Showing papers on "Quantum state published in 1981"

Statistical distance and Hilbert space

Abstract: A concept of "statistical distance" is defined between different preparations of the same quantum system, or in other words, between different rays in the same Hilbert space. Statistical distance is determined entirely by the size of statistical fluctuations occurring in measurements designed to distinguish one state from another. It is not related, a priori, to the usual distance (or angle) between rays. One finds, however, that these two kinds of distance are in fact the same, a result which depends on certain peculiarities of quantum mechanics.

N -Level Coherence Vector and Higher Conservation Laws in Quantum Optics and Quantum Mechanics

Abstract: The presence of unitary group generators in the time evolution of $N$-level quantum systems is shown to suggest a class of new nonlinear constants of motion, and to permit the description of the evolution in terms of the rotations of a real coherence vector.

Can we make sense out of the measurement process in relativistic quantum mechanics

Abstract: We study the instantaneity of the state-reduction process in relativistic quantum mechanics. The conclusion of various authors that this instantaneity will restrict the set of relativistic observables to purely local ones (i.e., that the measurement of any nonlocal property of a system at a well-defined time would give rise to violations of relativistic causality) is found to be erroneous, and experiments (of a kind not encountered before in measurement theory) are described whereby certain nonlocal properties of some simple physical systems can be measured at a well-defined time without violating causality. The attempts of certain authors to reconcile the reduction process with the covariance of the relativistic quantum state are considered and found wanting, and it is argued that the covariance of relativistic quantum theories resides exclusively in the experimental probabilities, and not in the underlying quantum states. The problem of nonlocal measurement is considered in general: distinctions (which are not to be met with in the nonrelativistic case) arise in relativistic quantum mechanics between what can be measured for fermions and what can be measured for bosons, between what can be measured for individual systems and what can be measured for ensembles, and between what kinds of states can be verified by measurement and what kinds of states can be prepared by measurement; and these pose difficult questions about the nature of measurement itself.

Quantum difference nonlinear Schrödinger equation

Abstract: The quantum inverse problem method is applied to the nonlinear Schrodinger equation on a one-dimensional chain. The commutation relations of field operators are noncanonical. The generating functional of quantum integrals of the motion, creation and annihilation operators of the eigenstates are constructed.

Multidimensional wave functions from classical trajectories

Abstract: A new technique is developed to generate semiclassical wave functions The method uses only information already available from a standard semiclassical quantization of a system Linear superpositions of Gaussian coherent states that lie along quantizing classical trajectories are used, with phases given by the action integrals plus a Maslov‐type correction Wave functions generated in this way suffer from none of the problems with caustics that primitive semiclassical wave functions encounter The semiclassical wave functions are convenient for subsequent use in applications, eg, molecular spectra By generating wave functions for several simple systems, we show that under most circumstances these wave functions are very accurate approximations to the true quantum states

Laser cooling of trapped particles III: The Lamb-Dicke limit

Abstract: In this paper we consider the laser cooling of a trapped particle when the discrete nature of the quantum levels must be taken into account. We particularize the equations to the Lamb-Dicke limit when the oscillational, amplitude is much less than the optical wavelength. Then the quantum levels are coupled only to the neighbouring ones, and we can also find a small parameter to use for adiabatic elimination of rapidly varying terms. There emerges one rate equation for the probability distribution over the quantum states. The ultimate distribution is found to be of the Planckian type independently of the initial one. We solve the equation, generally and obtain the time evolution for an arbitrary initial distribution. In particular we look at an initially thermal, Poisson, or pure state distribution. For the thermal one we find that its shape is preserved during the cooling. The results are discussed.

A self-consistent approach to quantum field theory for extended particles

Abstract: A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincare group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.

Magnetic state selector

Abstract: An improvement in an atomic or molecular magnetic quantum state selector wherein the bore and gap spacing may be adjusted or calibrated precisely after assembly by providing adjustable segments in the supporting structure surrounding the pole tips. The adjustable bore and gaps make it feasible to construct small size state selectors with precision bore and gap dimensions which have heretofore been difficult or impossible to realize due to the unrealistically small dimensional tolerances which would be required in previous conceptions of these devices.

Spin quantum number in the ground state of the Mattis-Heisenberg model

Abstract: Total spin quantum number is rigorously calculated for a quantum version of the Mattis model of random spin systems. Crossover between three universality classes of the Ising model, theXY model, and the Heisenberg model is explicitly worked out in the presence of randomness. The randomness of the type of the Mattis model is shown to have no thermodynamic effects even in quantum systems.

On a Quantum Algebraic Approach to Phase Space

Abstract: We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms o f a matrix algebra in a phase space. This makes clear not only the similarities o f the two theories, but also certain essential differences, and lays a Jbundation for understanding their relationship. We use the Wigner-Moyal trans]brmation as a change o f representation in phase space, and we avoM the problem of"negative probabilities" by regarding the solutions o f our equations as constants o f the motion, rather than as statistical weight factors. We show a close relationship o f our work to that o f Prigogine and his group. We bring in a new nonnegative probability function, and we propose extensions o f the tlueory to cover thermodynamic processes invoh, ing entropy changes, as well as the usual reversible processes.

Classical Limit of the Number of Quantum States

Abstract: A heuristic principle in quantum mechanics says that the number of quantum states supported by a subset S of classical phase space (of dimension 2d) is given by h−d|S|, where h is Planck’s constant One precise version of this is that as h ➛ 0, hd times the number of energy eigenvalues ≤ E approaches the volume of the set in phase space with energy less than E We generalize this to apply to continuous spectrum as well, showing that hd times the number of states with energy below E and position in B ≡ hdtr(χB(Q)χ(-−∞,E) (H)) approaches the volume of the corresponding subset of phase space, for H = −h2Δ + V(Q), with mild regularity conditions on V (Q = multiplication by position) The quantity we study has a statistical interpretation, and it exhibits the resonances of H

On quantum solitons and their classical relatives: II. ‘‘Fermion–boson reciprocity’’ and classical vs quantum problem for the sine‐Gordon system

Abstract: Both quantum and classical sine–Gordon fields can be built out of the fundamental free neutral massive excitations, which quantally obey the Bose–Einstein statistics. At the roots of the ’’boson‐fermion reciprocity’’ invented by Coleman, lies the spin 1/2 approximation of the underlying Bose system. By generalizing the coherent state methods to incorporate non‐Fock quantum structures and to give account of the so‐called boson transformation theory, we construct the carrier Hilbert space HSG for quantum soliton operators. The h/→0 limit of state expectation values of these operators among pure coherentlike states in HSG reproduces the classical sine–Gordon field. The related (classical and quantum) spin 1/2 xyz Heisenberg model field is built out of the fundamental sine–Gordon excitations, and hence can be consistently defined on the appropriate subset of the quantum soliton Hilbert space Hxyz . A correct classical limit is here shown to arise for the Heisenberg system: phase manifolds of the classical Hei...

Quantum rate theory of relaxation in symmetrical microscopic systems II: Preparation of initial states

Abstract: The preparation process of initial quantum states for the relaxation in symmetrical molecular complexes is studied theoretically. It is shown that the possibility of preparing a definite quasistable molecular complex is drastically dependent on the magnitude of the minimal experimental error to detect this complex in real measurements. Consequences of the theory on the existence of classical and non classical structures of the 2-norbornyl cation as intermediate complex in chemical reactions are discussed.

A classical stochastic description of the quantum lattice gas model

Abstract: Here we represent the quantum states of the finite lattice gas as a probability measure on a space Ω of finite sequences of zeros and ones All relevant observables, like functions of the Hamiltonian (and the Hamiltonian itself) and number operators, are written as real functions on Ω, thus we achieve a complete representation

A geometrical approach to elementary particles

Abstract: Starting from abstract quantum states of spin 1/2, the rishon states as introduced by Harari and Shupe, and projecting them onto a three-dimensional space, one describes a geometrical model of elementary particles in which leptons, quarks and hadrons are treated on the same footing. Their internal quantum numbers are thus related to the rishon content of these particles or states. A basic hypothesis on the lepton and quark generations allows a coherent graphical representation of elementary particles which gives a clear comprehension of their possible decay modes and seems to limit to four the generation number of leptons. An empirical mass formula for higher quark generation is then proposed leading to a prediction for t-quark mass value. The possible existence of exotic particles is then considered.