1,346 research outputs found
Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length
An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the
Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is
considered from the perspective of the radial Schr\"odinger equations on 3D
spaces of any (either positive, zero or negative) constant curvature. Further
to Stevenson, we show in detail how to get the hypergeometric wavefunction for
the hydrogen atom case. Finally, we make a comparison between the ``space
curvature" effects and minimal length effects for the hydrogen spectrumComment: 6 pages, v
Perturbation spectrum in inflation with cutoff
It has been pointed out that the perturbation spectrum predicted by inflation
may be sensitive to a natural ultraviolet cutoff, thus potentially providing an
experimentally accessible window to aspects of Planck scale physics. A priori,
a natural ultraviolet cutoff could take any form, but a fairly general
classification of possible Planck scale cutoffs has been given. One of those
categorized cutoffs, also appearing in various studies of quantum gravity and
string theory, has recently been implemented into the standard inflationary
scenario. Here, we continue this approach by investigating its effects on the
predicted perturbation spectrum. We find that the size of the effect depends
sensitively on the scale separation between cutoff and horizon during
inflation.Comment: 6 pages; matches version accepted by PR
Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
In the context of a two-parameter deformation of the
canonical commutation relation leading to nonzero minimal uncertainties in both
position and momentum, the harmonic oscillator spectrum and eigenvectors are
determined by using techniques of supersymmetric quantum mechanics combined
with shape invariance under parameter scaling. The resulting supersymmetric
partner Hamiltonians correspond to different masses and frequencies. The
exponential spectrum is proved to reduce to a previously found quadratic
spectrum whenever one of the parameters , vanishes, in which
case shape invariance under parameter translation occurs. In the special case
where , the oscillator Hamiltonian is shown to coincide
with that of the q-deformed oscillator with and its eigenvectors are
therefore --boson states. In the general case where , the eigenvectors are constructed as linear combinations of
--boson states by resorting to a Bargmann representation of the latter
and to -differential calculus. They are finally expressed in terms of a
-exponential and little -Jacobi polynomials.Comment: LaTeX, 24 pages, no figure, minor changes, additional references,
final version to be published in JP
Field theory on evolving fuzzy two-sphere
I construct field theory on an evolving fuzzy two-sphere, which is based on
the idea of evolving non-commutative worlds of the previous paper. The
equations of motion are similar to the one that can be obtained by dropping the
time-derivative term of the equation derived some time ago by Banks, Peskin and
Susskind for pure-into-mixed-state evolutions. The equations do not contain an
explicit time, and therefore follow the spirit of the Wheeler-de Witt equation.
The basic properties of field theory such as action, gauge invariance and
charge and momentum conservation are studied. The continuum limit of the scalar
field theory shows that the background geometry of the corresponding continuum
theory is given by ds^2 = -dt^2+ t d Omega^2, which saturates locally the
cosmic holographic principle.Comment: Typos corrected, minor changes, 23 pages, no figures, LaTe
1-D Harmonic Oscillator in Snyder Space, the Classic and the Quantum
The 1-D dimension harmonic oscillator in Snyder space is investigated in its
classical and quantum versions. The classical trajectory is obtained and the
semiclassical quantization from the phase space trajectories is discussed. In
the meanwhile, an effective cutoff to high frequencies is found. The quantum
version is developed and an equivalent usual harmonic oscillator is obtained
through an effective mass and an effective frequency introduced in the model.
This modified parameters give us an also modified energy spectra.Comment: 8 pages, 2 figure
One dimensional Coulomb-like problem in deformed space with minimal length
Spectrum and eigenfunctions in the momentum representation for 1D Coulomb
potential with deformed Heisenberg algebra leading to minimal length are found
exactly. It is shown that correction due to the deformation is proportional to
square root of the deformation parameter. We obtain the same spectrum using
Bohr-Sommerfeld quantization condition.Comment: 11 pages, typos corrected, references adde
Ultraviolet cut off, black hole-radiation equilibrium and big bang
In the presence of a minimal uncertainty in length, there exists a critical
temperature above which the thermodynamics of a gas of radiation changes
drastically.
We find that the equilibrium temperature of a system composed of a
Schwarzschild black hole surrounded by radiation is unaffected by these
modifications. This is in agreement with works related to the robustness of the
Hawking evaporation. The only change the deformation introduces concerns the
critical volume at which the system ceases to be stable.
On the contrary, the evolution of the very early universe is sensitive to the
new behavior. We readdress the shortcomings of the standard big bang
model(flatness, entropy and horizon problems) in this context, assuming a
minimal coupling to general relativity. Although they are not solved, some
qualitative differences set in.Comment: 10 pages revtex, 1 figur
WKB approximation in deformed space with minimal length
The WKB approximation for deformed space with minimal length is considered.
The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in
presence of deformation is that the WKB approximation is valid for intermediate
quantum numbers and can be invalid for small as well as very large quantum
numbers. The correctness of the rule is verified by comparing obtained results
with exact expressions for corresponding spectra.Comment: 13 pages Now it is avaible at http://stacks.iop.org/0305-4470/39/37
Online Demodulation and Trigger for Flux-ramp Modulated SQUID Signals
Due to the periodic characteristics of SQUIDs, a suitable linearization technique is required for SQUID-based readout. Flux-ramp modulation is a common linearization technique and is typically applied for the readout of a microwave SQUID multiplexer as well as since recently also for dc-SQUIDs. Flux-ramp modulation requires another stage in the signal processing chain to demodulate the SQUID output signal before further processing. For cryogenic microcalorimeters, the signal contains events that are given by a fast exponentially rising and slowly exponentially decaying pulses shape. The events shall be detected by a trigger engine and recorded by a storage logic. Since the data rate can be decreased significantly by demodulation and event detection, it is desirable to do both steps on the deployed fast FPGA logic during measurement before passing the data to a general-purpose processor. In this contribution, we show the implementation of efficient multi-channel flux-ramp demodulation computed at run-time on a SoC-FPGA. Furthermore, a concept and implementation for an online trigger and buffer mechanism with its theoretical trigger loss rates depending on buffer size is presented. Both FPGA modules can be operated with up to 500 MHz clock frequency and can efficiently process 32 channels. Correct functionality and data reduction capability of the modules are demonstrated in measurements utilizing magnetic microcalorimeter irradiated with an Iron-55 source for event generation and read out by a microwave SQUID multiplexer
Horizon Problem Remediation via Deformed Phase Space
We investigate the effects of a special kind of dynamical deformation between
the momenta of the scalar field of the Brans-Dicke theory and the scale factor
of the FRW metric. This special choice of deformation includes linearly a
deformation parameter. We trace the deformation footprints in the cosmological
equations of motion when the BD coupling parameter goes to infinity. One class
of the solutions gives a constant scale factor in the late time that confirms
the previous result obtained via another approach in the literature. This
effect can be interpreted as a quantum gravity footprint in the coarse grained
explanation. The another class of the solutions removes the big bang
singularity, and the accelerating expansion region has an infinite temporal
range which overcomes the horizon problem. After this epoch, there is a
graceful exiting by which the universe enters in the radiation dominated era.Comment: 13 pages, 2 figures, to appear in GER
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