Showing papers on "Open quantum system published in 1988"

Quantum correlations: A generalized Heisenberg uncertainty relation.

Abstract: A theoretical result for correlated quantum systems is presented which leads to a noise commutation relation and a generalized Heisenberg uncertainty relation. These relations imply an inherent and unavoidable extra noise in quantum measurements beyond that already included in the Heisenberg lower bound. These relations lead directly to model-independent lower bounds on inherent noise, useful in a variety of applications, including balanced homodyne detection and quantum optical linear amplifiers.

What are Quantum Jumps

Abstract: This paper answers the title question by giving an operational definition of quantum jumps based on measurement theory. This definition forms the basis of a theory of quantum jumps which leads to a number of testable predictions. Experiments are proposed to test the theory. The suggested experiments also test the quantum Zeno paradox, i.e., they test the proposition that frequent observation of a quantum system inhibits quantum jumps in that system.

Aspects of chaos in nuclear physics

Abstract: This article addresses the role of such concepts as chaos and predictability in the context of nuclear physics. The topic of this article is closely linked with such diverse areas as random-matrix theory, chaos in classical dynamical systems, statistical mechanics of small quantum systems, and the theory of disordered solids. We present recent information on nuclear data and on their analysis in terms of random-matrix models, a summary of work done on classical chaotic systems, on their quantum analogues, and on special systems like the hydrogen atom in a strong magnetic field. Also, we discuss how random-matrix models can be used to simulate chaotic behaviour in small quantum systems, the role of symmetries (isospin, parity, and time-reversal) in chaotic quantum (nuclear) systems, and how chaos surfaces in experimental and theoretical investigations in molecular physics, in the physics of small clusters, and the analysis of conductance fluctuations in solids. (AIP)

Equivalence relations between deterministic and quantum mechanical systems

Abstract: Several quantum mechanical models are shown to be equivalent to certain deterministic systems because a basis can be found in terms of which the wave function does not “spread.” This suggests that apparently indeterministic behavior typical for a quantum mechanical world can be the result of locally deterministic laws of physics. We show how certain deterministic systems allow the construction of a Hilbert space and a Hamiltonian so that at long distance scales they may appear to behave as quantum field theories, including interactions but as yet no mass term. These observations are suggested to be useful for building theories at the Planck scale.

Quantum chaos in a schematic shell model

Abstract: To test the connection between chaotic classical motion and quantum spectral and overlap statistics, we examine a schematic three-orbital shell model. This system is novel in that the quantum phase space is compact and the momentum dependence of the classical Hamiltonian is nonstandard. We find good agreement with the expected behavior of the spectral statistics and reasonable agreement for the overlap distributions. Also, there is evidence that the eigenvector statistics are more sensitive to the details of the classical dynamics than are the eigenvalues.

Hybrid mechanics: A combination of classical and quantum mechanics

Abstract: Because classical mechanics is so much easier to handle than quantum mechanics, the time evolution of wave functions for molecular dynamics is often calculated using semiclassical methods. The errors of such methods grow, in general, faster than linearly with time, although they may be quite small for small, but finite times. We therefore propose to use a semiclassical method to calculate the quantum mechanical time propagator for a finite time step (say 1/10 of a vibrational period) and to use this propagator and quantum mechanics for longer times. To describe the quantum time propagator we use a basis set that can describe regions in phase space that are not necessarily rectangular, but can have any shape, that will become important in applications to higher dimensions. We give numerical examples to demonstrate the accuracy of the method.

Experimental approaches to the quantum measurement paradox

Abstract: I examine the question of how far experiments that look for the effects of superposition of macroscopically distinct states are relevant to the classic measurement paradox of quantum mechanics. Existing experiments on superconducting devices confirm the predictions of the quantum formalism extrapolated to the macroscopic level, and to that extent provide strong circumstantial evidence for its validity at this level, but do not directly test the principle of superposition of macrostates. A more ambitious experiment, not obviously infeasible with current technology, could provide a direct test between quantum mechanics and a whole class of theories embodying the postulate of realism at the macroscopic level.

Quantum theory of fourth-order interference.

Abstract: The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.

Realistic quantum probability

Abstract: A mathemetical framework for a realistic quantum probability theory is presented. The basic elements of this framework are measurements and amplitudes. Definitions of the various concepts are motivated by guidelines from the path integral formalism for quantum mechanics. The operational meaning of these concepts is discussed. Superpositions of amplitude functions are investigated and superselection sectors are shown to occur in a natural way. It is shown that this framework includes traditional nonrelativistic quantum mechanics as a special case. Proofs of most of the theorems will appear elsewhere.

Non-integrable quantum phase in the evolution of a spin-1 system : a physical consequence of the non-trivial topology of the quantum state-space

Abstract: 2014 When a quantum state evolves in such a way as to describe a closed loop in the space of pure state density matrices, it must, as a consequence of the non trivial topology of this space acquire a path-dependent phase. When the state vector | 03C8 ~ evolution is such that 03C8 | d/dt | 03C8 > = 0, the resulting phase is that introduced by Aharanov and Anandan (thereafter called the A.A. phase). Mathematically this condition corresponds to a parallel transport of | 03C8 ~ by a connection defined on a fiber bundle. This paper contains an elementary and self-contained discussion of the A.A. phase for a spin-1 system. In this case, the phase appears as the holonomy of the natural connection over the complex projective space P2(C). Experimental verification of these ideas requires expressions for both the phase in terms of the path and a Hamiltonian which will parallely transports the state vector along the path. They are given in terms of four directly measurable quantities which parametrize the pure state spin-1 density matrices. It is not possible to measure directly the A.A. phase on an isolated system ; it requires the separating and subsequent bringing together of two subsystems which undergo different evolutions. We suggest two ways in which, in principle, the A.A. phase might be measured in the laboratory. J. Phys. France 49 (1988) 187-199 FTVRIER 1988, Classification Physics Abstracts 03.65 42.50 (+ ) Permanent address : Dept. of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, G.B. (*) Laboratoire Propre du Centre National de la Recherche Scientifique, associd a 1’Ecole Normale Sup6rieure et a l’Universit6 de Paris-Sud, France. Introduction. One of the most fundamental tenets of Quantum Mechanics is the Superposition Principle. Superficially this would seem to imply that the theory is basically a linear one. However, by virtue of the equally fundamental assumption that two wave funcArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01988004902018700

Coherent population trapping in N-level quantum systems

Abstract: A multilevel quantum system interacting with an intense laser field is shown to exhibit many invariants, or constants of evolution, under various conditions Our results also apply to other similar physical problems

Quantum kinematics of spacetime. II. A model quantum cosmology with real clocks

Abstract: Nonrelativistic model quantum cosmologies are studied in which the basic time variable is the position of a clock indicator and the time parameter of the Schr\"odinger equation is an unobservable label. Familiar Schr\"odinger-Heisenberg quantum mechanics emerges if the clock is ideal---arbitrarily accurate for arbitrarily long times. More realistically, however, the usual formulation emerges only as an approximation appropriate to states of this model universe in which part of the system functions approximately as an ideal clock. It is suggested that the quantum kinematics of spacetime theories such as general relativity may be analogous to those of this model. In particular it is suggested that our familiar notion of time in quantum mechanics is not an inevitable property of a general quantum framework but an approximate feature of specific initial conditions.

Quantum propensiton theory: a testable resolution of the wave/particle dilemma

Abstract: In this paper I put forward a new micro realistic, fundamentally probabilistic, propensiton version of quantum theory. According to this theory, the entities of the quantum domain - electrons, photons, atoms - are neither particles nor fields, but a new kind of fundamentally probabilistic entity, the propensiton - entities which interact with one another probabilistically. This version of quantum theory leaves the Schroedinger equation unchanged, but reinterprets it to specify how propensitons evolve when no probabilistic transitions occur. Probabilisitic transitions occur (...) when new "particles" are created as a result of inelastic interactions. All measurements are just special cases of this. This propensiton version of quantum theory, I argue, solves the wave/particle dilemma, is free of conceptual problems that plague orthodox quantum theory, recovers all the empirical success of orthodox quantum theory, and at the same time yields as yet untested predictions that differ from those of orthodox quantum theory

Quantum mechanics without wave functions

Abstract: The phase space formulation of quantum mechanics is based on the use of quasidistribution functions. This technique was pioneered by Wigner, whose distribution function is perhaps the most commonly used of the large variety that we find discussed in the literature. Here we address the question of how one can obtain distribution functions and hence do quantum mechanics without the use of wave functions.

Quantization and phase-space methods for slowly varying optical fields in a dispersive nonlinear medium.

Abstract: We consider the quantization of slowly varying optical fields in a dispersive nonlinear medium and the application of phase-space methods to the resulting quantum field equations. A pragmatic approach to the quantization of the electromagnetic field is adopted whereby we apply canonical quantization to the Hamiltonian expressed in terms of the slowly varying electric field envelope, all approximations (quasimonochromatic and paraxial) having been made at the classical level. This approach allows us to include material dispersion, diffraction, and nonlinearity. Using phase-space methods we then develop a c-number functional Fokker-Planck equation from which the quantum statistical properties of propagating optical fields can be deduced.

The quantum chaos problem

Abstract: This review describes the present state of the quantum chaos problem: The problem of determining the specific properties of autonomous and nonautonomous quantum systems with few degrees of freedom whose classical analogs have an unstable (stochastic) motion and also that of determining the relationships between these properties and the characteristics of the classical stochastic situation. The criteria for quantum chaos which have been established to date are examined and compared for autonomous systems. These criteria make use of properties of the energy spectrum, the wave functions in various representations, the matrices of operators other than the Hamiltonian, and particular features of the evolution of time-varying states (wave packets) in such systems. For nonautonomous systems, the conditions for the applicability of classical dynamics for describing observables and certain specific quantum-mechanical effects (tunneling through a separatrix and a global quantum resonance) are analyzed.

Observable effects of the quantum adiabatic phase for noncyclic evolution.

Abstract: It is pointed out that, contrary to naive expectation, the gauge structure or Berry connection recently found in slowly varying quantum systems gives rise to observable effects even for noncyclic evolutions corresponding to open paths in parameter space. We propose to test such effects in muon spin resonance and in level-crossing resonance in muon-spin-rotation spectroscopy. In our proposals either the probe or the system itself has a lifetime much shorter than the period of one adiabatic cycle.

Supersymmetric quantum mechanics: two simple examples

Abstract: Supersymmetry is exhibited in two of the simplest quantum mechanical systems and used to solve the corresponding spectral and scattering problems; these systems are the delta potential and the sech2 x potential.