Showing papers on "Quantum state published in 1988"

Models for universal reduction of macroscopic quantum fluctuations

Abstract: This paper adopts the hypothesis that the absence of macroscopic quantum fluctuations is due to a certain universal mechanism. Such a mechanism has recently been proposed by Ghirardi et al. [Phys. Rev. D 34, 470 (1986)], and here we recapitulate a compact version of it. K\'arolyh\'azy [Nuovo Cimento 52, 390 (1966)] showed earlier the possible role of gravity and, along this line, we construct here a new parameter-free unification of micro- and macrodynamics. We apply gravitational measures for reducing macroscopic quantum fluctuations of the mass density. This model leads to classical trajectories in the macroscopic limit of translational motion. For massive objects, unwanted macroscopic superpositions of quantum states become destroyed in very short times. The relation between state-vector and density-operator formalisms has also been discussed. We only anticipate the need for elaborating characteristic predictions of the model in the region separating micro- and macroscopic properties.

Wormholes in spacetime.

Abstract: Any reasonable theory of quantum gravity will allow closed universes to branch off from our nearly flat region of spacetime. I describe the possible quantum states of these closed universes. They correspond to wormholes which connect two asymptotically Euclidean regions, or two parts of the same asymptotically Euclidean region. I calculate the influence of these wormholes on ordinary quantum fields at low energies in the asymptotic region. This can be represented by adding effective interactions in flat spacetime which create or annihilate closed universes containing certain numbers of particles. The effective interactions are small except for closed universes containing scalar particles in the spatially homogeneous mode. If these scalar interactions are not reduced by sypersymmetry, it may be that any scalar particles we observe would have to be bound states of particles of higher spin, such as the pion. An observer in the asymptotically flat region would not be able to measure the quantum state of closed universes that branched off. He would therefore have to sum over all possibilities for the closed universes. This would mean that the final state would appear to be a mixed quantum state, rather than a pure quantum state.

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.

Quantum Coherence Down the Wormhole

Abstract: It is shown that pure quantum states will appear to decay into mixed states in any theory of quantum gravity that allows the topology of spacetime to be non simply connected. The reason is that the final state may contain little closed universes. There is no way one can detect the existence of these closed universes, or measure their quantum state. This means that the part of the final state that is in asymptotically flat spacetime, appears to be in a mixed state. The loss of quantum coherence in particle collisions is estimated. It comes from a wormhole connecting two asymptotically euclidean regions. The effect would be significant for scalar particles. It would make any scalar field that was not coupled to a Yang-Mills field constant throughout spacetime. It could have an important effect on Higgs particles but the effect would be small for particles of higher spin.

Phase space structure in classically chaotic regions and the nature of quantum eigenstates

Abstract: The authors review recent work concerning phase space structure relevant to energy relaxation and chemical reactions. Another example is shown, and that is for the local to normal mode transition in classically chaotic regions. The main purpose of the paper is to investigate the nature of the quantum eigenstates under such a condition, and they investigate what happens to the local and normal mode character of eigenstates when there is widespread chaos and there is extensive exchange of energy between two local modes and local and normal modes classically. They show that the quantum local-normal transition does not change significantly as classical chaos spreads. They relate this to the size of the flux across various phase space structures and present evidence that the quantum mechanics is essentially regular even when chaos is so widespread that, near the dissociation energy, chaotic regions can support approximately 10 quantum states. To further demonstrate this regularity, they quantitize some of the noninvariant phase space structure.

Wave Function of the Universe

Abstract: The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\ensuremath{\Lambda}g0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.

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

Photon-number distributions for quantum fields generated in nonlinear optical processes

Abstract: We show that in a large class of nonlinear optical processes which are used to generate the squeezed states of the radiation field, the quantum state of the generated radiation is given by a Gaussian Wigner function. This is so even when losses in the medium are included. The photon-number distributions for such fields are evaluated. The number distributions exhibit oscillatory character for the range of parameters for which the field is squeezed.

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.

Regular/irregular phase space structure of HCN/HNC

Abstract: A detailed 3D classical nonlinear mechanical analysis of HCN/HNC system is carried out and the results are compared with 2D quantum mechanical vibrational calculations as well as with the recent 3D quantum calculations of Bacic and Light. HCN is marked by regular behavior which persists at high energies when the stretching modes are excited. Chaotic trajectories located in the HNC well are those which lead to isomerization of HNC. The regular/irregular phase space structure agrees well with the corresponding assignment of quantum states. A multiple resonance among the vibrational modes of HCN, located at the top of the effective barrier of isomerization, is considered as the classical cause of the lack of delocalization of the wave functions found in the 3D quantum calculations.

Quantization of the continuous Heisenberg ferromagnet

Abstract: The quantization of the continuous anisotropic Heisenberg ferromagnet with uniaxial anisotropy is performed by means of the quantum inverse scattering method. The space of quantum states is shown to possess the positive metric only in the su(1, 1) case (the magnet on the hyperboloid). The requirement of complete integrability leads, in the anisotropic case, to a deformation of the algebra of observables. The problem of local integrals of motion is discussed. The Hamiltonian is constructed for two-particle states.

Extended wave description of a massive spin-0 particle

Abstract: The two-wave space-time description of a massive spin-0 particle in the external electromagnetic field is developed. In the nonrelativistic limit the spacelike counterpart of the Schrodinger equation is derived. In particular, it implies the existence of spacelike quantum states for a bound charged particle. The statistical interpretation of spacelike quantum states is proposed and the spacelike counterpart of the Heisenberg uncertainty relation is obtained.

Comment on "Obtainment of thermal noise from a pure quantum state"

Abstract: Yurke and Potasek [Phys. Rev. A 36, 3464 (1987)] have shown that pure states of correlated pairs of quantum systems can lead to mixed-state behavior if only one of the systems is observed. We note that such behavior is well known and describe how the mixed-state properties of these states have led to their application in thermodynamical problems via the thermofield formalism. The correlations have been found to lead to manifestly nonclassical behavior (such as squeezing) if both systems are observed.

Wehrl's entropy of spin states and Lieb's conjecture

Abstract: Wehrl's entropy is the entropy of the probability distribution in the phase space corresponding to the Q representation (antinormal ordering of operators) of a quantum state in terms of coherent states. The Hilbert space of a system of N spins (or N two-level atoms) is of 2N dimensions. The subspace with maximum total spin N/2 is of N+1 dimensions. All discussions are restricted within this subspace. The probability amplitude for an arbitrary pure state in this subspace is a polynomial of degree N which can be factorised into the product of N linear factors and each root can be identified with one point on the unit sphere. Hence, an arbitrary state in the subspace can be represented geometrically by N unit vectors. The general expression for the Wehrl entropy is obtained as a finite series expansion in terms of some symmetric functions of sin2( omega ij/2), where omega ij is the angle between a pair of unit vectors. The special cases of coherent and almost coherent spin states are then considered.

Quantized energy levels in Si inversion layers: A simplified self‐consistent approach

Abstract: A quasi‐analytical approximation scheme has been derived to calculate energies, wave functions and populations for the quantum states of electrons in p‐Si inversion layers. The analytical character of the wave functions is preserved throughout the computation, and the usual constraint of satisfying Poisson’s and Schrodinger’s equations self‐consistently everywhere in space is bypassed by putting forward physically justified guesses for the functional form of the wave function and the inversion layer potential, and imposing the equality of the first few electrical and quantum‐mechanical moments. The values obtained compare favorably with earlier results extracted from purely numerical methods.

Environmental effects on radiative lifetimes and mass renormalization, according to stochastic electrodynamics.

Abstract: The environmental effects on the mass renormalization and on the rate of radiative transitions, produced by the presence of conducting objects that alter the electromagnetic-field structure, are studied from the point of view of stochastic electrodynamics. The mass correction is shown to be a tensor that depends on both position and direction of motion. A fluctuation-dissipation theorem is obtained, which leads to the independence of quantum states from environmental changes; only the radiative corrections are affected by the surroundings. The results obtained are discussed in the light of recent experiments and of earlier quantum theoretical calculations.