36 research outputs found
Classical dynamics on three dimensional fuzzy space: Connecting the short and long length scales
We derive the path integral action for a particle moving in three dimensional
fuzzy space. From this we extract the classical equations of motion. These
equations have rather surprising and unconventional features: They predict a
cut-off in energy, a generally spatial dependent limiting speed, orbital
precession remarkably similar to the general relativistic result, flat velocity
curves below a length scale determined by the limiting velocity and included
mass, displaced planar motion and the existence of two dynamical branches of
which only one reduces to Newtonian dynamics in the commutative limit. These
features place strong constraints on the non-commutative parameter and
coordinate algebra to avoid conflict with observation and may provide a
stringent observational test for this scenario of non-commutativity.Comment: 21 pages, 4 figure
On Hilbert-Schmidt operator formulation of noncommutative quantum mechanics
This work gives value to the importance of Hilbert-Schmidt operators in the
formulation of a noncommutative quantum theory. A system of charged particle in
a constant magnetic field is investigated in this framework
A possible method for non-Hermitian and non--symmetric Hamiltonian systems
A possible method to investigate non-Hermitian Hamiltonians is suggested
through finding a Hermitian operator and defining the annihilation and
creation operators to be -pseudo-Hermitian adjoint to each other. The
operator represents the -pseudo-Hermiticity of Hamiltonians.
As an example, a non-Hermitian and non--symmetric Hamiltonian with
imaginary linear coordinate and linear momentum terms is constructed and
analyzed in detail. The operator is found, based on which, a real
spectrum and a positive-definite inner product, together with the probability
explanation of wave functions, the orthogonality of eigenstates, and the
unitarity of time evolution, are obtained for the non-Hermitian and
non--symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be
coupled when it is extended to the canonical noncommutative space with
noncommutative spatial coordinate operators and noncommutative momentum
operators as well. Our method is applicable to the coupled Hamiltonian. Then
the first and second order noncommutative corrections of energy levels are
calculated, and in particular the reality of energy spectra, the
positive-definiteness of inner products, and the related properties (the
probability explanation of wave functions, the orthogonality of eigenstates,
and the unitarity of time evolution) are found not to be altered by the
noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1
figure, clarifications made clearer; v4: 19 pages, the main context is
completely rewritten; v5: 25 pages, title slightly changed, clarifications
added, the final version to appear in PLOS ON
On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
We consider one-dimensional Schroedinger-type operators in a bounded interval
with non-self-adjoint Robin-type boundary conditions. It is well known that
such operators are generically conjugate to normal operators via a similarity
transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians
in quantum mechanics, we study properties of the transformations in detail. We
show that they can be expressed as the sum of the identity and an integral
Hilbert-Schmidt operator. In the case of parity and time reversal boundary
conditions, we establish closed integral-type formulae for the similarity
transformations, derive the similar self-adjoint operator and also find the
associated "charge conjugation" operator, which plays the role of fundamental
symmetry in a Krein-space reformulation of the problem.Comment: 27 page
Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type
We propose a noncommutative version of the Euclidean Lie algebra E 2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra
Dung removal increases under higher dung beetle functional diversity regardless of grazing intensification
Dung removal by macrofauna such as dung beetles is an important process for nutrient cycling in pasturelands. Intensification of farming practices generally reduces species and functional diversity of terrestrial invertebrates, which may negatively affect ecosystem services. Here, we investigate the effects of cattle-grazing intensification on dung removal by dung beetles in field experiments replicated in 38 pastures around the world. Within each study site, we measured dung removal in pastures managed with low- and high-intensity regimes to assess between-regime differences in dung beetle diversity and dung removal, whilst also considering climate and regional variations. The impacts of intensification were heterogeneous, either diminishing or increasing dung beetle species richness, functional diversity, and dung removal rates. The effects of beetle diversity on dung removal were more variable across sites than within sites. Dung removal increased with species richness across sites, while functional diversity consistently enhanced dung removal within sites, independently of cattle grazing intensity or climate. Our findings indicate that, despite intensified cattle stocking rates, ecosystem services related to decomposition and nutrient cycling can be maintained when a functionally diverse dung beetle community inhabits the human-modified landscape
Non-unitary Evolution of Quantum Logics
In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a non-Boolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, a notion that we introduce in order to cope with the temporal aspect of the logical structure of quantum theory