22 research outputs found
Time-dependent q-deformed coherent states for generalized uncertainty relations
We investigate properties of generalized time-dependent q-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e. the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest's theorem hold at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented
Is cell-mediated immune response related to nutritional state, but unaffected by concomitant malarial infection ?
Milne quantization for non-Hermitian systems
We generalize the Milne quantization condition to non-Hermitian systems. In the general case the underlying nonlinear Ermakov–Milne–Pinney equation needs to be replaced by a nonlinear integral differential equation. However, when the system is PT-symmetric or/and quasi/pseudo-Hermitian the equations simplify and one may employ the original energy integral to determine its quantization. We illustrate the working of the general framework with the Swanson model and two explicit examples for pairs of supersymmetric Hamiltonians. In one case both partner Hamiltonians are Hermitian and in the other a Hermitian Hamiltonian is paired by a Darboux transformation to a non-Hermitian one
Noncommutative quantum mechanics -- a perspective on structure and spatial extent
We explore the notion of spatial extent and structure, already alluded to in
earlier literature, within the formulation of quantum mechanics on the
noncommutative plane. Introducing the notion of average position and its
measurement, we find two equivalent pictures: a constrained local description
in position containing additional degrees of freedom, and an unconstrained
nonlocal description in terms of the position without any other degrees of
freedom. Both these descriptions have a corresponding classical theory which
shows that the concept of extended, structured objects emerges quite naturally
and unavoidably there. It is explicitly demonstrated that the conserved energy
and angular momentum contain corrections to those of a point particle. We argue
that these notions also extend naturally to the quantum level. The local
description is found to be the most convenient as it manifestly displays
additional information about structure of quantum states that is more subtly
encoded in the nonlocal, unconstrained description. Subsequently we use this
picture to discuss the free particle and harmonic oscillator as examples.Comment: 25 pages, no figure
Supersymmetry breaking in noncommutative quantum mechanics
Supersymmetric quantum mechanics is formulated on a two dimensional
noncommutative plane and applied to the supersymmetric harmonic oscillator. We
find that the ordinary commutative supersymmetry is partially broken and only
half of the number of supercharges are conserved. It is argued that this
breaking is closely related to the breaking of time reversal symmetry arising
from noncommutativity
PT-symmetric noncommutative spaces with minimal volume uncertainty relations
We provide a systematic procedure to relate a three dimensional q-deformed
oscillator algebra to the corresponding algebra satisfied by canonical
variables describing noncommutative spaces. The large number of possible free
parameters in these calculations is reduced to a manageable amount by imposing
various different versions of PT-symmetry on the underlying spaces, which are
dictated by the specific physical problem under consideration. The
representations for the corresponding operators are in general non-Hermitian
with regard to standard inner products and obey algebras whose uncertainty
relations lead to minimal length, areas or volumes in phase space. We analyze
in particular one three dimensional solution which may be decomposed to a two
dimensional noncommutative space plus one commuting space component and also
into a one dimensional noncommutative space plus two commuting space
components. We study some explicit models on these type of noncommutative
spaces.Comment: 18 page
Non-contiguous finished genome sequencing and description of Enterococcus timonensis sp. nov. isolated from human sputum
International audienc