4,018 research outputs found
The Schwinger Model on a circle: relation between Path Integral and Hamiltonian approaches
We solve the massless Schwinger model exactly in Hamiltonian formalism on a
circle. We construct physical states explicitly and discuss the role of the
spectral flow and nonperturbative vacua. Different thermodynamical correlation
functions are calculated and after performing the analytical continuation are
compared with the corresponding expressions obtained for the Schwinger model on
the torus in Euclidean Path Integral formalism obtained before.Comment: 40 page
Relativistic Harmonic Oscillator Revisited
The familiar Fock space commonly used to describe the relativistic harmonic
oscillator, for example as part of string theory, is insufficient to describe
all the states of the relativistic oscillator. We find that there are three
different vacua leading to three disconnected Fock sectors, all constructed
with the same creation-annihilation operators. These have different spacetime
geometric properties as well as different algebraic symmetry properties or
different quantum numbers. Two of these Fock spaces include negative norm
ghosts (as in string theory) while the third one is completely free of ghosts.
We discuss a gauge symmetry in a worldline theory approach that supplies
appropriate constraints to remove all the ghosts from all Fock sectors of the
single oscillator. The resulting ghost free quantum spectrum in d+1 dimensions
is then classified in unitary representations of the Lorentz group SO(d,1).
Moreover all states of the single oscillator put together make up a single
infinite dimensional unitary representation of a hidden global symmetry
SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these
new results in string theory and other areas of physics and mathematics are
briefly mentioned.Comment: 41 pages, 2 figures, LaTe
Loschmidt echo with a non-equilibrium initial state: early time scaling and enhanced decoherence
We study the Loschmidt echo (LE) in a central spin model in which a central
spin is globally coupled to an environment (E) which is subjected to a small
and sudden quench at so that its state at , remains the same as
the ground state of the initial environmental Hamiltonian before the quench;
this leads to a non-equilibrium situation. This state now evolves with two
Hamiltonians, the final Hamiltonian following the quench and its modified
version which incorporates an additional term arising due to the coupling of
the central spin to the environment. Using a generic short-time scaling of the
decay rate, we establish that in the early time limit, the rate of decay of the
LE (or the overlap between two states generated from the initial state evolving
through two channels) close to the quantum critical point (QCP) of E is
independent of the quenching. We do also study the temporal evolution of the LE
and establish the presence of a crossover to a situation where the quenching
becomes irrelevant. In the limit of large quench amplitude the non-equilibrium
initial condition is found to result in a drastic increase in decoherence at
large times, even far away from a QCP. These generic results are verified
analytically as well as numerically, choosing E to be a transverse Ising chain
where the transverse field is suddenly quenched.Comment: 5 pages, 6 figures; New results, figures and references added, title
change
Reduced coherence in double-slit diffraction of neutrons
In diffraction experiments with particle beams, several effects lead to a
fringe visibility reduction of the interference pattern. We theoretically
describe the intensity one can measure in a double-slit setup and compare the
results with the experimental data obtained with cold neutrons. Our conclusion
is that for cold neutrons the fringe visibility reduction is due not to
decoherence, but to initial incoherence.Comment: 4 pages LaTeX, 2 figure
The General Correlation Function in the Schwinger Model on a Torus
In the framework of the Euclidean path integral approach we derive the exact
formula for the general N-point chiral densities correlator in the Schwinger
model on a torusComment: 17 pages, misprints corrected, references adde
On the precise connection between the GRW master-equation and master-equations for the description of decoherence
We point out that the celebrated GRW master-equation is invariant under
translations, reflecting the homogeneity of space, thus providing a particular
realization of a general class of translation-covariant Markovian
master-equations. Such master-equations are typically used for the description
of decoherence due to momentum transfers between system and environment.
Building on this analogy we show the exact relationship between the GRW
master-equation and decoherence master-equations, further providing a
collisional decoherence model formally equivalent to the GRW master-equation.
This allows for a direct comparison of order of magnitudes of relevant
parameters. This formal analogy should not lead to confusion on the utterly
different spirit of the two research fields, in particular it has to be
stressed that the decoherence approach does not lead to a solution of the
measurement problem. Building on this analogy however the feasibility of the
extension of spontaneous localization models in order to avoid the infinite
energy growth is discussed. Apart from a particular case considered in the
paper, it appears that the amplification mechanism is generally spoiled by such
modifications.Comment: 9 pages, latex, no figures, to appear on J. Phys.
Quantum decoherence of the damped harmonic oscillator
In the framework of the Lindblad theory for open quantum systems, we
determine the degree of quantum decoherence of a harmonic oscillator
interacting with a thermal bath. It is found that the system manifests a
quantum decoherence which is more and more significant in time. We also
calculate the decoherence time and show that it has the same scale as the time
after which thermal fluctuations become comparable with quantum fluctuations.Comment: Talk at the XI International Conference on Quantum Optics
(ICQO'2006), May 2006, Minsk (Belarus), 9 page
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