2,017 research outputs found
The energy spectrum of complex periodic potentials of the Kronig-Penney type
We consider a complex periodic PT-symmetric potential of the Kronig-Penney
type, in order to elucidate the peculiar properties found by Bender et al. for
potentials of the form , and in particular the absence of
anti-periodic solutions. In this model we show explicitly why these solutions
disappear as soon as , and spell out the consequences for the
form of the dispersion relation.Comment: 4 pages, 2 figure
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
Quantum field dynamics of the slow rollover in the linear delta expansion
We show how the linear delta expansion, as applied to the slow-roll
transition in quantum mechanics, can be recast in the closed time-path
formalism. This results in simpler, explicit expressions than were obtained in
the Schr\"odinger formulation and allows for a straightforward generalization
to higher dimensions. Motivated by the success of the method in the
quantum-mechanical problem, where it has been shown to give more accurate
results for longer than existing alternatives, we apply the linear delta
expansion to four-dimensional field theory.
At small times all methods agree. At later times, the first-order linear
delta expansion is consistently higher that Hartree-Fock, but does not show any
sign of a turnover. A turnover emerges in second-order of the method, but the
value of at the
turnover. In subsequent applications of the method we hope to implement the
calculation in the context of an expanding universe, following the line of
earlier calculations by Boyanovsky {\sl et al.}, who used the Hartree-Fock and
large-N methods. It seems clear, however, that the method will become
unreliable as the system enters the reheating stage.Comment: 17 pages, 9 figures, revised version with extra section 4.2 including
second order calculatio
PT-Symmetry Quantum Electrodynamics--PTQED
The construction of -symmetric quantum electrodynamics is
reviewed. In particular, the massless version of the theory in 1+1 dimensions
(the Schwinger model) is solved. Difficulties with unitarity of the -matrix
are discussed.Comment: 11 pages, 1 figure, contributed to Proceedings of 6th International
Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physic
Dual PT-Symmetric Quantum Field Theories
Some quantum field theories described by non-Hermitian Hamiltonians are
investigated. It is shown that for the case of a free fermion field theory with
a mass term the Hamiltonian is -symmetric. Depending on the
mass parameter this symmetry may be either broken or unbroken. When the symmetry is unbroken, the spectrum of the quantum field theory is real. For
the -symmetric version of the massive Thirring model in
two-dimensional space-time, which is dual to the -symmetric scalar
Sine-Gordon model, an exact construction of the operator is given. It
is shown that the -symmetric massive Thirring and Sine-Gordon models
are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon
models with appropriately shifted masses.Comment: 9 pages, 1 figur
Non-perturbative calculations of a global U(1) theory at finite density and temperature
We use an optimised hopping parameter expansion for the free energy (linear
delta expansion) to study the phase transitions at finite temperature and
finite charge density in a global U(1) scalar Higgs sector on the lattice at
large lattice couplings. We are able to plot out phase diagrams in lattice
parameter space and find that the standard second-order phase transition with
temperature at zero chemical potential becomes first order as the chemical
potential increases.Comment: 24 pages, 11 figure
Bound States of Non-Hermitian Quantum Field Theories
The spectrum of the Hermitian Hamiltonian
(), which describes the quantum anharmonic oscillator, is real and
positive. The non-Hermitian quantum-mechanical Hamiltonian , where the coupling constant is real and positive, is
-symmetric. As a consequence, the spectrum of is known to be
real and positive as well. Here, it is shown that there is a significant
difference between these two theories: When is sufficiently small, the
latter Hamiltonian exhibits a two-particle bound state while the former does
not. The bound state persists in the corresponding non-Hermitian -symmetric quantum field theory for all dimensions
but is not present in the conventional Hermitian field theory.Comment: 14 pages, 3figure
Relationship between tinnitus pitch and edge of hearing loss in individuals with a narrow tinnitus bandwidth
Objective: Psychoacoustic measures of tinnitus, in particular dominant tinnitus pitch and its relationship to the shape of the audiogram, are important in determining and verifying pathophysiological mechanisms of the condition. Our previous study postulated that this relationship might vary between different groups of people with tinnitus. For a small subset of participants with narrow tinnitus bandwidth, pitch was associated with the audiometric edge, consistent with the tonotopic reorganization theory. The current study objective was to establish this relationship in an independent sample. Design: This was a retrospective design using data from five studies conducted between 2008 and 2013.
Study sample: From a cohort of 380 participants, a subgroup group of 129 with narrow tinnitus bandwidth were selected.
Results: Tinnitus pitch generally fell within the area of hearing loss. There was a statistically significant correlation between dominant tinnitus pitch and edge frequency; higher edge frequency being associated with higher dominant tinnitus pitch. However, similar to our previous study, for the majority of participants pitch was more than an octave above the edge frequency.
Conclusions: The findings did not support our prediction and are therefore not consistent with the reorganization theory postulating tinnitus pitch to correspond to the audiometric edge
Integral elastic, electronic-state, ionization, and total cross sections for electron scattering with furfural
8 págs.; 2 figs.; 2 tabs.We report absolute experimental integral cross sections (ICSs) for electron impact excitation of bands of electronic-states in furfural, for incident electron energies in the range 20-250 eV. Wherever possible, those results are compared to corresponding excitation cross sections in the structurally similar species furan, as previously reported by da Costa et al. [Phys. Rev. A 85, 062706 (2012)] and Regeta and Allan [Phys. Rev. A 91, 012707 (2015)]. Generally, very good agreement is found. In addition, ICSs calculated with our independent atom model (IAM) with screening corrected additivity rule (SCAR) formalism, extended to account for interference (I) terms that arise due to the multi-centre nature of the scattering problem, are also reported. The sum of those ICSs gives the IAM-SCAR+I total cross section for electron-furfural scattering. Where possible, those calculated IAM-SCAR+I ICS results are compared against corresponding results from the present measurements with an acceptable level of accord being obtained. Similarly, but only for the band I and band II excited electronic states, we also present results from our Schwinger multichannel method with pseudopotentials calculations. Those results are found to be in good qualitative accord with the present experimental ICSs. Finally, with a view to assembling a complete cross section data base for furfural, some binary-encounter-Bethe-level total ionization cross sections for this collision system are presented.D.B.J. thanks the Australian Research Council (ARC) for
financial support provided through a Discovery Early Career
Research Award, while M.J.B. also thanks the ARC for their
support. M.J.B. acknowledges the Brazilian agency CNPq
for his “Special Visiting Professor” position at the Federal
University of Juiz de Fora. G.G. acknowledges partial financial
support from the Spanish Ministry MINECO (Project No.
FIS2012-31230) and the European Union COST Action No.
CM1301 (CELINA). Finally R.F.C., M.T.doN.V, M.H.F.B,
and M.A.P.L. also acknowledge support from CNPq, while
M.T.doN.V. thanks FAPESPPeer Reviewe
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
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