75,581 research outputs found
Green Functions for the Wrong-Sign Quartic
It has been shown that the Schwinger-Dyson equations for non-Hermitian
theories implicitly include the Hilbert-space metric. Approximate Green
functions for such theories may thus be obtained, without having to evaluate
the metric explicitly, by truncation of the equations. Such a calculation has
recently been carried out for various -symmetric theories, in both quantum
mechanics and quantum field theory, including the wrong-sign quartic
oscillator. For this particular theory the metric is known in closed form,
making possible an independent check of these approximate results. We do so by
numerically evaluating the ground-state wave-function for the equivalent
Hermitian Hamiltonian and using this wave-function, in conjunction with the
metric operator, to calculate the one- and two-point Green functions. We find
that the Green functions evaluated by lowest-order truncation of the
Schwinger-Dyson equations are already accurate at the (6-8)% level. This
provides a strong justification for the method and a motivation for its
extension to higher order and to higher dimensions, where the calculation of
the metric is extremely difficult
Extending PT symmetry from Heisenberg algebra to E2 algebra
The E2 algebra has three elements, J, u, and v, which satisfy the commutation
relations [u,J]=iv, [v,J]=-iu, [u,v]=0. We can construct the Hamiltonian
H=J^2+gu, where g is a real parameter, from these elements. This Hamiltonian is
Hermitian and consequently it has real eigenvalues. However, we can also
construct the PT-symmetric and non-Hermitian Hamiltonian H=J^2+igu, where again
g is real. As in the case of PT-symmetric Hamiltonians constructed from the
elements x and p of the Heisenberg algebra, there are two regions in parameter
space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in
which all the eigenvalues are real and a region of broken PT symmetry in which
some of the eigenvalues are complex. The two regions are separated by a
critical value of g.Comment: 8 pages, 7 figure
The quantum anharmonic oscillator in the Heisenberg picture and multiple scale techniques
Multiple scale techniques are well-known in classical mechanics to give
perturbation series free from resonant terms. When applied to the quantum
anharmonic oscillator, these techniques lead to interesting features concerning
the solution of the Heisenberg equations of motion and the Hamiltonian
spectrum.Comment: 18 page
Symmetry Considerations for the Detection of Second-Harmonic Generation in Cuprates in the Pseudogap phase
A proposal to test the proposed time-reversal and inversion breaking phase in
the Pseudogap region of the Cuprate compounds through the variation of
Second-harmonic generation intensity with temperature and polarization and
angle of incidence is presented.Comment: 7 pages, 2 figures include
Entanglement Efficiencies in PT-Symmetric Quantum Mechanics
The degree of entanglement is determined for an arbitrary state of a broad
class of PT-symmetric bipartite composite systems. Subsequently we quantify the
rate with which entangled states are generated and show that this rate can be
characterized by a small set of parameters. These relations allow one in
principle to improve the ability of these systems to entangle states. It is
also noticed that many relations resemble corresponding ones in conventional
quantum mechanics.Comment: Published version with improved figures, 5 pages, 2 figure
Continuous canonical correlation analysis
Given a bivariate distribution, the set of canonical correlations and functions
is in general finite or countable. By using an inner product between
two functions via an extension of the covariance, we find all the canonical
correlations and functions for the so-called Cuadras-Aug´e copula and prove
the continuous dimensionality of this distribution
Nuclear weapons and European interests : Discussions in the Assembly of the Western European Union, 1955–1975
In the 1950s and 1960s the Defence Committee of the Western European Union (WEU) Assembly submitted a series of conspicuous reports on nuclear control issues, culminating in a plea for an Atlantic nuclear force. The article analyses the reports and discussions in the Assembly in the field of defence as well as its attempts to have their recommendations adopted by national parliaments. Internal political and national differences notwithstanding, the representatives in the WEU Assembly developed a clear understanding of European interests.
Our shifting perspectives on the oceans
In the last 15 years new research findings have radically reshaped our understanding of human effects on ocean ecosystems. Here I describe five major shifts in perspective that reveal our impacts to be more severe and persistent than previously appreciated. Firstly, scientists have delved deep into the past and found that the global expansion of European nations across the planet caused the large-scale loss of marine megafauna. In the past century, expansion of industrial scale fishing has continued the process, massively reducing the biomass of exploited species. Secondly, once depleted we are finding that populations rarely rebound rapidly, contrary to a widespread belief in greater resilience of marine compared to terrestrial species. Thirdly, marine ecosystems are being shifted into alternative states that are less desirable from the human perspective and may be stable. It could be difficult, or impossible in some cases, to reverse impacts once inflicted. Fourthly, marine species are at risk of extinction. Loss of shallow water marine habitats is proceeding as rapidly as on land, many species have small geographic ranges, and many possess life history characteristics that leave them highly susceptible to overexploitation. Finally, the deep sea is not beyond harm. Depletion of shallow water fisheries and technological advances are opening up the deep to exploitation and its collateral impacts. If we are to reverse these negative trends we must establish large-scale networks of marine reserves that are off limits to damaging activities and fishing. Such reserves would protect biodiversity, and recover and sustain the world's fisheries productivity
Keeping a reflective journal : reflections of a mature student
Reflective journals are used increasingly in Higher Education. Examples from an unstructured journal kept by the author in her role as a new Mechanical Engineering student raise issue of what 'ought' to be in journals, how emotional effects should be dealt with and how the subjective nature of reflection may cause problems for assessment
Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane
We consider the Edwards-Anderson Ising spin glass model on the half-plane with zero external field and a wide range of choices, including
mean zero Gaussian, for the common distribution of the collection J of i.i.d.
nearest neighbor couplings. The infinite-volume joint distribution
of couplings J and ground state pairs with periodic
(respectively, free) boundary conditions in the horizontal (respectively,
vertical) coordinate is shown to exist without need for subsequence limits. Our
main result is that for almost every J, the conditional distribution
is supported on a single ground state pair.Comment: 20 pages, 3 figure
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