Showing papers on "Quantum state published in 1984"
TL;DR: In this article, it was shown that in a simple minisuperspace model this boundary condition leads to a wave function which can be interpreted as a superposition of quantum states which are peaked around a family of classical solutions of the field equations.
628 citations
TL;DR: In this paper, it is shown that if a quantum system has a classically chaotic analog, the overlap tends to a very small value, with small fluctuations, while if the classical analog is regular, it remains appreciable and its fluctuations are much larger.
Abstract: The evolution of a quantum state is altered when a small perturbation is added to the Hamiltonian. As time progresses, the overlap of the perturbed and unperturbed states gives an indication of the stability of quantum motion. It is shown that if a quantum system has a classically chaotic analog, this overlap tends to a very small value, with small fluctuations. On the other hand, if the classical analog is regular, the overlap remains appreciable (on a time average) and its fluctuations are much larger.
544 citations
TL;DR: In this article, the quantum motion of a periodically kicked rotator is shown to be related to Anderson's problem of moving a quantum particle in a one-dimensional lattice in the presence of a static-random potential.
Abstract: The quantum motion of a periodically kicked rotator is shown to be related to Anderson's problem of motion of a quantum particle in a one-dimensional lattice in the presence of a static-random potential. Classically, the first problem is nonintegrable and, for certain values of the parameters, exhibits chaos and diffusion in phase space; in the second problem, diffusion takes place in configuration space. Quantum phase interference, however, is known to suppress diffusion in Anderson's problem and to produce quasiperiodic motion. By establishing a mapping between the two systems we show that a similar effect determines the dynamics of the quantum rotator. As a result its wave functions are localized in phase space and their time evolution is quasiperiodic. This result explains the quantum recurrences and boundedness of the energy found in recent numerical work.
316 citations
TL;DR: In this article, it was shown that integrable classical motion and ergodic classical motion information can indeed be obtained on not quite this, but a closely related correlation function for the two types of motion.
Abstract: Through the rule that there is one quantum state per Planck cell in phase space, classical mechanics supplies an ‘average’ semiclassical density of states for a system with bound motion. Can it supply more refined ‘averages’ such as the correlation function for the density of states ? I shall argue that for the two extreme cases of integrable classical motion and ergodic classical motion information can indeed be obtained on not quite this, but a closely related correlation function. The results for the two types of motion are markedly different.
272 citations
TL;DR: In this paper, a general formulation of quantum mechanics within the lowest Landau level in two dimensions was developed, making use of Bargmann's Hilbert space of analytic functions and a simple algorithm for the projection of any quantum operator onto the subspace of the lowest landau level.
Abstract: We develop a general formulation of quantum mechanics within the lowest Landau level in two dimensions. Making use of Bargmann's Hilbert space of analytic functions we obtain a simple algorithm for the projection of any quantum operator onto the subspace of the lowest Landau level. With this scheme we obtain the Schr\"odinger equation in both real-space and coherent-state representations. A Gaussian interaction among the particles leads to a particularly simple form in which the eigenvalue condition reduces to a purely algebraic property of the polynomial wave function. Finally, we formulate path integration within the lowest Landau level using the coherent-state representation. The techniques developed here should prove to be convenient for the study of the anomalous quantum Hall effect and other phenomena involving electron-electron interactions.
245 citations
TL;DR: In this article, the authors implemented unimolecular rate theory for various types of reactions for any looseness of transition state, and the rate constant k(EJ) was weighted with the initial E and J distributions.
239 citations
TL;DR: In this article, the principle of equivalence is extended to reference frames described by quantum states and a consistent discription of such frames is obtained which resolves a variety of apparent paradoxes associated with such a description.
Abstract: Frames of reference attached to quantum-mechanical objects of finite mass are considered. A consistent discription of such frames is obtained which resolves a variety of apparent paradoxes associated with such a description. The main result of the present work is a formalism wherein the principle of equivalence is extended to reference frames described by quantum states.
166 citations
TL;DR: In this paper, the authors analyze the behavior of the subsystem and elucidate the meaning and interrelation of several ubiquitous concepts in the following context: weak coupling limit, Markovian limit, rotating-wave approximation (RWA), and low-temperature behavior.
Abstract: Statistical fluctuations in linear quantum-mechanical systems are shown to result from a projection of the total quantum system onto a restricted subspace. The resulting equations of motion are of the generalized Langevin form, with fluctuating and dissipative terms. These terms are related by a quantum-mechanical fluctuation-dissipation relation that ensures thermal equilibration. We analyze the dynamical behavior of the subsystem and elucidate the meaning and interrelation of several ubiquitous concepts in the following context: weak-coupling limit, Markovian limit, rotating-wave approximation (RWA), and low-temperature behavior. The three most salient consequences of our analysis are as follows: (1) The time scale for the correlation of fluctuations and the dissipation can be quite distinct, (2) the traditional implementation of the RWA only gives valid results in the strict weak-coupling limit, and (3) a reformulation of the RWA valid at arbitrary coupling strengths, and hence at arbitrarily low temperatures, is possible.
144 citations
TL;DR: In this article, a quaternionic Hilbert module, a closed linear vector space with many of the properties of a Hilbert space, is studied, and the propositional system formed by the subspaces of such a space satisfy the axioms of quantum theory.
133 citations
TL;DR: In this article, it is shown that information about correlations between a clock and another physical system can be represented just as well in a single "timeless" quantum state as in a whole history of states and that it is therefore not necessary to include time as a basic element in the description of the world.
Abstract: coordinate time is not observable, but “clock time” is observable, Therefore, any statement about temporal evolution can be replaced, without loss of observational content, by a statement about correlations between a clock and another physical system. We show that information about such correlations can be represented just as well in a single “timeless” quantum state as in a whole history of states. It is therefore not necessary to include “time” as a basic element in the description of the world.
120 citations
01 Jan 1984
TL;DR: In this paper, the authors describe a new formalism for analyzing a particular class of nonlinear optical devices, called two-photon devices, which operate as follows: several modes of the electromagnetic field are coupled via a nonlinearity in some material; two of the modes are the device's "signal" modes, the rest are "pump" modes; photons are created or destroyed in the signal modes two at a time.
Abstract: In this paper we describe a new formalism for analyzing a particular class of nonlinear optical devices. We call these devices two-photon devices because they operate as follows: several modes of the electromagnetic field are coupled via a nonlinearity in some material; two of the modes are the device’s “signal” modes, the rest are “pump” modes; photons are created or destroyed in the signal modes two at a time. Examples include parametric amplifiers and four-wave mixers. Two-photon devices are to be contrasted with one-photon devices, such as the laser, in which photons are created or destroyed in the signal mode one at a time. The formalism used in one-photon optics uses variables and quantum states suited to describing the output of a one-photon device.
TL;DR: In this paper, the generalization of the detailed balance condition is discussed in the framework of algebraic quantum statistical mechanics, and the generalized balance condition can be seen as a special case of the balance condition.
Abstract: The generalization of the detailed balance condition is discussed in the framework of algebraic quantum statistical mechanics.
TL;DR: In this paper, it was shown that energy and momentum are conserved only because of the asymptotic field equations and that this requires a large area in which the evolution of density operator can be localized to a few Planck lengths.
Book•
01 Jan 1984
TL;DR: The translation between microscopic and macroscopic behavior is discussed in this paper, where it is shown that the first law of entropy and the Second Law of Entropy can be expressed as follows:
Abstract: The Translation Between Microscopic and Macroscopic Behavior. Microscopic Behaviors and Quantum States. SMALL SYSTEMS. Statistics for Small Systems. Statistics for Systems of Many Elements. INTERNAL ENERGY. Internal Energy and Equipartition. Internal Energy and the First Law. ENTROPY. The States of a System. Entropy and the Second Law. INTERACTIONS. The Thermal Interaction. The Mechanical Interaction. The Diffusive Interaction. CONSTRAINTS. Models. Natural Constraints. Imposed Constraints. Engines and Refrigerators. CLASSICAL STATISTICS. Probabilities and Microscopic Behaviors. Equipartition. Maxwell Distribution for Gases. Transport Processes In Gases. Magnetic Properties of Materials. The Partition Function. Chemical Equilibrium. Equilibrium Between Phases. QUANTUM STATISTICS. The Occupants of Quantum States. Survey of Applications. Blackbody Radiation. The Thermal Properties of Solids. Semiconductors and Insulators. Low Temperatures. Index.
TL;DR: In this paper, the probability of transitions induced by the variation of the interaction potential between quantum states corresponding to the two sheets of the dispersion surface is calculated and the predictions of this theory are found to be in agreement with direct solutions of the Takagi-Taupin equations as well as with the experimental results.
Abstract: The propagation of neutron waves in a deformed crystal is considered from the point of view of quantum mechanics. Instead of solving the Takagi-Taupin equations the probability of transitions, induced by the variation of the interaction potential, between quantum states corresponding to the two sheets of the dispersion surface is calculated. In this way transmission and reflection coefficients for an incident plane wave are obtained after a simple analytical calculation for a wide class of crystal deformations. The predictions of this theory are found to be in agreement with direct solutions of the Takagi-Taupin equations as well as with the experimental results.
TL;DR: In this article, the construction of physical occupation and transition probabilities in non-Hermitian, effective-Hamiltonian models of coupled near-resonant discrete states which decay to a continuum is analyzed.
Abstract: The construction of physical occupation and transition probabilities in non-Hermitian, effective-Hamiltonian models of coupled near-resonant discrete states which decay to a continuum is analyzed. We consider for definiteness the particular physical example of atomic multiphoton ionization. The possibility of finite duration and arbitrary modulation of this interaction, and of the subsequent ionization and/or decay, in such a system allows us to invoke "adiabatic switching" considerations in conventional $S$-matrix theory. The effective Hamiltonian $\stackrel{^}{H}(t)$ is derived for both stationary and time-dependent Schr\"odinger equations. These derivations yield the same effective $\stackrel{^}{H}(t)$, and further reveal that this operator is associated with discrete-state-projected "incoming" scattering states. The Hermitian conjugate operator ${\stackrel{^}{H}}^{\ifmmode\dagger\else\textdagger\fi{}}(t)$ is similarly shown to be associated with discrete-state "outgoing" scattering states. This shows that effective-Hamiltonian theories are intrinsically $S$-matrix theories. This fact, in turn, is employed to construct transition amplitudes. The possibility of resonance in the atom-field interaction requires that both the projected incoming states and projected outgoing states be employed in this construction. The projected incoming and outgoing states in the (discrete) bound space are quite conveniently described by effective time-dependent Schr\"odinger equations, supplemented by initial- and final-state boundary conditions. The fact of independent-exponential decay from each mode throughout the history of the interaction, for an arbitrary initial superposition state, in the adiabatic limit, suggests a practical construction for intermediate-time bound-state probabilities. This construction permits the formal definition of individual-state probabilities, which satisfy a generalized adiabatic theorem, and leads to the satisfying result that the total bound-state probability at all intermediate times is the sum of complex-mode probabilities. In marked contrast to the conventional norm-of-state definition of nonionization probability, this sum does not have oscillations at intermediate times, in the limit of adiabatic modulation of the interaction. Superposition-state probabilities, however, exhibit oscillations at intermediate times. The resulting non-Hermitian quantum dynamics is especially suited, and even essential, for an accurate description of near-resonance ionization. Precise matching of the time-dependent $\stackrel{^}{H}(t)$ and ${\stackrel{^}{H}}^{\ifmmode\dagger\else\textdagger\fi{}}(t)$ with bases of their instantaneous eigenstates is required by approximate unitarity in the discrete decaying space, for a consistent theory. We illustrate these considerations in a general way in the context of resolvent-operator techniques. The implementation of the theory in both its time-dependent and stationary-state formulations is presented in an Appendix, for the completely general two-state non-Hermitian Hamiltonian. The results of these formulations are found to agree, in the adiabatic limit, to all orders in the non-Hermitian interaction. The utility of direct diagonalization of the effective $\stackrel{^}{H}(t)$, advocated by Armstrong and Baker, is transparent. The overall context of interpretation of their earlier work is, however, significantly altered. Similar considerations apply for nonswitchable interactions, such as for $K$-meson decays. These results represent a practical generalization of quantum mechanics to non-Hermitian systems. The utility, and the necessity, of such a generalization has considerable theoretical interest, and direct experimental implications.
TL;DR: In this paper, a Fock-like field theoretical approach was introduced to the description of quantum cosmology. And the total transition amplitude between two quantum states of the state functional of the ADM geometry was calculated in the case of Bianchi class A models.
Abstract: Within the ADM technique of Hamiltonian cosmology, in the case of Bianchi class A models, we introduce a Fock-like, field theoretical approach to the description of quantum cosmology. We then calculate the total transition amplitude between two quantum states of the state functional of the ADM geometry.
TL;DR: In this article, the propagation of quantized electromagnetic fields through optically isotropic media with cubic optical nonlinearity is considered and analytical solutions are presented in closed form showing that the light field can emerge from the medium in a squeezed quantum state.
Abstract: The propagation of quantized electromagnetic fields through optically isotropic media with cubic optical nonlinearity is considered. Analytical solutions are presented in closed form showing that the light field can emerge from the medium in a squeezed quantum state. A detailed numerical analysis of the results is performed and presented graphically. Over 90 per cent of the squeezing permitted by quantum-mechanical theory is achieved in this way. The dependence of the squeezing effect on the polarization state of the field and the nonlinear molecular parameters is also discussed.
01 Apr 1984
TL;DR: In this paper, the authors investigated the influence of regular and chaotic motion on the nature of the intermode vibrational energy transfer after local excitation in two-dimensional non-separable oscillator systems.
Abstract: The classical as well as the quantum dynamics of two-dimensional nonseparable oscillator systems is studied in order to investigate the influence of regular and chaotic motion on the nature of the intermode vibrational energy transfer after local excitation. Representative sets of initial conditions - each element representing a single phase space cell — were chosen. For the classical problem one phase space point per cell was used while for the quantum problem minimum uncertainty wave packets (harmonic oscillator coherent states) with position and momentum expectation values corresponding to the classical values were taken as initial quantum states. For both types of motion information entropies were determined from time averaged probabilities. These entropies are compared with “ergodic limit entropies”. The latter correspond to a statistical preparation of the initial states. Although there is only a weak correspondence between single-trajectory motion and wave packet dynamics, some general predictions about the quantum dynamics can be made from the classical results for a time scale of chemical interest. No sharp transition is found for the wave packet dynamics going from the classically regular to the irregular energy region. However, one can estimate the probability for an arbitrarily prepared local minimum uncertainty wave packet to possess statistical (RRKM) or non statistical (non-RRKM) dynamics from the analysis of a sample of classical trajectories each starting in a phase space cell of the bound area of the Hamiltonian, i.e., the nature of unimolecular reactions can be roughly predicted from the potential energy surface and a sample group of classical trajectories.
TL;DR: In this article, the authors formalize the propensity interpretation in the framework of state-property structures and prove that the set L of all properties is a complete atomic orthomodular lattice and that the probabilistic aspect of the system is entirely determined by its deterministic aspect.
Abstract: In quantum physics the tests of most properties do not have predetermined outcomes. The latter have nevertheless well‐defined probabilities of being realized during a test. Following Popper we interpret these probabilities as physical propensities. A first purpose of the present article is to formalize the propensity interpretation in the framework of state‐property structures. Next, Gleason’s theorem asserts that in the Hilbert space there exists a unique propensity function (i.e., one probability measure for each state vector); the propensities are thus uniquely determined by the state vector. Conversely, we prove that if the state‐property structure admits one and only one propensity function, then the set L of all properties is a complete atomic orthomodular lattice. We point out that according to our assumption the probabilistic aspect of the system is entirely determined by its deterministic aspect. Assuming furthermore that each property can be ideally tested, it follows that L is isomorphic to the...
TL;DR: In this article, the problem of characterising those quantum logics which can be identified with the lattice of projections in a JBW-algebra or a von Neumann algebra is considered.
Abstract: The problem of characterising those quantum logics which can be identified with the lattice of projections in a JBW-algebra or a von Neumann algebra is considered. For quantum logics which satisfy the countable chain condition and which have no TypeI2 part, a characterisation in terms of geometric properties of the quantum state space is given.
TL;DR: In this article, a new proof of the indeterminacy relation of the standard energy deviation and lifetime of a pure quantum state is given by means of the Mandelstam-Tamm inequality.
Abstract: A new proof of the indeterminacy relation of the standard energy deviation and lifetime of a pure quantum state is given by means of the Mandelstam-Tamm inequality.
TL;DR: In this article, it was shown that the Hose-Taylor criterion of quantum quasiperiodicity can be recovered from low-order non-degenerate perturbation theory.
Abstract: We show that the Hose–Taylor criterion of quantum quasiperiodicity can be recovered from low‐order nondegenerate perturbation theory. It is seen that this mnemonic, which purports to identify energy levels which can be obtained by quantizing classical quasiperiodic motions, can lead to contradictions when applied to systems which are more semiclassical than that treated previously. These discrepancies arise since the criterion is both perturbation scheme and basis set dependent: the correlation between the semiclassical quantization and such a definition of quantum quasiperiodic behavior is not straightforward. As the underlying search is for a quantum KAM‐like theory (in particular for near‐separable systems which are typical of molecular vibrational Hamiltonians) some possibilities are discussed.
TL;DR: The change in the meaning of observables and states in quantum physics as compared with classical physics is discussed and shown to account for the novel formal properties of quantum observables as mentioned in this paper.
Abstract: The change in the meaning of observables and states in quantum physics as compared with classical physics is discussed and shown to account for the novel formal properties of quantum observables and states. The special character of observation interactions in quantum physics, in particular the discontinuous reductions of state vectors during measurements, is readily understood if the novel meaning of quantum states is taken into account.
TL;DR: In this article, the ontological status of these "perspectives of potentialities" is discussed, and it is conjectured that they propagate from the location of a measurement to the origins of all frames of reference at the speed of light.
Abstract: Recent investigations have conclusively proved that, because of their collapse, quantum states transform noncovariantly under Lorentz transformations. This result is shown to imply that quantum states do not represent probability distributions for the results of measurements. They represent, rather, perspectives of such probability distributions from the point of view of the frame of reference in which they are given. The ontological status of these “perspectives of potentialities” is discussed. It is conjectured that they propagate from the location of a measurement to the origins of all frames of reference at the speed of light.
TL;DR: In this article, it is argued that the impossibility of observing coherent superpositions of certain macroscopically distinguishable quantum states is a combined effect of collective dissipation processes generated by an interaction of the N -particle system with external quantum fields and a coarse-grained character of real measurements.
TL;DR: In this article, the free NO 2 molecule is prepared into a well defined, isolated quantum state and its properties and dynamical behaviour are investigated. But the results of these experiments are contradictory to our knowledge on the properties and dynamics of a molecule in isolated quantum states.
TL;DR: The mathematical problem of the existence of the mean value and variance of unbounded observables is studied in this paper, where the authors consider both pure states and quantum mixtures, with particular care for the problems that arise in the latter case.
Abstract: In this paper we examine, in the framework of Hilbert-space quantum mechanics, the mathematical problem of the existence of the mean value and variance of unbounded observables. We consider both pure states and quantum mixtures, with particular care for the problems that arise in the latter case.
TL;DR: In this article, a conformally covariant formalism is developed for the open string and a recursive construction is presented which permits the counting of physical states of any given mass, spin, and parity.
Abstract: The classical field-dependent parametrization covariant Hamiltonian formulation of the open and the closed string is discussed. The formalism is not applicable to the open string. A conformally covariant formalism is developed for the open string. The Rohrlich gauge conditions are justified and applied. The parametrization of classical solutions is not uniquely fixed; the generators of rigid time translation in the parameter space remain first class. The constraints and gauge conditions are taken into account in the quantum theory as conditions on physical states. The required invariance of physical states under rigid displacement of parameter time leads to a mass superselection rule. The set of physical string quantum states is analogous to the set of states constructed by Di Vecchia, Del Guidice, and Fubini. A recursive construction is presented which permits the counting of physical states of any given mass, spin, and parity. Physical states lie on linearly rising Regge trajectories with one universal slope. The intercept of the leading trajectory is constrained only by the requirement that there be no tachyonic physical states. The quantization is carried out in four space-time dimensions.
01 Jan 1984
TL;DR: In this article, it was shown that it is not possible to reproduce or clone an incident photon in an arbitrary quantum state in the linear light amplifier, since it would imply a violation of the uncertainty principle, so fundamental limitations are imposed on the amplifier.
Abstract: The linear light amplifier has recently generated renewed discussion in connection with the question whether it is possible to reproduce or clone an incident photon in an arbitrary quantum state. [l–3] If exact cloning were possible, this would imply a violation of the uncertainty principle, so that some fundamental limitations are imposed on the amplifier. The same limitations prevent light amplifiers, when inserted into one or more arms of an interferometer, from allowing us to determine which path through the interferometer a given photon followed.[4] What prevents precise cloning of a photon is the existence of spontaneous and unpredictable photon emissions in any amplification mechanism,[2,3] so that there is only a stochastic connection between the incoming and outgoing photons. This is the subject of the present article.