67 research outputs found
Physical interpretation of stochastic Schroedinger equations in cavity QED
We propose physical interpretations for stochastic methods which have been
developed recently to describe the evolution of a quantum system interacting
with a reservoir. As opposed to the usual reduced density operator approach,
which refers to ensemble averages, these methods deal with the dynamics of
single realizations, and involve the solution of stochastic Schr\"odinger
equations. These procedures have been shown to be completely equivalent to the
master equation approach when ensemble averages are taken over many
realizations. We show that these techniques are not only convenient
mathematical tools for dissipative systems, but may actually correspond to
concrete physical processes, for any temperature of the reservoir. We consider
a mode of the electromagnetic field in a cavity interacting with a beam of two-
or three-level atoms, the field mode playing the role of a small system and the
atomic beam standing for a reservoir at finite temperature, the interaction
between them being given by the Jaynes-Cummings model. We show that the
evolution of the field states, under continuous monitoring of the state of the
atoms which leave the cavity, can be described in terms of either the Monte
Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger
equation, depending on the system configuration. We also show that the Monte
Carlo Wave-Function approach leads, for finite temperatures, to localization
into jumping Fock states, while the diffusion equation method leads to
localization into states with a diffusing average photon number, which for
sufficiently small temperatures are close approximations to mildly squeezed
states.Comment: 12 pages RevTeX 3.0 + 6 figures (GIF format; for higher-resolution
postscript images or hardcopies contact the authors.) Submitted to Phys. Rev.
The Particle Spectrum of Heterotic Compactifications
Techniques are presented for computing the cohomology of stable, holomorphic
vector bundles over elliptically fibered Calabi-Yau threefolds. These
cohomology groups explicitly determine the spectrum of the low energy,
four-dimensional theory. Generic points in vector bundle moduli space manifest
an identical spectrum. However, it is shown that on subsets of moduli space of
co-dimension one or higher, the spectrum can abruptly jump to many different
values. Both analytic and numerical data illustrating this phenomenon are
presented. This result opens the possibility of tunneling or phase transitions
between different particle spectra in the same heterotic compactification. In
the course of this discussion, a classification of SU(5) GUT theories within a
specific context is presented.Comment: 77 pages, 3 figure
SU(4) Instantons on Calabi-Yau Threefolds with Z_2 x Z_2 Fundamental Group
Structure group SU(4) gauge vacua of both weakly and strongly coupled
heterotic superstring theory compactified on torus-fibered Calabi-Yau
threefolds Z with Z_2 x Z_2 fundamental group are presented. This is
accomplished by constructing invariant, stable, holomorphic rank four vector
bundles on the simply connected cover of Z. Such bundles can descend either to
Hermite-Yang-Mills instantons on Z or to twisted gauge fields satisfying the
Hermite-Yang-Mills equation corrected by a non-trivial flat B-field. It is
shown that large families of such instantons satisfy the constraints imposed by
particle physics phenomenology. The discrete parameter spaces of those families
are presented, as well as a lower bound on the dimension of the continuous
moduli of any such vacuum. In conjunction with Z_2 x Z_2 Wilson lines, these
SU(4) gauge vacua can lead to standard-like models at low energy with an
additional U(1)_{B-L} symmetry. This U(1)_{B-L} symmetry is very helpful in
naturally suppressing nucleon decay.Comment: 68 pages, no figure
- …