673 research outputs found
Ring diagrams and electroweak phase transition in a magnetic field
Electroweak phase transition in a magnetic field is investigated within the
one-loop and ring diagram contributions to the effective potential in the
minimal Standard Model. All fundamental fermions and bosons are included with
their actual values of masses and the Higgs boson mass is considered in the
range . The effective potential is real at
sufficiently high temperature. The important role of fermions and -bosons in
symmetry behaviour is observed. It is found that the phase transition for the
field strengths G is of first order but the baryogenesis
condition is not satisfied. The comparison with the hypermagnetic field case is
done.Comment: 16 pages, Latex, changed for a mistake in the numerical par
On (Cosmological) Singularity Avoidance in Loop Quantum Gravity
Loop Quantum Cosmology (LQC), mainly due to Bojowald, is not the cosmological
sector of Loop Quantum Gravity (LQG). Rather, LQC consists of a truncation of
the phase space of classical General Relativity to spatially homogeneous
situations which is then quantized by the methods of LQG. Thus, LQC is a
quantum mechanical toy model (finite number of degrees of freedom) for LQG(a
genuine QFT with an infinite number of degrees of freedom) which provides
important consistency checks. However, it is a non trivial question whether the
predictions of LQC are robust after switching on the inhomogeneous fluctuations
present in full LQG. Two of the most spectacular findings of LQC are that 1.
the inverse scale factor is bounded from above on zero volume eigenstates which
hints at the avoidance of the local curvature singularity and 2. that the
Quantum Einstein Equations are non -- singular which hints at the avoidance of
the global initial singularity. We display the result of a calculation for LQG
which proves that the (analogon of the) inverse scale factor, while densely
defined, is {\it not} bounded from above on zero volume eigenstates. Thus, in
full LQG, if curvature singularity avoidance is realized, then not in this
simple way. In fact, it turns out that the boundedness of the inverse scale
factor is neither necessary nor sufficient for curvature singularity avoidance
and that non -- singular evolution equations are neither necessary nor
sufficient for initial singularity avoidance because none of these criteria are
formulated in terms of observable quantities.After outlining what would be
required, we present the results of a calculation for LQG which could be a
first indication that our criteria at least for curvature singularity avoidance
are satisfied in LQG.Comment: 34 pages, 16 figure
Spectral Statistics in Chaotic Systems with Two Identical Connected Cells
Chaotic systems that decompose into two cells connected only by a narrow
channel exhibit characteristic deviations of their quantum spectral statistics
from the canonical random-matrix ensembles. The equilibration between the cells
introduces an additional classical time scale that is manifest also in the
spectral form factor. If the two cells are related by a spatial symmetry, the
spectrum shows doublets, reflected in the form factor as a positive peak around
the Heisenberg time. We combine a semiclassical analysis with an independent
random-matrix approach to the doublet splittings to obtain the form factor on
all time (energy) scales. Its only free parameter is the characteristic time of
exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho
Signature of Chaotic Diffusion in Band Spectra
We investigate the two-point correlations in the band spectra of spatially
periodic systems that exhibit chaotic diffusion in the classical limit. By
including level pairs pertaining to non-identical quasimomenta, we define form
factors with the winding number as a spatial argument. For times smaller than
the Heisenberg time, they are related to the full space-time dependence of the
classical diffusion propagator. They approach constant asymptotes via a regime,
reflecting quantal ballistic motion, where they decay by a factor proportional
to the number of unit cells. We derive a universal scaling function for the
long-time behaviour. Our results are substantiated by a numerical study of the
kicked rotor on a torus and a quasi-one-dimensional billiard chain.Comment: 8 pages, REVTeX, 5 figures (eps
Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization
The explicit analytical expression for the distribution function of
parametric derivatives of energy levels ("level velocities") with respect to a
random change of scattering potential is derived for the chaotic quantum
systems belonging to the quasi 1D universality class (quantum kicked rotator,
"domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.
External Fields as a Probe for Fundamental Physics
Quantum vacuum experiments are becoming a flexible tool for investigating
fundamental physics. They are particularly powerful for searching for new light
but weakly interacting degrees of freedom and are thus complementary to
accelerator-driven experiments. I review recent developments in this field,
focusing on optical experiments in strong electromagnetic fields. In order to
characterize potential optical signatures, I discuss various low-energy
effective actions which parameterize the interaction of particle-physics
candidates with optical photons and external electromagnetic fields.
Experiments with an electromagnetized quantum vacuum and optical probes do not
only have the potential to collect evidence for new physics, but
special-purpose setups can also distinguish between different particle-physics
scenarios and extract information about underlying microscopic properties.Comment: 12 pages, plenary talk at QFEXT07, Leipzig, September 200
Dissipative quantum chaos: transition from wave packet collapse to explosion
Using the quantum trajectories approach we study the quantum dynamics of a
dissipative chaotic system described by the Zaslavsky map. For strong
dissipation the quantum wave function in the phase space collapses onto a
compact packet which follows classical chaotic dynamics and whose area is
proportional to the Planck constant. At weak dissipation the exponential
instability of quantum dynamics on the Ehrenfest time scale dominates and leads
to wave packet explosion. The transition from collapse to explosion takes place
when the dissipation time scale exceeds the Ehrenfest time. For integrable
nonlinear dynamics the explosion practically disappears leaving place to
collapse.Comment: 4 pages, 4 figure
Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space
We investigate the properties of eigenstates and local density of states
(LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical
correspondence in energy representation. To construct the classical
counterparts of LDOS and the structure of eigenstates (SES), the effects of the
boundary are first incorporated (via a canonical transformation) into an
effective potential, rendering the one-particle motion in the 2D rippled
billiard equivalent to that of two-interacting particles in 1D geometry. We
show that classical counterparts of SES and LDOS in the case of strong chaotic
motion reveal quite a good correspondence with the quantum quantities. We also
show that the main features of the SES and LDOS can be explained in terms of
the underlying classical dynamics, in particular of certain periodic orbits. On
the other hand, statistical properties of eigenstates and LDOS turn out to be
different from those prescribed by random matrix theory. We discuss the quantum
effects responsible for the non-ergodic character of the eigenstates and
individual LDOS that seem to be generic for this type of billiards with a large
number of transverse channels.Comment: 13 pages, 18 figure
Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall
We consider the electromagnetic field in a cavity with a periodically
oscillating perfectly reflecting boundary and show that the mathematical theory
of circle maps leads to several physical predictions. Notably, well-known
results in the theory of circle maps (which we review briefly) imply that there
are intervals of parameters where the waves in the cavity get concentrated in
wave packets whose energy grows exponentially. Even if these intervals are
dense for typical motions of the reflecting boundary, in the complement there
is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i,
42.60.Da, 42.65.Y
Semiclassical quantisation of space-times with apparent horizons
Coherent or semiclassical states in canonical quantum gravity describe the
classical Schwarzschild space-time. By tracing over the coherent state
wavefunction inside the horizon, a density matrix is derived.
Bekenstein-Hawking entropy is obtained from the density matrix, modulo the
Immirzi parameter. The expectation value of the area and curvature operator is
evaluated in these states. The behaviour near the singularity of the curvature
operator shows that the singularity is resolved. We then generalise the results
to space-times with spherically symmetric apparent horizons.Comment: 52 pages, 4 figure
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