9,881 research outputs found
Elementary solution to the time-independent quantum navigation problem
A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realizes a required quantum process or task, under the influence of a prevailing ‘background’ Hamiltonian that cannot be manipulated. When the task is to transform one quantum state into another, finding the solution in closed form to the problem is nontrivial even in the case of timeindependent Hamiltonians. An elementary solution, based on trigonometric analysis, is found here when the Hilbert space dimension is two. Difficulties arising from generalizations to higher-dimensional systems are discussed
Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian
The differential-equation eigenvalue problem associated with a
recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of
the Riemann zeta function, is analyzed using Fourier and WKB analysis. The
Fourier analysis leads to a challenging open problem concerning the formulation
of the eigenvalue problem in the momentum space. The WKB analysis gives the
exact asymptotic behavior of the eigenfunction
Operator-valued zeta functions and Fourier analysis
The Riemann zeta function is defined as the infinite sum
, which converges when . The Riemann
hypothesis asserts that the nontrivial zeros of lie on the line
. Thus, to find these zeros it is necessary to
perform an analytic continuation to a region of complex for which the
defining sum does not converge. This analytic continuation is ordinarily
performed by using a functional equation. In this paper it is argued that one
can investigate some properties of the Riemann zeta function in the region
by allowing operator-valued zeta functions to act on test
functions. As an illustration, it is shown that the locations of the trivial
zeros can be determined purely from a Fourier series, without relying on an
explicit analytic continuation of the functional equation satisfied by
.Comment: 8 pages, version to appear in J. Pays.
Accrediting and the Sherman Act
The shortcomings of the Sherman Act as it relates to private accrediting are examined in order to assist courts in minimizing the anticompetitive features of accreditation and maximizing its procompetitive benefits. A lack of clear legal principles to guide factual analysis and to facilitate the granting of summary judgment in appropriate cases has led to unfocused and protracted litigation
Note on exponential families of distributions
We show that an arbitrary probability distribution can be represented in
exponential form. In physical contexts, this implies that the equilibrium
distribution of any classical or quantum dynamical system is expressible in
grand canonical form.Comment: 5 page
Photoproduction of K^+ Mesons in Hydrogen
The photoproduction of K^+ mesons in hydrogen has been measured with the purpose of extending the previous CalTech measurements to smaller angles, and obtaining better absolute values for the cross sections. The technique of Donoho and Walker, using a magnetic spectrometer and a time-of-flight measurement to detect the K^+ mesons, was modified so as to achieve a better discrimination against pions and scattered protons. The results obtained are in fairly good agreement with the more extensive measurements made at Cornell by a somewhat different method
Must a Hamiltonian be Hermitian?
A consistent physical theory of quantum mechanics can be built on a complex
Hamiltonian that is not Hermitian but instead satisfies the physical condition
of space-time reflection symmetry (PT symmetry). Thus, there are infinitely
many new Hamiltonians that one can construct that might explain experimental
data. One would think that a quantum theory based on a non-Hermitian
Hamiltonian violates unitarity. However, if PT symmetry is not broken, it is
possible to use a previously unnoticed physical symmetry of the Hamiltonian to
construct an inner product whose associated norm is positive definite. This
construction is general and works for any PT-symmetric Hamiltonian. The
dynamics is governed by unitary time evolution. This formulation does not
conflict with the requirements of conventional quantum mechanics. There are
many possible observable and experimental consequences of extending quantum
mechanics into the complex domain, both in particle physics and in solid state
physics.Comment: Revised version to appear in American Journal of Physic
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