10,545 research outputs found
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
Variational Ansatz for PT-Symmetric Quantum Mechanics
A variational calculation of the energy levels of a class of PT-invariant
quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 -
(ix)^N with N positive and x complex is presented. Excellent agreement is
obtained for the ground state and low lying excited state energy levels and
wave functions. We use an energy functional with a three parameter class of
PT-symmetric trial wave functions in obtaining our results.Comment: 9 pages -- one postscript figur
Complex periodic potentials with real band spectra
This paper demonstrates that complex PT-symmetric periodic potentials possess
real band spectra. However, there are significant qualitative differences in
the band structure for these potentials when compared with conventional real
periodic potentials. For example, while the potentials V(x)=i\sin^{2N+1}(x),
(N=0, 1, 2, ...), have infinitely many gaps, at the band edges there are
periodic wave functions but no antiperiodic wave functions. Numerical analysis
and higher-order WKB techniques are used to establish these results.Comment: 8 pages, 7 figures, LaTe
Simulation of granular soil behaviour using the bullet physics library
A physics engine is computer software which provides a simulation of certain physical systems, such as rigid body dynamics, soft body dynamics and fluid dynamics. Physics engines were firstly developed for using in animation and gaming industry ; nevertheless, due to fast calculation speed they are attracting more and more attetion from researchers of the engineering fields. Since physics engines are capable of performing fast calculations on multibody rigid dynamic systems, soil particles can be modeled as distinct rigid bodies. However, up to date, it is not clear to what extent they perform accurately in modeling soil behaviour from a geotechnical viewpoint. To investigate this, examples of pluviation and vibration-induced desification were simulated using the physics engine called Bullet physics library. In order to create soil samples, first, randomly shaped polyhedrons, representing gravels, were generated using the Voronoi tessellation approach. Then, particles were pluviated through a funnel into a cylinder. Once the soil particles settled in a static state, the cylinder was subjected to horizontal sinusoidal vibration for a period of 20 seconds. The same procedure for sample perparation was performed in the laboratory. The results of pluviation and vibration tests weere recorded and compared to those of simulations. A good agreement has been found between the results of simulations and laboratory tests. The findings in this study reinforce the idea that physics engines can be employed as a geotechnical engineering simulation tool
Accuracy of gravitational physics tests using ranges to the inner planets
A number of different types of deviations from Kepler's laws for planetary orbits can occur in nonNewtonian metric gravitational theories. These include secular changes in all of the orbital elements and in the mean motion, plus additional periodic perturbations in the coordinates. The first order corrections to the Keplerian motion of a single planet around the Sun due to the parameterized post Newtonian theory parameters were calculated as well as the corrections due to the solar quadrupole moment and a possible secular change in the gravitational constant. The results were applied to the case of proposed high accuracy ranging experiments from the Earth to a Mercury orbiting spacecraft in order to see how well the various parameters can be determined
The Complexity of Scheduling for p-norms of Flow and Stretch
We consider computing optimal k-norm preemptive schedules of jobs that arrive
over time. In particular, we show that computing the optimal k-norm of flow
schedule, is strongly NP-hard for k in (0, 1) and integers k in (1, infinity).
Further we show that computing the optimal k-norm of stretch schedule, is
strongly NP-hard for k in (0, 1) and integers k in (1, infinity).Comment: Conference version accepted to IPCO 201
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
All Hermitian Hamiltonians Have Parity
It is shown that if a Hamiltonian is Hermitian, then there always exists
an operator P having the following properties: (i) P is linear and Hermitian;
(ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an
eigenstate of P with eigenvalue (-1)^n. Given these properties, it is
appropriate to refer to P as the parity operator and to say that H has parity
symmetry, even though P may not refer to spatial reflection. Thus, if the
Hamiltonian has the form H=p^2+V(x), where V(x) is real (so that H possesses
time-reversal symmetry), then it immediately follows that H has PT symmetry.
This shows that PT symmetry is a generalization of Hermiticity: All Hermitian
Hamiltonians of the form H=p^2+V(x) have PT symmetry, but not all PT-symmetric
Hamiltonians of this form are Hermitian
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