5,849 research outputs found
General boundary quantum field theory: Timelike hypersurfaces in Klein-Gordon theory
We show that the real massive Klein-Gordon theory admits a description in
terms of states on various timelike hypersurfaces and amplitudes associated to
regions bounded by them. This realizes crucial elements of the general boundary
framework for quantum field theory. The hypersurfaces considered are
hyperplanes on the one hand and timelike hypercylinders on the other hand. The
latter lead to the first explicit examples of amplitudes associated with finite
regions of space, and admit no standard description in terms of ``initial'' and
``final'' states. We demonstrate a generalized probability interpretation in
this example, going beyond the applicability of standard quantum mechanics.Comment: 25 pages, LaTeX; typos correcte
Scale invariant thermodynamics of a toroidally trapped Bose gas
We consider a system of bosonic atoms in an axially symmetric harmonic trap
augmented with a two dimensional repulsive Gaussian optical potential. We find
an expression for the grand free energy of the system for configurations
ranging from the harmonic trap to the toroidal regime. For large tori we
identify an accessible regime where the ideal gas thermodynamics of the system
are found to be independent of toroidal radius. This property is a consequence
of an invariant extensive volume of the system that we identify analytically in
the regime where the toroidal potential is radially harmonic. In considering
corrections to the scale invariant transition temperature, we find that the
first order interaction shift is the dominant effect in the thermodynamic
limit, and is also scale invariant. We also consider adiabatic loading from the
harmonic to toroidal trap configuration, which we show to have only a small
effect on the condensate fraction of the ideal gas, indicating that loading
into the scale invariant regime may be experimentally practical.Comment: 10 pages, 3 figures, to appear in Phys. Rev. A, typos corrected,
references added, rewritten to emphasize generalized volume. Results
unchange
Interactions of cosmological gravitational waves and magnetic fields
The energy momentum tensor of a magnetic field always contains a spin-2
component in its anisotropic stress and therefore generates gravitational
waves. It has been argued in the literature (Caprini & Durrer \cite{CD}) that
this gravitational wave production can be very strong and that back-reaction
cannot be neglected. On the other hand, a gravitational wave background does
affect the evolution of magnetic fields. It has also been argued (Tsagas et al.
\cite{Tsagas:2001ak},\cite{Tsagas:2005ki}) that this can lead to very strong
amplification of a primordial magnetic field. In this paper we revisit these
claims and study back reaction to second order.Comment: Added references, accepted for publication in PR
Adiabatic Creation of Atomic Squeezing in Dark States vs. Decoherences
We study the multipartite correlations of the multi-atom dark states, which
are characterized by the atomic squeezing beyond the pairwise entanglement. It
is shown that, in the photon storage process with atomic ensemble via
electromagnetically induced transparency (EIT) mechanism, the atomic squeezing
and the pairwise entanglement can be created by adiabatically manipulating the
Rabi frequency of the classical light field on the atomic ensemble. We also
consider the sudden death for the atomic squeezing and the pairwise
entanglement under various decoherence channels. An optimal time for generating
the greatest atomic squeezing and pairwise entanglement is obtained by studying
in details the competition between the adiabatic creation of quantum
correlation in the atomic ensemble and the decoherence that we describe with
three typical decoherence channels.Comment: 11 pages, 13 figure
O(N) symmetry-breaking quantum quench: Topological defects versus quasiparticles
We present an analytical derivation of the winding number counting
topological defects created by an O(N) symmetry-breaking quantum quench in N
spatial dimensions. Our approach is universal in the sense that we do not
employ any approximations apart from the large- limit. The final result is
nonperturbative in N, i.e., it cannot be obtained by %the usual an expansion in
1/N, and we obtain far less topological defects than quasiparticle excitations,
in sharp distinction to previous, low-dimensional investigations.Comment: 6 pages of RevTex4-1, 1 figure; to be published in Physical Review
The Adiabatic Invariance of the Action Variable in Classical Dynamics
We consider one-dimensional classical time-dependent Hamiltonian systems with
quasi-periodic orbits. It is well-known that such systems possess an adiabatic
invariant which coincides with the action variable of the Hamiltonian
formalism. We present a new proof of the adiabatic invariance of this quantity
and illustrate our arguments by means of explicit calculations for the harmonic
oscillator.
The new proof makes essential use of the Hamiltonian formalism. The key step
is the introduction of a slowly-varying quantity closely related to the action
variable. This new quantity arises naturally within the Hamiltonian framework
as follows: a canonical transformation is first performed to convert the system
to action-angle coordinates; then the new quantity is constructed as an action
integral (effectively a new action variable) using the new coordinates. The
integration required for this construction provides, in a natural way, the
averaging procedure introduced in other proofs, though here it is an average in
phase space rather than over time.Comment: 8 page
Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach
Here we have studied first and second-order intertwining approach to generate
isospectral partner potentials of position-dependent (effective) mass
Schroedinger equation. The second-order intertwiner is constructed directly by
taking it as second order linear differential operator with position depndent
coefficients and the system of equations arising from the intertwining
relationship is solved for the coefficients by taking an ansatz. A complete
scheme for obtaining general solution is obtained which is valid for any
arbitrary potential and mass function. The proposed technique allows us to
generate isospectral potentials with the following spectral modifications: (i)
to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the
spectrum unaffected. To explain our findings with the help of an illustration,
we have used point canonical transformation (PCT) to obtain the general
solution of the position dependent mass Schrodinger equation corresponding to a
potential and mass function. It is shown that our results are consistent with
the formulation of type A N-fold supersymmetry [14,18] for the particular case
N = 1 and N = 2 respectively.Comment: Some references have been adde
Above-well, Stark, and potential-barrier resonances of an open square well in a static external electric field
Besides the well known Stark resonances, which are localized in the potential
well and tunnel through the potential barrier created by the dc-field,
"strange" long and short-lived resonances are analytically obtained. These
resonances are not localized inside the potential well. We show that the narrow
ones are localized above the potential well. These narrow resonances give rise
to a {\it peak structure} in a 1D scattering experiment. We also show that the
broad overlapping resonances are associated with the static electric field
potential barrier. These "strange" overlapping resonances do not give rise to a
{\it peak structure} in a 1D scattering experiment. We propose a 2D
experimental set-up where in principle these short-lived states should be
observed as {\it peaks}. Broad overlapping resonances, associated only with the
static electric field potential barrier, could also have observable effects in
a array of quantum wells in the presence of a truncated static electric
field. This last problem is associated with the resonance tunnelling phenomena
which are used in the construction of resonance-tunnelling diodes and
transistors.Comment: submitted to Phys. Rev. A, April 08 200
Positive cosmological constant in loop quantum cosmology
The k=0 Friedmann Lemaitre Robertson Walker model with a positive
cosmological constant and a massless scalar field is analyzed in detail. If one
uses the scalar field as relational time, new features arise already in the
Hamiltonian framework of classical general relativity: In a finite interval of
relational time, the universe expands out to infinite proper time and zero
matter density. In the deparameterized quantum theory, the true Hamiltonian now
fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach
and in LQC. Irrespective of the choice of the self-adjoint extension, the big
bang singularity persists in the WDW theory while it is resolved and replaced
by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum
evolution is surprisingly insensitive to the choice of the self-adjoint
extension. This may be a special case of an yet to be discovered general
property of a certain class of symmetric operators that fail to be essentially
self-adjoint.Comment: 36 pages, 6 figures, RevTex
Reflection and Transmission at the Apparent Horizon during Gravitational Collapse
We examine the wave-functionals describing the collapse of a self-gravitating
dust ball in an exact quantization of the gravity-dust system. We show that
ingoing (collapsing) dust shell modes outside the apparent horizon must
necessarily be accompanied by outgoing modes inside the apparent horizon, whose
amplitude is suppressed by the square root of the Boltzmann factor at the
Hawking temperature. Likewise, ingoing modes in the interior must be
accompanied by outgoing modes in the exterior, again with an amplitude
suppressed by the same factor. A suitable superposition of the two solutions is
necessary to conserve the dust probability flux across the apparent horizon,
thus each region contains both ingoing and outgoing dust modes. If one
restricts oneself to considering only the modes outside the apparent horizon
then one should think of the apparent horizon as a partial reflector, the
probability for a shell to reflect being given by the Boltzmann factor at the
Hawking temperature determined by the mass contained within it. However, if one
considers the entire wave function, the outgoing wave in the exterior is seen
to be the transmission through the horizon of the interior outgoing wave that
accompanies the collapsing shells. This transmission could allow information
from the interior to be transferred to the exterior.Comment: 19 pages, no figures. To appear in Phys. Rev.
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