3,237 research outputs found
A proposal for a first class conversion formalism based on the symmetries of the Wess-Zumino terms
We propose a new procedure to embed second class systems by introducing
Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the
models. This formalism is based on the direct imposition that the new
Hamiltonian must be invariant by gauge-symmetry transformations. An
interesting feature in this approach is the possibility to find a
representation for the WZ fields in a convenient way, which leads to preserve
the gauge symmetry in the original phase space. Consequently, the
gauge-invariant Hamiltonian can be written only in terms of the original
phase-space variables. In this situation, the WZ variables are only auxiliary
tools that permit to reveal the hidden symmetries present in the original
second class model. We apply this formalism to important physical models: the
reduced-SU(2) Skyrme model, the Chern-Simons-Proca quantum mechanics and the
chiral bosons field theory. In all these systems, the gauge-invariant
Hamiltonians are derived in a very simple way.Comment: Revised version. Title changed for Gauging by symmetries. To appear
in IJMP
Equivalence between different classical treatments of the O(N) nonlinear sigma model and their functional Schrodinger equations
In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma
model in its original version as a second-class constrained field theory and
then as a first-class constrained field theory. We treat the model as a
second-class constrained field theory by two different methods: the
unconstrained and the Dirac second-class formalisms. We show that the
Hamiltonians for all these versions of the model are equivalent. Then, for a
particular factor-ordering choice, we write the functional Schrodinger equation
for each derived Hamiltonian. We show that they are all identical which
justifies our factor-ordering choice and opens the way for a future
quantization of the model via the functional Schrodinger representation.Comment: Revtex version, 17 pages, substantial change
Temperature Measurement and Phonon Number Statistics of a Nanoelectromechanical Resonator
Measuring thermodynamic quantities can be easy or not, depending on the
system that is being studied. For a macroscopic object, measuring temperatures
can be as simple as measuring how much a column of mercury rises when in
contact with the object. At the small scale of quantum electromechanical
systems, such simple methods are not available and invariably detection
processes disturb the system state. Here we propose a method for measuring the
temperature on a suspended semiconductor membrane clamped at both ends. In this
method, the membrane is mediating a capacitive coupling between two
transmission line resonators (TLR). The first TLR has a strong dispersion, that
is, its decaying rate is larger than its drive, and its role is to pump in a
pulsed way the interaction between the membrane and the second TLR. By
averaging the pulsed measurements of the quadrature of the second TLR we show
how the temperature of the membrane can be determined. Moreover the statistical
description of the state of the membrane, which is directly accessed in this
approach is significantly improved by the addition of a Josephson Junction
coupled to the second TLR.Comment: 9 pages, 5 figures. To appear in New Journal of Physic
Canonical transformation for stiff matter models in quantum cosmology
In the present work we consider Friedmann-Robertson-Walker models in the
presence of a stiff matter perfect fluid and a cosmological constant. We write
the superhamiltonian of these models using the Schutz's variational formalism.
We notice that the resulting superhamiltonians have terms that will lead to
factor ordering ambiguities when they are written as operators. In order to
remove these ambiguities, we introduce appropriate coordinate transformations
and prove that these transformations are canonical using the symplectic method.Comment: Revtex4 Class, 3 pages, No Figure
Capacitive Coupling of Two Transmission Line Resonators Mediated by the Phonon Number of a Nanoelectromechanical Oscillator
Detection of quantum features in mechanical systems at the nanoscale
constitutes a challenging task, given the weak interaction with other elements
and the available technics. Here we describe how the interaction between two
monomodal transmission-line resonators (TLRs) mediated by vibrations of a
nano-electromechanical oscillator can be described. This scheme is then
employed for quantum non-demolition detection of the number of phonons in the
nano-electromechanical oscillator through a direct current measurement in the
output of one of the TLRs. For that to be possible an undepleted field inside
one of the TLR works as a amplifier for the interaction between the mechanical
resonator and the remaining TLR. We also show how how the non-classical nature
of this system can be used for generation of tripartite entanglement and
conditioned mechanical coherent superposition states, which may be further
explored for detection processes.Comment: 6 pages, 5 figure
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