1,228 research outputs found
Coherent states and the reconstruction of pure spin states
Coherent states provide an appealing method to reconstruct efficiently the pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s + 1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeros of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stem-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase space which are smaller than (h) over bar
PT-symmetry and its spontaneous breakdown explained by anti-linearity
The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PE-symmetric Harniltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PE. In this framework, the concept of a spontaneously broken PE-symmetry is not needed
Reconstruction of the spin state
System of 1/2 spin particles is observed repeatedly using Stern-Gerlach
apparatuses with rotated orientations. Synthesis of such non-commuting
observables is analyzed using maximum likelihood estimation as an example of
quantum state reconstruction. Repeated incompatible observations represent a
new generalized measurement. This idealized scheme will serve for analysis of
future experiments in neutron and quantum optics.Comment: 4 pages, 1 figur
A quantum search for zeros of polynomials
A quantum mechanical search procedure to determine the real zeros of a polynomial is introduced. It is based on the construction of a spin observable whose eigenvalues coincide with the zeros of the polynomial. Subsequent quantum mechanical measurements of the observable output directly the numerical values of the zeros. Performing the measurements is the only computational resource involved
Chaos and quantum-nondemolition measurements
The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ‘‘deterministic randomness’’ in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity
Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field
The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck’s constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution
Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems
Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because another formulation can be given to unitary perturbation theory. When worked out for quantum spin systems, this variant is found to be formally equivalent to canonical perturbation theory applied to nearly integrable systems consisting of classical spins. In particular, it becomes possible to locate the quantum-mechanical operator-valued equivalent of the frequency denominators that may cause divergence of the classical perturbation series. The results that are established here link the concept of quantum-mechanical integrability to a technical question, namely, the behavior of specific perturbation series
Signatures of quantum integrability and nonintegrability in the spectral properties of finite Hamiltonian matrices
For a two-spin model which is (classically) integrable on a five-dimensional
hypersurface in six-dimensional parameter space and for which level
degeneracies occur exclusively (with one known exception) on four-dimensional
manifolds embedded in the integrability hypersurface, we investigate the
relations between symmetry, integrability, and the assignment of quantum
numbers to eigenstates. We calculate quantum invariants in the form of
expectation values for selected operators and monitor their dependence on the
Hamiltonian parameters along loops within, without, and across the
integrability hypersurface in parameter space. We find clear-cut signatures of
integrability and nonintegrability in the observed traces of quantum invariants
evaluated in finite-dimensional invariant Hilbert subspaces, The results
support the notion that quantum integrability depends on the existence of
action operators as constituent elements of the Hamiltonian.Comment: 11 page
Structure of nonlinear gauge transformations
Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations
(NGT) defined in terms of a wave function do not form a group. To get
a group property one has to consider transformations that act differently on
different branches of the complex argument function and the knowledge of the
value of is not sufficient for a well defined NGT. NGT that are well
defined in terms of form a semigroup parametrized by a real number
and a nonzero which is either an integer or . An extension of NGT to projectors and general density matrices
leads to NGT with complex . Both linearity of evolution and Hermiticity
of density matrices are gauge dependent properties.Comment: Final version, to be published in Phys.Rev.A (Rapid Communication),
April 199
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