284 research outputs found
The q-harmonic oscillators, q-coherent states and the q-symplecton
The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton
Nonlinear self-flipping of polarization states in asymmetric waveguides
Waveguides of subwavelength dimensions with asymmetric geometries, such as
rib waveguides, can display nonlinear polarization effects in which the
nonlinear phase difference dominates the linear contribution, provided the
birefringence is sufficiently small. We demonstrate that self-flipping
polarization states can appear in such rib waveguides at low (mW) power levels.
We describe an optical power limiting device with optimized rib waveguide
parameters that can operate at low powers with switching properties
Spin dynamics of low-dimensional excitons due to acoustic phonons
We investigate the spin dynamics of excitons interacting with acoustic
phonons in quantum wells, quantum wires and quantum disks by employing a
multiband model based on the Luttinger Hamiltonian. We also use the
Bir-Pikus Hamiltonian to model the coupling of excitons to both longitudinal
acoustic phonons and transverse acoustic phonons, thereby providing us with a
realistic framework in which to determine details of the spin dynamics of
excitons. We use a fractional dimensional formulation to model the excitonic
wavefunctions and we demonstrate explicitly the decrease of spin relaxation
time with dimensionality. Our numerical results are consistent with
experimental results of spin relaxation times for various configurations of the
GaAs/AlGaAs material system. We find that longitudinal and
transverse acoustic phonons are equally significant in processes of exciton
spin relaxations involving acoustic phonons.Comment: 24 pages, 3 figure
On the Hydrogen Atom via Wigner-Heisenberg Algebra
We extend the usual Kustaanheimo-Stiefel mapping to study and
discuss a constrained super-Wigner oscillator in four dimensions. We show that
the physical hydrogen atom is the system that emerges in the bosonic sector of
the mapped super 3D system.Comment: 14 pages, no figure. This work was initiated in collaboration with
Jambunatha Jayaraman (In memory), whose advises and encouragement were
fundamental. http://www.cbpf.b
Fast transport of Bose-Einstein condensates
We propose an inverse method to accelerate without final excitation the
adiabatic transport of a Bose Einstein condensate. The method, applicable to
arbitrary potential traps, is based on a partial extension of the
Lewis-Riesenfeld invariants, and provides transport protocols that satisfy
exactly the no-excitation conditions without constraints or approximations.
This inverse method is complemented by optimizing the trap trajectory with
respect to different physical criteria and by studying the effect of noise
Construction of a universal quantum computer
We construct a universal quantum computer following Deutsch’s original proposal of a universal quantum Turing machine (UQTM). Like Deutsch’s UQTM, our machine can emulate any classical Turing machine and can execute any algorithm that can be implemented in the quantum gate array framework but under the control of a quantum program, and hence is universal. We present the architecture of the machine, which consists of a memory tape and a processor and describe the observables that comprise the registers of the processor and the instruction set, which includes a set of operations that can approximate any unitary operation to any desired accuracy and hence is quantum computationally universal. We present the unitary evolution operators that act on the machine to achieve universal computation and discuss each of them in detail and specify and discuss explicit program halting and concatenation schemes. We define and describe a set of primitive programs in order to demonstrate the universal nature of the machine. These primitive programs facilitate the implementation of more complex algorithms and we demonstrate their use by presenting a program that computes the NAND function, thereby also showing that the machine can compute any classically computable function.Antonio A. Lagana, M. A. Lohe, and Lorenz von Smeka
Bogomol'nyi Equations of Maxwell-Chern-Simons vortices from a generalized Abelian Higgs Model
We consider a generalization of the abelian Higgs model with a Chern-Simons
term by modifying two terms of the usual Lagrangian. We multiply a dielectric
function with the Maxwell kinetic energy term and incorporate nonminimal
interaction by considering generalized covariant derivative. We show that for a
particular choice of the dielectric function this model admits both topological
as well as nontopological charged vortices satisfying Bogomol'nyi bound for
which the magnetic flux, charge and angular momentum are not quantized. However
the energy for the topolgical vortices is quantized and in each sector these
topological vortex solutions are infinitely degenerate. In the nonrelativistic
limit, this model admits static self-dual soliton solutions with nonzero finite
energy configuration. For the whole class of dielectric function for which the
nontopological vortices exists in the relativistic theory, the charge density
satisfies the same Liouville equation in the nonrelativistic limit.Comment: 30 pages(4 figures not included), RevTeX, IP/BBSR/93-6
Kink fluctuation asymptotics and zero modes
In this paper we propose a refinement of the heat kernel/zeta function
treatment of kink quantum fluctuations in scalar field theory, further
analyzing the existence and implications of a zero energy fluctuation mode.
Improved understanding of the interplay between zero modes and the kink heat
kernel expansion delivers asymptotic estimations of one-loop kink mass shifts
with remarkably higher precision than previously obtained by means of the
standard Gilkey-DeWitt heat kernel expansion.Comment: 21 pages, 8 figures, to be published in The European Physical Journal
Coupling coefficients of SO(n) and integrals over triplets of Jacobi and Gegenbauer polynomials
The expressions of the coupling coefficients (3j-symbols) for the most
degenerate (symmetric) representations of the orthogonal groups SO(n) in a
canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical
or tree bases [with SO(n) restricted to SO(n'})\times SO(n''), n'+n''=n] are
considered, respectively, in context of the integrals involving triplets of the
Gegenbauer and the Jacobi polynomials. Since the directly derived
triple-hypergeometric series do not reveal the apparent triangle conditions of
the 3j-symbols, they are rearranged, using their relation with the
semistretched isofactors of the second kind for the complementary chain
Sp(4)\supset SU(2)\times SU(2) and analogy with the stretched 9j coefficients
of SU(2), into formulae with more rich limits for summation intervals and
obvious triangle conditions. The isofactors of class-one representations of the
orthogonal groups or class-two representations of the unitary groups (and, of
course, the related integrals involving triplets of the Gegenbauer and the
Jacobi polynomials) turn into the double sums in the cases of the canonical
SO(n)\supset SO(n-1) or U(n)\supset U(n-1) and semicanonical SO(n)\supset
SO(n-2)\times SO(2) chains, as well as into the_4F_3(1) series under more
specific conditions. Some ambiguities of the phase choice of the complementary
group approach are adjusted, as well as the problems with alternating sign
parameter of SO(2) representations in the SO(3)\supset SO(2) and SO(n)\supset
SO(n-2)\times SO(2) chains.Comment: 26 pages, corrections of (3.6c) and (3.12); elementary proof of
(3.2e) is adde
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