with respect to fine details of simple fragmentation processes.
Abstract: It is pointed out that the photodissociation of H2O in the first absorption band is an ideal process for studies which can lead to an understanding of the basic principles of simple fragmentation phenomena. With modern quantum methods, this fragmentation can be studied on an ab initio basis, and theoretical predictions can be compared with experimental results. The present investigation is concerned with the preparation of a single rotational state in an excited vibrational state, taking into account a procedure based on the use of a tunable IR laser. The conducted experiment demonstrates that photodissociation of single, selectable states is possible. New insight is obtained with respect to fine details of simple fragmentation processes. 10 references.
74 citations
TL;DR: An operational procedure is given for determining experimentally the Wigner function for an ensemble of particles, and closely parallels the method one might use in classical mechanics to determine a (true) phase-space probability density.
Abstract: An operational procedure is given for determining experimentally, in principle at least, the Wigner function for an ensemble of particles. This manner of "measuring" a quantum state, whether pure or mixed, via its Wigner function, seems the simplest possible, and closely parallels the method one might use in classical mechanics to determine a (true) phase-space probability density.
57 citations
TL;DR: A general representation of the thermal quantum state for any interacting quantum system such as fermi, bose and quantum spin systems is given in this article, where a fundamental equation of quantum non-equilibrium systems is obtained on the basis of the time-dependent thermal quantum states.
Abstract: A general representation of the thermal quantum state is given for any interacting quantum system such as fermi, bose and quantum spin systems. A fundamental equation of quantum non-equilibrium systems is obtained on the basis of the time-dependent thermal quantum state \(|\varPsi(t)\rangle\).
56 citations
TL;DR: Spectra of reactive intermediates, of highly vibrationally excited molecules, and even of molecules in the process of falling apart have been recorded, leading to greater understanding of the molecular structure and dynamics of small gas-phase molecules.
Abstract: It is now possible to resolve completely the initial and final quantum states in chemical processes. Spectra of reactive intermediates, of highly vibrationally excited molecules, and even of molecules in the process of falling apart have been recorded. This information has led to greater understanding of the molecular structure and dynamics of small gas-phase molecules. Many of the concepts and spectroscopic techniques that have been developed will be valuable throughout chemistry.
40 citations
TL;DR: In this article, the question of joint localization of a particle on bounded position and momentum value sets and the relevance of this question to the interpretation of positionmomentum uncertainty relations is surveyed.
Abstract: Uncertainty relations and complementarity of canonically conjugate position and momentum observables in quantum theory are discussed with respect to some general coupling properties of a function and its Fourier transform. The question of joint localization of a particle on bounded position and momentum value sets and the relevance of this question to the interpretation of position-momentum uncertainty relations is surveyed. In particular, it is argued that the Heisenberg interpretation of the uncertainty relations can consistently be carried through in a natural extension of the usual Hilbert space frame of the quantum theory.
24 citations
TL;DR: In this paper, a nonlinear equation of motion for a single isolated two-level quantum system was proposed, which implies the existence of new nonmechanical individual quantum states.
Abstract: We propose a new nonlinear equation of motion for a single isolated two-level quantum system. The resulting generalized two-level quantum dynamical theory entails a new alternative resolution of the long-standing dilemma on the nature of entropy and irreversibility. Even for a single isolated degree of freedom, in addition to the individual mechanical states for which all the results of conventional quantum mechanics remain valid, our theory implies the existence of new nonmechanical individual quantum states. These states have nonzero individual entropy and, by virtue of a constant-energy, internal redistribution mechanism, relax irreversibly toward stable equilibrium. We discuss the possibility of an experimental verification of these conclusions by means of a high-resolution, essentially single-particle, magnetic-resonance experiment.
21 citations
TL;DR: In this paper, the structure of the so-called DHB quantum theory was analyzed and the operational Hilbert space quantum theory is reconstructed from the (weak) projection postulate and the complementarity principle.
Abstract: Some classical and quantum theories are characterized within the convexity approach to probabilistic physical theories. In particular, the structure of the so-called DHB quantum theory will be analyzed. It turns out that the natural generalization of the standard Hubert space quantum mechanics, the operational one, is such a theory. The operational Hilbert space quantum theory will be reconstructed from the (weak) projection postulate and the complementarity principle. This is then used to argue that the DHB quantum theory is identical with the operational Hilbert space quantum theory.
20 citations
TL;DR: It is shown that these characteristic functions allow a universal differentiating procedure for calculating averages of arbitrary ordered noncommuting observables and satisfy the same criterion of non-negative definiteness as the Fourier transforms of the everywhere non- negative probability distribution.
Abstract: Fourier transforms of the von Neumann density operators could be regarded as functions on a Lie group whose infinitesimal generators correspond to dynamical variables characterizing a given quantum system. Called ``characteristic functions'' in this paper, they are discussed with a view to reformulating quantum statistical mechanics in a group-theoretical formalism. It is shown that these characteristic functions allow a universal differentiating procedure for calculating averages of arbitrary ordered noncommuting observables and satisfy the same criterion of non-negative definiteness as the Fourier transforms of the everywhere non-negative probability distribution (the characteristic functions in classical probability theory). The group-theoretical characteristic-function formalism is especially useful in providing easy reductions of the dynamics of complicated quantum systems to the evolutions of a set of quantum variables that are of particular interest. As examples of applications, the following results are derived: (a) a hierarchy of equations of motion for subsystems of a given N-body quantum system (a quantum analog of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy), (b) an equation of motion for centers of mass of two interacting quantum systems, and (c) the behavior of spin fluctuations of an ideal spin gas in the thermodynamic limit.
TL;DR: It is shown that any such vacuum state of the theory has a two-point function possessing the Hadamard singularity structure required by standard renormalization theory and must be a second-order adiabatic vacuum.
Abstract: We examine the constraints on the construction of Fock spaces for scalar fields in spatially flat Robertson-Walker space-times imposed by requiring that the vacuum state of the theory have a two-point function possessing the Hadamard singularity structure required by standard renormalization theory. It is shown that any such vacuum state must be a second-order adiabatic vacuum. We discuss the global requirements on the two-point function for it to possess the Hadamard form at all times if it possesses it at one time.
TL;DR: In this paper, a quantum state represented by its wave function satisfying the Schrodinger equation is considered and the transition probabilities of these processes are explicitly built in two circumstances: in the general case, but in an expansion in the time difference, and exactly, but for Gaussian processes.
Abstract: Starting from a quantum state represented by its wave function Ψ(x), satisfying the Schrodinger equation, we determine stochastic processes which provide the same time evolution for the probability densityν(x)=¦Ψ(x)¦2. The transition probabilities of these processes are explicitly built in two circumstances: in the general case, but in an expansion in the time difference, and exactly, but for Gaussian processes. This allows us to discuss the correspondence between quantum states and stochastic processes, which appears not to be one-to-one, but, on the contrary, to associate with the same state an infinity of processes which differ in the fluctuation correlations of the random variable.
TL;DR: In this article, the concept of statistical π algebras is introduced and the representation theorems are proved for two extreme cases of classical and quantum π-algebra.
Abstract: Following the idea of Zadeh, the concept of a statistical (or fuzzy)σ algebra is introduced. For two extreme cases of classical and quantum statisticalσ algebras the representation theorems are proved. The basic feature distinguishing these two cases is the possibility of producing nontrivial superpositions of pure quantum states, which is absent in the classical case.
TL;DR: In this article, the authors show that the photon noise reduction is very sensitive to the spatial and temporal coherence properties of the squeezed field, and that photon noise is not appreciably reduced with incoherent sources of squeezed field.
Abstract: The sensitivity of the interferometric methods for detection of gravitational waves is limited at the moment by photon noise. This noise can theoretically be reduced by entering in one input part of the interferometer a field in a particular quantum state, the so called squeezed state. A wide variety of non-linear processes, such as the degenerate four wave mixing, can realize the transformation of coherent states of the field into squeezed states. We show that the photon noise reduction is very sensitive to the spatial and temporal coherence properties of the squeezed field, and that photon noise is not appreciably reduced with incoherent sources of squeezed field.
TL;DR: In this article, the authors assume that the branching into the different product states is independent of the initial quantum states of the reactants, and derive an expression for the state-to-state cross section in terms of the stateto-all one, as well as microcanonical rate constants.
Abstract: We assume that, having arrived at the transition state, the branching into the different product states is independent of the initial quantum states of the reactants. This assumption plus the familiar transition state approximation (that the reaction rate is the rate of the passage across the barrier) yields an expression for the state‐to‐state cross section in terms of the state‐to‐all one, as well as microcanonical rate constants. Models, adiabatic correlations, purely statistical considerations, or collinear computations can provide the required input for the theory. Exact quantal computations on the 3D H + H2 reaction are found to satisfy the assumed factorization quite well. Furthemore, reaction probabilities derived from a line‐of‐centers model, with a barrier height dependent on the approach angle, account for the probabilities derived from the exact quantal computation.
TL;DR: In this article, Ramaswamy a critique le critere a 50% for le mouvement quantique regulier avance par Hose et Taylor, en disant qu'il s'agit d'un schema de perturbation and depend du systeme de base.
Abstract: Dans un article recent, Ramaswamy a critique le critere a 50% pour le mouvement quantique regulier avance par Hose et Taylor, en disant qu'il s'agit d'un schema de perturbation et qu'il depend du systeme de base. On montre que cette critique est erronee
TL;DR: In this article, a construction of time evolution for linear boson models of quantum statistical mechanics is presented, where the main result is a theorem on convergence to a quasifree moment functional in the course of linear time evolution.
Abstract: This paper contains a construction of time evolution for linear boson models of quantum statistical mechanics. The main result is a theorem on convergence to a quasifree moment functional in the course of linear time evolution. A connection between linear evolution of the moment functional and evolution of the corresponding state of an infinite quantum system is discussed. Bibliography: 30 titles.
TL;DR: In this paper, the useful analogy between stationary quantum states of the particle confined to the finite area and standing waves of a continuous medium is mostly treated incorrectly and the weak points of such presentations are indicated and the correct elementary explanation of energy quantisation is given.
Abstract: The useful analogy between stationary quantum states of the particle confined to the finite area and standing waves of a continuous medium is mostly treated incorrectly. The weak points of such presentations are indicated and the correct elementary explanation of energy quantisation is given.
TL;DR: In this paper, it is argued that this resolution of the EPR paradox relies on a reinterpretation of the concept of the quantum state that contradicts the basic axioms of quantum theory and is internally inconsistent.
TL;DR: In this paper, the physical properties of the quantum states are connected to the mathematical properties of an iterated map, and the connection between the mathematical property of iterated maps and the physical property of electronic systems is analyzed.
Abstract: The authors analyse the connection between the mathematical properties of iterated maps and the physical properties of electronic systems. Specifically, they treat a linear disordered chain of one-orbital atoms governed by a tight-binding Hamiltonian. The physical properties of the quantum states are connected to the mathematical properties of the orbits of an iterated map.
TL;DR: In this paper, the first quantum correction to the ground state energy and the spin wave spectrum for a Heisenberg antiferromagnetic linear chain in a magnetic field was calculated, and a consistent treatment of quantum corrections, obtained through an expansion in 1/S, is required to obtain a self energy that satisfies the Goldstone theorem.
Abstract: The authors calculate the first quantum correction to the ground state energy and to the spin wave spectrum for a Heisenberg antiferromagnet in a magnetic field. A consistent treatment of quantum corrections, obtained through an expansion in 1/S, is required to obtain a self-energy that satisfies the Goldstone theorem. They find that in the Heisenberg antiferromagnetic linear chain the two-sublattice ground state becomes unstable for any S because of the quantum fluctuations in presence of an applied magnetic field. This finding is in accord with rigorous results for S=1/2.
TL;DR: In this paper, a convergence lower bound to the critical screening parameter associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states.
Abstract: Converging lower bound to the critical screening parameterD
c
associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10−3% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD
≈ [0.764435n
−2+0.617737n
−3]−1 wheren is the principal quantum number. The predictedD
c
for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.
TL;DR: In this paper, a theoretical calculation shows how to monitor the state of a simple model atom without interfering with its quantum state. But Heisenberg's principle remains intact, and it is shown how to do so without violating the principle of noninterference.
Abstract: A neat theoretical calculation shows how to monitor the state of a simple model atom without interfering with its quantum state. But Heisenberg's principle remains intact.
TL;DR: In this article, the uncertainty relation in discrete quantum mechanics is obtained up to the lowest order correction to the continuum one, and the distinguishing feature of this new uncertainty relation is that the minimal uncertainty is not only a function of the fundamental constant l of the discreteness of the theory, but also the dynamics of the system, in contrast to the usual minimal uncertainty ( ℏ 2 ) which is the same for all dynamical systems in continuum quantum mechanics.
01 Jan 1985
TL;DR: In this article, the systematics of electron quantum states in atoms are reviewed along with the atomic terms and the filling-order of the electronic subshells, and the normal electronic configurations and terms of atomic particles are presented, together with the Hartree-Fock and asymptotic parameters of valence electron wavefunctions.
Abstract: The systematics of electron quantum states in atoms is briefly reviewed along with the systematics of atomic terms and the filling-order of the electronic subshells. The normal electronic configurations and terms of atomic particles are presented, together with the Hartree-Fock and asymptotic parameters of valence electron wavefunctions and radial expectation values.
TL;DR: In this article, the necessary and sufficient condition that the given observable has a finite mean value in the given state was shown to be satisfied, and it was suggested that such states are physically unrealizable.
Abstract: Given an observable and a state of a quantum system, we prove the necessary and sufficient condition that the given observable has a finite mean value in the given state. If the condition is not satisfied, then the mean value of the observable diverges: it is suggested that such states are physically unrealizable.