968 research outputs found

### Dimensional enhancement of kinetic energies

Simple thermodynamics considers kinetic energy to be an extensive variable
which is proportional to the number, N, of particles. We present a quantum
state of N non-interacting particles for which the kinetic energy increases
quadratically with N. This enhancement effect is tied to the quantum
centrifugal potential whose strength is quadratic in the number of dimensions
of configuration space.Comment: 9 pages, accepted by Phys. Rev.

### On the Squeezed Number States and their Phase Space Representations

We compute the photon number distribution, the Q distribution function and
the wave functions in the momentum and position representation for a single
mode squeezed number state using generating functions which allow to obtain any
matrix element in the squeezed number state representation from the matrix
elements in the squeezed coherent state representation. For highly squeezed
number states we discuss the previously unnoted oscillations which appear in
the Q function. We also note that these oscillations can be related to the
photon-number distribution oscillations and to the momentum representation of
the wave function.Comment: 16 pages, 9 figure

### Sagnac Effect of Goedel's Universe

We present exact expressions for the Sagnac effect of Goedel's Universe. For
this purpose we first derive a formula for the Sagnac time delay along a
circular path in the presence of an arbitrary stationary metric in cylindrical
coordinates. We then apply this result to Goedel's metric for two different
experimental situations: First, the light source and the detector are at rest
relative to the matter generating the gravitational field. In this case we find
an expression that is formally equivalent to the familiar nonrelativistic
Sagnac time delay. Second, the light source and the detector are rotating
relative to the matter. Here we show that for a special rotation rate of the
detector the Sagnac time delay vanishes. Finally we propose a formulation of
the Sagnac time delay in terms of invariant physical quantities. We show that
this result is very close to the analogous formula of the Sagnac time delay of
a rotating coordinate system in Minkowski spacetime.Comment: 26 pages, including 4 figures, corrected typos, changed reference

### Dropping cold quantum gases on Earth over long times and large distances

We describe the non-relativistic time evolution of an ultra-cold degenerate
quantum gas (bosons/fermions) falling in Earth's gravity during long times (10
sec) and over large distances (100 m). This models a drop tower experiment that
is currently performed by the QUANTUS collaboration at ZARM (Bremen, Germany).
Starting from the classical mechanics of the drop capsule and a single particle
trapped within, we develop the quantum field theoretical description for this
experimental situation in an inertial frame, the corotating frame of the Earth,
as well as the comoving frame of the drop capsule. Suitable transformations
eliminate non-inertial forces, provided all external potentials (trap, gravity)
can be approximated with a second order Taylor expansion around the
instantaneous trap center. This is an excellent assumption and the harmonic
potential theorem applies. As an application, we study the quantum dynamics of
a cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-field
approximation. Due to the instantaneous transformation to the rest-frame of the
superfluid wave packet, the long-distance drop (100m) can be studied easily on
a numerical grid.Comment: 18 pages latex, 5 eps figures, submitte

- â€¦