4,937 research outputs found
Moving Atom-Field Interactions: Quantum Motional Decoherence and Relaxation
The reduced dynamics of an atomic qubit coupled both to its own quantized
center of mass motion through the spatial mode functions of the electromagnetic
field, as well as the vacuum modes, is calculated in the influence functional
formalism. The formalism chosen can describe the entangled non-Markovian
evolution of the system with a full account of the coherent back-action of the
environment on the qubit. We find a slight increase in the decoherence due to
the quantized center of mass motion and give a condition on the mass and qubit
resonant frequency for which the effect is important. In optically resonant
alkali-metal atom systems, we find the effect to be negligibly small. The
framework presented here can nevertheless be used for general considerations of
the coherent evolution of qubits in moving atoms in an electromagnetic field.Comment: 9 pages, 1 figure, minor change
Diffeomorphisms as Symplectomorphisms in History Phase Space: Bosonic String Model
The structure of the history phase space of a covariant field system
and its history group (in the sense of Isham and Linden) is analyzed on an
example of a bosonic string. The history space includes the time map
from the spacetime manifold (the two-sheet) to a
one-dimensional time manifold as one of its configuration variables. A
canonical history action is posited on such that its restriction to
the configuration history space yields the familiar Polyakov action. The
standard Dirac-ADM action is shown to be identical with the canonical history
action, the only difference being that the underlying action is expressed in
two different coordinate charts on . The canonical history action
encompasses all individual Dirac-ADM actions corresponding to different choices
of foliating . The history Poisson brackets of spacetime fields
on induce the ordinary Poisson brackets of spatial fields in the
instantaneous phase space of the Dirac-ADM formalism. The
canonical history action is manifestly invariant both under spacetime
diffeomorphisms Diff and temporal diffeomorphisms Diff. Both of
these diffeomorphisms are explicitly represented by symplectomorphisms on the
history phase space . The resulting classical history phase space
formalism is offered as a starting point for projection operator quantization
and consistent histories interpretation of the bosonic string model.Comment: 45 pages, no figure
Consistent thermodynamics for spin echoes
Spin-echo experiments are often said to constitute an instant of
anti-thermodynamic behavior in a concrete physical system that violates the
second law of thermodynamics. We argue that a proper thermodynamic treatment of
the effect should take into account the correlations between the spin and
translational degrees of freedom of the molecules. To this end, we construct an
entropy functional using Boltzmann macrostates that incorporates both spin and
translational degrees of freedom. With this definition there is nothing special
in the thermodynamics of spin echoes: dephasing corresponds to Hamiltonian
evolution and leaves the entropy unchanged; dissipation increases the entropy.
In particular, there is no phase of entropy decrease in the echo. We also
discuss the definition of macrostates from the underlying quantum theory and we
show that the decay of net magnetization provides a faithful measure of entropy
change.Comment: 15 pages, 2 figs. Changed figures, version to appear in PR
The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
We provide an in-depth and thorough treatment of the validity of the
rotating-wave approximation (RWA) in an open quantum system. We find that when
it is introduced after tracing out the environment, all timescales of the open
system are correctly reproduced, but the details of the quantum state may not
be. The RWA made before the trace is more problematic: it results in incorrect
values for environmentally-induced shifts to system frequencies, and the
resulting theory has no Markovian limit. We point out that great care must be
taken when coupling two open systems together under the RWA. Though the RWA can
yield a master equation of Lindblad form similar to what one might get in the
Markovian limit with white noise, the master equation for the two coupled
systems is not a simple combination of the master equation for each system, as
is possible in the Markovian limit. Such a naive combination yields inaccurate
dynamics. To obtain the correct master equation for the composite system a
proper consideration of the non-Markovian dynamics is required.Comment: 17 pages, 0 figures
Tomographic Representation of Minisuperspace Quantum Cosmology and Noether Symmetries
The probability representation, in which cosmological quantum states are
described by a standard positive probability distribution, is constructed for
minisuperspace models selected by Noether symmetries. In such a case, the
tomographic probability distribution provides the classical evolution for the
models and can be considered an approach to select "observable" universes. Some
specific examples, derived from Extended Theories of Gravity, are worked out.
We discuss also how to connect tomograms, symmetries and cosmological
parameters.Comment: 15 page
Generalization of Classical Statistical Mechanics to Quantum Mechanics and Stable Property of Condensed Matter
Classical statistical average values are generally generalized to average
values of quantum mechanics, it is discovered that quantum mechanics is direct
generalization of classical statistical mechanics, and we generally deduce both
a new general continuous eigenvalue equation and a general discrete eigenvalue
equation in quantum mechanics, and discover that a eigenvalue of quantum
mechanics is just an extreme value of an operator in possibility distribution,
the eigenvalue f is just classical observable quantity. A general classical
statistical uncertain relation is further given, the general classical
statistical uncertain relation is generally generalized to quantum uncertainty
principle, the two lost conditions in classical uncertain relation and quantum
uncertainty principle, respectively, are found. We generally expound the
relations among uncertainty principle, singularity and condensed matter
stability, discover that quantum uncertainty principle prevents from the
appearance of singularity of the electromagnetic potential between nucleus and
electrons, and give the failure conditions of quantum uncertainty principle.
Finally, we discover that the classical limit of quantum mechanics is classical
statistical mechanics, the classical statistical mechanics may further be
degenerated to classical mechanics, and we discover that only saying that the
classical limit of quantum mechanics is classical mechanics is mistake. As
application examples, we deduce both Shrodinger equation and state
superposition principle, deduce that there exist decoherent factor from a
general mathematical representation of state superposition principle, and the
consistent difficulty between statistical interpretation of quantum mechanics
and determinant property of classical mechanics is overcome.Comment: 10 page
Quantum Theory of Non-Relativistic Particles Interacting with Gravity
We investigate the effects of the gravitational field on the quantum dynamics
of non-relativistic particles. We consider N non-relativistic particles,
interacting with the linearized gravitational field. Using the Feynman - Vernon
influence functional technique, we trace out the graviton field, to obtain a
master equation for the system of particles to first order in . The
effective interaction between the particles, as well as the self-interaction is
non-local in time and in general non-markovian. We show that the gravitational
self-interaction cannot be held responsible for decoherence of microscopic
particles due to the fast vanishing of the diffusion function. For macroscopic
particles though, it leads to diagonalization to the energy eigenstate basis, a
desirable feature in gravity induced collapse models. We finally comment on
possible applications.Comment: Latex,14 pages, replaced to correct the titl
Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field
We derive the stochastic equations and consider the non-Markovian dynamics of
a system of multiple two-level atoms in a common quantum field. We make only
the dipole approximation for the atoms and assume weak atom-field interactions.
From these assumptions we use a combination of non-secular open- and
closed-system perturbation theory, and we abstain from any additional
approximation schemes. These more accurate solutions are necessary to explore
several regimes: in particular, near-resonance dynamics and low-temperature
behavior. In detuned atomic systems, small variations in the system energy
levels engender timescales which, in general, cannot be safely ignored, as
would be the case in the rotating-wave approximation (RWA). More problematic
are the second-order solutions, which, as has been recently pointed out, cannot
be accurately calculated using any second-order perturbative master equation,
whether RWA, Born-Markov, Redfield, etc.. This latter problem, which applies to
all perturbative open-system master equations, has a profound effect upon
calculation of entanglement at low temperatures. We find that even at zero
temperature all initial states will undergo finite-time disentanglement
(sometimes termed "sudden death"), in contrast to previous work. We also use
our solution, without invoking RWA, to characterize the necessary conditions
for Dickie subradiance at finite temperature. We find that the subradiant
states fall into two categories at finite temperature: one that is temperature
independent and one that acquires temperature dependence. With the RWA there is
no temperature dependence in any case.Comment: 17 pages, 13 figures, v2 updated references, v3 clarified results and
corrected renormalization, v4 further clarified results and new Fig. 8-1
Quantum chaos in open systems: a quantum state diffusion analysis
Except for the universe, all quantum systems are open, and according to
quantum state diffusion theory, many systems localize to wave packets in the
neighborhood of phase space points. This is due to decoherence from the
interaction with the environment, and makes the quasiclassical limit of such
systems both more realistic and simpler in many respects than the more familiar
quasiclassical limit for closed systems. A linearized version of this theory
leads to the correct classical dynamics in the macroscopic limit, even for
nonlinear and chaotic systems. We apply the theory to the forced, damped
Duffing oscillator, comparing the numerical results of the full and linearized
equations, and argue that this can be used to make explicit calculations in the
decoherent histories formalism of quantum mechanics.Comment: 18 pages standard LaTeX + 9 figures; extensively trimmed; to appear
in J. Phys.
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